Perry’s Chemical Engineers’ Handbook ABOUT THE EDITORS Dr. Don W. Green is Emeritus Distinguished Professor of Chemical and Petroleum Engineering at the University of Kansas (KU). He holds a B.S. in petroleum engineering from the University of Tulsa, and M.S. and Ph.D. degrees in chemical engineering from the University of Oklahoma. He is the coeditor of the sixth edition of Perry’s Chemical Engineers’ Handbook, and editor of the seventh and eighth editions. He has authored/coauthored 70 refereed publications, over 100 technical meeting presentations, and is coauthor of the first and second editions of the SPE textbook Enhanced Oil Recovery. Dr. Green has won numerous teaching awards at KU, including the Honors for Outstanding Progressive Educator (HOPE) Award and the Chancellor’s Club Career Teaching Award, the highest teaching recognitions awarded at the University. He has also been featured as an outstanding educator in ASEE’s Chemical Engineering Education Journal. He received the KU School of Engineering Distinguished Engineering Service Award (DESA), and has been designated an Honorary Member of both SPE and AIME and a Fellow of the AIChE. Dr. Marylee Z. Southard is Associate Professor of Chemical and Petroleum Engineering at the University of Kansas. She holds B.S., M.S., and Ph.D. degrees in chemical engineering from the University of Kansas. Dr. Southard’s research deals with small molecule drug formulations; but her industrial background is in production and process development of inorganic chemical intermediates. Dr. Southard’s work in inorganic chemicals production has included process engineering, design, and product development. She has consulted for industrial and pharmaceutical chemical production and research companies. She teaches process design and project economics, and has won several university-wide teaching awards, including the Honors for Outstanding Progressive Educator (HOPE) Award and the Kemper Teaching Fellowship. She has authored 1 patent, 15 refereed publications, and numerous technical presentations. Her research interests are in biological and pharmaceutical mass transport. She is a senior member of AIChE and ASEE. PERRY’S CHEMICAL ENGINEERS’ HANDBOOK NINTH EDITION New York Chicago San Francisco Athens London Madrid Mexico City Milan New Delhi Singapore Sydney Toronto Editor-in-Chief Don W. Green Emeritus Distinguished Professor of Chemical and Petroleum Engineering, University of Kansas Associate Editor Marylee Z. Southard Associate Professor of Chemical & Petroleum Engineering, University of Kansas Copyright © 2019 by McGraw-Hill Education. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 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McGraw-Hill Education has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. Contents For the detailed contents of any section, consult the title page of that section. See also the alphabetical index in the back of the handbook. Section Unit Conversion Factors and Symbols Marylee Z. Southard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Marylee Z. Southard, Richard L. Rowley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Physical and Chemical Data Bruce A. Finlayson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Mathematics J. Richard Elliott, Carl T. Lira, Timothy C. Frank, Paul M. Mathias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Thermodynamics Geoffrey D. Silcox, James J. Noble, Phillip C. Wankat, Kent S. Knaebel . . . . . . . . . . . . . . . . . . . . . . . . 5 Heat and Mass Transfer James N. Tilton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Fluid and Particle Dynamics Tiberiu M. Leib, Carmo J. Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Reaction Kinetics Thomas F. Edgar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Process Control Process Economics James R. Couper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Transport and Storage of Fluids Heat-Transfer Equipment Meherwan P. Boyce, Victor H. Edwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Richard L. Shilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Psychrometry, Evaporative Cooling, and Solids Drying John P. Hecht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Michael F. Doherty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Distillation Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment Timothy C. Frank . . . . . . . . . . . . . . . . . 15 M. Douglas LeVan, Giorgio Carta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Adsorption and Ion Exchange Gas–Solid Operations and Equipment Liquid-Solid Operations and Equipment Reactors Henry Z. Kister . . . . . . . . . . . . . 14 Ted M. Knowlton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Wayne J. Genck. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Carmo J. Pereira, Tiberiu M. Leib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Bioreactions and Bioprocessing Gregory Frank, Jeffrey Chalmers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Solids Processing and Particle Technology Waste Management Process Safety Karl V. Jacob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Louis Theodore, Paul S. Farber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Daniel A. Crowl, Robert W. Johnson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Energy Resources, Conversion, and Utilization Materials of Construction Shabbir Ahmed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Lindell R. Hurst, Jr., Edward R. Naylor, Emory A. Ford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Index follows Section 25 v This page intentionally left blank Contributors D. Shabbir Ahmed, Ph.D. Chemical Engineer, Chemical Sciences and Engineering Division, Argonne National Laboratory (Section Editor, Sec. 24, Energy Resources, Conversion, and Utilization) Brooke Albin, M.S.E. Chemical Engineer, MATRIC (Mid-Atlantic Technology, Research and Innovation Center), Charleston, WV; Member, American Institute of Chemical Engineers, American Filtration Society (Crystallization from the Melt) (Sec. 18, Liquid-Solid Operations and Equipment) John Alderman, M.S., P.E., C.S.P. Managing Partner, Hazard and Risk Analysis, LLC (Electrical Area Classification, Fire Protection Systems) (Sec. 23, Process Safety) Paul Amyotte, Ph.D., P.Eng. Professor of Chemical Engineering and C.D. Howe Chair in Process Safety, Dalhousie University; Fellow, Chemical Institute of Canada; Fellow, Canadian Academy of Engineering (Dust Explosions) (Sec. 23, Process Safety) Frank A. Baczek, B.S. Sr. Research Advisor, FLSmidth USA, Inc. (Gravity Sedimentation Operations) (Sec. 18, LiquidSolid Operations and Equipment) Wayne E. Beimesch, Ph.D. Technical Associate Director (Retired), Corporate Engineering, The Procter & Gamble Company (Drying Equipment, Operation and Troubleshooting) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Ray Bennett, Ph.D., P.E., CEFEI Senior Principal Engineer, Baker Engineering and Risk Consultants, Inc.; Member, American Petroleum Institute 752, 753, and 756 (Estimation of Damage Effects) (Sec. 23, Process Safety) B. Wayne Bequette, Ph.D. Professor of Chemical and Biological Engineering, Rensselaer Polytechnic Institute (Unit Operations Control, Advanced Control Systems) (Sec. 8, Process Control) Patrick M. Bernhagen, P.E., B.S. Director of Sales—Fired Heater, Amec Foster Wheeler North America Corp.; API Subcommittee on Heat Transfer Equipment API 530, 536, 560, and 561 (Compact and Nontubular Heat Exchangers) (Sec. 11, Heat-Transfer Equipment) Michael J. Betenbaugh, Ph.D. Professor of Chemical and Biomolecular Engineering, Johns Hopkins University; Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and Bioprocessing Technologies and Trends) (Sec. 20, Bioreactions and Bioprocessing) Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member, National Academy of Engineering (Sec. 3, Mathematics) Meherwan P. Boyce, Ph.D., P.E. (Deceased) Chairman and Principal Consultant, The Boyce Consultancy Group, LLC; Fellow, American Society of Mechanical Engineers (U.S.); Fellow, National Academy Forensic Engineers (U.S.); Fellow, Institution of Mechanical Engineers (U.K.); Fellow, Institution of Diesel and Gas Turbine Engineers (U.K.); Registered Professional Engineer (Texas), Chartered Engineer (U.K.); Sigma Xi, Tau Beta Pi, Phi Kappa Phi. (Section Coeditor, Sec. 10, Transport and Storage of Fluids) Jeffrey Breit, Ph.D. Principal Scientist, Capsugel; Member, American Association of Pharmaceutical Scientists (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing) vii viii COnTRIBUTORS Laurence G. Britton, Ph.D. Process Safety Consultant; Fellow, American Institute of Chemical Engineers; Fellow, Energy Institute; Member, Institute of Physics (U.K.) (Flame Arresters) (Sec. 23, Process Safety) nathan Calzadilla, M.S.E. Research Program Assistant, Johns Hopkins Medicine, Chemical and Biomolecular Engineering, Johns Hopkins University; Member, American Institute of Chemical Engineers (Emerging Biopharmaceutical and Bioprocessing Technologies and Trends) (Sec. 20, Bioreactions and Bioprocessing) John W. Carson, Ph.D. President, Jenike & Johanson, Inc., Founding member and past chair of ASTM Subcommittee D18.24, “Characterization and Handling of Powders and Bulk Solids” (Bulk Solids Flow and Hopper Design) (Sec. 21, Solids Processing and Particle Technology) Giorgio Carta, Ph.D. Lawrence R. Quarles Professor, Department of Chemical Engineering, University of Virginia; Member, American Institute of Chemical Engineers, American Chemical Society (Section Coeditor, Sec. 16, Adsorption and Ion Exchange) Jeffrey Chalmers, Ph.D. Professor of Chemical and Biomolecular Engineering, The Ohio State University; Member, American Institute of Chemical Engineers; American Chemical Society; Fellow, American Institute for Medical and Biological Engineering (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing) J. Wayne Chastain, B.S., P.E., CCPSC Engineering Associate, Eastman Chemical Company; Member, American Institute of Chemical Engineers (Layer of Protection Analysis) (Sec. 23, Process Safety) Wu Chen, Ph.D. Principal Research Scientist, The Dow Chemical Company; Fellow, American Filtration and Separations Society (Expression) (Sec. 18, Liquid-Solid Operations and Equipment) Martin P. Clouthier, M.Sc., P.Eng. Director, Jensen Hughes Consulting Canada Ltd. (Dust Explosions) (Sec. 23, Process Safety) James R. Couper, D.Sc. Professor Emeritus, The Ralph E. Martin Department of Chemical Engineering, University of Arkansas—Fayetteville (Section Editor, Sec. 9, Process Economics) Daniel A. Crowl, Ph.D., CCPSC AIChE/CCPS Staff Consultant; Adjunct Professor, University of Utah; Professor Emeritus of Chemical Engineering, Michigan Technological University; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Section Coeditor, Sec. 23, Process Safety) Rita D’Aquino, M.E. Consultant, Member, American Institute of Chemical Engineers (Pollution Prevention) (Sec. 22, Waste Management) Michael Davies, Ph.D. President and CEO, Braunschweiger Flammenfilter GmbH (PROTEGO), Member, American Institute of Chemical Engineers; Member, National Fire Protection Association (Flame Arresters) (Sec. 23, Process Safety) Sheldon W. Dean, Jr., ScD, P.E. President, Dean Corrosion Technology, Inc.; Fellow, Air Products and Chemicals, Inc., Retired; Fellow, ASTM; Fellow, NACE; Fellow, AIChE; Fellow, Materials Technology Institute (Corrosion Fundamentals, Corrosion Prevention) (Sec. 25, Materials of Construction) Dennis W. Dees, Ph.D. Senior Electrochemical Engineer, Chemical Sciences and Engineering Division, Argonne National Laboratory (Electrochemical Energy Storage) (Sec. 24, Energy Resources, Conversion, and Utilization) Vinay P. Deodeshmukh, Ph.D. Sr. Applications Development Manager—High Temperature and Corrosion Resistant Alloys, Haynes International Inc. (Corrosion Fundamentals, High-Temperature Corrosion, Nickel Alloys) (Sec. 25, Materials of Construction) Shrikant Dhodapkar, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Gas–Solids Separations) (Sec. 17, Gas–Solid Operations and Equipment); (Feeding, Metering, and Dosing) (Sec. 21, Solids Processing and Particle Technology) David S. Dickey, Ph.D. Consultant, MixTech, Inc.; Fellow, American Institute of Chemical Engineers; Member, North American Mixing Forum (NAMF); Member, American Chemical Society; Member, American Society of Mechanical Engineers; Member, Institute of Food Technology (Mixing and Processing of Liquids and Solids & Mixing of Viscous Fluids, Pastes, and Doughs) (Sec. 18, Liquid-Solid Operations and Equipment) Michael F. Doherty, Ph.D. Professor of Chemical Engineering, University of California—Santa Barbara (Section Editor, Sec. 13, Distillation) Arthur M. Dowell, III, P.E., B.S. President, A M Dowell III PLLC; Fellow, American Institute of Chemical Engineers; Senior Member, Instrumentation, Systems and Automation Society (Risk Analysis) (Sec. 23, Process Safety) Brandon Downey, B.A.Sc. Principal Engineer, R&D, Lonza; Member, American Institute of Chemical Engineers (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing) Karin nordström Dyvelkov, Ph.D. GEA Process Engineering A/S Denmark (Drying Equipment, Fluidized Bed Dryers, Spray Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) COnTRIBUTORS ix Thomas F. Edgar, Ph.D. Professor of Chemical Engineering, University of Texas—Austin (Section Editor, Sec. 8, Process Control) Victor H. Edwards, Ph.D., P.E. Principal, VHE Technical Analysis; Fellow and Life Member, American Institute of Chemical Engineers; Member, American Association for the Advancement of Science, American Chemical Society, National Society of Professional Engineers; Life Member, New York Academy of Sciences; Registered Professional Engineer (Texas), Phi Lambda Upsilon, Sigma Tau (Section Coeditor, Sec. 10, Transport and Storage of Fluids) J. Richard Elliott, Ph.D. Professor, Department of Chemical and Biomolecular Engineering, University of Akron; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics) Dirk T. Van Essendelft, Ph.D. Chemical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Coal) (Sec. 24, Energy Resources, Conversion, and Utilization) James R. Fair, Ph.D., P.E. (Deceased) Professor of Chemical Engineering, University of Texas; Fellow, American Institute of Chemical Engineers; Member, American Chemical Society, American Society for Engineering Education, National Society of Professional Engineers (Section Editor of the 7th edition and major contributor to the 5th, 6th, and 7th editions) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Yi Fan, Ph.D. Associate Research Scientist, The Dow Chemical Company (Solids Mixing) (Sec. 21, Solids Processing and Particle Technology) Paul S. Farber, P.E., M.S. Principal, P. Farber & Associates, LLC, Willowbrook, Illinois; Member, American Institute of Chemical Engineers, Air & Waste Management Association (Section Coeditor, Sec. 22, Waste Management) Hans K. Fauske, D.Sc. Emeritus President and Regent Advisor, Fauske and Associates, LLC; Fellow, American Institute of Chemical Engineers; Fellow, American Nuclear Society; Member, National Academy of Engineering (Pressure Relief Systems) (Sec. 23, Process Safety) Zbigniew T. Fidkowski, Ph.D. (Sec. 13, Distillation) Process Engineer, Evonik Industries (Distillation Systems, Batch Distillation) Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering, University of Washington; Member, National Academy of Engineering (Section Editor, Sec. 3, Mathematics) Emory A. Ford, Ph.D. Associate Director, Materials Technology Institute, Chief Scientist and Director of Research, Lyondell/Bassel Retired, Fellow Materials Technology Institute (Section Coeditor, Sec. 25, Materials of Construction) Gregory Frank, Ph.D. Principal Engineer, Amgen Inc.; Fellow, American Institute of Chemical Engineers; Member, Society of Biological Engineering; North American Mixing Forum; Pharmaceutical Discovery, Development, and Manufacturing Forum (Section Coeditor, Sec. 20, Bioreactions and Bioprocessing) Timothy C. Frank, Ph.D. Fellow, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 4, Thermodynamics; Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Walter L. Frank, B.S., P.E., CCPSC President, Frank Risk Solutions, Inc.; AIChE/CCPS Staff Consultant; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Hazards of Vacuum, Hazards of Inerts) (Sec. 23, Process Safety) Ben J. Freireich, Ph.D. Technical Director, Particulate Solid Research, Inc. (Solids Mixing, Size Enlargement) (Sec. 21, Solids Processing and Particle Technology) James D. Fritz, Ph.D. Consultant, NACE International certified Material Selection Design Specialist; Member of the Metallic Materials and Materials Joining Subcommittees of the ASME Bioprocessing Equipment Standard, the Ferrous Specifications Subcommittee of the ASME Boiler & Pressure Vessel Code, and ASM International (Stainless Steels) (Sec. 25, Materials of Construction) Kevin L. Ganschow, B.S., P.E. Senior Staff Materials Engineer, Chevron Corporation; Registered Professional Mechanical Engineer (California) (Ferritic Steels) (Sec. 25, Materials of Construction) Wayne J. Genck, Ph.D. President, Genck International; consultant on crystallization and precipitation; Member, American Chemical Society, American Institute of Chemical Engineers, Association for Crystallization Technology, International Society of Pharmaceutical Engineers (ISPE) (Section Editor, Sec. 18, Liquid-Solid Operations and Equipment) Craig G. Gilbert, B.Sc. Global Product Manager-Paste, FLSmidth USA, Inc.; Member, Society for Mining, Metallurgy, and Exploration; Mining and Metallurgical Society of America; Registered Professional Engineer (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment) x COnTRIBUTORS Roy A. Grichuk, P.E. Piping Director, Fluor, BSME, P.E.; Member, American Society of Mechanical Engineers, B31 Main Committee, B31MTC Committee, and B31.3 Committee; Registered Professional Engineer (Texas) (Piping) (Sec. 10, Transport and Storage of Fluids) Juergen Hahn, Ph.D. Professor of Biomedical Engineering, Rensselaer Polytechnic Institute (Advanced Control Systems, Bioprocess Control) (Sec. 8, Process Control) Roger G. Harrison, Ph.D. Professor of Chemical, Biological, and Materials Engineering and Professor of Biomedical Engineering, University of Oklahoma; Member, American Institute of Chemical Engineers, American Chemical Society, American Society for Engineering Education, Oklahoma Higher Education Hall of Fame; Fellow, American Institute for Medical and Biological Engineering (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) John P. Hecht, Ph.D. Technical Section Head, Drying and Particle Processing, The Procter & Gamble Company; Member, American Institute of Chemical Engineers (Section Editor, Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Matthew K. Heermann, P.E., B.S. Consultant—Fossil Power Environmental Technologies, Sargent & Lundy LLC, Chicago, Illinois (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management) Dennis C. Hendershot, M.S. Process Safety Consultant; Fellow, American Institute of Chemical Engineers (Inherently Safer Design and Related Concepts, Hazard Analysis, Key Procedures) (Sec. 23, Process Safety) Taryn Herrera, B.S. Process Engineer, Manager Separations Laboratory, FLSmidth USA, Inc. (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment) Darryl W. Hertz, B.S. Senior Manager, Value Improvement Group, KBR, Houston, Texas (Front-End Loading, Value-Improving Practices) (Sec. 9, Process Economics) Bruce S. Holden, M.S. Principal Research Scientist, The Dow Chemical Company; Fellow, American Institute of Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Predrag S. Hrnjak, Ph.D. Will Stoecker Res. Professor of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign; Principal Investigator—U of I Air Conditioning and Refrigeration Center; Assistant Professor, University of Belgrade; International Institute of Chemical Engineers; American Society of Heat, Refrigerating, and Air Conditioning Engineers (Refrigeration) (Sec. 11, Heat-Transfer Equipment) Lindell R. Hurst, Jr., M.S., P.E. Senior Materials and Corrosion Engineer, Shell Global Solutions (US) Inc. Retired, Registered Professional Metallurgical Engineer (Alabama, Ohio, North Dakota) (Section Coeditor, Sec. 25, Materials of Construction) Karl V. Jacob, B.S. Fellow, The Dow Chemical Company; Lecturer, University of Michigan; Fellow, American Institute of Chemical Engineers (Section Editor, Sec. 21, Solids Processing and Particle Technology) Pradeep Jain, M.S. Senior Fellow, The Dow Chemical Company (Feeding, Metering, and Dosing) (Sec. 21, Solids Processing and Particle Technology) David Johnson, P.E., M.Ch.E. (Sec. 11, Heat-Transfer Equipment) Retired (Thermal Design of Heat Exchangers, Condensers, Reboilers) Robert W. Johnson, M.S.Ch.E. President, Unwin Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 23, Process Safety) Hugh D. Kaiser, P.E., B.S., M.B.A. Principal Engineer, WSP USA; Fellow, American Institute of Chemical Engineers; Registered Professional Engineer (Indiana, Nebraska, Oklahoma, and Texas) (Storage and Process Vessels) (Sec. 10, Transport and Storage of Fluids) Ian C. Kemp, M.A. (Cantab) Scientific Leader, GlaxoSmithKline; Fellow, Institution of Chemical Engineers; Associate Member, Institution of Mechanical Engineers (Psychrometry, Solids-Drying Fundamentals, Freeze Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Pinch Analysis) (Sec. 24, Energy Resources, Conversion, and Utilization) Pradip R. Khaladkar, M.S., P.E. Principal Consultant, Materials Engineering Group, Dupont Company (Retired), Registered Professional Engineer (Delaware), Fellow, Materials Technology Institute, St. Louis (Nonmetallic Materials) (Sec. 25, Materials of Construction) Henry Z. Kister, M.E., C.Eng., C.Sc. Senior Fellow and Director of Fractionation Technology, Fluor Corporation; Member, National Academy of Engineering (NAE); Fellow, American Institute of Chemical Engineers; Fellow, Institution of Chemical Engineers (U.K.); Member, Institute of Energy (Section Editor, Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Kent S. Knaebel, Ph.D. President, Adsorption Research, Inc.; Member, American Institute of Chemical Engineers, International Adsorption Society; Professional Engineer (Ohio) (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer) COnTRIBUTORS xi Ted M. Knowlton, Ph.D. Technical Consultant and Fellow, Particulate Solid Research, Inc.; Member, American Institute of Chemical Engineers (Section Editor, Sec. 17, Gas–Solid Operations and Equipment) James F. Koch, M.S. Senior Process Engineering Specialist, The Dow Chemical Company (Size Reduction, Screening) (Sec. 21, Solids Processing and Particle Technology) Tim Langrish, D. Phil. School of Chemical and Biomolecular Engineering, The University of Sydney, Australia (Solids-Drying Fundamentals, Cascading Rotary Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Tim J. Laros, M.S. Owner, Filtration Technologies, LLC, Park City, UT; Member, Society for Mining, Metallurgy, and Exploration (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) Tiberiu M. Leib, Ph.D. Principal Consultant, The Chemours Company (retired); Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors) M. Douglas LeVan, Ph.D. J. Lawrence Wilson Professor of Engineering Emeritus, Department of Chemical and Biomolecular Engineering, Vanderbilt University; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Section Coeditor, Sec. 16, Adsorption and Ion Exchange) Wenping Li, Ph.D. R&D Director, Agrilectric Research Company; Member, American Filtration and Separations Society, American Institute of Chemical Engineers (Expression) (Sec. 18, Liquid-Solid Operations and Equipment) Eugene L. Liening, M.S., P.E. Manufacturing & Engineering Technology Fellow, The Dow Chemical Company Retired; Fellow, Materials Technology Institute; Registered Professional Metallurgical Engineer (Michigan) (Corrosion Testing) (Sec. 25, Materials of Construction) Dirk Link, Ph.D. Chemist, National Energy Technology Laboratory, U.S. Department of Energy (Nonpetroleum Liquid Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Carl T. Lira, Ph.D. Associate Professor, Department of Chemical and Materials Engineering, Michigan State University; Member, American Institute of Chemical Engineers; Member, American Chemical Society; Member, American Society of Engineering Educators (Section Coeditor, Sec. 4, Thermodynamics) Peter J. Loftus, D. Phil. Chief Scientist, Primaira LLC, Member, American Society of Mechanical Engineers (Heat Generation) (Sec. 24, Energy Resources, Conversion, and Utilization) Michael F. Malone, Ph.D. Professor of Chemical Engineering and Vice-Chancellor for Research and Engagement, University of Massachusetts—Amherst (Batch Distillation, Enhanced Distillation) (Sec. 13, Distillation) Paul E. Manning, Ph.D. Director CRA Marketing and Business Development, Haynes International (Nickel Alloys) (Sec. 25, Materials of Construction) Chad V. Mashuga, Ph.D., P.E. Assistant Professor of Chemical Engineering, Texas A&M University (Flammability, Combustion and Flammability Hazards, Explosions, Vapor Cloud Explosions, Boiling-Liquid Expanding-Vapor Explosions) (Sec. 23, Process Safety) Paul M. Mathias, Ph.D. Senior Fellow and Technical Director, Fluor Corporation; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 4, Thermodynamics); (Design of Gas Absorption Systems) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Paul McCurdie, B.S. Product Manager-Vacuum Filtration, FLSmidth USA, Inc. (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) James K. McGillicuddy, B.S. Product Specialist, Centrifuges, Andritz Separation Inc.; Member, American Institute of Chemical Engineers (Centrifuges) (Sec. 18, Liquid-Solid Operations and Equipment) John D. McKenna, Ph.D. Principal, ETS, Inc.; Member, American Institute of Chemical Engineers, Air and Waste Management Association (Air Pollution Management of Stationary Sources) (Sec. 22, Waste Management) Terence P. Mcnulty, Ph.D. President, T. P. McNulty and Associates, Inc.; consultants in mineral processing and extractive metallurgy; Member, National Academy of Engineering; Member, American Institute of Mining, Metallurgical, and Petroleum Engineers; Member, Society for Mining, Metallurgy, and Exploration; Member, The Metallurgical Society; Member Mining and Metallurgical Society of America (Leaching) (Sec. 18, Liquid-Solid Operations and Equipment) Greg Mehos, Ph.D., P.E. Senior Project Engineer, Jenike & Johanson, Inc. (Bulk Solids Flow and Hopper Design) (Sec. 21, Solids Processing and Particle Technology) Georges A. Melhem, Ph.D. President and CEO, IoMosaic; Fellow, American Institute of Chemical Engineers (Emergency Relief Device Effluent Collection and Handling) (Sec. 23, Process Safety) Valerie S. Monical, B.S. Fellow, Ascend Performance Materials, Inc. (Phase Separation) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) xii COnTRIBUTORS Ronnie Montgomery Technical Manager, Process Control Systems, IHI Engineering and Construction International Corporation; Member, Process Industries Practices, Process Controls Function Team; Member, International Society of Automation (Flow Measurement) (Sec. 10, Transport and Storage of Fluids) David A. Moore, B.Sc., M.B.A., P.E., C.S.P. President, AcuTech Consulting Group; Member, ASSE, ASIS, NFPA (Security) (Sec. 23, Process Safety) Charles G. Moyers, Ph.D. Senior Chemical Engineering Consultant, MATRIC (Mid-Atlantic Technology, Research and Innovation Center), Charleston, WV; Fellow, American Institute of Chemical Engineers (Crystallization from the Melt) (Sec. 18, Liquid-Solid Operations and Equipment) William E. Murphy, Ph.D., P.E. Professor of Mechanical Engineering, University of Kentucky; American Society of Heating, Refrigerating, and Air-Conditioning Engineers; American Society of Mechanical Engineers; International Institute of Refrigeration (Air Conditioning) (Sec. 11, Heat-Transfer Equipment) Edward R. naylor, B.S., M.S. Senior Materials Engineering Associate, AkzoNobel; Certified API 510, 570, 653 and Fixed Equipment Source Inspector (Section Coeditor, Sec. 25, Materials of Construction) James J. noble, Ph.D., P.E., Ch.E. [U.K.] Research Affiliate, Department of Chemical Engineering, Massachusetts Institute of Technology; Fellow, American Institute of Chemical Engineers; Member, New York Academy of Sciences (Heat Transfer Coeditor, Sec. 5, Heat and Mass Transfer) W. Roy Penney, Ph.D., P.E. Professor Emeritus, Department of Chemical Engineering, University of Arkansas; Fellow, American Institute of Chemical Engineers (Gas-in-Liquid Dispersions) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Clint Pepper, Ph.D. Director, Lonza; Member, American Institute of Chemical Engineers (Product Attribute Control) (Sec. 20, Bioreactions and Bioprocessing) Carmo J. Pereira, Ph.D., M.B.A. DuPont Fellow, E. I. du Pont de Nemours and Company; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 7, Reaction Kinetics; Sec. 19, Reactors) Demetri P. Petrides, Ph.D. President, Intelligen, Inc.; Member, American Institute of Chemical Engineers, American Chemical Society (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Thomas H. Pratt, Ph.D., P.E., C.S.P. Retired; Emeritus Member, NFPA 77 (Static Electricity) (Sec. 23, Process Safety) Richard W. Prugh, M.S., P.E., C.S.P. Principal Process Safety Consultant, Chilworth Technology, Inc., a Dekra Company; Fellow, American Institute of Chemical Engineers; Member, National Fire Protection Association (Toxicity) (Sec. 23, Process Safety) Massood Ramezan, Ph.D., P.E. Sr. Technical Advisor, KeyLogic Systems, Inc. (Coal Conversion) (Sec. 24, Energy Resources, Conversion, and Utilization) George A. Richards, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas, Liquefied Petroleum Gas, Other Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) John R. Richards, Ph.D. Research Fellow, E. I. du Pont de Nemours and Company (retired); Fellow, American Institute of Chemical Engineers (Polymerization Reactions) (Sec. 7, Reaction Kinetics) James A. Ritter, Ph.D. L. M. Weisiger Professor of Engineering and Carolina Distinguished Professor, Department of Chemical Engineering, University of South Carolina; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Sorption Equilibrium, Process Cycles, Equipment) (Sec. 16, Adsorption and Ion Exchange) Richard L. Rowley, Ph.D. Professor Emeritus of Chemical Engineering, Brigham Young University (Section Coeditor, Sec. 2, Physical and Chemical Data) Scott R. Rudge, Ph.D. Chief Operating Officer and Chairman, RMC Pharmaceutical Solutions, Inc.; Adjunct Professor, Chemical and Biological Engineering, University of Colorado; Vice President, Margaux Biologics, Scientific Advisory Board, Sundhin Biopharma (Downstream Processing: Primary Recovery and Purification); Member, American Chemical Society, International Society of Pharmaceutical Engineers, American Association for the Advancement of Science, Parenteral Drug Association (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Adel F. Sarofim, Sc.D. Deceased; Presidential Professor of Chemical Engineering, Combustion, and Reactors, University of Utah; Member, American Institute of Chemical Engineers, American Chemical Society, Combustion Institute (Radiation) (Sec. 5, Heat and Mass Transfer) David K. Schmalzer, Ph.D., P.E. Argonne National Laboratory (Retired), Member, American Chemical Society, American Institute of Chemical Engineers (Resources and Reserves, Liquid Petroleum Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) COnTRIBUTORS xiii Fred Schoenbrunn, B.S. Director-Sedimentation Products, Member, Society of Metallurgical and Exploration Engineers of the American Institute of Minting, Metallurgical and Petroleum Engineers; Registered Professional Engineer (Gravity Sedimentation Operations) (Sec. 18, Liquid-Solid Operations and Equipment) A. Frank Seibert, Ph.D., P.E. Technical Manager, Separations Research Program, The University of Texas at Austin; Fellow, American Institute of Chemical Engineers (Sec. 15, Liquid-Liquid Extraction and Other Liquid-Liquid Operations and Equipment) Yongkoo Seol, Ph.D. Geologist, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas) (Sec. 24, Energy Resources, Conversion, and Utilization) Lawrence J. Shadle, Ph.D. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Coke) (Sec. 24, Energy Resources, Conversion, and Utilization) Robert R. Sharp, P.E., Ph.D. Environmental Consultant; Professor of Environmental Engineering, Manhattan College; Member, American Water Works Association; Water Environment Federation Section Director (Wastewater Management) (Sec. 22, Waste Management) Dushyant Shekhawat, Ph.D., P.E. Chemical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Natural Gas, Fuel and Energy Costs) (Sec. 24, Energy Resources, Conversion, and Utilization) Richard L. Shilling, P.E., B.E.M.E. Senior Engineering Consultant, Heat Transfer Research, Inc.; American Society of Mechanical Engineers (Section Editor, Sec. 11, Heat-Transfer Equipment) nicholas S. Siefert, Ph.D., P.E. Mechanical Engineer, National Energy Technology Laboratory, U.S. Department of Energy (Other Solid Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Geoffrey D. Silcox, Ph.D. Professor of Chemical Engineering, University of Utah; Member, American Institute of Chemical Engineers, American Chemical Society (Heat Transfer Section Coeditor, Sec. 5, Heat and Mass Transfer) Cecil L. Smith, Ph.D. Principal, Cecil L. Smith Inc. (Batch Process Control, Telemetering and Transmission, Digital Technology for Process Control, Process Control and Plant Safety) (Sec. 8, Process Control) (Francis) Lee Smith, Ph.D. Principal, Wilcrest Consulting Associates, LLC, Katy, Texas; Partner and General Manager, Albutran USA, LLC, Katy, Texas (Front-End Loading, Value-Improving Practices) (Sec. 9, Process Economics); (Evaporative Cooling) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying); (Energy Recovery) (Sec. 24, Energy Resources, Conversion, and Utilization) Joseph D. Smith, Ph.D. Professor of Chemical and Biochemical Engineering, Missouri University of Science and Technology (Thermal Energy Conversion and Utilization) (Sec. 24, Energy Resources, Conversion, and Utilization) Daniel J. Soeder, M.S. Director, Energy Resources Initiative, South Dakota School of Mines & Technology (Gaseous Fuels) (Sec. 24, Energy Resources, Conversion, and Utilization) Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education (Section Editor, Sec. 1, Unit Conversion Factors and Symbols); (Section Editor, Sec. 2, Physical and Chemical Data) Thomas O. Spicer III, Ph.D., P.E. Professor; Maurice E. Barker Chair in Chemical Engineering, Chemical Hazards Research Center Director, Ralph E. Martin Department of Chemical Engineering, University of Arkansas; Fellow, American Institute of Chemical Engineers (Atmospheric Dispersion) (Sec. 23, Process Safety) Jason A. Stamper, M. Eng. Technology Leader, Drying and Particle Processing, The Procter & Gamble Company; Member, Institute for Liquid Atomization and Spray Systems (Drying Equipment, Fluidized Bed Dryers, Spray Dryers) (Sec. 12, Psychrometry, Evaporative Cooling, and Solids Drying) Daniel E. Steinmeyer, P.E., M.S. Distinguished Science Fellow, Monsanto Company (retired); Fellow, American Institute of Chemical Engineers; Member, American Chemical Society (Phase Dispersion, Liquid in Gas Systems) (Sec. 14, Equipment for Distillation, Gas Absorption, Phase Dispersion, and Phase Separation) Gary J. Stiegel, P.E., M.S. Technology Manager (Retired), National Energy Technology Laboratory, U.S. Department of Energy (Coal Conversion) (Sec. 24, Energy Resources, Conversion, and Utilization) Angela Summers, Ph.D., P.E. President, SIS-TECH; Adjunct Professor, Department of Environmental Management, University of Houston–Clear Lake; Fellow, International Society of Automation; Fellow, American Institute of Chemical Engineers; Fellow, AIChE Center for Chemical Process Safety (Safety Instrumented Systems) (Sec. 23, Process Safety) Richard C. Sutherlin, B.S., P.E. Richard Sutherlin, PE, Consulting, LLC; Registered Professional Metallurgical Engineer (Oregon) (Reactive Metals) (Sec. 25, Materials of Construction) Ross Taylor, Ph.D. Distinguished Professor of Chemical Engineering, Clarkson University (Simulation of Distillation Processes) (Sec. 13, Distillation) xiv COnTRIBUTORS Louis Theodore, Eng.Sc.D. Consultant, Theodore Tutorials, Professor of Chemical Engineering, Manhattan College; Member, Air and Waste Management Association (Section Coeditor, Sec. 22, Waste Management) Susan A. Thorneloe, M.S. U.S. EPA/Office of Research & Development, National Risk Management Research Laboratory; Member, Air and Waste Management Association, International Waste Working Group (Sec. 22, Waste Management) James n. Tilton, Ph.D., P.E. DuPont Fellow, Chemical and Bioprocess Engineering, E. I. du Pont de Nemours & Co.; Member, American Institute of Chemical Engineers; Registered Professional Engineer (Delaware) (Section Editor, Sec. 6, Fluid and Particle Dynamics) Paul W. Todd, Ph.D. Chief Scientist Emeritus, Techshot, Inc.; Member, American Institute of Chemical Engineers (Downstream Processing: Primary Recovery and Purification) (Sec. 20, Bioreactions and Bioprocessing) Krista S. Walton, Ph.D. Professor and Robert “Bud” Moeller Faculty Fellow, School of Chemical & Biomolecular Engineering, Georgia Institute of Technology; Member, American Institute of Chemical Engineers, American Chemical Society, International Adsorption Society (Adsorbents) (Sec. 16, Adsorption and Ion Exchange) Phillip C. Wankat, Ph.D. Clifton L. Lovell Distinguished Professor of Chemical Engineering Emeritus, Purdue University; Member, American Institute of Chemical Engineers (Mass Transfer Coeditor, Sec. 5, Heat and Mass Transfer) Kenneth n. Weiss, P.E., BCEE, B.Ch.E, M.B.A. Managing Partner, ERM; Member, Air and Waste Management Association (Introduction to Waste Management and Regulatory Overview) (Sec. 22, Waste Management) W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow, American Institute of Chemical Engineers (Section Coeditor, Sec. 2, Physical and Chemical Data) Ronald J. Willey, Ph.D., P.E. Professor, Department of Chemical Engineering, Northeastern University; Fellow, American Institute of Chemical Engineers (Case Histories) (Sec. 23, Process Safety) Todd W. Wisdom, M.S. Director-Separations Technology, FLSmidth USA, Inc.; Member, American Institute of Chemical Engineers (Filtration) (Sec. 18, Liquid-Solid Operations and Equipment) John L. Woodward, Ph.D. Senior Principal Consultant, Baker Engineering and Risk Consultants, Inc.; Fellow, American Institute of Chemical Engineers (Discharge Rates from Punctured Lines and Vessels) (Sec. 23, Process Safety) Preface to the ninth Edition “This handbook is intended to supply both the practicing engineer and the student with an authoritative reference work that covers comprehensively the field of chemical engineering as well as important related fields.” —John H. Perry, 1934 Chemical engineering is generally accepted to have had its origin in the United Kingdom (U.K.) during the latter part of the nineteenth century, largely in response to the industrial revolution and growth in the demand for industrial chemicals. To answer this demand, chemical companies began to mass-produce their products, which meant moving from batch processing to continuous operation. New processes and equipment, in turn, called for new methods. Initially, continuous reactions and processing were implemented largely by plant operators, mechanical engineers, and industrial chemists. Chemical engineering evolved from this advancement of the chemical industry, creating engineers who were trained in chemistry as well as the fundamentals of engineering, physics, and thermodynamics. As an academic discipline, the earliest reported chemical engineering lectures were given in the United Kingdom. George Davis is generally recognized as the first chemical engineer, lecturing at the Manchester Technical School (later the University of Manchester) in 1887. The first American chemical engineering courses were taught at MIT in 1888. Davis also proposed an appropriate professional society that evolved with the industrial and academic profession, ultimately called the Society of Chemical Industry (1881). His initial proposal was for a society of chemical engineers but the name was changed because so few chemical engineers existed at that time. From there, the American Institute of Chemical Engineers, AIChE (1908), and the U.K.-origin Institution of Chemical Engineers, IChemE (1922), were created. As the discipline advanced, important approaches to describing and designing chemical and physical processes developed. George Davis is credited with an early description of what came to be termed “unit operations,” although he did not use that specific term. Arthur D. Little coined the phrase in 1908 in a report to the president of MIT and developed the concept and applications with William H. Walker. Walker later defined “unit operations” in his 1923 seminal textbook published by McGraw-Hill, Principles of Chemical Engineering, coauthored with Warren K. Lewis and William H. McAdams. Other concepts developed over time, including chemical reactor engineering, transport phenomena, and use of computers to enhance mathematical simulation, have increased our ability to understand and design chemical/physical industrial processes. Chemical engineering concepts and methods have been applied in increasingly diverse fields, including environmental engineering, pharmaceutical processing, microelectronics, and biological/biosimilar engineering. The first known handbook of chemical engineering was in two volumes, written by George Davis, and published in the United Kingdom in 1901. A second edition followed in 1904. The emphasis was on materials and their properties; laboratory equipment and techniques; steam production and distribution; power and its applications; moving solids, liquids, and gases; and solids handling. In the preface, Davis acknowledged the advances in industrial chemistry made in Germany, especially in commercial organic chemistry. He also noted the “severe competition” coming from America “in the ammoniasoda industry.” The first US handbook was edited by Donald M. Liddell and published by McGraw-Hill in 1922. It was a two-volume book with thirty-one contributing writers. It dealt with many of the same topics as in the Davis handbook, but also had significantly more emphasis on operations such as leaching, crystallization, evaporation, and drying. Perry’s Chemical Engineers’ Handbook originated from a decision by McGraw-Hill in 1930 (during the Great Depression) to develop a new handbook of chemical engineering. Receiving support for the project from DuPont Company, they selected John H. Perry to be the editor. Perry had earned a Ph.D. from MIT in 1922 in Physical Chemistry and Chemical Engineering. He subsequently worked for the US Bureau of Mines, next as a chemist for a DuPont subsidiary in Cleveland, OH, then moved to Wilmington, DE, to work for DuPont as a chemist in the company’s experimental station, and back to xv xvi PREFACE TO THE nInTH EDITIOn Cleveland, still with DuPont. Family lore says that Perry was a very hard worker, dedicated to chemical engineering, and willing to basically live two lives: one as a full-time engineer for DuPont and the other as editor of the handbook. On weekends he would hitchhike to New York, go to the Chemist’s Club with a packet of galley proofs and a carton of cigarettes, and work all weekend, sometimes for 24 hours at a time. His work on the book extended through 1933, leading to publication of the first edition in January 1934. There were 63 contributors, 14 from the DuPont Company and 21 from different universities, all experts in their respective technical areas. The first sentence in the preface was applicable then as well as for this ninth edition: “This handbook is intended to supply both the practicing engineer and the student with an authoritative reference work that covers comprehensively the field of chemical engineering as well as important related fields.” Several chemical engineers, serving as editor or coeditor, have guided the preparation of the different editions over the years. John H. Perry was editor of the first (1934), second (1941), and third (1950) editions before his untimely death in 1953. The position of editor passed to his only child, Robert H. Perry (Bob), a notable chemical engineer in his own right. Bob had a Ph.D. in chemical engineering from the University of Delaware and was working in industry at the time of his father’s death. In 1958, he took a position as professor and later chair of the Department of Chemical Engineering at the University of Oklahoma. He was the editor of the fourth (1963) edition, coedited with Cecil H. Chilton and assisted by Sidney D. Kirkpatrick, and the fifth (1973) edition, coedited with Chilton. For the sixth edition, Bob asked Don W. Green, his first Ph.D. student and now a professor of Chemical and Petroleum Engineering at the University of Kansas, to assist him. Tragically, Bob Perry’s work on the handbook ceased when he was killed in an accident south of London in November 1978. Green assumed responsibility as editor and completed the sixth edition (1984), assisted by a colleague at KU, James O. Maloney. The first five editions were titled The Chemical Engineers’ Handbook. Beginning with the sixth edition, the book was renamed Perry’s Chemical Engineers’ Handbook in honor of the father and son. Green was also editor of the seventh (1997) and eighth (2008) editions, with Maloney assisting on the seventh edition. Robert H. Perry was listed as the “late editor” for the seventh and eighth editions; honoring his ideas that carried over to these recent editions. To create the ninth edition, Green brought on Marylee Z. Southard, a colleague with industrial, consulting, and academic experience in chemical engineering. The organization of this ninth edition replicates the logic of the eighth edition, although content changes are extensive. The first group of sections includes comprehensive tables with unit conversions and fundamental constants, physical and chemical data, methods to predict properties, and basics of mathematics most useful to engineers. The second group, comprising the fourth through the ninth sections, covers fundamentals of chemical engineering. The third and largest group of sections deals with processes, including heat transfer operations, distillation, gas–liquid processes, chemical reactors, and liquid–liquid processes. The last group of sections covers auxiliary information, including waste management, safety and handling of hazardous materials, energy sources, and materials of construction. In 2012, McGraw-Hill launched Access Engineering (ACE), an electronic engineering reference tool for professionals, academics, and students. This edition of Perry’s Chemical Engineers’ Handbook is a part of ACE, as was the eighth edition. Beyond the complete text of the handbook, ACE provides: • Interactive graphs • Video tutorials for example problems given in the handbook • Excel spreadsheets to solve guided and user-defined problems in different areas, such as heat transfer or fluid flow • Curriculum maps for use in complementing engineering course content All 25 sections have been updated to cover the latest advances in technology related to chemical engineering. Notable updates and completely new materials include: • Sec. 2 includes new and updated chemical property data produced by the Design Institute for Physical Properties (DIPPR) of AIChE • Sec. 4 on thermodynamics fundamentals has been redesigned to be more practical, and less theoretical than in earlier editions, to suit the practicing engineer and student pursuing applications • A new Sec. 20, “Bioreactions and Bioprocessing,” has been added in response to the significant, large-scale growth of commercial processes for nonfood products since the end of the twentieth century • Sec. 21 on solids handling operations and equipment has been rewritten by industrial experts in their field A group of 147 professionals, serving as section editors and contributors, has worked on this ninth edition. Their names, affiliations, and writing responsibilities are listed herein as part of the front material and on the title page of their respective sections. These authors are known experts in their field, with many having received professional awards and named as Fellows of their professional societies. Since the publication of the eighth edition, we have lost two major contributors to Perry’s Chemical Engineers’ Handbook. Dr. Adel F. Sarofim died in December 2011. He was a section coeditor/contributor in the radiation subsection from the fifth edition (1973) through this current ninth edition. Dr. Sarofim, a Professor Emeritus at MIT, was a recognized pioneer in the development of combustion science and radiation heat transfer. He received numerous U.S. and international prizes for his work. Dr. Meherwan P. Boyce died in December 2017. He was the editor for the “Transport and Storage of Fluids” section in the seventh edition and co-section editor for the eighth and current editions. Dr. Boyce was founder of Boyce Engineering International. He was also known for his role as the first director of the Turbomachinery Laboratory and founding member of the Turbomachinery Symposium. On this 85th anniversary of Perry’s Chemical Engineers’ Handbook, we celebrate the memory of its creators, Dr. John H. Perry and Dr. Robert H. Perry. Often referred to as “the Bible of Chemical Engineering,” this handbook is the gold standard as a source of valuable information to innumerable chemical engineers. We dedicate this ninth edition to chemical engineers who carry on the profession, creating solutions, products, and processes needed in the challenging world ahead. We hope this edition will provide information and focus for you—to work for the quality and improvement of human life and the earth we inhabit. DON W. GREEN Editor-in-Chief MARYLEE Z. SOUTHARD Associate Editor Section 1 Unit Conversion Factors and Symbols Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education Table 1-1 Table 1-2a Table 1-2b Table 1-3 Table 1-4 Table 1-5 UnITS AnD SYMBOLS Standard SI Quantities and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Derived Units of SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derived Units of SI That Have Special Names . . . . . . . . . . . . . . . . . . . . SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Greek Alphabet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . United States Traditional System of Weights and Measures . . . . . . 1-2 1-2 1-2 1-2 1-2 1-3 Table 1-6 Table 1-7 COnVERSIOn FACTORS Common Units and Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . Alphabetical Listing of Common Unit Conversions . . . . . . . . . . . . . . 1-4 1-5 Table 1-8 Table 1-9 Table 1-10 Table 1-11 Table 1-12 Table 1-13 Table 1-14 Conversion Factors: Commonly Used and Traditional Units to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Conversion Factors to SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density Conversion Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematic Viscosity Conversion Formulas. . . . . . . . . . . . . . . . . . . . . . . Values of the Ideal Gas Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 1-15 1-17 1-17 1-17 1-17 1-18 1-1 1-2 UnIT COnVERSIOn FACTORS AnD SYMBOLS UnITS AnD SYMBOLS TABLE 1-2b Derived Units of SI That Have Special names TABLE 1-1 Standard SI Quantities and Units Quantity or “dimension” SI unit SI unit symbol (“abbreviation”) Base quantity or “dimension” m length meter kg kilogram mass s second time A ampere electric current K kelvin thermodynamic temperature mol mole* amount of substance cd candela luminous intensity Supplementary quantity or “dimension” rad radian plane angle sr steradian solid angle *When the mole is used, the elementary entities must be specified; they may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. TABLE 1-2a Common Derived Units of SI Quantity Unit Symbol acceleration angular acceleration angular velocity area concentration (mass) concentration (molar) current density density, mass electric charge density electric field strength electric flux density energy density entropy heat capacity heat flux density, irradiance luminance magnetic field strength molar energy molar entropy molar heat capacity moment of force permeability permittivity radiance radiant intensity specific energy specific entropy specific heat capacity specific volume surface tension thermal conductivity velocity viscosity, dynamic viscosity, kinematic volume wave number meter per second squared radian per second squared radian per second square meter kilogram per cubic meter mole per cubic meter ampere per square meter kilogram per cubic meter coulomb per cubic meter volt per meter coulomb per square meter joule per cubic meter joule per kelvin joule per kelvin watt per square meter candela per square meter ampere per meter joule per mole joule per mole-kelvin joule per mole-kelvin newton-meter henry per meter farad per meter watt per square meter-steradian watt per steradian joule per kilogram joule per kilogram-kelvin joule per kilogram-kelvin cubic meter per kilogram newton per meter watt per meter-kelvin meter per second pascal-second square meter per second cubic meter reciprocal meter m/s2 rad/s2 rad/s m2 kg/m3 mol/m3 A/m2 kg/m3 C/m3 V/m C/m2 J/m3 J/K J/K W/m2 cd/m2 A/m J/mol J/(mol ⋅ K) J/(mol ⋅ K) N⋅m H/m F/m W/(m2 ⋅ sr) W/sr J/kg J/(kg ⋅ K) J/(kg ⋅ K) m3/kg N/m W/(m ⋅ K) m/s Pa ⋅ s m2/s m3 1/m Quantity absorbed dose activity (of radionuclides) capacitance conductance electric potential, potential difference, electromotive force electric resistance energy, work, quantity of heat force frequency (of a periodic phenomenon) illuminance inductance luminous flux magnetic flux magnetic flux density power, radiant flux pressure, stress quantity of electricity, electric charge Unit Symbol gray becquerel farad siemens volt Gy Bq F S V J/kg l/s C/V A/V W/A Formula ohm joule newton hertz lux henry lumen weber tesla watt pascal coulomb Ω J N Hz lx H lm Wb T W Pa C V/A N⋅m (kg ⋅ m)/s2 1/s lm/m2 Wb/A Cd ⋅ sr V⋅s Wb/m2 J/s N/m2 A⋅s TABLE 1-3 SI Prefixes Multiplication factor 1 000 000 000 1 000 000 1 000 1 000 000 000 000 1 000 000 000 000 000 1 18 000 = 10 000 = 1015 000 = 1012 000 = 109 000 = 106 000 = 103 100 = 102 10 = 101 0.1 = 10-1 0.01 = 10-2 0.001 = 10-3 0.000 001 = 10-6 0.000 000 001 = 10-9 0.000 000 000 001 = 10-12 0.000 000 000 000 001 = 10-15 0.000 000 000 000 000 001 = 10-18 Prefix Symbol exa peta tera giga mega kilo hecto* deka* deci* centi milli micro nano pico femto atto E P T G M k h da d c m µ n p f a *Generally to be avoided. TABLE 1-4 Greek Alphabet alpha = A, α beta = B, b gamma = Γ, γ delta = Δ, δ epsilon = Ε, ε zeta = Ζ, ζ eta = Η, η theta = Θ, θ iota = Ι, ι kappa = Κ, κ lambda = Λ, λ mu = Μ, µ nu xi omicron pi rho sigma tau upsilon phi chi psi omega = Ν, ν = Ξ, ξ = Ο, ο = Π, π = Ρ, ρ = Σ, σ = Τ, τ = Υ, υ = Φ, φ = Χ, χ = Ψ, ψ = Ω, ω UnITS AnD SYMBOLS TABLE 1-5 United States Traditional System of Weights and Measures Linear Measure 12 inches (in) or (″) = 1 foot ( ft) or (′) 3 feet = 1 yard (yd) 16.5 feet   = 1 rod (rd) 5.5 yards  5280 feet  = 1 mile (mi) 320 rods   1 mil = 0.001 in Nautical: 6080.2 feet = 1 nautical mile 6 feet = 1 fathom 120 fathoms = 1 cable length 1 knot (kn) = 1 nautical mile per hour 60 nautical miles = 1° of latitude Square Measure 144 square inches (sq in) or (in2) = 1 sq ft ( ft2) 9 sq ft ( ft2) = 1 sq yd (yd2) 30.25 sq yd = 1 sq rod, pole, or perch  10 sq chains  160 sq rods =   = 1 acre 43.560 sq ft    640 acres = 1 sq mi = 1 section 1 circular in (area of circle of 1-in diameter) = 0.7854 sq in 1 sq in = 1.2732 circular in 1 circular mil = area of circle of 0.001-in diameter 1,000,000 circular mils = 1 circular in Circular Measure 60 seconds (″) = 1 minute or (′) 60 minutes (′) = 1 degree (1°) 90 degrees (90°) = 1 quadrant 360 degrees (360°) = 1 circumference  1 radian (rad) 57.29578 degrees =   57 17 ′ 44.81′′ Volume Measure Solid: 1728 cubic in (cu in) (in3) = 1 cubic foot (cu ft) ( ft3) 27 cu ft = 1 cubic yard (cu yd) (yd3) Dry Measure: 2 pints = 1 quart 8 quarts = 1 peck 4 pecks = 1 bushel 1 U.S. Winchester bushel = 2150.42 cubic inches (in3) Liquid: 4 gills = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) 7.4805 gallons = 1 cubic foot ( ft3) Apothecaries’ Liquid: 60 minims (min. or ) = 1 fluid dram or drachm 8 drams ( ) = 1 fluid ounce 16 ounces (oz. ) = 1 pint Avoirdupois Weight 16 drams = 437.5 grains (gr) = 1 ounce (oz) 16 ounces = 7000 grains = 1 pound (lb) 100 pounds = 1 hundredweight (cwt) 2000 pounds = 1 short ton; 2240 pounds = 1 long ton Troy Weight 24 grains (gr) = 1 pennyweight (dwt) 20 pennyweights = 1 ounce (oz) 12 ounces = 1 pound (lb) Apothecaries’ Weight 20 grains (gr) = 1 scruple ( ) 3 scruples = 1 dram ( ) 8 drams = 1 ounce ( ) 12 ounces = 1 pound (lb) 1-3 1-4 UnIT COnVERSIOn FACTORS AnD SYMBOLS COnVERSIOn FACTORS TABLE 1-6 Common Units and Conversion Factors* Mass (M) Length (L) Area (L2) Volume (L3) Time (θ) 1 pound mass = 453.5924 grams = 0.45359 kilogram = 7000 grains 1 slug = 32.174 pounds mass 1 ton (short) = 2000 pounds mass 1 ton (long) = 2240 pounds mass 1 ton (metric) = 1000 kilograms = 2204.62 pounds mass 1 pound-mole = 453.59 gram-moles 1 foot = 30.480 centimeters = 0.3048 meter 1 inch = 2.54 centimeters = 0.0254 meter 1 mile (U.S.) = 1.60935 kilometers 1 yard = 0.9144 meter 1 square foot = 929.0304 square centimeters = 0.09290304 square meter 1 square inch = 6.4516 square centimeters 1 square yard = 0.836127 square meter 1 cubic foot = 28,316.85 cubic centimeters = 0.02831685 cubic meter = 28.31685 liters = 7.481 gallons (U.S.) 1 gallon = 3.7853 liters = 231 cubic inches 1 hour (h) = 60 minutes (min) = 3600 seconds (s) Temperature (T) 1 centigrade or Celsius degree = 1.8 Fahrenheit degrees Temperature, Kelvin = T °C + 273.15 Temperature, Rankine = T °F + 459.7 Temperature, Fahrenheit = 9/5 T °C + 32 Temperature, Celsius or centigrade = 5/9 (T °F - 32) Temperature, Rankine = 1.8T K Force (F) 1 pound force = 444,822.2 dynes = 4.448222 newtons (N) = 32.174 poundals 2 Pressure (F/L ) Normal atmospheric pressure note: U.S. Customary units, or British units, on left and SI units on right. *Adapted from Faust et al., Principles of Unit Operations, John Wiley & Sons, 1980. 1 atm = 760 millimeters of mercury at 0°C (density 13.5951 g/cm3) = 29.921 inches of mercury at 32°F = 14.696 pounds force/square inch = 33.899 feet of water at 39.1°F = 1.01325 × 106 dynes/square centimeter = 1.01325 × 105 newtons/square meter Density (M/L3) 1 pound mass/cubic foot = 0.01601846 gram/cubic centimeter = 16.01846 kilograms/cubic meter Energy (H or FL) 1 British thermal unit = 251.98 calories = 1054.4 joules = 777.97 foot-pounds force = 10.409 liter-atmospheres = 0.2930 watthour Diffusivity (L2/θ) 1 square foot/hour = 0.258 cm2/s = 2.58 × 10-5 m2/s Viscosity (M/Lθ) 1 pound mass/foot-hour = 0.00413 g/cm s = 0.000413 kg/m s 1 centipoise (cP) = 0.01 poise (P) = 0.01 g/cm s = 0.001 kg/m s = 0.000672 lbm/ft s = 0.0000209 lbf -s/ft2 Thermal conductivity [H/θ L2(T/L)] 1 Btu/h ft2 (°F/ft) = 0.00413 cal/s cm2 (°C/cm) = 1.728 J/s m2 (°C/m) Heat transfer coefficient 1 Btu/h ft2 °F = 5.678 J/s m2 °C Heat capacity (H/MT ) 1 Btu/lbm °F = 1 cal/g °C = 4184 J/kg °C Gas constant 1.987 Btu/lbm mol °R = 1.987 cal/mol K = 82.057 atm cm3/mol K = 0.7302 atm ft3/lbmol °F = 10.73 (lbf /in2) ( ft3)/lb mol °R = 1545 (lbf /ft2) ( ft3)/lb mol °R = 8.314 (N/m2) (m3)/mol K Gravitational acceleration g = 9.8066 m/s2 = 32.174 ft/s2 COnVERSIOn FACTORS 1-5 TABLE 1-7 Alphabetical Listing of Common Unit Conversions To Convert from acres acres acres acre-feet ampere-hours (absolute) angstrom units angstrom units angstrom units atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres atmospheres bags (cement) barrels (cement) barrels (oil) barrels (oil) barrels (U.S. liquid) barrels (U.S. liquid) barrels per day bars bars bars board feet boiler horsepower boiler horsepower Btu Btu Btu Btu Btu Btu Btu Btu Btu Btu Btu per cubic foot Btu per hour Btu per minute Btu per pound Btu per pound per degree Fahrenheit Btu per pound per degree Fahrenheit Btu per second Btu per square foot per hour Btu per square foot per minute Btu per square foot per second for a temperature gradient of 1°F per inch Btu (60°F) per degree Fahrenheit Bushels (U.S. dry) Bushels (U.S. dry) calories, gram calories, gram calories, gram calories, gram calories, gram calories, gram, per gram per degree C To Multiply by square feet square meters square miles cubic meters Coulombs (absolute) inches meters microns or micrometers millimeters of mercury at 32°F dynes per square centimeter newtons per square meter feet of water at 39.1°F grams per square centimeter inches of mercury at 32°F pounds per square foot pounds per square inch pounds (cement) pounds (cement) cubic meters gallons cubic meters gallons gallons per minute atmospheres newtons per square meter pounds per square inch cubic feet Btu per hour kilowatts calories (gram) celsius heat units (chu or pcu) foot-pounds horsepower-hours joules liter-atmospheres pounds carbon to CO2 pounds water evaporated from and at 212°F cubic foot–atmospheres kilowatt-hours joules per cubic meter watts horsepower joules per kilogram calories per gram per degree celsius joules per kilogram per degree kelvin watts joules per square meter per second kilowatts per square foot calories, gram (15°C), per square centimeter per second for a temperature gradient of 1°C per centimeter calories per degree Celsius 43,560 4074 0.001563 1233 3600 3.937 × 10-9 1 × 10-10 1 × 10-4 760 1.0133 × 106 101,325 33.90 1033.3 29.921 2116.3 14.696 94 376 0.15899 42 0.11924 31.5 0.02917 0.9869 1 × 105 14.504 1 ⁄12 33,480 9.803 252 0.55556 777.9 3.929 × 10-4 1055.1 10.41 6.88 × 10-5 0.001036 cubic feet cubic meters Btu foot-pounds joules liter-atmospheres horsepower-hours joules per kilogram per kelvin 1.2444 0.03524 3.968 × 10-3 3.087 4.1868 4.130 × 10-2 1.5591 × 10-6 4186.8 0.3676 2.930 × 10-4 37,260 0.29307 0.02357 2326 1 4186.8 1054.4 3.1546 0.1758 1.2405 453.6 To Convert from To calories, kilogram calories, kilogram per second candle power (spherical) carats (metric) centigrade heat units centimeters centimeters centimeters centimeters centimeters centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters of mercury at 0°C centimeters per second centimeters of water at 4°C centistokes circular mils circular mils circular mils cords cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic foot–atmospheres cubic foot–atmospheres cubic feet of water (60°F) cubic feet per minute cubic feet per minute cubic feet per second cubic feet per second cubic inches cubic yards curies curies degrees drams (apothecaries’ or troy) drams (avoirdupois) dynes ergs Faradays fathoms feet feet per minute feet per minute feet per (second)2 feet of water at 39.2°F foot-poundals foot-poundals foot-poundals foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds force foot-pounds per second foot-pounds per second furlongs gallons (U.S. liquid) kilowatt-hours kilowatts lumens grams Btu Angstrom units feet inches meters microns or micrometers atmospheres feet of water at 39.1°F newtons per square meter pounds per square foot pounds per square inch feet per minute newtons per square meter square meters per second square centimeters square inches square mils cubic feet cubic feet gallons ounces (U.S. fluid) quarts (U.S. fluid) Bushels (U.S.) cubic centimeters cubic meters cubic yards gallons liters foot-pounds liter-atmospheres pounds cubic centimeters per second gallons per second gallons per minute million gallons per day cubic meters cubic meters disintegrations per minute coulombs per minute radians grams grams newtons joules Coulombs (abs.) feet meters centimeters per second miles per hour meters per (second)2 newtons per square meter Btu joules liter-atmospheres Btu calories, gram foot-poundals horsepower-hours kilowatt-hours liter-atmospheres joules horsepower kilowatts miles barrels (U.S. liquid) Multiply by 0.0011626 4.185 12.556 0.2 1.8 1 × 108 0.03281 0.3937 0.01 10,000 0.013158 0.4460 1333.2 27.845 0.19337 1.9685 98.064 1 × 10-6 5.067 × 10-6 7.854 × 10-7 0.7854 128 3.532 × 10-5 2.6417 × 10-4 0.03381 0.0010567 0.8036 28,317 0.028317 0.03704 7.481 28.316 2116.3 28.316 62.37 472.0 0.1247 448.8 0.64632 1.6387 × 10-5 0.76456 2.2 × 1012 1.1 × 1012 0.017453 3.888 1.7719 1 × 10-5 1 × 10-7 96,500 6 0.3048 0.5080 0.011364 0.3048 2989 3.995 × 10-5 0.04214 4.159 × 10-4 0.0012856 0.3239 32.174 5.051 × 10-7 3.766 × 10-7 0.013381 1.3558 0.0018182 0.0013558 0.125 0.03175 (Continued ) 1-6 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-7 Alphabetical Listing of Common Unit Conversions (Continued ) To Convert from gallons gallons gallons gallons gallons gallons per minute gallons per minute grains grains grains per cubic foot grains per gallon grams grams grams grams grams grams grams per cubic centimeter grams per cubic centimeter grams per liter grams per liter grams per square centimeter grams per square centimeter hectares hectares horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (British) horsepower (metric) horsepower (metric) hours (mean solar) inches inches of mercury at 60°F inches of water at 60°F joules (absolute) joules (absolute) joules (absolute) joules (absolute) joules (absolute) joules (absolute) kilocalories kilograms kilograms force kilograms per square centimeter kilometers kilowatt-hours kilowatt-hours kilowatts knots (international) knots (nautical miles per hour) lamberts liter-atmospheres liter-atmospheres liters liters liters lumens micromicrons microns To Multiply by cubic meters cubic feet gallons (imperial) liters ounces (U.S. fluid) cubic feet per hour cubic feet per second grams pounds grams per cubic meter parts per million drams (avoirdupois) drams (troy) grains kilograms pounds (avoirdupois) pounds (troy) pounds per cubic foot pounds per gallon grains per gallon pounds per cubic foot pounds per square foot pounds per square inch acres square meters btu per minute btu per hour foot-pounds per minute foot-pounds per second watts horsepower (metric) pounds carbon to CO2 per hour pounds water evaporated per hour at 212°F foot-pounds per second kilogram-meters per second seconds meters newtons per square meter newtons per square meter Btu (mean) calories, gram (mean) cubic foot–atmospheres foot-pounds kilowatt-hours liter-atmospheres joules pounds (avoirdupois) newtons pounds per square inch 0.003785 0.13368 0.8327 3.785 128 8.021 0.002228 0.06480 1 ⁄7000 2.2884 17.118 0.5644 0.2572 15.432 0.001 0.0022046 0.002679 62.43 8.345 58.42 0.0624 2.0482 0.014223 2.471 10,000 42.42 2545 33,000 550 745.7 1.0139 0.175 miles Btu foot-pounds horsepower meters per second miles per hour 0.6214 3414 2.6552 × 106 1.3410 0.5144 1.1516 candles per square inch cubic foot–atmospheres foot-pounds cubic feet cubic meters gallons watts microns or micrometers angstrom units 2.054 0.03532 74.74 0.03532 0.001 0.26418 0.001496 1 × 10-6 1 × 104 2.64 542.47 75.0 3600 0.0254 3376.9 248.84 9.480 × 10-4 0.2389 0.3485 0.7376 2.7778 × 10-7 0.009869 4186.8 2.2046 9.807 14.223 To Convert from microns miles (nautical) miles (nautical) miles miles miles per hour miles per hour milliliters millimeters millimeters of mercury at 0°C millimicrons mils mils minims (U.S.) minutes (angle) minutes (mean solar) newtons ounces (avoirdupois) ounces (avoirdupois) ounces (U.S. fluid) ounces (troy) pints (U.S. liquid) poundals pounds (avoirdupois) pounds (avoirdupois) pounds (avoirdupois) pounds per cubic foot pounds per cubic foot pounds per square foot pounds per square foot pounds per square inch pounds per square inch pounds per square inch pounds force pounds force per square foot pounds water evaporated from and at 212°F pound-celsius units (pcu) quarts (U.S. liquid) radians revolutions per minute seconds (angle) slugs slugs slugs square centimeters square feet square feet per hour square inches square inches square yards stokes tons (long) tons (long) tons (metric) tons (metric) tons (metric) tons (short) tons (short) tons (refrigeration) tons (British shipping) tons (U.S. shipping) torr (mm mercury, 0°C) watts watts watts watthours yards To Multiply by meters feet miles (U.S. statute) feet meters feet per second meters per second cubic centimeters meters newtons per square meter microns inches meters cubic centimeters radians seconds kilograms kilograms ounces (troy) cubic meters ounces (apothecaries’) cubic meters newtons grains kilograms pounds (troy) grams per cubic centimeter kilograms per cubic meter atmospheres kilograms per square meter atmospheres kilograms per square centimeter newtons per square meter newtons newtons per square meter horsepower-hours 1 × 10-6 6080 1.1516 5280 1609.3 1.4667 0.4470 1 0.001 133.32 0.001 0.001 2.54 × 10-5 0.06161 2.909 × 10-4 60 0.10197 0.02835 0.9115 2.957 × 10-5 1.000 4.732 × 10-4 0.13826 7000 0.45359 1.2153 0.016018 16.018 4.725 × 10-4 4.882 0.06805 0.07031 Btu cubic meters degrees radians per second radians g pounds kilograms pounds square feet square meters square meters per second square centimeters square meters square meters square meters per second kilograms pounds kilograms pounds tons (short) kilograms pounds Btu per hour cubic feet cubic feet newtons per square meter Btu per hour joules per second kilogram-meters per second joules meters 1.8 9.464 × 10-4 57.30 0.10472 4.848 × 10-6 1 14.594 32.17 0.0010764 0.0929 2.581 × 10-5 6.452 6.452 × 10-4 0.8361 1 × 10-4 1016 2240 1000 2204.6 1.1023 907.18 2000 12,000 42.00 40.00 133.32 3.413 1 0.10197 3600 0.9144 6894.8 4.4482 47.88 0.379 COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units The following unit symbols are used in the table: Unit symbol Name A a Bq C cd Ci d °C ° dyn F fc G g gr Unit symbol ampere annum (year) becquerel coulomb candela curie day degree Celsius degree dyne farad footcandle gauss gram grain Name Gy H h ha Hz J K L, ℓ, l lm lx m min ′ N naut mi Unit symbol gray henry hour hectare hertz joule kelvin liter lumen lux meter minute minute newton U.S. nautical mile Name Oe Ω Pa rad r S s ″ sr St T t V W Wb oersted ohm pascal radian revolution siemens second second steradian stokes tesla tonne volt watt weber note: Copyright SPE-AIME, The SI Metric System of Units and SPE’s Tentative Metric Standard, Society of Petroleum Engineers, Dallas, 1977. Quantity Customary or commonly used unit SI unit Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Space, time Length naut mi mi chain link fathom yd ft in in mil km km m m m m m cm mm cm µm Length/length ft/mi m/km 3 1.852* 1.609 344* 2.011 68* 2.011 68* 1.828 8* 9.144* 3.048* 3.048* 2.54* 2.54 2.54* E + 00 E + 00 E + 01 E - 01 E + 00 E - 01 E - 01 E + 01 E + 01 E + 00 E + 01 1.893 939 E - 01 Length/volume ft/U.S. gal ft/ft3 ft/bbl m/m m/m3 m/m3 8.051 964 1.076 391 1.917 134 E + 01 E + 01 E + 00 Area mi2 section acre ha yd2 ft2 in2 km2 ha ha m2 m2 m2 mm2 cm2 2.589 988 2.589 988 4.046 856 1.000 000* 8.361 274 9.290 304* 6.451 6* 6.451 6* E + 00 E + 02 E - 01 E + 04 E - 01 E - 02 E + 02 E + 00 Area/volume ft2/in3 ft2/ft3 m2/cm3 m2/m3 5.699 291 3.280 840 E - 03 E + 00 Volume m3 acre ⋅ ft km3 m3 ha ⋅ m m3 m3 m3 dm3 m3 dm3 m3 dm3 dm3 dm3 dm3 cm3 cm3 cm3 4.168 182 1.233 482 1.233 482 7.645 549 1.589 873 2.831 685 2.831 685 4.546 092 4.546 092 3.785 412 3.785 412 1.136 523 9.463 529 4.731 765 2.841 307 2.957 353 1.638 706 E + 00 E + 03 E - 01 E + 01 E - 01 E - 02 E + 01 E - 03 E + 00 E - 03 E + 00 E + 00 E - 01 E - 01 E + 01 E + 01 E + 01 yd3 bbl (42 U.S. gal) ft3 U.K. gal U.S. gal U.K. qt U.S. qt U.S. pt U.K. fl oz U.S. fl oz in3 L L L L L L Volume/length (linear displacement) bbl/in bbl/ft ft3/ft U.S. gal/ft m3m m3/m m3/m m3/m L/m 6.259 342 5.216 119 9.290 304* 1.241 933 1.241 933 E + 00 E - 01 E - 02 E - 02 E + 01 Plane angle rad deg (°) min (′) sec (″) rad rad rad rad 1 1.745 329 2.908 882 4.848 137 E - 02 E - 04 E - 06 Solid angle sr sr 1 *An asterisk indicates that the conversion factor is exact. (Continued ) 1-7 1-8 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Quantity Time Customary or commonly used unit SI unit Alternate SI unit a d s min s h year week h min Conversion factor; multiply customary unit by factor to obtain SI unit 1 7.0* 3.6* 6.0* 6.0* 1.666 667 E + 00 E + 03 E + 01 E + 01 E - 02 1.016 047 9.071 847 5.080 234 4.535 924 4.535 924 3.110 348 2.834 952 6.479 891 E + 00 E - 01 E + 01 E + 01 E - 01 E + 01 E + 01 E + 01 4.535 924 4.461 58 1.195 30 E - 01 E - 02 E - 03 2.326 000 2.326 000 6.461 112 4.184* 9.224 141 E - 03 E + 00 E - 04 E + 00 E + 00 4.184* 2.326 000 E + 03 E + 00 2.787 163 2.787 163 7.742 119 2.320 800 2.320 800 6.446 667 3.725 895 3.725 895 1.034 971 4.184* 3.581 692 E - 01 E + 02 E - 02 E - 01 E + 02 E - 02 E - 02 E + 01 E - 02 E + 00 E - 01 E + 03 E + 00 E + 01 E - 02 Mass, amount of substance Mass U.K. ton U.S. ton U.K. cwt U.S. cwt lbm oz (troy) oz (av) gr Mg Mg kg kg kg g g mg Amount of substance lbmmol std m3 (0°C, 1 atm) std ft3 (60°F, 1 atm) kmol kmol kmol t t Enthalpy, calorific value, heat, entropy, heat capacity cal/g cal/lbm MJ/kg kJ/kg kWh/kg kJ/kg J/kg Caloric value, enthalpy (mole basis) kcal/(g ⋅ mol) Btu/(lb ⋅ mol) kJ/kmol kJ/kmol Caloric value (volume basis—solids and liquids) Btu/U.S. gal MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kWh/m3 MJ/m3 kJ/m3 kJ/dm3 Caloric value, enthalpy (mass basis) Btu/lbm Btu/U.K. gal Btu/ft3 cal/mL ( ft ⋅ lbf)/U.S. gal J/g J/g kJ/dm3 kJ/dm3 Caloric value (volume basis—gases) cal/mL kcal/m3 Btu/ft3 kJ/m3 kJ/m3 kJ/m3 kWh/m3 J/dm3 J/dm3 J/dm3 Specific entropy Btu/(lbm ⋅ °R) cal/(g ⋅ K) kcal/(kg ⋅ °C) kJ/(kg ⋅ K) kJ/(kg ⋅ K) kJ/(kg ⋅ K) J/(g ⋅ K) J/(g ⋅ K) J/(g ⋅ K) 4.184* 4.184* 3.725 895 1.034 971 4.186 8* 4.184* 4.184* Specific heat capacity (mass basis) kWh/(kg ⋅ °C) Btu/(lbm ⋅ °F) kcal/(kg ⋅ °C) kJ/(kg ⋅ K) kJ/(kg ⋅ K) kJ/(kg ⋅ K) J/(g ⋅ K) J/(g ⋅ K) J/(g ⋅ K) 3.6* 4.186 8* 4.184* E + 03 E + 00 E + 00 Specific heat capacity (mole basis) Btu/(lb ⋅ mol ⋅ °F) cal/(g ⋅ mol ⋅ °C) kJ/(kmol ⋅ K) kJ/(kmol ⋅ K) 4.186 8* 4.184* E + 00 E + 00 E + 00 E + 00 E + 00 Temperature, pressure, vacuum Temperature (absolute) °R K K K 5/9 1 Temperature (traditional) °F °C 5/9(°F + 32) Temperature (difference) °F K, °C 5/9 Pressure atm (760 mmHg at 0°C or 14,696 psi) MPa kPa bar MPa kPa MPa kPa bar kPa kPa kPa kPa kPa Pa Pa Pa 1.013 250* 1.013 250* 1.013 250* 1.0* 1.0* 6.894 757 6.894 757 6.894 757 3.376 85 2.488 4 1.333 224 9.806 38 4.788 026 1.333 224 1.0* 1.0* bar mmHg (0°C) = torr µmHg (0°C) µ bar mmHg = torr (0°C) cmH2O (4°C) lbf /ft2 (psf) mHg (0°C) bar dyn/cm2 *An asterisk indicates that the conversion factor is exact. E - 01 E + 02 E + 00 E + 01 E + 02 E - 03 E + 00 E - 02 E + 00 E - 01 E - 01 E - 02 E - 02 E - 01 E + 05 E - 01 COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Customary or commonly used unit SI unit Vacuum, draft inHg (60°F) inH2O (39.2°F) inH2O (60°F) mmHg (0°C) = torr cmH2O (4°C) kPa kPa kPa kPa kPa 3.376 85 2.490 82 2.488 4 1.333 224 9.806 38 E + 00 E - 01 E - 01 E - 01 E -02 Liquid head ft in m mm cm 3.048* 2.54* 2.54* E - 01 E + 01 E + 00 psi/ft kPa/m 2.262 059 E + 01 kg/m3 g/m3 kg/m3 g/cm3 kg/m3 kg/m3 g/cm3 kg/m3 kg/m3 1.601 846 1.601 846 1.198 264 1.198 264 9.977 633 1.601 846 1.601 846 1.0* 1.601 846 E + 01 E + 04 E + 02 E - 01 E + 01 E + 01 E - 02 E + 03 E + 01 ft /lbm U.K. gal/lbm U.S. gal/lbm m3/kg m3/g dm3/kg dm3/kg dm3/kg 6.242 796 6.242 796 6.242 796 1.002 242 8.345 404 E - 02 E - 05 E + 01 E + 01 E + 00 Specific volume (mole basis) L/(gmol) ft3/(lbmol) m3/kmol m3/kmol 1 6.242 796 E - 02 Specific volume bbl/U.S. ton bbl/U.K. ton m3/t m3/t 1.752 535 1.564 763 E - 01 E - 01 Yield bbl/U.S. ton bbl/U.K. ton U.S. gal/U.S. ton U.S. gal/U.K. ton dm3/t dm3/t dm3/t dm3/t 1.752 535 1.564 763 4.172 702 3.725 627 E + 02 E + 02 E + 00 E + 00 Concentration (mass/mass) wt % wt ppm kg/kg g/kg mg/kg 1.0* 1.0* 1 E - 02 E + 01 lbm/bbl g/U.S. gal g/U.K. gal lbm/1000 U.S. gal lbm/1000 U.K. gal gr/U.S. gal gr/ft3 lbm/1000 bbl mg/U.S. gal gr/100 ft3 kg/m3 kg/m3 kg/m3 g/m3 g/m3 g/m3 mg/m3 g/m3 g/m3 mg/m3 2.853 010 2.641 720 2.199 692 1.198 264 9.977 633 1.711 806 2.288 351 2.853 010 2.641 720 2.288 351 E + 00 E - 01 E - 01 E + 02 E + 01 E + 01 E + 03 E + 00 E - 01 E + 01 ft3/ft3 bbl/(acreft) vol % U.K. gal/ft3 U.S. gal/ft3 mL/U.S. gal mL/U.K. gal vol ppm U.K. gal/1000 bbl U.S. gal/1000 bbl U.K. pt/1000 bbl m3/m3 m3/m3 m3/m3 dm3/m3 dm3/m3 dm3/m3 dm3/m3 cm3/m3 dm3/m3 cm3/m3 cm3/m3 cm3/m3 Concentration (mole/volume) (lbmol)/U.S. gal (lbmol)/U.K. gal (lbmol)/ft3 std ft3 (60°F, 1 atm)/bbl kmol/m3 kmol/m3 kmol/m3 kmol/m3 Concentration (volume/mole) U.S. gal/1000 std ft3 (60°F/60°F) bbl/million std ft3 (60°F/60°F) dm3/kmol Quantity Pressure drop/length Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Density, specific volume, concentration, dosage Density lbm/ft3 lbm/U.S. gal lbm/U.K. gal lbm/ft3 g/cm3 lbm/ft3 Specific volume ft3/lbm 3 Concentration (mass/volume) Concentration (volume/volume) *An asterisk indicates that the conversion factor is exact. 3 dm /kmol cm3/g cm3/g L/t L/t L/t L/t g/dm3 g/L mg/dm3 mg/dm3 mg/dm3 mg/dm3 mg/dm3 3 L/m L/m3 L/m3 L/m3 L/m3 1 1.288 931 1.0* 1.605 437 1.336 806 2.641 720 2.199 692 1 1.0* 2.859 403 2.380 952 3.574 253 E - 04 E - 02 E + 02 E + 02 E - 01 E - 01 E - 03 E + 01 E + 01 E + 00 1.198 264 9.977 644 1.601 846 7.518 21 E + 02 E + 01 E + 01 E - 03 L/kmol 3.166 91 E + 00 L/kmol 1.330 10 E - 01 (Continued ) 1-9 1-10 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Quantity Customary or commonly used unit SI unit Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Facility throughput, capacity Throughput (mass basis) U.K. ton/yr U.S. ton/yr U.K. ton/day U.S. ton/day U.K. ton/h U.S. ton/h lbm/h Throughput (volume basis) bbl/day ft3/day bbl/h ft3/h U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min t/a t/a t/d t/h t/d t/h t/h t/h kg/h 1.016 047 9.071 847 1.016 047 4.233 529 9.071 847 3.779 936 1.016 047 9.071 847 4.535 924 E + 00 E - 01 E + 00 E - 02 E - 01 E - 02 E + 00 E - 01 E - 01 t/a m3/d m3/h m3/h m3/h m3/h L/s m3/h L/s m3/h L/s m3/h L/s 5.803 036 1.589 873 1.179 869 1.589 873 2.831 685 4.546 092 1.262 803 3.785 412 1.051 503 2.727 655 7.576 819 2.271 247 6.309 020 E + 01 E - 01 E - 03 E - 01 E - 02 E - 03 E - 03 E - 03 E - 03 E - 01 E - 02 E - 01 E - 02 kmol/h kmol/s 4.535 924 1.259 979 E - 01 E - 04 Throughput (mole basis) (lbmmol)/h Flow rate (mass basis) U.K. ton/min U.S. ton/min U.K. ton/h U.S. ton/h U.K. ton/day U.S. ton/day million lbm/yr U.K. ton/yr U.S. ton/yr lbm/s lbm/min lbm/h kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s kg/s 1.693 412 1.511 974 2.822 353 2.519 958 1.175 980 1.049 982 5.249 912 3.221 864 2.876 664 4.535 924 7.559 873 1.259 979 E + 01 E + 01 E - 01 E - 01 E - 02 E - 02 E + 00 E - 05 E - 05 E - 01 E - 03 E - 04 Flow rate (volume basis) bbl/day U.K. gal/h U.S. gal/h U.K. gal/min U.S. gal/min ft3/min ft3/s m3/d L/s m3/d L/s m3/s L/s m3/s L/s dm3/s dm3/s dm3/s dm3/s dm3/s dm3/s 1.589 873 1.840 131 2.831 685 3.277 413 4.416 314 4.416 314 7.865 791 7.865 791 1.262 803 1.051 503 7.576 820 6.309 020 4.719 474 2.831 685 E - 01 E - 03 E - 02 E - 04 E - 05 E - 02 E - 06 E - 03 E - 03 E - 03 E - 02 E - 02 E - 01 E + 01 Flow rate (mole basis) (lbmol)/s (lbmol)/h million scf/D kmol/s kmol/s kmol/s 4.535 924 1.259 979 1.383 45 E - 01 E - 04 E - 02 Flow rate/length (mass basis) lbm/(sft) lbm/(hft) kg/(sm) kg/(sm) 1.488 164 4.133 789 E + 00 E - 04 Flow rate/length (volume basis) U.K. gal/(min ⋅ ft) U.S. gal/(min ⋅ ft) U.K. gal/(h ⋅ in) U.S. gal/(h ⋅ in) U.K. gal/(h ⋅ ft) U.S. gal/(h ⋅ ft) m2/s m2/s m2/s m2/s m2/s m2/s 2.485 833 2.069 888 4.971 667 4.139 776 4.143 055 3.449 814 E - 04 E - 04 E - 05 E - 05 E - 06 E - 06 Flow rate/area (mass basis) lbm/(s ⋅ ft2) lbm/(h ⋅ ft2) kg/(s ⋅ m2) kg/(s ⋅ m2) 4.882 428 1.356 230 E + 00 E - 03 Flow rate/area (volume basis) ft3/(s ⋅ ft2) ft3/(min ⋅ ft2) U.K. gal/(h ⋅ in2) U.S. gal/(h ⋅ in2) U.K. gal/(min ⋅ ft2) U.S. gal/(min ⋅ ft2) U.K. gal/(h ⋅ ft2) U.S. gal/(h ⋅ ft2) m/s m/s m/s m/s m/s m/s m/s m/s 3.048* 5.08* 1.957 349 1.629 833 8.155 621 6.790 972 1.359 270 1.131 829 E - 01 E - 03 E - 03 E - 03 E - 04 E - 04 E - 05 E - 05 Flow rate 3 ft /day bbl/h ft3/h *An asterisk indicates that the conversion factor is exact. L/s L/s L/s L/s L/s L/s m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) m3/(s ⋅ m2) COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Quantity Customary or commonly used unit SI unit Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Energy, work, power kcal cal ft ⋅ lbf lbf ⋅ ft J (lbf ⋅ ft2)/s2 erg MJ kJ kWh MJ MJ kJ kWh MJ kJ kWh MJ kJ kJ kWh kJ kWh kJ kJ kJ kJ kJ kJ J 1.055 056 1.055 056 2.930 711 1.431 744 2.684 520 2.684 520 7.456 999 2.647 780 2.647 780 7.354 999 3.6* 3.6* 1.899 101 5.275 280 1.055 056 2.930 711 4.184* 4.184* 1.355 818 1.355 818 1.0* 4.214 011 1.0* E + 02 E + 05 E + 01 E + 01 E + 00 E + 03 E - 01 E + 00 E + 03 E - 01 E + 00 E + 03 E + 00 E - 04 E + 00 E - 04 E + 00 E - 03 E - 03 E - 03 E - 03 E - 05 E - 07 Impact energy kgf ⋅ m lbf ⋅ ft J J 9.806 650* 1.355 818 E + 00 E + 00 Surface energy erg/cm2 mJ/m2 1.0* E + 00 J/cm2 J/cm2 9.806 650* 2.101 522 E - 02 E - 03 Energy, work therm U.S. tonf ⋅ mi hp ⋅ h ch ⋅ h or CV ⋅ h kWh Chu Btu Specific-impact energy (kgf ⋅ m)/cm (lbf ⋅ ft)/in2 Power million Btu/h tons of refrigeration Btu/s kW hydraulic horsepower (hhp) hp (electric) hp [(550 ft ⋅ lbf)/s] ch or CV Btu/min ( ft ⋅ lbf)/s kcal/h Btu/h ( ft ⋅ lbf)/min MW kW kW kW kW kW kW kW kW kW W W W 2.930 711 3.516 853 1.055 056 1 7.460 43 7.46* 7.456 999 7.354 999 1.758 427 1.355 818 1.162 222 2.930 711 2.259 697 E - 01 E + 00 E + 00 Power/area Btu/(s ⋅ ft2) cal/(h ⋅ cm2) Btu/(h ⋅ ft2) kW/m2 kW/m2 kW/m2 1.135 653 1.162 222 3.154 591 E + 01 E - 02 E - 03 Heat-release rate, mixing power hp/ft3 cal/(h ⋅ cm3) Btu/(s ⋅ ft3) Btu/(h ⋅ ft3) kW/m3 kW/m3 kW/m3 kW/m3 2.633 414 1.162 222 3.725 895 1.034 971 E + 01 E + 00 E + 01 E - 02 Cooling duty (machinery) Btu/(bhp ⋅ h) W/kW 3.930 148 E - 01 Specific fuel consumption (mass basis) lbm/(hp ⋅ h) mg/J kg/kWh kg/MJ 1.689 659 6.082 774 E - 01 E - 01 Specific fuel consumption (volume basis) m3/kWh U.S. gal/(hp ⋅ h) U.K. pt/(hp ⋅ h) dm3/MJ dm3/MJ dm3/MJ mm3/J mm3/J mm3/J 2.777 778 1.410 089 2.116 806 E + 02 E + 00 E - 01 Fuel consumption U.K. gal/mi U.S. gal/mi mi/U.S. gal mi/U.K. gal dm3/100 km dm3/100 km km/dm3 km/dm3 L/100 km L/100 km km/L km/L 2.824 807 2.352 146 4.251 437 3.540 064 E + 02 E + 02 E - 01 E - 01 Velocity (linear), speed knot mi/h ft/s km/h km/h m/s cm/s m/s mm/s mm/s m/d mm/s mm/s 1.852* 1.609 344* 3.048* 3.048* 5.08* 8.466 667 3.527 778 3.048* 2.54* 4.233 333 E + 00 E + 00 E - 01 E + 01 E - 03 E - 02 E - 03 E - 01 E + 01 E - 01 ft/min ft/h ft/day in/s in/min *An asterisk indicates that the conversion factor is exact. 2 E - 01 E - 01 E - 01 E - 01 E - 02 E - 03 E + 00 E - 01 E - 02 (Continued ) 1-11 1-12 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Customary or commonly used unit SI unit Corrosion rate in/yr (ipy) mil/yr mm/a mm/a 2.54* 2.54* E + 01 E - 02 Rotational frequency r/min r/s rad/s 1.666 667 1.047 198 E + 02 E - 01 Acceleration (linear) ft/s2 m/s2 cm/s2 3.048* 3.048* E - 01 E + 01 Acceleration (rotational) rpm/s rad/s2 1.047 198 E - 01 Momentum (lbm ⋅ ft)/s (kg ⋅ m)/s 1.382 550 E - 01 Force U.K. tonf U.S. tonf kgf lbf dyn kN kN N N mN 9.964 016 8.896 443 9.806 650* 4.448 222 1.0 E + 00 E + 00 E + 00 E + 00 E - 02 Bending moment, torque U.S. tonf ⋅ ft kgf ⋅ m lbf ⋅ ft lbf ⋅ in kN ⋅ m N⋅m N⋅m N⋅m 2.711 636 9.806 650* 1.355 818 1.129 848 E + 00 E + 00 E + 00 E - 01 Bending moment/length (lbf ⋅ ft)/in (lbf ⋅ in)/in (N ⋅ m)/m (N ⋅ m)/m 5.337 866 4.448 222 E + 01 E + 00 Moment of inertia lbm ⋅ ft2 kg ⋅ m2 4.214 011 E - 02 Stress U.S. tonf/in2 kgf/mm2 U.S. tonf/ft2 lbf/in2 (psi) lbf/ft2 (psf) dyn/cm2 MPa MPa MPa MPa kPa Pa 1.378 951 9.806 650* 9.576 052 6.894 757 4.788 026 1.0* E + 01 E + 00 E - 02 E - 03 E - 02 E - 01 Quantity Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit N/mm2 N/mm2 N/mm2 N/mm2 Mass/length lbm/ft kg/m 1.488 164 E + 00 Mass/area structural loading, bearing capacity (mass basis) U.S. ton/ft2 lbm/ft2 Mg/m2 kg/m2 9.764 855 4.882 428 E + 00 E + 00 Diffusivity ft2/s m2/s ft2/h m2/s mm2/s m2/s 9.290 304* 1.0* 2.580 64* E - 02 E + 06 E - 05 Thermal resistance (°C ⋅ m2 ⋅ h)/kcal (°F ⋅ ft2 ⋅ h)/Btu (K ⋅ m2)/kW (K ⋅ m2)/kW 8.604 208 1.761 102 E + 02 E + 02 Heat flux Btu/(h ⋅ ft2) kW/m2 3.154 591 E - 03 W/(m ⋅ K) W/(m ⋅ K) (kJ ⋅ m)/(h ⋅ m2 ⋅ K) W/(m ⋅ K) W/(m ⋅ K) W/(m ⋅ K) 4.184* 1.730 735 6.230 646 1.162 222 1.442 279 1.162 222 E + 02 E + 00 E + 00 E + 00 E - 01 E - 01 Btu/(h ⋅ ft2 ⋅ °R) kcal/(h ⋅ m2 ⋅ °C) kW/(m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K) kJ/(h ⋅ m2 ⋅ K) kW/(m2 ⋅ K) kW/(m2 ⋅ K) 4.184* 2.044 175 1.162 222 5.678 263 2.044 175 5.678 263 1.162 222 E + 01 E + 01 E - 02 E - 03 E + 01 E - 03 E - 03 Volumetric heat-transfer coefficient Btu/(s ⋅ ft3 ⋅ °F) Btu/(h ⋅ ft3 ⋅ °F) kW/(m3 ⋅ K) kW/(m3 ⋅ K) 6.706 611 1.862 947 E + 01 E - 02 Surface tension dyn/cm mN/m Miscellaneous transport properties Thermal conductivity 2 (cal ⋅ cm)/(s ⋅ cm ⋅ °C) (Btu ⋅ ft)/(h ⋅ ft2 ⋅ °F) (kcal ⋅ m)/(h ⋅ m2 ⋅ °C) (Btu ⋅ in)/(h ⋅ ft2 ⋅ °F) (cal ⋅ cm)/(h ⋅ cm2 ⋅ °C) Heat-transfer coefficient Viscosity (dynamic) cal/(s ⋅ cm2 ⋅ °C) Btu/(s ⋅ ft2 ⋅ °F) cal/(h ⋅ cm2 ⋅ °C) Btu/(h ⋅ ft2 ⋅ °F) 2 (lbf ⋅ s)/in (lbf ⋅ s)/ft2 (kgf ⋅ s)/m2 lbm/( ft ⋅ s) (dyn ⋅ s)/cm2 cP lbm/( ft ⋅ h) *An asterisk indicates that the conversion factor is exact. Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s Pa ⋅ s 1 2 (N ⋅ s)/m (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 (N ⋅ s)/m2 6.894 757 4.788 026 9.806 650* 1.488 164 1.0* 1.0* 4.133 789 E + 03 E + 01 E + 00 E + 00 E - 01 E - 03 E - 04 COnVERSIOn FACTORS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Customary or commonly used unit SI unit Viscosity (kinematic) ft2/s in2/s m2/h ft2/h cSt m2/s mm2/s mm2/s m2/s mm2/s 9.290 304* 6.451 6* 2.777 778 2.580 64* 1 E - 02 E + 02 E + 02 E - 05 Permeability darcy millidarcy µm2 µm2 9.869 233 9.869 233 E - 01 E - 04 Thermal flux Btu/(h ⋅ ft2) Btu/(s ⋅ ft2) cal/(s ⋅ cm2) W/m2 W/m2 W/m2 3.152 1.135 4.184 E + 00 E + 04 E + 04 Mass-transfer coefficient (lbmol)/[h ⋅ ft2(lbmol/ft3)] (gmol)/[s ⋅ m2(gmol/L)] m/s m/s 8.467 1.0 E - 05 E + 01 Quantity Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Electricity, magnetism Admittance S S 1 Capacitance µF µF 1 Charge density C/mm3 C/mm3 1 Conductance S S S 1 1 (mho) Ω Conductivity S/m /m m /m S/m S/m mS/m 1 1 1 Current density A/mm2 A/mm2 1 1 Ω Ω 2 Displacement C/cm C/cm2 Electric charge C C 1 Electric current A A 1 Electric-dipole moment C⋅m C⋅m 1 Electric-field strength V/m V/m 1 Electric flux C C 1 Electric polarization C/cm2 C/cm2 1 Electric potential V mV V mV 1 1 Electromagnetic moment A ⋅ m2 A ⋅ m2 1 Electromotive force V V 1 Flux of displacement C C 1 Frequency cycles/s Hz 1 Impedance Ω Ω 1 Linear-current density A/mm A/mm 1 Magnetic-dipole moment Wb ⋅ m Wb ⋅ m 1 Magnetic-field strength A/mm Oe gamma A/mm A/m A/m 1 7.957 747 7.957 747 Magnetic flux mWb mWb 1 Magnetic-flux density mT G gamma mT T nT 1 1.0* 1 Magnetic induction mT mT 1 Magnetic moment A ⋅ m2 A ⋅ m2 1 Magnetic polarization mT mT 1 Magnetic potential difference A A 1 Magnetic-vector potential Wb/mm Wb/mm 1 Magnetization A/mm A/mm 1 Modulus of admittance S S 1 *An asterisk indicates that the conversion factor is exact. E + 01 E + 04 E - 04 (Continued ) 1-13 1-14 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-8 Conversion Factors: Commonly Used and Traditional Units to SI Units (Continued ) Customary or commonly used unit SI unit Modulus of impedance Ω Ω 1 Mutual inductance H H 1 Permeability µH/m µH/m 1 Permeance H H 1 Permittivity µF/m µF/m 1 Potential difference V V 1 Quantity Alternate SI unit Conversion factor; multiply customary unit by factor to obtain SI unit Quantity of electricity C C 1 Reactance Ω Ω 1 Reluctance H-1 H-1 1 Resistance Ω Ω 1 Resistivity Ω ⋅ cm Ω⋅m Ω ⋅ cm Ω⋅m 1 1 Self-inductance mH mH 1 Surface density of change mC/m2 mC/m2 1 Susceptance S S 1 Volume density of charge C/mm3 C/mm3 1 Absorbed dose rad Gy 1.0* Acoustical energy J J 1 Acoustical intensity W/cm2 W/m2 1.0* Acoustical power W W 1 Sound pressure N/m2 N/m2 1.0* Illuminance fc lx 1.076 391 E + 01 Illumination fc lx 1.076 391 E + 01 Acoustics, light, radiation 2 2 Irradiance W/m W/m 1 Light exposure fc ⋅ s lx ⋅ s 1.076 391 Luminance cd/m2 cd/m2 1 Luminous efficacy lm/W lm/W 1 2 2 E - 02 E + 04 E + 01 Luminous exitance lm/m lm/m 1 Luminous flux lm lm 1 Luminous intensity cd cd 1 Radiance W/m2 ⋅ sr W/m2 ⋅ sr 1 Radiant energy J J 1 Radiant flux W W 1 Radiant intensity W/sr W/sr 1 Radiant power W W 1 Wavelength Å nm 1.0* E - 01 Capture unit 10 cm m E + 01 m m 1.0* 1 1 Ci Bq 3.7* E + 10 -3 -1 Radioactivity *An asterisk indicates that the conversion factor is exact. -1 -1 -1 10-3 cm-1 COnVERSIOn FACTORS TABLE 1-9 Other Conversion Factors to SI Units The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m. To Convert from abampere abcoulomb abfarad abhenry abmho abohm abvolt acre ampere (international of 1948) angstrom are astronomical unit atmosphere bar barn barrel (petroleum 42 gal) barye British thermal unit (ISO/TC 12) British thermal unit (International Steam Table) British thermal unit (mean) British thermal unit (thermochemical) British thermal unit (39°F) British thermal unit (60°F) bushel (U.S.) cable caliber calorie (International Steam Table) calorie (mean) calorie (thermochemical) calorie (15°C) calorie (20°C) calorie (kilogram, International Steam Table) calorie (kilogram, mean) calorie (kilogram, thermochemical) carat (metric) Celsius (temperature) centimeter of mercury (0°C) centimeter of water (4°C) chain (engineer’s) chain (surveyor’s or Gunter’s) circular mil cord coulomb (international of 1948) cubit cup curie day (mean solar) day (sidereal) degree (angle) denier (international) dram (avoirdupois) dram (troy or apothecary) dram (U.S. fluid) dyne electron volt erg Fahrenheit (temperature) Fahrenheit (temperature) farad (international of 1948) faraday (based on carbon 12) faraday (chemical) faraday (physical) fathom fermi ( femtometer) fluid ounce (U.S.) foot To Multiply by ampere coulomb farad henry mho ohm volt meter2 ampere +01 1.00 +01 1.00 +09 1.00 -09 1.00 +09 1.00 -09 1.00 -08 1.00 +03 4.046 856 -01 9.998 35 meter meter2 meter newton/meter2 newton/meter2 meter2 meter3 newton/meter2 joule -10 1.00 +02 1.00 +11 1.495 978 +05 1.013 25 +05 1.00 -28 1.00 -01 1.589 873 -01 1.00 +03 1.055 06 joule +03 1.055 04 joule joule +03 1.055 87 +03 1.054 350 joule joule meter3 meter meter joule joule joule joule joule joule +03 1.059 67 +03 1.054 68 -02 3.523 907 +02 2.194 56 -04 2.54 +00 4.1868 +00 4.190 02 +00 4.184 +00 4.185 80 +00 4.181 90 +03 4.186 8 joule joule +03 4.190 02 +03 4.184 kilogram kelvin newton/meter2 newton/meter2 meter meter -04 2.00 tK = tC + 273.15 +03 1.333 22 +01 9.806 38 +01 3.048 +01 2.011 68 meter2 meter3 coulomb -10 5.067 074 +00 3.624 556 -01 9.998 35 meter meter3 disintegration/second second (mean solar) second (mean solar) radian kilogram/meter kilogram kilogram meter3 newton joule joule kelvin Celsius farad coulomb coulomb coulomb meter meter meter3 meter -01 4.572 -04 2.365 882 +10 3.70 +04 8.64 +04 8.616 409 -02 1.745 329 -07 1.111 111 -03 1.771 845 -03 3.887 934 -06 3.696 691 -05 1.00 -19 1.602 10 -07 1.00 tK = (5/9)(tF + 459.67) tC = (5/9)(tF - 32) -01 9.995 05 +04 9.648 70 +04 9.649 57 +04 9.652 19 +00 1.828 8 -15 1.00 -05 2.957 352 -01 3.048 To Convert from foot (U.S. survey) foot of water (39.2°F) footcandle footlambert furlong galileo gallon (U.K. liquid) gallon (U.S. dry) gallon (U.S. liquid) gamma gauss gilbert gill (U.K.) gill (U.S.) grad grad grain gram hand hectare henry (international of 1948) hogshead (U.S.) horsepower (550 ft lbf/s) horsepower (boiler) horsepower (electric) horsepower (metric) horsepower (U.K.) horsepower (water) hour (mean solar) hour (sidereal) hundredweight (long) hundredweight (short) inch inch of mercury (32°F) inch of mercury (60°F) inch of water (39.2°F) inch of water (60°F) joule (international of 1948) kayser kilocalorie (International Steam Table) kilocalorie (mean) kilocalorie (thermochemical) kilogram mass kilogram-force (kgf) kilopound-force kip knot (international) lambert lambert langley lbf (pound-force, avoirdupois) lbm (pound-mass, avoirdupois) league (British nautical) league (international nautical) league (statute) light-year link (engineer’s) link (surveyor’s or Gunter’s) liter lux maxwell meter micrometer mil mile (U.S. statute) mile (U.K. nautical) mile (international nautical) mile (U.S. nautical) millibar millimeter of mercury (0°C) To Multiply by meter newton/meter2 lumen/meter2 candela/meter2 meter meter/second2 meter3 meter3 meter3 tesla tesla ampere turn meter3 meter3 degree (angular) radian kilogram kilogram meter meter2 henry meter3 watt watt watt watt watt watt second (mean solar) second (mean solar) kilogram kilogram meter newton/meter2 newton/meter2 newton/meter2 newton/meter2 joule 1/meter joule -01 3.048 006 +03 2.988 98 +01 1.076 391 +00 3.426 259 +02 2.011 68 -02 1.00 -03 4.546 087 -03 4.404 883 -03 3.785 411 -09 1.00 -04 1.00 -01 7.957 747 -04 1.420 652 -04 1.182 941 -01 9.00 -02 1.570 796 -05 6.479 891 -03 1.00 -01 1.016 +04 1.00 +00 1.000 495 -01 2.384 809 +02 7.456 998 +03 9.809 50 +02 7.46 +02 7.354 99 +02 7.457 +02 7.460 43 +03 3.60 +03 3.590 170 +01 5.080 234 +01 4.535 923 -02 2.54 +03 3.386 389 +03 3.376 85 +02 2.490 82 +02 2.4884 +00 1.000 165 +02 1.00 +03 4.186 74 joule joule kilogram newton newton newton meter/second candela/meter2 candela/meter2 joule/meter2 newton +03 4.190 02 +03 4.184 +00 1.00 +00 9.806 65 +00 9.806 65 +03 4.448 221 -01 5.144 444 +04 1/π +03 3.183 098 +04 4.184 +00 4.448 221 kilogram -01 4.535 923 meter meter +03 5.559 552 +03 5.556 meter meter meter meter meter3 lumen/meter2 weber wavelengths Kr 86 meter meter meter meter meter meter newton/meter2 newton/meter2 +03 4.828 032 +15 9.460 55 -01 3.048 -01 2.011 68 -03 1.00 +00 1.00 -08 1.00 +06 1.650 763 -06 1.00 -05 2.54 +03 1.609 344 +03 1.853 184 +03 1.852 +03 1.852 +02 1.00 +02 1.333 224 (Continued ) 1-15 1-16 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-9 Other Conversion Factors to SI Units (Continued ) The first two digits of each numerical entry represent a power of 10. For example, the entry “-02 2.54” expresses the fact that 1 in = 2.54 × 10-2 m. To Convert from minute (angle) minute (mean solar) minute (sidereal) month (mean calendar) nautical mile (international) nautical mile (U.S.) nautical mile (U.K.) oersted ohm (international of 1948) ounce-force (avoirdupois) ounce-mass (avoirdupois) ounce-mass (troy or apothecary) ounce (U.S. fluid) pace parsec pascal peck (U.S.) pennyweight perch phot pica (printer’s) pint (U.S. dry) pint (U.S. liquid) point (printer’s) poise pole pound-force (lbf avoirdupois) pound-mass (lbm avoirdupois) pound-mass (troy or apothecary) poundal quart (U.S. dry) quart (U.S. liquid) rad (radiation dose absorbed) Rankine (temperature) rayleigh (rate of photon emission) rhe rod roentgen rutherford second (angle) To Multiply by radian second (mean solar) second (mean solar) second (mean solar) meter meter meter ampere/meter ohm newton kilogram kilogram meter3 meter meter newton/meter2 meter3 kilogram meter lumen/meter2 meter meter3 meter3 meter (newton-second)/meter2 meter newton -04 2.908 882 +01 6.00 +01 5.983 617 +06 2.628 +03 1.852 +03 1.852 +03 1.853 184 +01 7.957 747 +00 1.000 495 -01 2.780 138 -02 2.834 952 -02 3.110 347 -05 2.957 352 -01 7.62 +16 3.083 74 +00 1.00 -03 8.809 767 -03 1.555 173 +00 5.0292 +04 1.00 -03 4.217 517 -04 5.506 104 -04 4.731 764 -04 3.514 598 -01 1.00 +00 5.0292 +00 4.448 221 kilogram -01 4.535 923 kilogram -01 3.732 417 newton meter3 meter3 joule/kilogram -01 1.382 549 -03 1.101 220 -04 9.463 529 -02 1.00 kelvin 1/second-meter2 tK = (5/9)tR +10 1.00 meter2/(newtonsecond) meter coulomb/kilogram disintegration/second radian +01 1.00 +00 5.0292 -04 2.579 76 +06 1.00 -06 4.848 136 To Convert from To Multiply by second (ephemeris) second (mean solar) second second (ephemeris) second (sidereal) section scruple (apothecary) shake skein slug span statampere statcoulomb statfarad stathenry statmho statohm statute mile (U.S.) statvolt stere stilb stoke tablespoon teaspoon ton (assay) ton (long) ton (metric) ton (nuclear equivalent of TNT) ton (register) ton (short, 2000 lb) tonne torr (0°C) township unit pole volt (international of 1948) watt (international of 1948) yard year (calendar) year (sidereal) year (tropical) year 1900, tropical, Jan., day 0, hour 12 year 1900, tropical, Jan., day 0, hour 12 second (mean solar) meter2 kilogram second meter kilogram meter ampere coulomb farad henry mho ohm meter volt meter3 candela/meter2 meter2/second meter3 meter3 kilogram kilogram kilogram joule meter3 kilogram kilogram newton/meter2 meter2 weber volt watt meter second (mean solar) second (mean solar) second (mean solar) second (ephemeris) +00 1.000 000 Consult American Ephemeris and Nautical Almanac -01 9.972 695 +06 2.589 988 -03 1.295 978 -08 1.00 +02 1.097 28 +01 1.459 390 -01 2.286 -10 3.335 640 -10 3.335 640 -12 1.112 650 +11 8.987 554 -12 1.112 650 +11 8.987 554 +03 1.609 344 +02 2.997 925 +00 1.00 +04 1.00 -04 1.00 -05 1.478 676 -06 4.928 921 -02 2.916 666 +03 1.016 046 +03 1.00 +09 4.20 +00 2.831 684 +02 9.071 847 +03 1.00 +02 1.333 22 +07 9.323 957 -07 1.256 637 +00 1.000 330 +00 1.000 165 -01 9.144 +07 3.1536 +07 3.155 815 +07 3.155 692 +07 3.155 692 second +07 3.155 692 COnVERSIOn FACTORS TABLE 1-10 Temperature Conversion Formulas °F = (°C × 5/9) + 32 °C = (°F - 32) × 5/9 °R = °F + 459.67 K = °C + 273.15 K = °R × 5/9 TABLE 1-13 Values of the Ideal Gas Constant Temp. scale Temperature difference ΔT: °F = °C × 9/5 atm atm mmHg bar kg/cm2 atm mmHg TABLE 1-11 Density Conversion Formulas lb gal T,P lb ft 3 T,P = sp gr = sp gr T,P T,P Pressure units Volume units Kelvin Bé = 145 − 145 (heavier than H O) 2 sp gr   Tw = sp gr 60 /60 F − 1 0.005 API = 141.5 − 131.5 sp gr  Bé = 140 − 130 (lighter than H O) 2 sp gr cm3 liters liters liters liters ft3 ft3 Rankine atm in Hg mmHg lb/in2 abs lb/ft2 abs × 8.345406 × 62.42797 ft3 ft3 ft3 ft3 ft3 Kinematic Viscosity Conversion Formulas Viscosity scale Saybolt Universal Saybolt Furol Redwood No. 1 Range of t, s Kinematic viscosity, stokes* 32 < t < 100 t > 100 25 < t < 40 t > 40 34 < t < 100 t > 100 0.00226t - 1.95/t 0.00220t - 1.35/t 0.0224t - 1.84/t 0.0216t - 0.60/t 0.00260t - 1.79/t 0.00247t - 0.50/t 0.027t - 20/t 0.00147t - 3.74/t Redwood Admiralty Engler *1 stoke (St) = 1 cm2/s = 10-4 m2/s R Energy / (Weight ⋅ Temp) Weight units Energy units* g mol g mol g mol g mol g mol g mol g mol g mol lb mol lb mol lb mol calories joules (abs) joules (int) atm ⋅ cm3 atm ⋅ liters mmHg ⋅ liters bar ⋅ liters kg/(cm2)(liters) atm ⋅ ft3 mmHg ⋅ ft3 chu or pcu 1.9872 8.3144 8.3130 82.057 0.08205 62.361 0.08314 0.08478 1.314 998.9 1.9872 lb mol lb mol lb mol lb mol lb mol lb mol lb mol lb mol Btu hph kWh atm ⋅ ft3 in Hg ⋅ ft3 mmHg ⋅ ft3 (lb)( ft3)/in2 ft ⋅ lbf 1.9872 0.0007805 0.0005819 0.7302 21.85 555.0 10.73 1545.0 *Energy units are the product of pressure units and volume units. TABLE 1-12 1-17 1-18 UnIT COnVERSIOn FACTORS AnD SYMBOLS TABLE 1-14 Fundamental Physical Constants 1 sec = 1.00273791 sidereal seconds g0 = 9.80665 m/s2 1 liter = 0.001 cu m 1 atm = 101,325 newtons/sq m 1 mmHg (pressure) = (1⁄760) atm = 133.3224 newtons/sq m 1 int ohm = 1.000495 ± 0.000015 abs ohm 1 int amp = 0.999835 ± 0.000025 abs amp 1 int coul = 0.999835 ± 0.000025 abs coul 1 int volt = 1.000330 ± 0.000029 abs volt 1 int watt = 1.000165 ± 0.000052 abs watt 1 int joule = 1.000165 ± 0.000052 abs joule T0°C = 273.150 ± 0.010 K (PV)0°CP=0 = (RT)0°C = 2271.16 ± 0.04 abs joule/mole = 22,414.6 ± 0.4 cu cm atm/mole = 22.4146 ± 0.0004 liter atm/mole R = 8.31439 ± 0.00034 abs joule/deg mole = 1.98719 ± 0.00013 cal/deg mole = 82.0567 ± 0.0034 cu cm atm/deg mole = 0.0820567 ± 0.0000034 liter atm/deg mole ln 10 = 2.302585 R ln 10 = 19.14460 ± 0.00078 abs joule/deg mole = 4.57567 ± 0.00030 cal/deg mole N = (6.02283 ± 0.0022) × 1023/mole h = (6.6242 ± 0.0044) × 10-34 joule s c = (2.99776 ± 0.00008) × 108 m/s (h2/8 π2k) = (4.0258 ± 0.0037) × 10-39 g sq cm deg (h/8 π2c) = (2.7986 ± 0.0018) × 10-39 g cm Z = Nhc = 11.9600 ± 0.0036 abs joule cm/mole = 2.85851 ± 0.0009 cal cm/mole Z/R = hc/k = c2 = 1.43847 ± 0.00045 cm deg f = 96,501.2 ± 10.0 int coul/g-equiv or int joule/int volt g-equiv = 96,485.3 ± 10.0 abs coul/g-equiv or abs joule/abs volt g-equiv = 23,068.1 ± 2.4 cal/int volt g-equiv = 23,060.5 ± 2.4 cal/abs volt g-equiv e = (1.60199 ± 0.00060) × 10-19 abs coul = (1.60199 ± 0.00060) × 10-20 abs emu = (4.80239 ± 0.00180) × 10-10 abs esu 1 int electron-volt/molecule = 96,501.2 ± 10 int joule/mole = 23,068.1 ± 2.4 cal/mole 1 abs electron-volt/molecule = 96,485.3 ± 10. abs joule/mole = 23,060.5 ± 2.4 cal/mole 1 int electron-volt = (1.60252 ± 0.00060) × 10-12 erg 1 abs electron-volt = (1.60199 ± 0.00060) × 10-12 erg hc = (1.23916 ± 0.00032) × 10-4 int electron-volt cm = (1.23957 ± 0.00032) × 10-4 abs electron-volt cm k = (8.61442 ± 0.00100) × 10-5 int electron-volt/deg = (8.61727 ± 0.00100) × 10-5 abs electron-volt/deg = R/N = (1.38048 ± 0.00050) × 10-23 joule/deg 1 IT cal = (1⁄860) = 0.00116279 int watt-h = 4.18605 int joule = 4.18674 abs joule = 1.000654 cal 1 cal = 4.1840 abs joule = 4.1833 int joule = 41.2929 ± 0.0020 cu cm atm = 0.0412929 ± 0.0000020 liter atm 1 IT cal/g = 1.8 Btu/lb 1 Btu = 251.996 IT cal = 0.293018 int watt-h = 1054.866 int joule = 1055.040 abs joule = 252.161 cal 1 horsepower = 550 ft-lbf (wt)/s = 745.578 int watt = 745.70 abs watt 1 in = (1/0.3937) = 2.54 cm 1 ft = 0.304800610 m 1 lb = 453.5924277 g 1 gal = 231 cu in = 0.133680555 cu ft = 3.785412 × 10-3 cu m = 3.785412 liter sec = mean solar second Definition: g0 = standard gravity Definition: atm = standard atmosphere mmHg (pressure) = standard millimeter mercury int = international; abs = absolute amp = ampere coul = coulomb Absolute temperature of the ice point, 0°C PV = product for ideal gas at 0°C R = gas constant per mole ln = natural logarithm (base e) N = Avogadro number h = Planck constant c = velocity of light Constant in rotational partition function of gases Constant relating wave number and moment of inertia Z = constant relating wave number and energy per mole c2 = second radiation constant ℱ = Faraday constant e = electronic charge emu = electromagnetic unit of charge esu = electrostatic unit of charge Constant relating wave number and energy per molecule k = Boltzmann constant Definition of IT cal: IT = International steam tables cal = thermochemical calorie Definition: cal = thermochemical calorie Definition of Btu: Btu = IT British thermal unit cal = thermochemical calorie Definition of horsepower (mechanical): lb (wt) = weight of 1 lb at standard gravity Definition of inch: in = U.S. inch ft = U.S. foot (1 ft = 12 in) Definition: lb = avoirdupois pound Definition: gal = U.S. gallon Section 2 Physical and Chemical Data Marylee Z. Southard, Ph.D. Associate Professor of Chemical and Petroleum Engineering, University of Kansas; Senior Member, American Institute of Chemical Engineers; Member, American Society for Engineering Education (Section Coeditor, Physical and Chemical Data) Richard L. Rowley, Ph.D. Department of Chemical Engineering, Emeritus, Brigham Young University (Section Coeditor, Prediction and Correlation of Physical Properties) W. Vincent Wilding, Ph.D. Professor of Chemical Engineering, Brigham Young University; Fellow, American Institute of Chemical Engineers (Section Coeditor, Prediction and Correlation of Physical Properties) GEnERAL REFEREnCES PHYSICAL PROPERTIES OF PURE SUBSTAnCES Tables 2-1 2-2 Physical Properties of the Elements and Inorganic Compounds . . . . . Physical Properties of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 2-26 VAPOR PRESSURES Tables 2-3 Vapor Pressure of Water Ice from 0 to −40°C . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Vapor Pressure of Supercooled Liquid Water from 0 to −40°C . . . . . . . Vapor Pressures of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-5 Vapor Pressure (MPa) of Liquid Water from 0 to 100°C . . . . . . . . . . . . . . 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family . . . . . . . . . . . 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 . . . . . . . . . . . . . . . 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K . . . . . . . . . . . . . . . . . . . 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm . . . . . . . . . . . . . . 2-10 Vapor Pressures of Organic Compounds, up to 1 atm . . . . . . . . . . . . . . . . VAPOR PRESSURES OF SOLUTIOnS Tables 2-11 Partial Pressures of Water over Aqueous Solutions of HCl . . . . . . . . . . . Vapor Pressures of H3PO4 Aqueous: Partial Pressure of H2O Vapor (Fig. 2-1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions . . . 2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg . . . . . . . . . 2-14 Partial Pressures of HNO3 and H2O over Aqueous Solutions of HNO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15 Total Vapor Pressures of Aqueous Solutions of CH3COOH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 Partial Pressure of H2O over Aqueous Solutions of NH3 (psia) . . . . . . . . 2-17 Partial Pressures of H2O over Aqueous Solutions of Sodium Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46 2-46 2-46 2-46 2-46 2-46 2-47 2-50 2-53 2-59 2-63 2-78 2-78 2-79 2-80 2-80 2-81 2-82 2-83 2-18 Partial Pressures of H2O and CH3OH over Aqueous Solutions of Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium Hydroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Vapor Content in Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Content in Air at Pressures over Atmospheric (Fig. 2-2) . . . . . . . SOLUBILITIES Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-21 Solubility as a Function of Temperature and Henry’s Constant at 25°C for Gases in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Henry’s Constant H for Various Compounds in Water at 25°C . . . . . . . 2-23 Henry’s Constant H for Various Compounds in Water at 25°C from Infinite Dilution Activity Coefficients . . . . . . . . . . . . . . . . . . . . . . . . 2-24 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 Ammonia-Water at 10 and 20°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Carbon Dioxide (CO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27 Chlorine (Cl2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Chlorine Dioxide (ClO2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30 Hydrogen Sulfide (H2S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DEnSITIES Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References and Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Densities of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point to the Critical Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) . . . . . . . . . . . . . . 2-83 2-83 2-84 2-84 2-84 2-84 2-85 2-89 2-89 2-90 2-90 2-90 2-90 2-91 2-91 2-91 2-91 2-92 2-92 2-92 2-92 2-93 DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM Tables 2-33 Ammonia (NH3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100 2-34 Ammonium Chloride (NH4Cl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100 2-1 2-2 PHYSICAL AnD CHEMICAL DATA 2-35 Calcium Chloride (CaCl2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36 Ferric Chloride (FeCl3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37 Ferric Sulfate [Fe2(SO4)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38 Ferric Nitrate [Fe(NO3)3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-39 Ferrous Sulfate (FeSO4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40 Hydrogen Cyanide (HCN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41 Hydrogen Chloride (HCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42 Hydrogen Peroxide (H2O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43 Nitric Acid (HNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44 Perchloric Acid (HClO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45 Phosphoric Acid (H3PO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46 Potassium Bicarbonate (KHCO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-47 Potassium Carbonate (K2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-48 Potassium Chloride (KCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-49 Potassium Hydroxide (KOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-50 Potassium Nitrate (KNO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-51 Sodium Acetate (NaC2H3O2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52 Sodium Carbonate (Na2CO3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-53 Sodium Chloride (NaCl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-54 Sodium Hydroxide (NaOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-55 Sulfuric Acid (H2SO4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Densities of Aqueous Organic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-56 Acetic Acid (CH3COOH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-57 Methyl Alcohol (CH3OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-58 Ethyl Alcohol (C2H5OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-59 n-Propyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-60 Isopropyl Alcohol (C3H7OH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-61 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62 Hydrazine (N2H4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DEnSITIES OF MISCELLAnEOUS MATERIALS Tables 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65 Density (kg/m3) of Selected Elements as a Function of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LATEnT HEATS ....................................................... Unit Conversions Tables 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-67 Heats of Fusion of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . 2-68 Heats of Fusion of Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SPECIFIC HEATS Specific Heats of Pure Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-70 Heat Capacities of the Elements and Inorganic Compounds . . . . . . . . . 2-71 Specific Heat [kJ/(kg ⋅ K)] of Selected Elements. . . . . . . . . . . . . . . . . . . . . . 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol ⋅ K)] . . . . . 2-73 Specific Heats of Organic Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol ⋅ K)]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-76 Cp/Cv : Ratios of Specific Heats of Gases at 1 atm Pressure. . . . . . . . . . . . Specific Heats of Aqueous Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-77 Acetic Acid (at 38°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-78 Ammonia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-79 Ethyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-80 Glycerol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-81 Hydrochloric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-82 Methyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-83 Nitric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-84 Phosphoric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-85 Potassium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-86 Potassium Hydroxide (at 19°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-87 Normal Propyl Alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-88 Sodium Carbonate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-89 Sodium Chloride . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-90 Sodium Hydroxide (at 20°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-91 Sulfuric Acid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Heats of Miscellaneous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-92 Specific Heats of Miscellaneous Liquids and Solids. . . . . . . . . . . . . . . . . . 2-93 Oils (Animal, Vegetable, Mineral Oils) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-100 2-100 2-100 2-100 2-100 2-100 2-100 2-100 2-101 2-102 2-102 2-102 2-102 2-103 2-103 2-103 2-103 2-103 2-103 2-103 2-104 2-106 2-106 2-107 2-108 2-109 2-109 2-110 2-110 2-111 2-113 2-114 2-114 2-115 2-117 2-118 2-120 2-128 2-128 2-128 2-128 2-136 2-137 2-144 2-147 2-149 2-156 2-156 2-156 2-156 2-156 2-156 2-156 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-157 2-158 2-158 2-158 PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-158 Tables 2-94 Heats and Free Energies of Formation of Inorganic Compounds . . . . . 2-159 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and Net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-167 2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol), of Combustion Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-174 2-97 Ideal Gas Entropies s°, kJ/(kmol ⋅ K), of Combustion Products . . . . . . . 2-175 HEATS OF SOLUTIOn Tables 2-98 Heats of Solution of Inorganic Compounds in Water . . . . . . . . . . . . . . . . 2-99 Heats of Solution of Organic Compounds in Water (at Infinite Dilution and Approximately Room Temperature) . . . . . . . . . . . . . . . . . . THERMAL EXPAnSIOn AnD COMPRESSIBILITY Unit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Expansion of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-100 Linear Expansion of the Solid Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-101 Linear Expansion of Miscellaneous Substances . . . . . . . . . . . . . . . . . . . . 2-102 Volume Expansion of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-103 Volume Expansion of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Expansion: Joule-Thomson Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-104 Additional References Available for the Joule-Thomson Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-105 Approximate Inversion-Curve Locus in Reduced Coordinates (Tr = T/Tc ; Pr = P/Pc) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-106 Critical Constants and Acentric Factors of Inorganic and Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-107 Compressibilities of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-108 Compressibilities of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THERMODYnAMIC PROPERTIES Explanation of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-109 Thermodynamic Properties of Acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-110 Thermodynamic Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Dry Air (Fig. 2-3) . . . . . . . . . . . . . . . . . . 2-111 Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air, Moist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-112 Thermodynamic Properties of Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . 2-113 Thermodynamic Properties of Carbon Dioxide . . . . . . . . . . . . . . . . . . . . 2-114 Thermodynamic Properties of Carbon Monoxide . . . . . . . . . . . . . . . . . . Temperature-Entropy Diagram for Carbon Monoxide (Fig. 2-4) . . . . 2-115 Thermodynamic Properties of Ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Ethyl Alcohol (Fig. 2-5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-116 Thermodynamic Properties of Normal Hydrogen . . . . . . . . . . . . . . . . . . 2-117 Saturated Hydrogen Peroxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-118 Thermodynamic Properties of Hydrogen Sulfide . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Hydrogen Chloride at 1 atm (Fig. 2-6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-119 Thermodynamic Properties of Methane . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-120 Thermodynamic Properties of Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . 2-121 Thermodynamic Properties of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Nitrogen (Fig. 2-7) . . . . . . . . . . . . . . . . . 2-122 Thermodynamic Properties of Oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Oxygen (Fig. 2-8) . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Oxygen-Nitrogen Mixture at 1 atm (Fig. 2-9). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K Values (K = y/x) in Light-Hydrocarbon Systems (Fig. 2-10) . . . . . . . 2-123 Composition of Selected Refrigerant Mixtures . . . . . . . . . . . . . . . . . . . . . 2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 22. (Fig. 2-11) . . . . . . . . . . 2-125 Thermodynamic Properties of R-32, Difluoromethane . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 32. (Fig. 2-12) . . . . . . . . . . 2-126 Thermodynamic Properties of R-125, Pentafluoroethane. . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 125 (Fig. 2-13) . . . . . . . . . 2-127 Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane . . . Pressure-Enthalpy Diagram for Refrigerant 134a. (Fig. 2-14). . . . . . . . 2-176 2-178 2-179 2-179 2-179 2-179 2-180 2-181 2-181 2-182 2-182 2-182 2-182 2-182 2-182 2-182 2-183 2-190 2-190 2-190 2-190 2-190 2-191 2-191 2-191 2-191 2-192 2-194 2-198 2-199 2-199 2-200 2-202 2-204 2-206 2-207 2-209 2-210 2-212 2-213 2-215 2-216 2-218 2-220 2-222 2-223 2-225 2-226 2-226 2-227 2-228 2-230 2-231 2-233 2-234 2-236 2-237 2-239 PHYSICAL AnD CHEMICAL DATA 2-128 Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane . . . . . . . 2-129 Thermodynamic Properties of R-404A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-130 Thermodynamic Properties of R-407C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 407C (Fig. 2-15) . . . . . . . . 2-131 Thermodynamic Properties of R-410A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-132 Opteon YF (R-1234yf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure-Enthalpy Diagram for Refrigerant 1234yf (Fig. 2-16) . . . . . . 2-133 Thermophysical Properties of Saturated Seawater . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Sodium Hydroxide at 1 atm (Fig. 2-17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy-Concentration Diagram for Aqueous Sulfuric Acid at 1 atm (Fig. 2-18) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-134 Saturated Solid/Vapor Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-135 Thermodynamic Properties of Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-136 Thermodynamic Properties of Water Substance along the Melting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TRAnSPORT PROPERTIES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-137 Surface Tension σ (dyn/cm) of Various Liquids . . . . . . . . . . . . . . . . . . . . 2-138 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) . . . . . . . . 2-139 Viscosity of Inorganic and Organic Liquids (Pa∙s) . . . . . . . . . . . . . . . . . . 2-140 Viscosities of Liquids: Coordinates for Use with Fig . 2-19 . . . . . . . . . . . Nomograph for Viscosities of Liquids at 1 atm (Fig . 2-19) . . . . . . . . . 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) . . . . . . . . . . . . . . . . . . 2-142 Diffusivities in Liquids (25°C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-143 Transport Properties of Selected Gases at Atmospheric Pressure . . . 2-144 Prandtl Number of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-145 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids . . . . 2-147 Thermal Conductivity of Inorganic and Organic Liquids [W/(m ⋅ K)] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-148 Nomograph for Thermal Conductivity of Organic Liquids (Fig . 2-20) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-149 Thermal-Conductivity-Temperature Table for Metals and Nonmetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-150 Thermal Conductivity of Chromium Alloys . . . . . . . . . . . . . . . . . . . . . . . . 2-151 Thermal Conductivity of Some Alloys at High Temperature . . . . . . . . 2-152 Thermophysical Properties of Selected Nonmetallic Solid Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons . . . . . . . . . . . PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prediction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Property Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Estimation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory and Empirical Extension of Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corresponding States (CS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Contributions (GCs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computational Chemistry (CC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empirical QSPR Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Critical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-154 Ambrose Group Contributions for Critical Constants . . . . . . . . . . . . . . 2-155 Group Contributions for the Nannoolal et al . Method for Critical Constants and Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . 2-156 Intermolecular Interaction Corrections for the Nannoolal et al . Method for Critical Constants and Normal Boiling Point . . . . . . . . . . 2-157 Wilson-Jasperson First- and Second-Order Contributions for Critical Temperature and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Melting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Boiling Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-158 First-Order Groups and Their Contributions for Melting Point . . . . . 2-159 Second-Order Groups and Their Contributions for Melting Point . . . Characterizing and Correlating Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acentric Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radius of Gyration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dipole Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-240 2-242 2-244 2-246 2-247 2-249 2-258 2-259 2-260 2-260 2-261 2-262 2-265 2-266 2-266 2-266 2-266 2-266 2-267 2-274 2-281 2-282 2-283 2-285 2-288 2-288 2-288 2-289 2-296 2-298 2-305 2-306 2-307 2-307 2-307 2-308 2-311 2-311 2-311 2-314 2-314 2-314 2-314 2-315 2-315 2-315 2-315 2-315 2-315 2-315 2-315 2-317 2-318 2-320 2-321 2-321 2-321 2-322 2-322 2-323 2-323 2-324 2-324 Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dielectric Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-160 Wildman-Crippen Contributions for Refractive Index . . . . . . . . . . . . . . Vapor Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-161 Domalski-Hearing Group Contribution Values for Standard State Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gibbs Energy of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Latent Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Vaporization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enthalpy of Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-162 Cs (C—H) Group Values for Chickos Estimation of ∆Hfus . . . . . . . . . . . 2-163 Ct (Functional) Group Values for Chickos Estimation of ∆H fus . . . . . . Enthalpy of Sublimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-164 Group Contributions and Corrections for ∆Hsub . . . . . . . . . . . . . . . . . . . . Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-165 Benson and CHETAH Group Contributions for Ideal Gas Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-166 Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-167 Group Values and Nonlinear Correction Terms for Estimation of Solid Heat Capacity with the Goodman et al . Method . . . . . . . . . . . 2-168 Element Contributions to Solid Heat Capacity for the Modified Kopp’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-169 Simple Fluid Compressibility Factors Z (0) . . . . . . . . . . . . . . . . . . . . . . . . . . 2-170 Acentric Deviations Z (1) from the Simple Fluid Compressibility Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-171 Constants for the Two Reference Fluids Used in Lee-Kesler Method . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-172 Relationships for Eq . (2-70) for Common Cubic EoS . . . . . . . . . . . . . . . . Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-173 Reichenberg Group Contribution Values . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-174 Group Contributions for the Hsu et al . Method . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-175 UNIFAC-VISCO Group Interaction Parameters αmn . . . . . . . . . . . . . . . . Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-176 Correlation Parameters for Baroncini et al . Method for Estimation of Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pure Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-177 Knotts Group Contributions for the Parachor in Estimating Surface Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flammability Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flash Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flammability Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tables 2-178 Group Contributions for Quantities Used to Estimate Flammability Limits By Rowley et al . Method for Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-179 Ideal Gas Enthalpies of Formation and Average Heat Capacities of Combustion Gases for Use in Eq . (2-125) . . . . . . . . . . . . . . . . . . . . . . . Autoignition Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table 2-180 Group Contributions for Pintar Autoignition Temperature Method for Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 2-324 2-325 2-325 2-326 2-326 2-327 2-327 2-327 2-328 2-334 2-334 2-334 2-334 2-335 2-336 2-336 2-336 2-337 2-337 2-337 2-338 2-339 2-343 2-344 2-345 2-345 2-345 2-345 2-345 2-347 2-348 2-349 2-349 2-349 2-350 2-350 2-351 2-351 2-351 2-352 2-353 2-354 2-354 2-355 2-356 2-356 2-357 2-357 2-358 2-358 2-358 2-359 2-360 2-360 2-360 2-361 2-361 2-361 2-362 GEnERAL REFEREnCES Considerations of reader interest, space availability, the system or systems of units employed, copyright issues, etc., have all influenced the revision of material in previous editions for the present edition. Reference is made at numerous places to various specialized works and, when appropriate, to more general works. A listing of general works may be useful to readers in need of further information. ASHRAE Handbook—Fundamentals, SI edition, ASHRAE, Atlanta, 2005; Benedek, P., and F. Olti, Computer-Aided Chemical Thermodynamics of Gases and Liquids, Wiley, New York, 1985; Brule, M. R., L. L. Lee, and K. E. Starling, Chem. Eng., 86, 25, Nov. 19, 1979, pp. 155–164; Cox, J. D., and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, New York, 1970; Cox, J. D., D. D. Wagman, and V. A. Medvedev, CODATA Key Values for Thermodynamics, Hemisphere Publishing Corp., New York, 1989; Daubert, T. E., R. P. Danner, H. M. Sibel, and C. C. Stebbins, Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, Taylor & Francis, Washington, 1997; Domalski, E. S., and E. D. Hearing, Heat capacities and entropies of organic compounds in the condensed phase, vol. 3, J. Phys. Chem. Ref. Data 25(1):1–525, Jan-Feb 1996; Dykyj, J., and M. Repas, Saturated vapor pressures of organic compounds, Veda, Bratislava, 1979 (Slovak); Dykyj, J., M. Repas, and J. Svoboda, Saturated vapor pressures of organic compounds, Veda, Bratislava, 1984 (Slovak); Glushko, V. P., ed., Thermal Constants of Compounds, Issues I–X, Moscow, 1965–1982 (Russian only); Gmehling, J., Azeotropic Data, 2 vols., VCH Weinheim, Germany, 1994; Gmehling, J., and U. Onken, Vapor-Liquid Equilibrium Data Collection, Dechema Chemistry Data Series, Frankfurt, 1977–1978; International Data Series, Selected Data on Mixtures, Series A: Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; Kaye, S. M., Encyclopedia of Explosives and Related Items, U.S. Army R&D command, Dover, N.J., 1980; King, M. B., Phase Equilibrium in Mixtures, Pergamon, Oxford, 1969; Landolt-Boernstein, Numerical Data and Functional Relationships in Science and Technology (New Series), http://www.springeronline .com/sgw/cda/frontpage/0,11855,4-10113-2-95859-0,00.html; Lide, D. R., CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, Boca Raton, Fla., 2005; Lyman, W. J., W. F. Reehl, and D. H. Rosenblatt, Handbook of Chemical Property Estimation Methods, McGraw-Hill, New York, 1990; Majer, V., and V. Svoboda, Enthalpies of Vaporization of Organic Compounds: A Critical Review and Data Compilation, Blackwell Science, 1985; Majer V., V. Svoboda, and J. Pick, Heats of Vaporization of Fluids, Elsevier, Amsterdam, 1989 (general discussion); Marsh, K. N., Recommended Reference Materials for the Realization of Physicochemical Properties, Blackwell Science, 1987; NIST-IUPAC Solubility Data Series, Pergamon Press, http://www.iupac.org/publications/ ci/1999/march/solubility.html; Ohse, R. W., and H. von Tippelskirch, High Temp.—High Press., 9:367–385, 1977; Ohse, R. W., Handbook of Thermodynamic and Transport Properties of Alkali Metals, Blackwell Science Pubs., Oxford, England, 1985; Pedley, J. B., R. D. Naylor, and S. P. Kirby, Thermochemical Data of Organic Compounds, Chapman and Hall, New York, 1986; Physical Property Data for the Design Engineer, Hemisphere, New York, 1989; Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and 2-4 Liquids, 5th ed., McGraw-Hill, New York, 2001; Rothman, D., et al., Max Planck Inst. f. Stromungsforschung, Ber 6, 1978; Smith, B. D., and R. Srivastava, Thermodynamic Data for Pure Compounds, Part A: Hydrocarbons and Ketones, Elsevier, Amsterdam, 1986, Physical sciences data 25, http://www .elsevier.com/wps/find/bookseriesdescription.librarians/BS_PSD/description; Sterbacek, Z., B. Biskup, and P. Tausk, Calculation of Properties Using Corresponding States Methods, Elsevier, Amsterdam, 1979; Stull, D. R., E. F. Westrum, and G. C. Sink, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969; TRC Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research Center, National Institute of Standards and Technology, Boulder, Colo.; Young, D. A., “Phase Diagrams of the Elements,” UCRL Rep. 51902, 1975 republished in expanded form by the University of California Press, 1991; Zabransky, M., V. Ruzicka, Jr., V. Majer, and E. S. Domalski, Heat Capacity of Liquids: Critical Review and Recommended Values, J. Phys. Chem. Ref. Data, Monograph No. 6, 1996. Critical Data Sources Ambrose, D., “Vapor-Liquid Critical Properties,” N. P. L. Teddington, Middlesex, Rep. 107, 1980; Kudchaker, A. P., G. H. Alani, and B. J. Zwolinski, Chem. Revs. 68: 659–735, 1968; Matthews, J. F., Chem. Revs. 72: 71–100, 1972; Simmrock, K., R. Janowsky, and A. Ohnsorge, Critical Data of Pure Substances, Parts 1 and 2, Dechema Chemistry Data Series, 1986. Other recent references for critical data can be found in Lide, D. R., CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, Boca Raton, Fla., 2005. Publications on Thermochemistry Pedley, J. B., Thermochemical Data and Structures of Organic Compounds, 1, Thermodynamic Research Center, Texas A&M Univ., 1994 (976 pp., 3000 cpds.); Frenkel, M., et al., Thermodynamics of Organic Compounds in the Gas State, 2 vols., Thermodynamic Research Center, Texas A&M Univ., 1994 (1825 pp., 2000 cpds.); Barin, I., Thermochemical Data of Pure Substances, 2nd ed., 2 vols., VCH Weinheim, Germany, 1993 (1834 pp., 2400 substances); Gurvich, L. V., et al., Thermodynamic Properties of Individual Substances, 4th ed., 3 vols., Hemisphere, New York, 1989, 1990, and 1993 (2520 pp.); Lide, D. R., and G. W. A. Milne, Handbook of Data on Organic Compounds, 3rd ed., 7 vols., Chemical Rubber, Miami, 1993 (7000 pp.); Daubert, T. E., et al., Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation, extant 1995, Taylor & Francis, Bristol, Pa., 1995; Database 11, NIST, Gaithersburg, Md. U.S. Bureau of Mines publications include Bulletins 584, 1960 (232 pp.); 592, 1961 (149 pp.); 595, 1961 (68 pp.); 654, 1970 (26 pp.); Chase, M. W., et al., JANAF Thermochemical Tables, 3d ed., J. Phys. Chem. Ref. Data 14 suppl. 1, 1986 (1896 pp.); Journal of Physical and Chemical Reference Data is available online at http://listserv.nd .edu/cgi-bin/wa?×A2=ind0501&L=pamnet&F=&S=&P=8490 and at http:// www.nist.gov/srd/reprints.htm PHYSICAL PROPERTIES OF PURE SUBSTAnCES TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds* Abbreviations Used in the Table a., acid A., specific gravity with reference to air = 1 abs., absolute ac., acetic acid act., acetone al., 95 percent ethyl alcohol alk, alkali (i.e., aq. NaOH or KOH) am., amyl (C5H11) amor., amorphous anh., anhydrous aq., aqueous or water aq. reg., aqua regia atm., atmosphere or 760 mm. of mercury pressure bk., black brn., brown bz., benzene c., cold cb., cubic cc, cubic centimeter chl., chloroform col., colorless or white conc., concentrated cr., crystals or crystalline d., decomposes D., specific gravity with reference to hydrogen = 1 hyg., hygroscopic i., insoluble ign., ignites lq., liquid lt., light m. al., methyl alcohol mn., monoclinic nd., needles NH3, liquid ammonia NH4OH, ammonium hydroxide solution oct., octahedral or., orange pd., powder d. 50, decomposes at 50°C; 50 d., melts at 50°C with decomposition delq., deliquescent dil., dilute dk., dark eff., effloresces or efflorescent et., ethyl ether expl., explodes gel., gelatinous gly., glycerol (glycerin) gn., green h., hot hex., hexagonal Formula weights are based upon the International Atomic Weights in “Atomic Weights of the Elements 2001,” Pure Appl. Chem., 75, 1107, 2003, and are computed to the nearest hundredth . Refractive index, where given for a uniaxial crystal, is for the ordinary (ω) ray; where given for a biaxial crystal, the index given is for the median (β) value . Unless otherwise specified, the index is given for the sodium D-line (λ = 589 .3 µm) . Specific gravity values are given at room temperatures (15 to 20°C) unless otherwise indicated by the small figures which follow the value: thus, 5.6 184° indicates a specific gravity of 5 .6 for the substance at 18°C referred to water at 4°C . In this table the values for the specific gravity of gases are given with reference to air (A) = 1, or hydrogen (D) = 1 . Melting point is recorded in a certain case as 82 d . and in some other case as d . 82, the distinction being made in this manner to indicate that the former is a melting point with decomposition at 82°C, while in the latter decomposition only occurs at 82°C . Where a value such as −2H2O, 82 is given, it indicates loss of 2 moles of water per formula weight of the compound at a temperature of 82°C . Boiling point is given at atmospheric pressure (760 mm of mercury) unless otherwise indicated; thus, 8215 mm indicates the boiling point is 82°C when the pressure is 15 mm . Name Aluminum acetate, normal acetate, basic bromide bromide carbide chloride Formula Al Al(C2H3O2)3 Al(OH)(C2H3O2)2 AlBr3 AlBr3⋅6H2O Al4C3 AlCl3 Formula weight 26 .98 204 .11 162 .08 266 .69 374 .78 143 .96 133 .34 Color, crystalline form, and refractive index silv ., cb . wh . pd . wh ., amor . trig . col ., delq . cr . yel ., hex ., 2 .70 wh ., delq ., hex . Specific gravity 2 .7020° 3 .01 254° 2 .95 2 .44 25 ° 4 pl., plates pr., prisms or prismatic pyr., pyridine rhb., rhombic (orthorhombic) s., soluble satd., saturated sl., slightly soln., solution subl., sublimes sulf., sulfides tart. a., tartaric acid tet., tetragonal tr., transition tri., triclinic trig., trigonal v., very vac., in vacuo vl., violet volt., volatile or volatilizes wh., white yel., yellow ∞, soluble in all proportions <, less than >, greater than 42±, about or near 42 −3H2O, 100, loses 3 moles of water per formula weight at 100°C Solubility is given in parts by weight (of the formula shown at the extreme left) per 100 parts by weight of the solvent; the small superscript indicates the temperature . In the case of gases the solubility is often expressed in some manner as 510° cc which indicates that at 10°C, 5 cc of the gas are soluble in 100 g of the solvent . The symbols of the common mineral acids: H2SO4, HNO3, HCl, etc ., represent dilute aqueous solutions of these acids . See also special tables on Solubility . references: The information given in this table has been collected mainly from the following sources: Mellor, A Comprehensive Treatise on Inorganic and Theoretical Chemistry, Longmans, New York, 1922 . Abegg, Handbuch der anorganischen Chemie, S . Hirzel, Leipzig, 1905 . Gmelin-Kraut, Handbuch der anorganischen Chemie, 7th ed ., Carl Winter, Heidelberg; 8th ed ., Verlag Chemie, Berlin, 1924 . Friend, Textbook of Inorganic Chemistry, Griffin, London, 1914 . Winchell, Microscopic Character of Artificial Inorganic Solid Substances or Artificial Minerals, Wiley, New York, 1931 . International Critical Tables, McGraw-Hill, New York, 1926 . Tables annuelles internationales de constants et donnes numeriques, McGraw-Hill, New York . Annual Tables of Physical Constants and Numerical Data, National Research Council, Princeton, N .J ., 1943 . Comey and Hahn, A Dictionary of Chemical Solubilities, Macmillan, New York, 1921 . Seidell, Solubilities of Inorganic and Metal Organic Compounds, Van Nostrand, New York, 1940 . Melting point, °C 660 d . 200 d . 97 .5 d . 100 d . >2200 1945 .2atm . Boiling point, °C 2056 268 752mm 182 .7 ; subl . 178 Solubility in 100 parts Cold water i . s . i . s . s . d . to CH4 69 .8715° chloride AlCl3⋅6H2O col ., delq ., trig ., 1 .560 400 241 .43 fluoride (fluellite) AlF3⋅H2O col ., rhb ., 1 .490 2 .17 d . sl . s . 101 .99 fluoride Al2F6⋅7H2O wh ., cr . pd . −4H2O, 120 −6H2O, 250 i . 294 .06 hydroxide Al(OH)3 wh ., mn . 2 .42 −2H2O, 300 0 .00010418° 78 .00 nitrate Al(NO3)3⋅9H2O rhb ., delq . 73 d . 134 v . s . 375 .13 4atm . 25 ° nitride Al2N2 yel ., hex . 3 .05 4 2150 d . >1400 d . slowly 81 .98 oxide Al2O3 col ., hex ., 1 .67–8 3 .99 1999 to 2032 i . 101 .96 oxide (corundum) Al2O3 wh ., trig ., 1 .768 4 .00 1999 to 2032 2210 i . 101 .96 phosphate AlPO4 col ., hex . 2 .59 i . 121 .95 ∗By N . A . Lange, Ph .D ., Handbook Publishers, Inc ., Sandusky, Ohio . Abridged from table of Physical Constants of Inorganic Compounds in Lange’s Handbook of Chemistry. Hot water i . d . Other reagents s . HCl, H2SO4, alk . s . d . s .a .; i . NH4 salts s .al ., act ., CS2 s . al ., CS2 s . a .; i . act . s . et ., chl ., CCl4; i . bz . v . s . 50 al .; s . et . s . sl . s . i . v . s . d . i . i . i . s . a ., alk .; i . a . s . al ., CS2 s . alk . d . v . sl . s . a ., alk . v . sl . s . a ., alk . s . a ., alk .; i . ac . (Continued ) 2-5 2-6 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Aluminum (Cont.) potassium silicate (muscovite) potassium silicate (orthoclase) Aluminum potassium tartrate sodium fluoride (cryolite) sodium silicate sulfate Alum, ammonium (tschermigite) ammonium chrome Formula Formula weight 3Al2O3⋅K2O⋅6SiO2⋅2H2O Al2O3⋅K2O⋅6SiO2 AlK(C4H4O6)2 AlF3⋅3NaF Al2O3⋅Na2O⋅6SiO2 Al2(SO4)3 Al2(SO4)3⋅(NH4)2SO4⋅ 24H2O Cr2(SO4)3⋅(NH4)2SO4⋅ 24H2O Fe2(SO4)3⋅(NH4)2SO4⋅ 24H2O Al2(SO4)3⋅K2SO4⋅24H2O Cr2(SO4)3⋅K2SO4⋅24H2O Al2(SO4)3⋅Na2SO4⋅24H2O NH3 796 .61 556 .66 362 .22 209 .94 524 .44 342 .15 906 .66 956 .69 Color, crystalline form, and refractive index mn., 1.590 col., mn., 1.524 col. wh., mn., 1.3389 col., tri., 1.529 wh. cr. col., oct., 1.4594 gn . or vl ., oct ., 1 .4842 Specific gravity Melting point, °C 2.9 2.56 d. 1450 (1150) 2.90 2.61 2.71 1.64 204° 1000 1100 d. 770 93.5 1 .72 Boiling point, °C −20H2O, 120; −24H2O, 200 100 d . vl ., oct ., 1 .485 1 .71 40 948 .78 998 .81 916 .56 17 .03 col ., mn ., 1 .4564 red or gn ., cb ., 1 .4814 col ., oct ., 1 .4388 col . gas, 1 .325 (lq .) 92 89 61 −77 .7 −18H2O, 64 .5 77 .08 337 .09 79 .06 97 .94 114 .10 157 .13 wh ., hyg . cr . pl . mn . or rhb ., 1 .5358 col ., cb ., 1 .7108 col . pl . wh . cr . 114 d . 200 d . 35–60 subl . 542 d . 58 subl . d . 272 .21 wh . chloride (salammoniac) chloroplatinate chloroplatinite chlorostannate chromate cyanide dichromate ferrocyanide fluoride fluoride, acid formate NH4C2H3O2 NH4CN⋅Au(CN)3⋅H2O NH4HCO3 NH4Br (NH4)2CO3⋅H2O NH4HCO3⋅ NH2CO2NH4‡ (NH4)2CO3⋅ 2NH4HCO3⋅H2O NH4Cl (NH4)2PtCl6 (NH4)2PtCl4 (NH4)2SnCl6 (NH4)2CrO4 NH4CN (NH4)2Cr2O7 (NH4)4Fe(CN)6⋅6H2O NH4F NH4F⋅HF HCO2NH4 1 .76 264° 1 .83 1 .675 204° 0 .817−79° 0 .5971 (A) 1 .073 53 .49 443 .87 372 .97 367 .50 152 .07 44 .06 252 .06 392 .19 37 .04 57 .04 63 .06 wh ., cb ., 1 .639, 1 .6426 yel ., cb . tet . pink ., cb . yel ., mn . col ., cb . or ., mn . mn . wh ., hex . wh ., rhb ., 1 .390 col ., mn ., delq . hydrosulfide hydroxide molybdate molybdate, heptanitrate (α), stable −16° to 32° nitrate (β), stable 32° to 84° NH4HS NH4OH (NH4)2MoO4 (NH4)6Mo7O24⋅4H2O‡ NH4NO3 NH4NO3 51 .11 35 .05 196 .01 1235 .86 80 .04 80 .04 col ., rhb . in soln . only mn . col ., mn . col ., tet ., 1 .611 col ., rhb . or mn . nitrite osmochloride oxalate oxalate, acid perchlorate persulfate phosphate, monobasic phosphate, dibasic phosphate, meta- NH4NO2 (NH4)2OsCl6 (NH4)2C2O4⋅H2O NH4HC2O4⋅H2O NH4ClO4 (NH4)2S2O8 NH4H2PO4 (NH4)2HPO4 (NH4)4P4O12 64 .04 439 .02 142 .11 125 .08 117 .49 228 .20 115 .03 132 .06 388 .04 wh . nd . cb . col ., rhb . col ., trimetric col ., rhb ., 1 .4833 wh ., mn ., 1 .5016 col ., tet ., 1 .5246 col ., mn ., 1 .53 col ., mn . potassium (kalinite) potassium chrome sodium Ammonia† Ammonium acetate auricyanide bicarbonate bromide carbonate carbonate, carbamate carbonate, sesqui- 1 .573 2 .327 154° 124 −33 .4 d . 1 .5317° 3 .065 2 .4 1 .91712° 0 .79100° (A) 2 .15 2 .21 1212° 1 .266 d . 350 d . d . d . 2 .27 subl . 520 d . 180 36 d . 185 d . 114–116 d . 180; subl . in vac . subl . 120 d . 25 ° 4 25 ° 4 1 .66 1 .725 169 .6 1 .69 2 .93 204° 1 .501 1 .556 1 .95 1 .98 1 .803 194° 1 .619 2 .21 expl . i. i. s. sl. s. i. 31.30° 3.90° 21 .2 964 .38 ammonium iron Solubility in 100 parts Cold water d . 210 d . 210 s. i. 89100° ∞ 100° 25° Other reagents i. HCl d. a. i . al . s . al . 25° i . al . 5 .70° 20 106 .40° 89 .90° ∞93° 50 121 .745° 7 .496° 1484° s . 11 .90° 6810° 10015° 2515° v . s . 2730° 145 .6100° 2015° 5049° 29 .40° 0 .715° s . 33 .315° 40 .530° s . 47 .230° s . v . s . v . s . 1020° 77 .3100° 1 .25100° v . s . s . NH3; sl . s . al ., m . al . 0 .005 al . d . v . s . v . s . d . sl . s . act ., NH3; i . al . s . al . s . al .; i . act . i . al . s . al .; i . NH3 53180° s . al . v . s . s . d . 4425° 118 .30° 365 .835° s . 6765° 2 .5 s . 10 .90° 58 .20° 22 .70° 13115° s . i . al . i . al . 14 .820° al .; s . et . s . al .; sl . s . act . i . al . i . al . s . al ., et ., act . i . al ., CS2, NH3 s . al . d . i . al ., NH3 i . al . 30° 241 .8 58080° d . 0° d . d . d . 120 Hot water 11 .850° 100° 46 .9 d . 173 .2100° 3 .820° al ., 17 .120° m . al .; v . s . NH3 s . al . sl . s . al .; i . NH3 220° al .; s . act .; i . et . i . ac . i . act . Ammonium phosphomolybdate silicofluoride sulfamate sulfate (mascagnite) sulfate, acid sulfide sulfide, pentasulfite sulfite, acid tartrate thiocyanate vanadate, metaAntimony chloride, tri- (butter of antimony)∗ oxide, tri- (valentinite) oxide, tri- (senarmontite) sulfide, tri- (stibnite) (NH4)3PO4⋅12MoO3⋅ 3H2O (?) (NH4)2SiF6 NH4⋅SO3NH2 (NH4)2SO4 NH4HSO4 (NH4)2S (NH4)2S5 (NH4)2SO3⋅H2O NH4HSO3 (NH4)2C4H4O6 NH4CNS NH4VO3 Sb 1930 .39 178 .15 114 .12 132 .14 115 .11 68 .14 196 .40 134 .16 99 .11 184 .15 76 .12 116 .98 121 .76 yel. cb., 1.3696 col. pl. col., rhb., 1.5230 col., rhb., 1.480 yel.-wh. or.-red pr. col., mn. rhb. col., mn. col., mn., 1.685± col. cr. tin wh., trig. d. 0.0315° i. s. alk.; i. al., HNO3 55.5 35750° 103.3100° s. al.; i. act. 8760° 17020° 3.0570° i. 1.769 204° 1.78 132 235 d. 146.9 d. 1.41 2.03 124° 1.60 1.305 2.326 6.68425° d. d. d. 149.6 d. 630.5 1380 18.517.5° 1340° 70.60° 100 v. s. s. 10012° s. 450° 1200° 0.4418° i. 73.4 220.2 601.60° ∞72° 656 652 550 1570 2.01 SbCl3 228 .12 col., rhb., delq. 3.14 Sb2O3 Sb2O3 Sb2S3 291 .52 291 .52 339 .72 rhb ., 2 .35 cb ., 2 .087 bk ., rhb ., 4 .046 5 .67 5 .2 4 .64 20 ° 4 0° subl. d. 160 490 d. 170 i. al., act., CS2 v. sl. s. al.; i. act. 12025° NH3 i. al., act. sl. s. al. s. al., act., NH3, SO2 i. al., NH4Cl s. aq. reg., h. conc. H2SO4 s . al ., HCl, HBr, H2C4H4O6 s . HCl, KOH, H2C4H4O6 v . sl . s . sl . s . 0 .0001718° d . −2S, 135 629 i . i . 5 .268 .7° d . i . 5 .60° cc 35 .7100° d . d . 2 .2350° cc s . gly .; i . al . s . HCl; alk ., NH4HS, K2S; i . ac . s . HCl, alk ., NH4HS sulfide, pentatelluride, triAntimonyl potassium tartrate (tartar emetic) sulfate, normal sulfate, basic Argon Sb2S5 Sb2Te3 403 .85 626 .32 golden gray 4 .120 (SbO)KC4H4O6⋅½H2O (SbO)2SO4 (SbO)2SO4⋅Sb2(OH)4 Ar 333 .94 371 .58 683 .20 39 .95 wh ., rhb . wh . pd . wh . pd . col . gas 2 .60 4 .89 −½H2O, 100 −189 .2 −185 .7 Arsenic (crystalline) (α) Arsenic (black) (β) As4 As4 299 .69 299 .69 met ., hex . bk ., amor . 1 .65−288°; 1 .402−185 .7°; 1 .38 (A) 5 .72714° 4 .720° 81436atm . subl . 615 i . i . i . i . s . HNO3 s . HNO3, aq . reg ., aq . Cl2, h . alk . Arsenic (yellow) (γ) acid, orthoacid, metaacid, pyropentoxide sulfide, di- (realgar) As4 H3AsO4⋅½H2O HAsO3 H4As2O7 As2O5 As2S2 299 .69 150 .95 123 .93 265 .87 229 .84 213 .97 yel ., cb . col ., hyg . wh ., hyg . col . wh ., amor . red, mn ., 2 .68 −H2O, 160 50 H3AsO4 H3AsO4 76 .7100° d . s . alk . d . 565 16 .7 d . to form d . to form 59 .50° i . s . alk ., al . s . K2S, NaHCO3 sulfide, pentaArsenious chloride (butter of arsenic) hydride (arsine) oxide (arsenolite) oxide (claudetite) oxide As2S5 AsCl3 310 .17 181 .28 d . 500 130 0 .0001360° d . i . d . s . HNO3, alk . s . HCl, HBr, PCl3 AsH3 As2O3 As2O3 As2O3 −55; d . 230 20 cc sl . s . sl . s . 1 .210° sl . s . sl . s . sl . s . 2 .9340° Auric chloride cyanide Aurous chloride cyanide Cf. also under Gold Barium acetate acetate bromide ∗Usually the solution . † See special tables . ‡ Usual commercial form . sl . s . alk . i . al ., et . i . al ., et . s . HCl, alk ., Na2CO3; i . al ., et . s . HCl, al ., et .; sl . s . NH3 s . al . s . HCl, HBr; d . al . s . KCN; i . al ., et . Ba Ba(C2H3O2)2 Ba(C2H3O2)2⋅H2O BaBr2 2 .020° 2 .0–2 .5 d . 358 35 .5 d . d . 206 4 .086 (α)3 .50619°; (β)3 .25419° (α)tr . 267; (β)307 yel . oily lq . lq . 2 .163 −18 77 .95 197 .84 197 .84 197 .84 col . gas col ., cb ., fibrous, 1 .755 col ., mn ., 1 .92 amor . or vitreous 2 .695 (A) 3 .865 254° 3 .85 3 .738 −113 .5 subl . subl . 315 AuCl3⋅2H2O 339 .36 or . cr . d . v . s . v . s . Au(CN)3⋅6H2O AuCl AuCN 383 .11 232 .42 222 .98 yel . cr . yel . cr . 7 .4 d . 50 AuCl3, 170 d . d . 290 v . s . d . i . v . s . d . i . 137 .33 255 .42 273 .43 297 .14 silv . met . col . wh ., tri . pr ., 1 .517 col . 3 .5 2 .468 2 .19 4 .781 244° 850 1140 −H2O, 41 847 d . d . 58 .80° 7530°(anh .) 980° d . 75 .0100° 7940°(anh .) 149100° 5 .1515° gly . 2425° cc al . s . a .; d . al . i . al . v . s . m . al .; v . sl . s . act . (Continued ) 2-7 2-8 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Barium (Cont.) bromide carbonate (witherite) carbonate (α) carbonate (β) Barium chlorate chlorate chloride chloride chloride hydroxide hydroxide nitrate (nitrobarite) oxalate oxide peroxide peroxide phosphate, monobasic phosphate, dibasic phosphate, tribasic phosphate, pyrosilicofluoride sulfate (barite, barytes) sulfide, monosulfide, trisulfide, tetraBeryllium (glucinum) Bismuth carbonate, subchloride, dichloride, trinitrate nitrate, suboxide, trioxide, trioxide, trioxychloride Formula Formula weight Color, crystalline form, and refractive index 333.17 197.34 197.34 197.34 304.23 322.24 208.23 208.23 244.26 171.34 315.46 261.34 225.35 153.33 col., mn., 1.7266 wh., rhb., 1.676 wh., hex. wh. col. col., mn., 1.577 col., mn., 1.7361 col., cb. col., mn., 1.646 col., mn. col., mn., 1.5017 col., cb., 1.572 wh. cr. col., cb., 1.98 BaO2∗ BaO2⋅8H2O BaH4(PO4)2 BaHPO4 Ba3(PO4)2 Ba2P2O7 BaSiF6 BaSO4 169.33 313.45 331.30 233.31 601.92 448.60 279.40 233.39 gray or wh. pd. pearly sc. tri. wh., rhb. nd., 1.635 wh., cb. wh., rhb. pr. col., rhb., 1.636 BaS BaS3 BaS4⋅2H2O Be(Gl) Bi 169.39 233.52 301.62 9.01 208.98 Bi2O3⋅CO2⋅H2O BiCl2 BiCl3∗ Bi(NO3)3⋅5H2O BiONO3⋅H2O Bi2O3 Bi2O3 Bi2O3 BiOCl 527.98 279.89 315.34 485.07 305.00 465.96 465.96 465.96 260.43 col., cb., 2.155 yel.-gn. red, rhb. gray, met., hex. silv. wh. or reddish, hex. wh. pd. bk. nd. wh. cr. col., tri. hex. pl. yel., rhb. yel., tet. yel., cb. wh., amor. 6.86 4.86 4.75 2.82 4.92815° 8.9 8.55 8.20 7.7215° d. 163 230 d. 30 d. 260 820 860 tr. 704 wh., tri. 1.43515° 185 d. 2.32 2.54 1.85 1.49 2300 2450 577 d. d. 100 −7.2 61.83 H3BO3 Boron carbide oxide oxide (sassolite) Bromic acid Bromine B B4C B2O3 B2O3⋅3H2O HBrO3 Br2 10.81 55.25 69.62 123.67 128.91 159.81 gray or bk., amor. or mn. bk. cr. col. glass, 1.459 tri., 1.456 col.; in soln. only rhb., or red lq. Br2⋅10H2O Cd Cd(C2H3O2)2 Cd(C2H3O2)2⋅2H2O∗ CdCO3 339.96 112.41 230.50 266.53 172.42 red, oct. silv. met., hex. col. col., mn. wh., trig. chloride Melting point, °C BaBr2⋅2H2O BaCO3 BaCO3 BaCO3 Ba(ClO3)2 Ba(ClO3)2⋅H2O∗ BaCl2 BaCl2 BaCl2⋅2H2O† Ba(OH)2 Ba(OH)2⋅8H2O Ba(NO3)2 BaC2O4 BaO Boric acid hydrate Cadmium acetate acetate carbonate Specific gravity CdCl2 183.32 wh., cb. 3.69 4.29 3.179 3.856 244° 3.097 244° 4.495 2.18816° 3.24428° 2.658 5.72 4.958 4° 2.9 4.16515° 4.116° 3.920° 4.27915° 4.49915° 4.2515° 2.98820° 1.816 9.8020° 3.11920°; 5.87 (A) 8.6520° 2.341 2.01 4.2584° 4.047 25 ° 4 Boiling point, °C −2H2O, 100 tr. 811 to α tr. 982 to β 174090 atm. 414 d. 120 tr. 925 962 −2H2O, 100 d. d. 1450 77.9 592 −8H2O, 550 d. 1923 d. 400 d. 200 1284 271 d. 6.8 320.9 256 −H2O, 130 d. <500 568 Hot water Other reagents v. s. 0.002218° v. s. 0.0065100° s. al. s. a.; i. al. 0.002218° 20.350° s. 310° 0.0065100° 84.880° s. 59100° s. a.; i. al. 76.8100° 101.480° 2000± 39.30° 1.670° 5.615° 5.00° 0.00168° 1.50° d. d. d. tr. to mn. 1149 v. sl. s. 0.168 d. 0.015 i. 0.01 0.02617° 0.0001150° 2767 1450 d. s. 4115° i. i. d. s. v. s. sl. s. d. i. i. d. d. d. i. i. i. i. sl. s. i. i. i. i. i. sl. s. 2.660° 40.2100° i. i. 1.10° sl. s. v. s. 4.220° i. i. 15.7100° s. d. 3.1330° 1560 1560 −O, 800 −8H2O, 100 1580 d. Solubility in 100 parts Cold water d. 300 447 −5H2O, 80 1900± 2550 >3500 >1500 58.78 767 d. 960 s. i. v. s. v. s. i. 90 0° 34.2100° 0.002424° 90.880° 0.09100° 0.00028530° i. i. 147100° sl. s. al., act. sl. s. HCl, HNO3; i. al. sl. s. HCl, HNO3; i. al. v. sl. s. al.; i. et. sl. s. a.; i. al. s. a., NH4Cl; i. al. s. HCl, HNO3, abs. al.; i. NH3, act. s. dil. a.; i. act. s. dil. a.; i. al., et., act. s. a. s. a., NH4 salts s. a. s. a., NH4 salts sl. s. HCl, NH4Cl; i. al. s. conc. H2SO4; 0.006, 3% HCl d. HCl; i. al. i. al., CS2 s. dil. a., alk. s. aq. reg., conc. H2SO4, HNO3 s. a. s. al. 4219° act.; s. a.; i. al. s. a. s. a. s. a. s. a. s. a.; i. act., NH3, H2C4H4O6 22.220° gly., 0.2425° et.; s. al. s. HNO3; i. al. i. a. s. a., al., gly. s. al., et., alk., CS2 s. a., NH4NO3 s. m. al. s. al. s. a., KCN, NH4 salts; i. NH3 1.5215° al.; i. et., act. CdCl2 ⋅2½H2O Cd(CN)2 Cd(OH)2 Cd(NO3)2 Cd(NO3)2⋅4H2O∗ CdO CdO Cd2O CdSO4 CdSO4⋅H2O 3CdSO4⋅8H2O∗ CdSO4⋅4H2O CdSO4⋅7H2O CdS Ca Ca(C2H2O2)2⋅H2O Ca(AlO2)2 CaO⋅Al2O3⋅2SiO2 Ca3(AsO4)2 CaBr2 CaCO3 CaCO3 CaCl2∗ CaCl2⋅H2O CaCl2⋅6H2O Ca3(C6H5O7)2⋅4H2O CaCN2 Ca2Fe(CN)6⋅12H2O CaF2 Ca(HCO2)2 CaH2 Ca(OH)2 Ca(ClO)2⋅4H2O Ca2P2O6⋅2H2O Ca(C3H5O3)2⋅5H2O 228 .36 164 .45 146 .43 236 .42 308 .48 128 .41 128 .41 240 .82 208 .47 226 .49 769 .54 280 .53 334 .58 144 .48 40 .08 176 .18 158 .04 278 .21 398 .07 199 .89 100 .09 100 .09 110 .98 129 .00 219 .08 570 .49 80 .10 508 .29 78 .07 130 .11 42 .09 74 .09 215 .04 274 .13 308 .29 col., mn., 1.6513 3.327 wh., trig. col. col. nd. brn., cb. brn., amor, 2.49 gn., amor. rhb. mn. col., mn., 1.565 col. mn. yel.-or., hex., 2.506 silv. met., cb. wh. nd. col., rhb. or mn. tri., 1.5832 wh. pd. delq. nd. col., rhb., 1.6809 col., hex., 1.550 wh., delq., cb, 1.52 col., delq. col., trig., 1.417 col. nd. col., rhombohedral yel., tri., 1.5818 wh., cb., 1.4339 col., rhb. wh. cr. or pd. col., hex., 1.574 wh., feathery cr. granular col., eff. 4.79 154° CaO⋅MgO⋅2CO2 CaO⋅MgO⋅2SiO2 Ca(NO3)2 Ca(NO3)2⋅4H2O∗ Ca3N2 Ca(NO2)2⋅H2O CaC2O4 CaC2O4⋅H2O CaO 184 .40 216 .55 164 .09 236 .15 148 .25 150 .10 128 .10 146 .11 56 .08 trig ., 1 .68174 wh ., mn . col ., cb . col ., mn ., 1 .498 brn . cr . delq ., hex . col ., cb . col . col ., cb ., 1 .837 peroxide phosphate, monobasic phosphate, dibasic phosphate, tribasic phosphate, metaphosphate, pyrophosphate, pyro- (brushite) phosphide silicate (α) (pseudowollastonite) CaO2⋅8H2O CaH4(PO4)2⋅H2O CaHPO4⋅2H2O Ca3(PO4)2 Ca(PO3)2 Ca2P2O7 Ca2P2O7⋅5H2O Ca3P2 CaSiO3 216 .20 252 .07 172 .09 310 .18 198 .02 254 .10 344 .18 182 .18 116 .16 silicate (β) (wollastonite) sulfate (anhydrite) CaSiO3 CaSO4 116 .16 136 .14 pearly, tet . wh ., tri . wh ., mn . pl . wh ., amor . wh ., tet ., 1 .588 col ., biaxial, 1 .60 wh ., mn . red cr . col ., pseudo hex ., 1 .6150 or mn . col ., mn ., 1 .610 col ., rhb ., 1 .576, or mn ., 1 .50 chloride cyanide hydroxide nitrate nitrate oxide oxide oxide, subCadmium sulfate sulfate sulfate sulfate sulfate sulfide (greenockite) Calcium acetate aluminate aluminum silicate (anorthite) arsenate bromide carbonate (aragonite) carbonate (calcite) chloride (hydrophilite) chloride chloride citrate cyanamide ferrocyanide fluoride ( fluorite) formate hydride hydroxide hypochlorite hypophosphate lactate magnesium carbonate (dolomite) magnesium silicate (diopside) nitrate (nitrocalcite) nitrate nitride nitrite oxalate oxalate oxide ∗Usual commercial form . † The solubility of CaCO3 in H2O is greatly increased by increasing the amount of CO2 in the H2O . 2.455 174° 8.15 6.95 8.192 184° 4.691 244° 3.78620° 3.09 3.05 2.48 204° 4.58 1.5520° tr. 34 d. >200 d. 300 350 59.4 132 d. 900–1000 d. 1000 tr. 108 tr. 41.5 3.6720° 2.765 tr. 4 1750100atm. 810 d. 1600 1551 3.353 254° 2.93 2.711 254° 2.152 154° 760 d. 825 1339103atm. 772 >1600 29.92 −2H2O, 130 −6H2O, 200 −4H2O, 185 17° 1.68 1.7 3.18020° 2.015 1.7 2.2 2 .872 3 .3 2 .36 1 .82 2 .6317° 2 .2334° 2 .24° 2 .2 3 .32 2 .220 164° 2 .306 164° 3 .14 2 .82 3 .09 2 .25 2 .5115° 2 .905 2 .915 2 .96 subl. in N2, 980 1200 ± 30 1810 1330 d. d. 675 −H2O, 580 d. −2H2O, 200 −3H2O, 100 d . 730–760 1391 561 42 .7 900 d . −H2O, 200 2570 −8H2O, 100 −H2O, 100 d . 1670 975 1230 2850 expl . 275 d . 200 32659.5° i. i. 60.8100° s. 127.660° s. 0.01325° 1250° 0.001220°† 0.001425° 59.50° s. v. s. 0.08518° s. d. s. 0.001618° 16.10° d. 0.1850° delq.; d. i. 10.5 i. 312105° 0.002100° 0.002100° 347260° s. v. s. 0.09626° d. 15090° 0.001726° 18.4100 0 .03218° i . 1020° 2660° d . 770° 0 .0006713° i . Forms Ca(OH)2 sl . s . 0 .02 0 .0025 i . i . sl . s . d . 0 .009517° tr . 1193 to rhb . 180100° 76.50° s. 114.20° s. 350−5° 0.000001 d. 520° d. 24 .5° >1600 1540 tr . 1190 to α 1450(mn .) 16820° 0.024718° 0.0002625° 109.70° 2150° i. i. 0 .29820° Colloidal d. 45.580° 0.077100° d. ∞ i . 376151° v . s . d . 41790° 0 .001495° i . d . d . 0 .075100° d . i . 0 .1619100° 2.0515° m. al. s. a.; NH4OH, KCN s. a., NH4 salts; i. alk. v. s. a. s. al., NH3; i. HNO3 s. a., NH4 salts; i. alk. s. a., NH4 salts; i. alk. d. a., alk. i.act., NH3 i. al. i. al. i. al. s. a.; v. s. NH4OH s, a.; sl. s. al. sl. s. al. s. HCl s. dil. a. s. al., act.; sl. s. NH3 s. a., NH4Cl s. a., NH4Cl s. al. s. al. s. al. 0.006518° al. i. al. sl. s. a. i. al., et. d. a.; i. bz. s. NH4Cl d. a. s. HCl, H4P2O6 ∞h . al .; i . et . 1415° al .; s . amyl al ., NH3 s . dil . a .; i . abs . al . s . 90% al . s . a .; i . ac . s . a .; i . ac s . a .; i . al . s . a . d .; i . al ., et . s . a .; i . al ., ac . i . a . s . a . s . a .; i . NH4Cl s . dil . a .; i . al ., et . s . HCl s . a ., Na2S2O3, NH4 salts (Continued ) 2-9 2-10 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Calcium (Cont.) sulfate (gypsum) Formula Formula weight Color, crystalline form, and refractive index CaSO4⋅2H2O 172.17 col., mn., 1.5226 Ca(SH)2⋅6H2O CaS CaSO3⋅2H2O CaC4H4O6⋅4H2O Ca(CNS)2⋅3H2O CaS2O3⋅6H2O CaWO4 214.32 72.14 156.17 260.21 210.29 260.30 287.92 col. pr. col., cb. wh., cr., 1.595 col., rhb. wh., delq. cr. col., tri., 1.56 wh., tet., 1.9200 C C C CO2 12.01 12.01 12.01 44.01 bk., amor. col., cb., 2.4195 bk., hex. col. gas disulfide CS2 76.14 col. lq. monoxide CO 28.01 col., poisonous, odorless gas poisonous gas gas sulfhydrate sulfide (oldhamite) sulfite tartrate thiocyanate thiosulfate tungstate (scheelite) Carbon, cf. table of organic compounds Carbon, amorphous Carbon, diamond Carbon, graphite dioxide oxychloride (phosgene) oxysulfide suboxide thionyl chloride Ceric hydroxide hydroxynitrate oxide sulfate Cerium COCl2 COS C3O2 CSCl2 2CeO2⋅3H2O Ce(OH)(NO3)3⋅3H2O CeO2 Ce(SO4)2⋅4H2O Ce 98.92 60.08 68.03 114.98 398.28 397.18 172.11 404.30 140.12 Cerous sulfate sulfate Cesium Chloric acid Chlorine Ce2(SO4)3 Ce2(SO4)3⋅8H2O Cs HClO3⋅7H2O Cl2 568.42 712.54 132.91 210.57 70.91 hydrate Chloroplatinic acid Chlorostannic acid Chlorosulfonic acid Chromic acetate chloride chloride fluoride hydroxide Cl2⋅8H2O H2PtCl6⋅6H2O H2SnCl6⋅6H2O HO⋅SO2⋅Cl Cr2(C2H3O2)6⋅2H2O CrCl3 CrCl3⋅6H2O∗ CrF3 Cr(OH)3 215.03 517.90 441.54 116.52 494.29 158.36 266.45 108.99 103.02 Cr(OH)3⋅2H2O Cr(NO3)3⋅9H2O∗ Cr(NO3)3⋅7½H2O Cr2O3 Cr2(SO4)3 Cr2(SO4)3⋅5H2O Cr2(SO4)3⋅15H2O Cr2(SO4)3⋅18H2O Cr2S3 139.05 400.15 373.13 151.99 392.18 482.26 662.41 716.46 200.19 hydroxide nitrate nitrate oxide sulfate sulfate sulfate sulfate sulfide gas yel.-red lq. yel., gelatinous red, mn. wh. or pa. yel., cb. yel., rhb. steel gray, cb. or hex. wh., mn. or rhb. tri. silv. met., hex. lq. rhb., or gn.-yel. gas rhb. red-brn., delq. delq. col. lq. gn. pink, trig. vl. or gn., hex. pl. gn., rhb. gn. or blue, gelatinous gn. purple pr. purple, mn. dark gn., hex. rose pd. gn. vl. vl., cb., 1.564 brn.-bk. pd. Specific gravity 2.32 2.815° Melting point, °C −1½H2O, 128 Boiling point, °C −2H2O, 163 d. 15 −2H2O, 100 d. d. 650 Solubility in 100 parts Cold water Hot water 0.2230° 0.25750° v. s. d. 0.004318° 0.0370° s. 71.29° 0.2 v. s. d. 0.002790° 0.2285° v. s. d. Other reagents s. a., gly., Na2S2O3, NH4 salts s. al. s. a. s. H2SO3 sl. s. al. v. s. al. i. al. s. NH4Cl; i. a. 1.87316° 6.06 d. 1.8–2.1 3.5120° 2.2620° lq. 1.101−87°; 1.53 (A); solid 1.56−79° lq. 1.261 2220° ; 2.63 (A) ° lq. 0.814 −195 4 ; 0.968 (A) 1.392 194° lq. 1.24−87°; 2.10 (A) lq. 1.1140° 1.50915° >3500 >3500 >3500 −56.65.2atm. 4200 4200 4200 subl. −78.5 i. i. i. 179.70° cc i. i. i. 90.120° cc i. a., alk. i. a., alk. i. a., alk. s. a., alk. −108.6 46.3 0.20° 0.01450° s. al.; et. −207 −192 0.00440°; 3.50° cc v. s. sl. d. 1330° cc 0.001850° 2.3220° cc d. 40.330° cc s. al., Cu2Cl2 7.3 3.91 6.920° cb.; 6.7 hex. 3.91 2.88617° 1.9020° 1.28214.2° lq. 1.56−33.6°; 2.490° (A) 1.23 2.431 1.97128° 1.78725° 2.75715° 1.835 254° 3.8 5.21 3.012 1.86717° 1.722° 3.7719° 756mm −104 −138.2 8.2 −50.2760mm −107 7761mm 73.5 1950 645 1400 d. s. et. s. a.; sl. s. alk. carb.; i. alk d. i. s. d. i. i. 0° −8H2O, 630 28.5 <−20 −101.6 d. 9.6 60 19.2 −80 subl. 83 >1000 −2H2O, 100 36.5 100 1900 100 −S, 1350 670 d. 40 −34.6 151.5765mm 1200–1500 d. d. d. 100 d. −10H2O, 100 −12H2O, 100 s. ac., CCl4, bs.; d.a. v. s. alk., al. 18.98 250° d. v. s. 1.460°; 31010° cc s. v. s. s. d. s. i.§ v. s. d. i. i. i. s. s. i. i.† s. s. 12020° i. Slowly oxidized 0.4100° 7.640° 30° 0.57 ; 17730° cc v. s. sl. s. i. s. s. i. d. 67° d. d. s. H2SO4, HCl s. dil. H2SO4 s. dil. a.; i. al. s. a., al., NH3 s. alk. s. alk. s. al., et. d. al.; i. CS2 4.7615° m. al. i. a., act., CS2 s. al.; i. et. sl. s. a.; i. al., NH3 s. a., alk.; sl. s. NH3 s. a., alk. s. a., alk., al., act. sl. s. a. i. a. s. al., H2SO4 sl. s. al. s. al. s. h. HNO3 Chromium trioxide (chromic acid) Chromous chloride hydroxide oxide sulfate sulfide (daubrelite) Chromyl chloride Cobalt carbonyl sulfide, diCobaltic chloride chloride, dichro chloride, luteo chloride, praseo Cobaltic chloride, purpureo chloride, roseo hydroxide oxide sulfate sulfide Cobalto-cobaltic oxide Cobaltous acetate chloride chloride nitrate oxide sulfate sulfate sulfate (biebeorite) sulfide (syeporite) Copper Cupric acetate aceto-arsenite (Paris green) ammonium chloride Cr 52 .00 CrO3 CrCl2 Cr(OH)2 CrO CrSO4⋅7H2O CrS CrO2Cl2 Co Co(CO)4 CoS2 CoCl3 Co(NH3)3Cl3⋅H2O Co(NH3)6Cl3 Co(NH3)4Cl3⋅H2O Co(NH3)5Cl3 Co(NH3)5Cl3⋅H2O Co(OH)3 Co2O3 Co2(SO4)3 Co2S3 Co3O4 Co(C2H3O2)2⋅4H2O CoCl2 CoCl2⋅6H2O∗ Co(NO3)2⋅6H2O 99 .99 122 .90 86 .01 68 .00 274 .17 84 .06 154 .90 58 .93 170 .97 123 .06 165 .29 234 .40 267 .48 251 .43 250 .44 268 .46 109 .96 165 .86 406 .05 214 .06 240 .80 249 .08 129 .84 237 .93 291 .03 CoO CoSO4 CoSO4⋅H2O 74 .93 155 .00 173 .01 CoSO4⋅7H2O∗ CoS Cu Cu(C2H3O2)2 Cu(C2H3O2)2⋅H2O (CuOAs2O3)3⋅ Cu(C2H3O2)2∗ CuCl2⋅2NH4Cl⋅2H2O 281 .10 91 .00 63 .55 181 .63 199 .65 1013 .79 gray, met., cb. red, rhb. wh., delq. yel.-brn. bk. pd. blue bk. pd. dark red lq. silv. met., cb. or. cr. bk., cb. red cr. 7.1 1615 2.70 2.75 197 d. 3.97 1.92 8.920° 1.7318° 4.269 2.94 1550 −96.5 1480 51 subl. brn., cb. red pd. red pd., mn.(?), 1.639 red, mn., 1.483 brn. nd. yel.-red met., cb. 5.18 d. 100 −1½H2O, 100 d. 900 4.8 6.07 1.705318.7° 3.356 1.924 2525° 1.883 2525° −4H2O, 140 subl. 86 <100 5.68 3.71025° 3.13 d. 1800 d. 880 d. 1.948 2525° 5.4518° 8.9220° 1.930 204° 1.882 96.8 >1100 1083 −7H2O, 420 115 240 d. 1.98 d. 110 ammonium sulfate carbonate, basic (azurite) CuSO4⋅4NH3⋅H2O 2CuCO3⋅Cu(OH)2 245 .75 344 .67 blue, tet., 1.670, 1.744 blue, rhb. blue, mn., 1.758 carbonate, basic (malachite) chloride (eriochalcite) CuCO3⋅Cu(OH)2 CuCl2 221 .12 134 .45 dark gn., mn., 1.875 brn.-yel. pd. 3.9 3.054 d. 498 chloride chromate, basic cyanide dichromate ferricyanide ferrocyanide formate hydroxide lactate nitrate nitrate ∗Usual commercial form . † Also a soluble modification . CuCl2⋅2H2O CuCrO4⋅2CuO⋅2H2O Cu(CN)2 CuCr2O7⋅2H2O Cu3[Fe(CN)6]2 Cu2Fe(CN)6⋅7H2O Cu(HCO2)2 Cu(OH)2 Cu(C3H5O3)2⋅2H2O Cu(NO3)2⋅3H2O∗ Cu(NO3)2⋅6H2O 170 .48 374 .66 115 .58 315 .56 614 .54 465 .15 153 .58 97 .56 277 .72 241 .60 295 .65 gn., rhb., 1.684 yel.-brn. yel.-gn. bk., tri. yel.-gn. red-brn. blue, mn. blue, gelatinous dark blue, mn. blue, delq. blue, rhb. 2.3922.4° −2H2O, 110 −2H2O, 260 d. −2H2O, 100 277 .47 117.6 2900 d. 52 20° 1.7016 1.847 1.819 2525° 1.81 3.88 d. 150 d. 220 2.28618° 1.831 3.368 2.047 2.074 1049 −6H2O, 110 d. 114.5 −3H2O, 26.4 i. 164.9 v. s. d. i. 12.350° i. d. i. i. i. s. s. 4.260° v. s. 0.2320° 16.120° i. i. d. i. i. s. 457° 116.50° 84.030°(anh.) i. 25.60° s. 2300 3380° 0.0003818° i. s. 7.2 i. 33.80° 18.05 i. Forms Cu2Cl2 993 d. −H2O 3.9° i. 0° d. or., mn. gn., rhb. rhb. brick red bk. bk. blue cr. bk. cr. bk., cb. red-vl., mn., 1.542 blue cr. red, mn. red, mn., 1.4 dark gn., mn. gn. 2200 −HNO3, 170 21.5° 206.7 v. s. 100° i. i. d. s. 12.7446.5° 1.03146.5° 24.8716° i. i. i. s. 10596° 17780° 334.990° (anh.) i. 83100° s. s. i. s. HCl, dil. H2SO4; i. HNO3 s. H2SO4, al., et. sl. s. al.; i. et. s. conc. a. i. dil. HNO3 sl. s. al. v. s. a. s. et. s. a. s. al., et., CS2 s. HNO3, aq. reg. s. a.; al. i. al., NH4OH s. a.; i. al. i. al. sl. s. HCl s. a.; i. al. s. a. s. H2SO4 d. a. s. H2SO4; i. HCl, HNO3 s. a., al. 31 al.; 8.6 act. v. s. et., act. 10012.5° al.; s. act.; sl. s. NH3 s. a., NH4OH; i. al. 1.0418° m. al.; i. NH8 2.58° al. s. a., aq. reg. s. HNO3, h. H2SO4 20 7 al.; s. et.; gly. s. a., NH4OH 99.380° s. a. d. d. i. al. s. NH4OH, h. aq. NaHCO3 s. KCN; 0.03 aq. CO 5315° al.; 6815° m. al. i. 70.70° d. 107.9100° 110.40° i. i. sl. s. i. i. 12.5 i. 16.7 38140° 243.70° 192.4100° d. i. d. d. 45100° 66680° ∞ s. al.; et., NH4Cl s. HNO3, NH4OH s. KCN, C5H5N s. a.; NH4OH s. NH4OH; i. HCl s. NH4OH; i. a., NH8 0.25 al. s. a., NH4OH, KCN, al. sl. s. al. 10012.5° al. s . al . (Continued ) 2-11 2-12 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Formula Formula weight Color, crystalline form, and refractive index Cupric (Cont.) oxide (paramelaconite) oxide (tenorite) oxychloride phosphide sulfate (hydrocyanite) sulfate (blue vitriol or chalcanthite) sulfide (covellite) tartate Cuprous ammonium iodide carbonate chloride (nantokite) cyanide CuO CuO CuCl2⋅2CuO⋅4H2O Cu3P2 CuSO4 79 .55 79 .55 365 .60 252 .59 159 .61 CuSO4⋅5H2O∗ CuS CuC4H4O6⋅3H2O CuI⋅NH4I⋅H2O Cu2CO3 Cu2Cl2 Cu2(CN)2 249 .69 95 .61 265 .66 353 .41 187 .10 198 .00 179 .13 bk., cb. bk., tri., 2.63 blue-gn. bk. gn.-wh., rhb., 1.733 blue, tri., 1.5368 blue, hex. or mn., 1.45 1 gn. pd. rhb. pl. yel. wh., cb., 1.973 wh., mn. ferricyanide ferrocyanide fluoride hydroxide oxide (cuprite) Cuprous phosphide sulfide (chalcocite) sulfide Cyanogen Cu3Fe(CN)6 Cu4Fe(CN)6 Cu2F2 CuOH Cu2O Cu6P2 Cu2S Cu2S C2N2 402 .59 466 .13 165 .09 80 .55 143 .09 443 .22 159 .16 159 .16 52 .03 brn.-red brn.-red red cr. yel. red, cb., 2.705 gray-bk. bk., rhb. bk., cb. poisonous gas Fe(OH)(C2H3O2)2 190 .94 brn., amor. Cyanogen compounds, cf. table of organic compounds Ferric acetate, basic ammonium sulfate, cf. Alum chloride (molysite) chloride ferrocyanide (Prussian blue) hydroxide lactate nitrate oxide (hematite) sulfate sulfate (coquimbite) Ferroso-ferric chloride ferricyanide (Prussian green) oxide (magnetite; magnetic iron oxide) oxide, hydrated Ferrous ammonium sulfate FeCl3 FeCl3⋅6H2O∗ Fe4[Fe(CN)6]3 162 .20 270 .30 859 .23 bk.-brn., hex. delq. red-yel., delq. dark blue Fe(OH)3 Fe(C3H5O3)3 Fe(NO3)3⋅6H2O Fe2O3 106 .87 323 .06 349 .95 159 .69 red-brn . brn ., amor ., delq . rhb ., delq . red or bk ., trig ., 3 .042 rhb ., 1 .814 yel ., trig . yel ., delq . gn . bk ., cb ., 2 .42 Fe2(SO4)3 Fe2(SO4)3⋅9H2O FeCl2⋅2FeCl3⋅18H2O Fe4Fe3[Fe(CN)6]6 Fe3O4 399 .88 562 .02 775 .43 1662 .61 231 .53 303 .59 392 .14 chloride (lawrencite) Fe3O4⋅4H2O FeSO4⋅(NH4)2SO4⋅ 6H2O FeCl2 chloroplatinate ferricyanide (Turnbull’s blue) ferrocyanide formate hydroxide nitrate oxide FePtCl6⋅6H2O Fe3[Fe(CN)6]2 Fe2Fe(CN)6 Fe(HCO2)2⋅2H2O Fe(OH)2 Fe(NO3)2⋅6H2O FeO 571 .73 591 .43 323 .64 181 .91 89 .86 287 .95 71 .84 126 .75 bk . blue-gn ., mn ., 1 .4915 gn .-yel ., hex ., 1 .567 yel ., hex . dark blue blue-wh ., amor . Specific gravity 6.40 6.45 6.35 3.60615° Melting point, °C d. 1026 d. 1026 −3H2O, 140 d. d. >600 ° 2.286 15.6 4 4.6 −4H2O, 110 tr. 103 d. 4.4 3.53 2.9 d. 422 474.5 3.4 6.0 6.4 to 6.8 5.6 5.80 lq. 0.866−17.2°; 1.806 (A) 908 −½H2O, 360 1235 1100 1130 −34.4 Forms CuO, 650 −5H2O, 250 d. 220 1366 d. subl. 1100 −O, 1800 −20.5 Solubility in 100 parts Cold water i. i. i. i. 14.30° 24.30° 0.00003318° 0.0215° d. i. 1.5225° i. i. i. i. i. i. i. 0.000518° 0.000518° 45020° cc Hot water i. i. 75.4100° 205100° 0.1485° i. i. i. i. i. 11° 2.804 282 37 d . 3 .4 to 3 .9 −1½H2O, 500 1 .68420° 5 .12 35 1560 d . 3 .09718° 2 .1 d . 480 315 280 d . Other reagents s. a.; KCN, NH4Cl s. a., KCN, NH4Cl s. a. s. HNO3; i. HCl i. al. 1.18° al. s. HNO3, KCN s. a., KOH s. NH4I s. a., NH4OH s. HCl, NH4OH, al. s. KCN, HCl, NH4OH; sl. s. NH3 s. NH4OH; i. HCl s. NH4OH; i. NH4Cl s. HF, HCl, HNO3; i. al. s. a., NH4OH s. HCl, NH4Cl, NH4OH s. HNO3; i. HCl s. HNO3, NH4OH; i. act. s. HNO3, NH4OH; i. act. 230020° cc al.; 50018° cc et. s. a.; al. 0° 100° 74.4 2460° i . 535.8 ∞ d . v. s. al.; et. +HCl s . al ., act ., gly . s . HCl, conc . H2SO4; i . al ., et . s . a .; i . al ., et . i . et . s . al ., act . s . HCl i . v . s . 1500° i . i . v . s . ∞ d . d . s . i . s . d . h . HCl i . al . 5 .2 d . 50 d . 180 1538 d . sl . s . 440 s . i . i . 1 .864 d . d . i . 180° i . 10075° s . a . i . al . 64 .410° 105 .7100° 100 al .; s . act .; i . et . v . s . i . i . sl . s . 0 .00067 2000° i . v . s . 2 .7 delq . 2 .714 d . d . lt . gn . cr . bk . Boiling point, °C 3 .4 5 .7 60 .5 1420 i . H2SO4, NH3 s . abs . al . i . dil . a ., al . 30025° i . s . a ., NH4Cl s . a .; i . alk . phosphate (vivianite) Fe3(PO4)2⋅8H2O 501 .60 silicate sulfate (siderotilate) sulfate (copperas) sulfide cf. also under iron Fluoboric acid Fluorine FeSiO3 FeSO4⋅5H2O FeSO4⋅7H2O∗ FeS 131 .93 241 .98 278 .01 87 .91 HBF4 F2 87 .81 38 .00 Fluosilicic acid Gadolinium Gallium bromide Glucinum cf. Beryllium Gold Gold, colloidal Gold salts cf. under Auric and Aurous Hafnium Helium Hydrazine formate hydrate hydrochloride hydrochloride, dinitrate nitrate, disulfate sulfate Hydrazoic acid (azoimide) Hydriodic acid Hydriodic acid Hydriodic acid Hydriodic acid Hydriodic acid Hydrobromic acid Hydrobromic acid H2SiF6 Gd GaBr3 144 .09 157 .25 309 .44 delq . cr . Au Au 196 .97 196 .97 yel . met ., cb . blue to vl . 19 .320° 1063 2600 Hf He N2H4 N2H4⋅2HCO2H N2H4⋅H2O N2H4⋅HCl N2H4⋅2HCl N2H4⋅HNO3 N2H4⋅2HNO3 N2H4⋅½H2SO4 N2H4⋅H2SO4 HN3 HI HI⋅H2O HI⋅2H2O HI⋅3H2O HI⋅4H2O HBr HBr⋅H2O 178 .49 4 .00 32 .05 124 .10 50 .06 68 .51 104 .97 95 .06 158 .07 81 .08 130 .12 43 .03 127 .91 145 .93 163 .94 181 .96 199 .97 80 .91 98 .93 hex . col . gas col . lq . cb . col . yel . lq . wh ., cb . cr . nd . delq . pl . rhb . col . lq . col . gas col . lq . col . lq . col . lq . col . lq . col . gas; 1 .325 (lq .) col . lq . 12 .1 0 .1368 (A) 1 .011 154° >1700 <−272 .2 1 .4 128 −40 >3200(?) −268 .9 113 .5 Hydrobromic acid Hydrobromic acid Hydrochloric acid Hydrochloric acid Hydrochloric acid Hydrochloric acid Hydrocyanic acid (prussic acid) HBr (47 .8% in H2O) HBr⋅2H2O HCl† HCl (45 .2% in H2O) HCl⋅2H2O HCl⋅3H2O HCN 80 .91 118 .96 36 .46 36 .46 72 .49 90 .51 27 .03 Hydrofluoric acid Hydrofluoric acid Hydrogen HF HF (35 .35% in H2O) H2 20 .01 20 .01 2 .02 col . lq . wh . cr . col . gas; 1 .256 (lq .) col . lq . col . lq . col . lq . poisonous gas or col . lq ., 1 .254 gas or col . lq . col . lq . col . gas or cb . peroxide selenide sulfide Hydroxylamine hydrochloride nitrate sulfate ‡ H2O2 H2Se H2S NH2OH NH2OH⋅HCl NH2OH⋅HNO3 NH2OH⋅½H2SO4 ∗Usual commercial form . † Usual commercial form about 31 percent . ‡ Usual commercial forms 3 or 30 percent . 34 .01 80 .98 34 .08 33 .03 69 .49 96 .04 82 .07 blue, mn., 1.592, 1.603 mn. gn., tri., 1.536 blue-gn., mn. bk., hex. col. lq. gn .-yel . gas col . lq ., 1 .333 col . gas col . gas rhb ., delq . col ., mn . col . cr . col ., mn . 2.58 3.5 2.2 1.89914.8° 4.84 lq . 1 .51−187°; 1 .3115° (A) 1 .0321° 1 .42 1 .378 4 .40° (A) 1 .715° 2 .710° (A) 1 .78 1 .486 2 .11−15° 1 .2680° (A) 1 .48 ° 1 .46 −18.3 4 0 .69718° 0 .98813 .6° 1 .15 lq . 0 .0709−252 .7° 0 .06948 (A) 1 .438 204° 2 .12−42° 1 .1895 (A) 1 .3518° 1 .6717° 1550 i. i. s. a.; i. ac. 64 1193 −5H2O, 300 −7H2O, 300 d. s. 32.80° 0.00061618° s. 14950° i. al. i. al. s. a.; i. NH3 130 d. −187 ∞ d . ∞ s . al . −223 s . s . s . s . i . s . i . s . aq . reg ., KCN; i . a . s . aq . reg ., KCN; i . a . 0 .970° cc ∞ s . ∞ v . s . s . 174 .910° v . s . v . s . 3 .05522° ∞ 42,50010° cc ∞ ∞ ∞ ∞ 2210° 1 .0850° cc ∞ Absorbed by Pt s . al . ∞ v . s . v . s . v . s . ∞ al .; i . et . sl . s . al . s . al . 198 70 .7 104 85 254 −80 −50 .8 −43 −48 −36 .5 −86 118 .5739 .5mm subl . 140 d . 37 −35 .5 127774mm −67 126 −11 −111 −15 .35 0 −24 .4 −14 −83 −35 −259 .1 −0 .89 −64 −82 .9 34 151 48 170 d . 27 .6560° ∞ v . s . 130100° i . al . v . sl . s . abs . al . ∞ al . s . al . ∞ al . s . al . s . al . s . al . s . al . Stable at −15 .5° and 1 atm ., and at −11 .3° and 2 .5 atm . s . al . d . d . 26 ∞ s . 82 .30° ∞ ∞ ∞ ∞ 19 .4 120 −252 .7 ∞ 0° to 19 .4° v . s . 2 .10° cc 0 .8580° cc sl . s . Fe, Pd, Pt ∞ 3774° cc 4370° cc s . 83 .317° v . s . 32 .90° 27022 .5° cc 18640° cc d . v . s . d . 68 .590° s . a ., et .; i . petr . et s . CS2, COCl2 9 .5415° cc al .; s . CS2 s . a ., al . s . al .; i . et . v . s . abs . al . v . sl . s . al .; i . et ., abs . al . −85 760mm 151 .4 −42 −59 .6 56 .522mm d . d . <100 s . 56 .160° s . al ., et . s . al . s . al . s . al . ∞ al ., et . v . s . (Continued ) 2-13 2-14 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Formula Hypobromous acid Indium Iodic acid HBrO In HIO3 Iodine oxide, pentaIodoplatinic acid Iridium Iron, cast† pure steel white pig wrought carbide (cementite) carbonyl nitride silicide sulfide, di- (marcasite) sulfide, di- (pyrite) sulfide (pyrrhotite) Cf. also under ferric and ferrous Krypton Lanthanum Lead I2 I2O5 H2PtI6⋅9H2O Ir Fe Fe Fe Fe Fe Fe3C Fe(CO)5 Fe2N FeSi FeS2 FeS2 Fe7S8 Formula weight Color, crystalline form, and refractive index 96.91 114.82 175.91 yel. soft, tet. met. col., rhb. 253.81 333.81 1120.66 192.22 55.85 55.85 55.85 55.85 55.85 179.55 195.90 125.70 83.93 119.98 119.98 647.44 blue-bk., rhb. wh., trimetric brn., delq. mn. wh. met., cb. gray silv. met., cb. silv. gray gray gray pseudo hex. pa. yel. lq. gray yel.-gray, oct. yel., rhb. yel., cb. hex. Specific gravity Melting point, °C d. i. 576101° 0.01620° 187.412° s. d. i. i. i. i. i. i. i. i. d. i. 0.00049 0.0005 i. 0.0956660° 4.9320° 4.799 254° 113.5 d. 300 184.35 22.420° 7.03 7.8620° 7.6 to 7.8 7.6 to 7.8 7.86 7.4 1.45721° 6.35 6.1 204° 4.87 5.0 4.6 204° 2350 1275 1535 1375 1075 1505 1837 −21 d. >560 >4800 tr. 450 1171 d. >700 d. d. −151.8 1800 1620 3000 102.5760mm i. i. i. i. i. i. i. i. 11.050° cc d. i. 3.5760° cc 280 −3H2O, 75 22 19.70° 45.6415° s. v. s. v. s. 22150° 200100° s. 5.55 18.2 d. 140 d. >200 d. i. d. i. i. 0.45540° d. 0.05100° 4.75100° 0.0001120° i. d. i. d. 190 −H2O, 130 d. 470 0.6730° 0.00000720° i. 1.616° 0.014 38.80° 3.34100° i. i. 18100° d. d. red heat 888 i. 0.006818° i. col. gas lead gray silv. met., cb. 2.818 (A) 6.1520° 11.337 2020° −169 826 327.5 Pb(C2H3O2)2 Pb(C2H3O2)2⋅3H2O† Pb(C2H3O2)2⋅10H2O Pb2(C2H3O2)3OH Pb(C2H3O2)2⋅ Pb(OH)2⋅H2O Pb(C2H3O2)2⋅ 2Pb(OH)2 PbH4(AsO4)2 PbHAsO4 Pb(AsO3)2 Pb2As2O7 PbN6 PbBr2 325.29 379.33 505.44 608.54 584.52 wh. cr. wh., mn. wh., rhb. wh. wh. nd. 3.251 204° 2.55 1.689 807.72 wh. nd. 489.07 347.13 453.04 676.24 291.24 367.01 tri., 1.82 wh., mn., 1.9097 hex. rhb., 2.03 col. nd. col., rhb. 4.4615° 5.94 6.4215° 6.85 1515° 6.66 802 expl. 350 373 carbonate (cerussite) carbonate, basic (hydrocerussite; white lead) chloride (cotunnite) chromate (crocoite) chromate, basic formate hydroxide nitrate PbCO3 2PbCO3⋅Pb(OH)2† 267.21 775.63 wh., rhb., 2.0763 wh., hex. 6.6 6.14 d. 315 d. 400 PbCl2 PbCrO4 PbCrO4⋅PbO Pb(HCO2)2 3PbO⋅H2O Pb(NO3)2 278.11 323.19 546.39 297.23 687.61 331.21 5.80 6.12 501 844 4.56 7.592 4.53 oxide, suboxide, mono- (litharge) Pb2O PbO 430.40 223.20 wh., rhb., 2.2172 yel., mn., 2.42 or.-yel. nd. wh., rhb. cb. col., cb. or mn., 1.7815 bk., amor. yel., tet. 8.34 9.53 oxide, mono (massicotite) PbO 223.20 yel., rhb., 2.61 8.0 arsenate, monobasic arsenate, dibasic (schultenite) arsenate, metaarsenate, pyroazide bromide Hot water s. i. 2860° 155 110 d. 83.80 138.91 207.20 acetate, basic Solubility in 100 parts Cold water 4050mm 1450 7.320° 4.6290° Kr La Pb acetate acetate (sugar of lead) acetate acetate, basic acetate, basic Boiling point, °C −H2O, 280 918 954760mm d. i. sl. s. 138.8100° Other reagents s. a. v. s. 87% al.; i. abs. al. et., chl. s. al., KI, et. i. abs. al., et., chl. sl. s. aq. reg., aq. Cl2 s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a.; i. alk. s. a. s. al., H2SO4, alk. s. HCl, H2SO4 i. aq. reg. i. dil. a. i. dil. a. sl. s. al., bz. s. a. s. HNO3; i. c. HCl, H2SO4 s. gly.; v. sl. s. al. s. gly.; sl. s. al. sl. s. al. s. al. s. al. s. HNO3 s. HNO3, NaOH s. HNO3 s. HCl, HNO3; i. sc. v. s. ac.; i. NH4OH s. a., KBr.; sl. s. NH3; i. al. s. a., alk.; i. NH3, al. s. ac.; sl. s. aq. CO2 sl. s. dil. HCl, NH3, i. al. s. a., alk.; i. NH3, ac. s. a., alk. i. al. s. a., alk. 8.822° al. s. a., alk. s. alk., PbAc, NH4Cl, CaCl2 oxide, mono- PbO 223 .20 amor. 9.2 to 9.5 oxide, red (minium) oxide, sesquioxide, di- (plattnerite) silicate sulfate (anglesite) Pb3O4 Pb2O3 PbO2 PbSiO3 PbSO4 685 .60 462 .40 239 .20 283 .28 303 .26 9.1 Pb(HSO4)2 ⋅H2O PbSO4⋅PbO PbS Pb(CNS)2 Li LiC7H5O2 LiBr 419 .36 526 .46 239 .27 323 .36 6 .94 128 .05 86 .85 LiBr⋅2H2O Li2CO3 LiCl 122 .88 73 .89 42 .39 citrate fluoride formate hydride hydroxide hydroxide nitrate nitrate oxide phosphate, monobasic phosphate, tribasic phosphate, tribasic salicylate sulfate sulfate sulfate, acid Lutecium Magnesium acetate acetate aluminate (spinel) Li3C6H5O7⋅4H2O LiF LiHCO2⋅H2O LiH LiOH LiOH⋅H2O LiNO3 LiNO3⋅3H2O Li2O LiH2PO4 Li3PO4 Li3PO4⋅12H2O LiC7H5O3 Li2SO4 Li2SO4⋅H2O† LiHSO4 Lu Mg Mg(C2H3O2)2 Mg(C2H3O2)2⋅4H2O† MgO⋅Al2O3 281 .98 25 .94 69 .97 7 .95 23 .95 41 .96 68 .95 122 .99 29 .88 103 .93 115 .79 331 .98 144 .05 109 .94 127 .96 104 .01 174 .97 24 .31 142 .39 214 .45 142 .26 red, amor. red-yel., amor. brn., tet., 2.229 col., mn., 1.961 wh., mn. or rhb., 1.8823 cr. col., mn. lead gray, cb., 3.912 col., mn. silv. met. cb. wh. leaflets wh., delq., cb., 1.784 wh. pr. col., mn., 1.567 wh., delq., cb., 1.662 wh. cr. wh., cb., 1.3915 col., rhb. wh., cb. wh. cr. col., mn. col., trig., 1.735 col. col ., 1 .644 col . wh ., rhb . wh ., trig . col . col ., mn ., 1 .465 col ., mn ., 1 .477 pr . ammonium chloride ammonium phosphate (struvite) ammonium sulfate (boussingaultite) benzoate carbonate (magnesite) carbonate (nesquehonite) carbonate, basic (hydromagnesite) Magnesium chloride (chloromagnesite) chloride (bischofite) hydroxide (brucite) nitride oxide (magnesia; periclase) perchlorate MgCl2⋅NH4Cl⋅6H2O MgNH4PO4⋅6H2O 256 .79 245 .41 sulfate, acid sulfate, basic (lanarkite) sulfide (galena) thiocyanate Lithium benzoate bromide bromide carbonate chloride ∗See also a table of alloys . † Usual commercial form . MgSO4⋅(NH4)2SO4⋅ 6H2O Mg(C7H5O2)2⋅3H2O MgCO3 MgCO3⋅3H2O 3MgCO3⋅Mg(OH)2⋅3H2O MgCl2 MgCl2⋅6H2O Mg(OH)2 Mg3N2 MgO Mg(ClO4)2† † 360 .60 i. i. 9.375 6.49 6.2 d. 500 d. 360 d. 290 766 1170 i. i. i. i. 0.00280° i. i. i. 6.92 7.5 3.82 0.5320° d. 977 1120 d. 190 186 1336 ± 5 25 ° 4 547 1265 0.000118° 0.004418° 0.0000918° 0.0520° d. 3325° 1430° (2H2O) 2.110° 2.068 254° 44 618 614 d. 1360 24620° 1.540° 670° 3.464 2.29521.5° 1.46 0.820 2.54 1.83 2.38 2 .013 254° 2 .461 2 .53717 .5° 1 .645 d. 870 −H2O, 94 680 445 261 29.88 2 .22 2 .06 2 .12313° silv . met ., hex . wh . wh ., mn . pr ., 1 .491 col . cb ., 1 .718–23 1 .7420° 1 .42 1 .454 3 .6 651 323 80 2135 wh ., rhb ., delq . col ., rhb ., 1 .496 1 .456 1 .715 −4H2O, 195 d . 100 1 .72 wh . pd . wh ., trig . 1 .700 col ., rhb ., 1 .501 wh ., rhb ., 1 .530 3 .037 1 .852 2 .16 −3H2O, 110 d . 350 −H2O, 100 d . 95 .21 col ., hex ., 1 .675 2 .32525° 712 wh ., delq ., mn ., 1 .507 wh ., trig ., 1 .5617 gn .-yel ., amor . col ., cb ., 1 .7364 wh ., delq . 1 .56 2 .4 3 .65 2 .6025° 1110 >120 320 .58 84 .31 138 .36 365 .31 203 .30 58 .32 100 .93 40 .30 223 .21 925± d. subl . <1000 >100 837 100 d . 860 −H2O, 130 170 .5 col ., mn . 1670 118 d . d . d . 2800 d . 3600 0.72100° 127.5100° 66.7100° 0.13535° 346.6104° 0 .03418° v . sl . s . 12826° 35 .340° 43 .60° d . v . sl . s . v . sl . s . i . v . s . v . s . i . sl . s . d . v . s . v . s . 16 .7 0 .02310° s . 0 .019580° 0° 25° d . i. s. d. 40100° 266100° (1H2O) 61.215° 0.2718° 49.20° d. 12.70° 22.310° 53.40° v. s. forms LiOH 16 .86 1412 0.005640° 17.5100° 26.880° 19470° ∞ 29 .9100° 35100° s. alk., PbAc, NH4Cl, CaCl2 s. ac., h. HCl s. a., alk. s. ac., h. alk.; i. al. s. a. s. conc. a., NH4 salts; i. al. sl. s. H2SO4 sl. s. H2SO4 s. a.; i. alk. s. KCNS, HNO3 s. a., NH3 7.725°, 1078° al. s. al., act. s. al. s. dil. a.; i. al., act., NH3 2.4815° al.; s. et. sl. s. al., et. s. HF; i. act. sl. s. al., et. i. et. sl. s. al. sl. s. al. s. al., NH3 s . a ., NH4Cl; i . act . v . s . al . i . act ., 80% al . i . 80% al . s . a ., NH4 salts 5 .2515° m . al . v . s . al . v . sl . s . dil . HCl; i . dil . HNO3 s . a .; i . al . 100° 130 4 .5 (anh .) 0 .0106 0 .151819° 0 .04 d . 0 .011 s . act . s . a ., aq . CO2; i . act ., NH3 s . a ., aq . CO2 s . a ., NH4 salts; i . al . 52 .80° 73100° 50 al . 0° 281 0 .000918° i . 0 .00062 99 .625° s . 100° 918 d . v . s . 50 al . s . NH4 salts, dil . a . s . a .; i . al . s . a ., NH4 salts; i . al . 2425 al ., 51 .825° m . al .; 0 .29 et . (Continued ) 2-15 2-16 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Magnesium (Cont.) peroxide phosphate, pyrophosphate, pyropotassium chloride (carnallite) potassium sulfate (picromerite) silicofluoride sodium chloride sulfate sulfate (epsom salt; epsomite) Manganese acetate acetate carbonate (rhodocrosite) Formula Formula weight Color, crystalline form, and refractive index Specific gravity Melting point, °C 2.59822° 2.56 ° 1.60 19.4 4 2.15 ° 1.788 17.5 4 expl. 275 1383 −3H2O, 100 265 d. 72 d. MgO2 Mg2P2O7 Mg2P2O7⋅3H2O MgCl2⋅KCl⋅6H2O MgSO4⋅K2SO4⋅6H2O MgSiF6⋅6H2O MgCl2⋅NaCl⋅H2O MgSO4 MgSO4⋅7H2O∗ Mn Mn(C2H3O2)2 Mn(C2H3O2)2⋅4H2O∗ MnCO3 56 .30 222 .55 276 .60 277 .85 402 .72 274 .47 171 .67 120 .37 246 .47 54 .94 173 .03 245 .09 114 .95 wh. pd. col., mn., 1.604 wh., amor. delq., rhb., 1.475 mn., 1.4629 col., trig., 1.3439 col. col. col., rhb., 1.4554 gray-pink met. chloride (scacchite) chloride MnCl2 MnCl2⋅4H2O∗ 125 .84 197 .91 chloride, perhydroxide (ous) (pyrochroite) hydroxide (ic) (manganite) nitrate oxide (ous) (manganosite) oxide (ic) oxide, di- (pyrolusite; polianite) sulfate (ous) sulfate (ous) (szmikite) MnCl4 Mn(OH)2 Mn2O3⋅H2O Mn(NO3)2⋅6H2O MnO Mn2O3 MnO2∗ 196 .75 88 .95 175 .89 287 .04 70 .94 157 .87 86 .94 rose, delq., cb. rose red, delq., mn. 1 .575 gn . wh ., trig . brn ., rhb ., 2 .24 rose red, mn . gray-gn ., cb ., 2 .16 brn .-bk ., cb . bk ., rhb . MnSO4 MnSO4⋅H2O 151 .00 169 .02 red-wh . pa . pink, mn ., 1 .595 sulfate (ous) MnSO4⋅2H2O 187 .03 2 .52615° 15° sulfate (ous) MnSO4⋅3H2O 205 .05 sulfate (ous) MnSO4⋅4H2O∗ 223 .06 sulfate (ous) MnSO4⋅5H2O 241 .08 sulfate (ous) MnSO4⋅6H2O 259 .09 sulfate (ous) sulfate (ic) Mercuric acetate bromide carbonate, basic chloride (corrosive sublimate) fulminate hydroxide oxide (montroydite) oxychloride (kleinite) silicofluoride, basic sulfate sulfate, basic (turpeth) Mercurous acetate bromide carbonate pa. pink, mn. rose, trig., 1.817 2.66 1.68 7.220° 1.74 204° 1.589 3.125 1185 70 d. 1260 2.977 254° 2.01 650 58.0 3 .25818° 3 .258 1 .8221° 5 .18 4 .81 5 .026 d . d . 25 .8 1650 −0, 1080 −0, >230 3 .235 2 .87 700 Stable 57 to 117 Stable 40 to 57 2 .356 pink, rhb . or mn ., 1 .518 pink, tri ., 1 .508 2 .107 15° 2 .103 MnSO4⋅7H2O 277 .11 pink, mn . or rhb . 2 .092 Mn2(SO4)3 Hg(C2H3O2)2 HgBr2 HgCO3⋅2HgO HgCl2 Hg(CNO)2 Hg(OH)2 HgO HgCl2⋅3HgO HgSiF6⋅HgO⋅3H2O HgSO4 HgSO4⋅2HgO HgC2H3O2 HgBr Hg2CO3 398 .06 318 .68 360 .40 693 .78 271 .50 284 .62 234 .60 216 .59 921 .26 613 .30 296 .65 729 .83 259 .63 280 .49 461 .19 gn ., delq . cr . wh . pl . wh ., rhb . brn .-red wh ., rhb ., 1 .859 cb . 3 .24 3 .270 6 .053 yel . or red, rhb ., 2 .5 yel ., hex . yel . nd . wh ., rhb . yel ., tet . wh . sc . wh ., tet . yel . pd . 11 .14 7 .93 5 .44 4 .42 6 .47 6 .44 7 .307 Boiling point, °C Hot water i. i. sl. s. d. 81.775° s. s. 68.3100° 17840° 63.40° 1518° 123.8100° ∞ s. al., m. al. s. aq. CO2, dil. a.; l. NH3, al. s. al.; i. et., NH3 s . al .; i . et . 129 .5 s . 0 .00220° i . 4260° i . i . i . s . i . i . ∞ i . i . i . s . al ., et . s . a ., NH4 salts; i . alk . s . h . H2SO4 v . s . al . s . a ., NH4Cl s . a .; i . act . s . HCl; i . HNO3, act . d . 850 530° 98 .4748° 7350° 79 .77100° s . al .; i . et . 85 .2735° 106 .855° 1900 1190 −H2O, 106; −4H2O, 200 5° Stable 30 to 40 −4H2O, 450 s. 64.550° 74 .22 99 .3157° 13616° 16950° 5° 142 200 Stable −5 to +8 Stable −10 to −5; 19 d . d . 160 d . 237 2040° 2479° d . d . subl . 345 d . 130 −7H2O, 280 322 304 0° 25114° v . s . 2510° 0 .520° i . 3 .60° sl . s . i . 0 .005225° i . d . d . 0 .005 0 .7513° 7 × 10−9 i . d . 100100° 25100° 176 s. a. s. a.; i. alk. s. a.; i. al. d. al. d. HF s. al. s. al. s. dil. a. i . al . 35° Stable 8 to 18 277 expl . −H2O, 175 d . 100 d . 260 Other reagents i. i. i. 64.519° d. 19.260° 64.817.5° s. 26.90° 72.40° d. s. s. 0.006525° d. Stable 18 to 30 Solubility in 100 parts Cold water 61 .3100° i . 0 .041100° d . 0 .167100° d . i . d . s . HCl, dil . H2SO4; l . s . al . sl . d . 25 .20° al .; v . sl . s . et . s . aq . CO2, NH4Cl 3325° 99% al .; 33 et . s . NH4OH, al . s . a . s . a .; i . al . s . HCl s . a . s . a .; i . al ., act ., NH8 s . a .; i . al . s . H2SO4, HNO3; i . al . s . a .; i . al ., act . s . NH4Cl HgCl 236 .04 wh., tet., 1.9733 7.150 302 383.7 0.00140° 0.000743° iodide nitrate Mercurous oxide HgI HgNO3⋅H2O Hg2O 327 .49 280 .61 417 .18 yel., tet. wh. mn. bk. 7.70 4.7853.9° 9.8 290 d. 70 d. 100 subl. 140; 310d. expl. 2 × 10−8 v. s. i. v. sl. s. d. 0.0007 sulfate Mercury† Molybdenum Hg2SO4 Hg Mo 497 .24 200 .59 95 .94 wh., mn. silv. lq. or hex.(?) gray, cb. 7.56 13.54620° 10.2 d. −38.87 2620 ± 10 0.05516.5° i. i. 0.092100° i. i. MoCl2 166 .85 yel., amor. 3.714 254° d. i. i. 25 ° 4 d. i. d. chloride (calomel) MoCl3 202 .30 dark red pd. chloride, tetra- MoCl4 237 .75 brn., delq. volt. d. s. d. chloride, penta- MoCl5 273 .21 bk. cr. 2.928 254° 194 268 s. d. MoO3 MoS2 MoS3 MoS4 H2MoO4 H2MoO4⋅H2O Nd Ne 143 .94 160 .07 192 .14 224 .20 161 .95 161 .95 144 .24 20 .18 col., rhb. bk., hex., 4.7 red-brn. brn. pd. yel-wh., hex. yel., mn. yellowish col. gas 4.5019.5° 4.80114° 795 1185 d. d. d. 115 −H2O, 70 840 −248.67 subl. 0.10718° i. sl. s. i. v. sl. s. 0.13318° d. 2.60° cc 2.10679° i. s. i. sl. s. 2.1370° s. aq. reg., Hg(NO3)2; sl. s. HNO3, HCl; i. al., etc. s. KI; i. al. s. HNO3; i. al., et. s. h. ac.; i. alk., dil. HCl, NH3 s. H2SO4, HNO3 s. HNO3; i. HCl s. h. conc. H2SO4; i. HCl, HF, NH3, dil. H2SO4, Hg s. HCl, H2SO4, NH4OH, al., et. s. HNO3, H2SO4; v. sl. s. al., et. s. HNO3, H2SO4; sl. s. al., et. s. HNO3, H2SO4; i. abs. al., et. s. a., NH4OH s. H2SO4, aq. reg. s. alk. sulfides s. alk. sulfides; i. NH3 s. NH4OH, H2SO4; i. NH s. a., NH4OH, NH4, salts 1.145° cc s. lq. O2, al., act., bz. i. s. dil. HNO3; sl. s. H2SO4, HCl; i. NH3 i. al. chloride, dichloride, tri- oxide, tri- (molybdite) sulfide, di- (molybdenite) sulfide, trisulfide, tetraMolybdic acid Molybdic acid Neodymium Neon Neptunium Nickel acetate ammonium chloride ammonium sulfate Np Ni 239 239 .05 58 .69 1.798 1.645 1.923 d. 2.575 4.64 284° carbonyl chloride chloride 170 .73 129 .60 237 .69 chloride, ammonia cyanide dimethylglyoxime NiCl2⋅6NH3 Ni(CN)2⋅4H2O NiC8H14O4N4 lq. yel., delq. gn., delq., mn., 1.57± 231 .78 182 .79 288 .91 gn. pl. scarlet red cr. formate hydroxide (ic) hydroxide (ous) nitrate nitrate, ammonia oxide, mono- (bunsenite) Ni(HCO2)2⋅2H2O Ni(OH)3 Ni(OH)2⋅¼H2O Ni(NO3)2⋅6H2O Ni(NO3)2⋅4NH3⋅2H2O NiO 184 .76 109 .72 97 .21 290 .79 286 .86 74 .69 2-17 potassium cyanide sulfate ∗Usual commercial form . † See also Tables 2-28 and 2-280 . Ni(CN)2⋅2KCN⋅H2O NiSO4 258 .97 154 .76 1.3117° 3.544 gn. cr. bk. lt. gn. gn., mn. 4.36 2.05 gn .-bk ., cb ., 2 .37 7 .45 red yel ., mn . yel ., cb . 2.154 11° 1 .875 3 .68 −245.9 Produced by Neutron bombardment of U 1452 2900 i. gn. pr. gn., delq., mn. blue-gn., mn., 1.5007 gn., cb. yel., delq. gn., delq. vl. pd. trig. lt. gn., rhb. lt. gn. 1.837 3.715 −2H2O, 200 238 8.9020 176 .78 291 .18 394 .99 422 .59 218 .50 272 .55 320 .68 841 .29 118 .70 587 .59 3.12415° 6.920° lq. 1.204−245.9° 0.674 (A) silv. met., cb. Ni(C2H3O2)2 NiCl2⋅NH4Cl⋅6H2O NiSO4⋅(NH4)2SO4⋅ 6H2O Ni(BrO3)2⋅6H2O NiBr2 NiBr2⋅3H2O NiBr2⋅6NH3 NiPtBr6⋅6H2O NiCO3 2NiCO3⋅3Ni(OH)2⋅ 4H2O Ni(CO)4 NiCl2 NiCl2⋅6H2O∗ bromate bromide bromide bromide, ammonia bromoplatinate carbonate carbonate, basic 3.578 356.9 3700 16.6 15025° 2.53.5° v. s. 39.288° d. d. −3H2O, 200 28 112.80° 1999° v. s. 156100° 316100° d. s. NH4OH s. al., et., NH4OH s. al., et., NH4OH i. c. NH4OH d. d. 0.009325° i. i. d. s. a. s. a., NH4 salts 0.0189.8° 53.80° 180 i. 87.6100° v. s. s. aq. reg., HNO3, al., et. s. NH4OH, al.; i. NH3 v. s. al. s. i. i. d. i. i. s. NH4OH; i. al. s. KCN; i. dil. KCl s. abs. al., a.; i. ac., NH4OH i. v. sl. s. ∞56 .7° −25 subl. 43751mm 973 −4H2O, 200 subl. 250 d. d. d. d. 56.7 Forms Ni2O3 at 400 −H2O, 100 −SO3, 840 136.7 v. sl. s. (NH4)2SO4 s. i. v. sl. s. 243.00° v . s . i . i . s. a., NH4OH, NH4Cl s. a., NH4OH; i. alk. s . NH4OH; i . abs . al . i . al . s . a ., NH4OH s . 27 .20° 76 .7100° d . a . i . al ., et ., act . (Continued ) 2-18 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Formula Formula weight Color, crystalline form, and refractive index Nickel (Cont.) sulfate NiSO4⋅6H2O∗ 262 .85 sulfate (morenosite) Nitric acid Nitric acid Nitric acid Nitro acid sulfite Nitrogen NiSO4⋅7H2O HNO3 HNO3⋅H2O HNO3⋅3H2O NO2HSO3 N2 280 .86 63 .01 81 .03 117 .06 127 .08 28 .01 Nitrogen oxide, mono- (ous) N2O 44 .01 col . gas oxide, di- (ic) NO or (NO)2 col . gas oxide, tri- N2O3 30 .01 60 .01 76 .01 gn. mn. or blue, tet., 1.5109 gn., rhb., 1.4893 col. lq. col . lq . col . lq . col ., rhb . col . gas or cb . cr . red-brn . gas or blue lq . or solid yel . lq ., col . solid, red-brn . gas wh ., rhb . oxide, tetra- (per- or di-) NO2 or (NO2)2 oxide, penta- N2O5 46 .01 92 .01 108 .01 oxybromide oxychloride NOBr NOCl 109 .91 65 .46 brn . lq . red-yel . lq . or gas Nitroxyl chloride Osmium chloride, dichloride, trichloride, tetraOxygen NO2Cl Os OsCl2 OsCl3 OsCl4 O2 81 .46 190 .23 261 .14 296 .59 332 .04 32 .00 yel .-brn . gas blue, hex . gn ., delq . brn ., cb . red-yel . nd . col . gas or hex . solid Ozone O3 48 .00 Palladium Pd 106 .42 silv . met ., cb . PdBr2 PdCl2 PdCl2⋅2H2O Pd(CN)2 266 .23 177 .33 213 .36 158 .45 brn . brn ., cb . brn . pr . yel . Pd2H Pd(NH3)2Cl2 HClO4 HClO4⋅H2O HClO4⋅2H2O∗ 73 .6% anh . HIO4 HIO4⋅2H2O HMnO4 HMoO4⋅2H2O H2S2O8 PONH2⋅(OH)2 H7P(Mo2O7)6⋅28H2O PH3 213 .85 211 .39 100 .46 118 .47 136 .49 met . red or yel ., tet . unstable, col . lq fairly stable nd . stable lq ., col . bromide (ous) chloride chloride cyanide hydride Palladous dichlorodiammine Perchloric acid Perchloric acid Perchloric acid Periodic acid Periodic acid Permanganic acid Permolybdic acid Persulfuric acid Phosphamic acid Phosphatomolybdic acid Phosphine Phosphonium chloride PH4Cl 191 .91 227 .94 119 .94 196 .98 194 .14 97 .01 2365 .71 34 .00 70 .46 col . gas wh . cr . delq ., mn . exists only in solution wh . cr . hyg . cr . cb . yel . cb . col . gas wh ., cb . Specific gravity Melting point, °C Boiling point, °C Solubility in 100 parts Cold water Hot water Other reagents 2.07 tr. 53.3 −6H2O, 280 13150° 280100° v. s. NH4OH, al. 1.948 1.502 98–100 −42 −38 −18 .5 73 d . −209 .86 −6H2O, 103 86 117.830° ∞ ∞ ∞ −195 .8 63.50° ∞ ∞ 263−20° d . 2 .350° cc s. al. expl . with al . d . al . d . al . s . H2SO4 sl . s . al . −102 .3 −90 .7 130 .520° cc −161 −151 7 .340° cc 60 .8224° cc 0 .0100° −102 3 .5 s . 1 .026−252 .5° 0 .808−195 .8° 12 .50° (D) lq . 1 .226−89° 1 .530 (A) lq . 1 .269−150 .2° 1 .0367 (A) 1 .4472° 20° 1 .448 −9 .3 21 .3 d . 1 .6318° 30 47 s . >1 .0 1 .417−12° 2 .31 (A) lq . 1 .3214° 22 .4820° −55 .5 −64 .5 −2 −5 .5 d . d . <−30 2700 5 >5300 26 .6 cc al .; 3 .5 cc H2SO4; s . aq . FeSO4 s . a ., et . s . HNO3, H2SO4, chl ., CS2 Forms HNO3 s . fuming H2SO4 −218 .4 −183 −251 −112 0 .4940° cc 060° cc s . oil turp ., oil cinn . 1555 2200 i . i . i . s . s . i . i . s . s . i . s . aq . reg ., h . H2SO4; i . NH3 s . HBr s . HCl, act ., al . s . HCl, act ., al . s . HCN, KCN, NH4OH; i . dil . a . 500 d . d . 11 .06 2 .5 1 .768 224° 1 .88 1 .71 254° s . H2SO4, al . d i . s . d . sl . s . s . d . 4 .890° cc d . 560–600 1 .14−188° 1 .426−252 .5° 1 .1053 (A) 1 .71−183° 3 .03−80° 1 .658 (A) 12 .020° 111550° 1 .5520° cc i . 2 .630° cc 1 .7100° cc sl . s . aq . reg ., HNO3; i . NH3 s . NaCl, al ., et . s . a ., alk ., al .; sl . s . et . s . HCl, al . sl . s . al ., s . fused Ag d . −90° lq . 0 .746 1 .146 (A) −112 50 −17 .8 1618mm d . 200 d . 138 d . 110 subl . 110 <60 d . 78 −132 .5 46atm . 28 s . s . s . v . s . −25H2O, 140 −85 s . v . s . v . s . v . s . v . s . v . s . s . 2617° cc subl . d . s . a ., NH4OH s . al . v . s . d . v . s . d . v . s . d . 100° i . sl . s . al ., et . d . al . i . al . s . HNO8 s . Cu2Cl2, al ., et . Phosphoric acid, hypoPhosphoric acid, meta- H4P2O6 HPO3 Phosphoric acid, orthoPhosphoric acid, pyro- † 4 H3PO H4P2O7 98 .00 177 .98 col., rhb. wh. nd. 1.834 Phosphorous acid, hypoPhosphorous acid, orthoPhosphorous acid, pyroPhosphorus, black Phosphorus, red Phosphorus, yellow H3PO2 H3PO3 H4P2O5 P4 P4 P4 66 .00 82 .00 145 .98 123 .90 123 .90 123 .90 syrupy col . nd . rhombohedral red, cb . yel ., hex ., 2 .1168 1.49318.8° 1 .65121 .2° PCl3 PCl5 137 .33 208 .24 col ., fuming lq . delq ., tet . chloride, trichloride, pentaoxide, pentaoxychloride Phosphotungstic acid Platinum chloride (ic) chloride (ous) chloride (ic) cyanide (ous) Plutonium Plutonium Potassium P2O5 POCl3 H3PO4⋅12WO3⋅xH2O Pt PtCl4 161 .98 79 .98 141 .94 153 .33 2880 .05 195 .08 336 .89 cr. vitreous, delq. wh ., delq ., amor . col ., fuming lq . yel .-gn . cr . silv . met ., cb . 18.2° 2 .69 2 .2020° 1 .8220°; lq . 1 .74544 .5° ° 1 .574 20.8 4 solid 1 .6; 3 .60295° (A) 2 .387 1 .675 21 .4520° lq . 191755° brn . PtCl2 265 .98 brn . PtCl4⋅8H2O Pt(CN)2 Pu Pu K 481 .01 247 .11 238 .05 239 .05 39 .10 red, mn . yel .-brn . acetate KC2H3O2 98 .14 acetate, acid KH(C2H3O2)2 158 .19 aluminate K2(AlO2)2⋅3H2O 250 .20 amide KNH2 55 .12 arsenate (monobasic) KH2AsO4 180 .03 auricyanide KAu(CN)4⋅1⋅5H2O 367 .16 aurocyanide KAu(CN)2 288 .10 bicarbonate KHCO3 100 .12 bisulfate KHSO4 136 .17 bromate KBrO3 167 .00 bromide KBr 119 .00 carbonate K2CO3 138 .21 carbonate K2CO3⋅2H2O 174 .24 carbonate 2K2CO3⋅3H3O 330 .46 chlorate KClO3 122 .55 chloride (sylvite) KCl 74 .55 chloroplatinate K2PtCl6 485 .99 chromate (tarapacaite) K2CrO4 194 .19 cyanate KCNO 81 .12 cyanide KCN 65 .12 dichromate K2Cr2O7 294 .18 ferricyanide K3Fe(CN)6 329 .24 ferrocyanide K4Fe(CN)6⋅3H2O 422 .39 formate KHCO2 84 .12 hydride KH 40 .11 hydrosulfide KHS 72 .17 hydroxide KOH 56 .11 iodate KIO3 214 .00 iodide KI 166 .00 ∗One commercial form 70 to 72 per cent . † Common commercial form 85 per cent H3PO4 in aqueous solution . 2.2–2.5 silv . met ., cb . wh . pd . delq . nd . or pl . cr . yel .-grn . col ., tet ., 1 .5674 pl . rhb . mn ., 1 .482 rhb ., or mn ., 1 .480 trig . col ., cb ., 1 .5594 wh ., delq . pd ., 1 .531 rhb . mn . col ., mn ., 1 .5167 col ., cb ., 1 .4904 yel ., cb ., 1 .825± yel ., rhb ., 1 .7261 wh ., tet . wh ., cb ., delq ., 1 .410 red, tri . red, mn . pr ., 1 .5689 yel ., mn ., 1 .5772 col ., rhb . cb ., 1 .453 wh ., delq ., rhb . wh ., delq ., rhb . col ., mn . wh ., cb ., 1 .6670 55 subl. d. 70 s. s. 26° 42.35 61 −½H2O, 213 2340 80028° 26.5 74 38 d. d . 200 d . 130 ign . in air, 400 ign . in air, 725 280 ∞ 307 .30° d . i . i . 0 .0003 −111 .8 148 under pressure subl . 250 2 75 .95760mm subl . 160 d . d . 1755 4300 59043atm . 44 .1; ign . 34 107 .2760mm Forms H3PO4 d . s . i . 25° 45062° Forms H3PO4 v. s. Forms H3PO4 ∞ 73040° i . CS2 s . alk .; i . CS2, NH3, et . 0 .4 al .; 100010° CS2; 1 .50°, 1081° bs .; s . NH3 s . et ., chl ., CS2 s . CS2, C6H5COCl v . s . s . H2SO4; i . NH3, act . d . al . s . al ., et . s . aq . reg ., fused alk . i . 140 v . s . 5 .87 d . 581 i . i . 2 .43 −4H2O, 100 v . s . i . v . s . i . Produced by deuteron bombardment on U238 Produced by neutron bombardment on U238 0 .8620° 62 .3 760 lq . 0 .8342° 1 .8 292 148 d . 200 2 .867 2 .17 2 .35 3 .2717 .5° 2 .7525° 2 .29 2 .043 2 .13 2 .32 1 .988 3 .499 2 .73218° 2 .048 1 .5216° 2 .69 1 .84 1 .85317° 1 .91 0 .80 2 .0 2 .044 3 .89 3 .13 338 288 d . 200 d . 100–200 210 370 d . 730 891 368 790 d . 250 975 634 .5 398 d . −3HO2, 70 167 .5 d . 455 380 560 723 subl . 400 d . 1380 d . d . 400 1500 d . d . 1320 1330 d . 0° 217 d . s . d . 18 .876° s . 14 .3 22 .40° 36 .30° 3 .110° 53 .50° 105 .50° 1830° 129 .40° 3 .30° 27 .60° 0 .740° 58 .00° s . s . 4 .90° 334 .4° 27 .812 .2° 33118° d . s . 970° 4 .730° 127 .50° s. al. v. s. al., et. i . i . sl . s . d . 370 11° i. lq. CO2 Forms KOH 39690° d . v . s . v . s . 200100° 6060° 121 .6100° 49 .75100° 104100° 156100° 331100° 268100° 57100° 56 .7100° 5 .2100° 75 .6100° d . 122 .2108 .8° 80100° 77 .5100° 90 .696 .8° 65790° s . d . 178100° 32 .2100° 208100° s . al ., act .; sl . s . NH2; i . et . s . HCl, NH4OH; sl . s . NH3; i . al ., et . s . al ., et . i . alk . s . a ., al ., Hg 33 al .; i . et . s . ac . s . alk .; i al . d . al .; 3 .625° NH3 i . al . s . al . sl . s . al .; i . et . i . satd . K2CO3, al . d . al . sl . s . al .; i . act . sl . s . al ., et . i . al . 0 .83 al .; s . alk . s . al ., alk . i . al ., et . i . al . v . sl . s . al . s . gly .; 0 .919 .5° al .; 1 .3 h . al . i . al . s . act .; sl . s . al .; i . NH3 s . act .; i . NH3, al ., et . sl . s . al .; i . et . i . et ., bz ., CS2 s . al . v . s . al ., et .; i . NH3 s . KI; i . al ., NH3 420° al .; s . NH3; sl . s . et . (Continued ) 2-19 2-20 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Formula Formula weight Color, crystalline form, and refractive index Potassium (Cont.) iodide, triiodoplatinate manganate metabisulfite nitrate (saltpeter) nitrite oxalate oxalate, acid oxalate, acid oxide perchlorate permanganate persulfate phosphate, monobasic KI3 K2PtI6 K2MnO4 K2S2O5 KNO3 KNO2 K2C2O4⋅H2O KHC2O4∗ KHC2O4⋅½H2O K2O KClO4 KMnO4 K2S2O3 KH2PO4 419 .81 1034 .70 197 .13 222 .32 101 .10 85 .10 184 .23 128 .13 137 .13 94 .20 138 .55 158 .03 190 .32 136 .09 phosphate, dibasic phosphate, tribasic phosphate, metaphosphate, metaphosphate, pyrophthalate, acid platinocyanide silicate silicate, tetrasulfate (arcanite) sulfate, pyrosulfide, monosulfite sulfite, acid tartrate tartrate, acid thiocyanate K2HPO4 K3PO4 KPO3 K4P4O12⋅2H2O K4P2O7⋅3H2O KHC8H4O4 K2Pt(CN)4⋅3H2O K2SiO3 K2Si4O9⋅H2O K2SO4 K2S2O7 K2S⋅5H2O K2SO3⋅2H2O KHSO3 K2C4H4O6⋅½H2O KHC4H4O6∗ KCNS 174 .18 212 .27 118 .07 508 .31 384 .38 204 .22 431 .39 154 .28 352 .55 174 .26 254 .32 200 .34 194 .29 120 .17 235 .28 188 .18 97 .18 thiosulfate thiosulfate Praseodymium Radium bromide Radon (Niton) K2S2O3 3K2S2O3⋅H2O Pr Ra RaBr2 Rn 190 .32 588 .99 140 .91 226 .03 385 .83 222 .02 dark blue, delq., mn. cb. gn., rhb. mn., pl. col., rhb., 1.5038 pr. wh., mn. mn., 1.545 trimetric wh., cb. col., rhb., 1.4737 purple, rhb. wh., tri., 1.4669 col., delq., tet., 1.5095 wh., delq. wh., rhb. wh. pd. amor. delq. wh. cr. yel., rhb., 1.62± hyg. 1.521± rhb., 1.530 col., rhb., 1.4947 col. rhb., delq. wh., rhb. wh., mn. col., mn., 1.526 col., rhb. col., delq., mn., 1.660± col., cb. delq., mn. yel. wh., met. wh., mn. gas Rhenium Re 186 .21 hex. Rhodium chloride chloride Rubidium Rh RhCl3 RhCl3⋅4H2O Rb 102 .91 209 .26 281 .33 85 .47 gray-wh., cb. red dark red silv. wh. Ruthenium Ruthenium Samarium Scandium Selenic acid Selenic acid Selenium Selenium Ru Ru Sm (also Sa) Sc H2SeO4 H2SeO4⋅H2O Se8 Se8 101 .07 101 .07 150 .36 44 .96 144 .97 162 .99 631 .68 631 .68 bk., porous gray, hex. hex. pr. nd . red pd ., amor ., 2 .92 gray, trig ., 3 .00; red, hex . Specific gravity 3.498 5.18 10.6° 2.11 1.915 2.13 2.0 2.32 204° 2.524 114° 2.703 2.338 2.56417° 2.25814.5° 2.26414.5° 2.33 1.63 2.4516° 2.417 2.662 2.277 1.98 1.956 1.886 2.23 6.520° 5? 5.79 lq. 5.5; 111 (D) Melting point, °C 45 d. 190 d. 150 tr. 129; 333 297 d. d. d. Boiling point, °C d. 225 d. 400 d. 350 d. 400 d. <240 d. <100 256 d. 1340 tr. 450; 798 −2H2O, 100 −2H2O, 180 d. 976 d. 400 tr. 588 300 60 d. d. 190 172.3 d. 400 −H2O, 180 940 960 728 −71 1320 d. −3H2O, 300 −3H2O, 150 d. d. 500 d. 1140 subl. 900 −62 Solubility in 100 parts Cold water v. s. s. d. 250° 13.30° 2810° 28.70° 14.350° 2.20° Forms KOH 0.750° 2.830° 1.770° 14.80° Hot water s. KI, al. 12094° 246100° 413100° 83.2100° 48.1100° 51.5100° v. s. 21.8100° 32.3575° 1040° 83.590° 3325° 193.125° s. s. s. 10.225° sl. s. s. s. 7.350° s. s. 100 45.515° 12.517.5° 0.370° 1770° v. s. v. s. s. 83 v. s. 36 v. s. s. s. 24.1100° d. 96.10° 311.290° d. d. +H2 7020° 510° cc s. 8.560° cc >100 91.575° 278100° 6.1100° 21720° 3440 12.5 1955 d. 450 >2500 subl. 800± lq. 1.47588.5; 1.5320° 8.6 12.220° 7.7 2.5? 2.950 154° 2 .627 154° 4 .2625° 4 .80; 4 .50 38.5 >1950 2450 >1300 1200 58 26 50 220 Other reagents s. KOH sl. s. al.; i. et. 0.130° al.; i. et. v. s. NH3; sl. s. al. s. al., et. 0.10520° m. al.; i. et. s. H2SO4; d. al. i. al. i. al. sl. s. al. i. al. s. a. i. al. s. al., et. i. al. i. al. i. al., act., CS2 s. al., gly.; i. et. sl. s. al.; i. NH3 i. abs. al. sl. s. al. s. a., alk.; i. al., ac. 20.822° act.; s. al. i. al. d. a. s. al. i. HF, HCl; s. H2SO4; HNO3 sl. s. aq. reg., a. v. sl. s. alk.; i. aq. reg., a. s. HCl, al.; i. et. s. a., al. i. i. 700 i. i. v. s. d. i. i. i. i. sl. s. aq. reg., a. >2700 2400 260 205 688 688 130030° v . s . i . i . ∞60° s . H2SO4; d . al .; i . NH3 i . i . s . CS2, H2SO4, CH2I2 s . CS2, H2SO4 Selenium Selenous acid Silicic acid, metaSilicic acid, orthoSilicon, crystalline Se8 H2SeO3 H2SiO3 H4SiO4 Si Silicon, graphitic Si Silicon, amorphous carbide chloride, trichloride, tetra- Si SiC Si2Cl6 SiCl4 28.09 40.10 268.89 169.90 SiF4 SiH4 SiO2⋅xH2O SiO2 104.08 32.12 SiO2 SiO2 SiO2 Ag AgBr 60.08 60.08 60.08 107.87 187.77 carbonate chloride (cerargyrite) Ag2CO3 AgCl cyanide nitrate (lunar caustic) Sodium steel gray hex. amor., 1.41 amor. gray, cb., 3.736 4.825° 3.004 154° 2.1–2.3 1.57617° 2.420° cr. 2.0–2.5 brn., amor. blue-bk., trig., 2.654 lf. or lq. col., fuming lq., 1.412 gas col. gas iridescent, amor. col., cb. or tet., 1.487 2 3.17 1.580° 1.50 2600 i. 900° i. sl. s. i. i. 40090° i. sl. s. i. 2600 i. i. >2700 −1 −70 2600 subl. 2200 144760mm 57.6 i. i. d. d. i. i. 3.57 (A) lq. 0.68−185° 2.2 2.32 −95.7 −185 1600–1750 1710 −651810mm −112760mm subl. 1750 2230 v. s. d. i. i. i. hex., 1.5442 trig., rhb., 1.469 silv. met., cb. pa. yel., cb., 2.252 2.20 2.65020° 2.26 10.520° 6.473 254° tr. <1425 tr. 1670 960.5 434 2230 2230 2230 1950 d. 700 i. i. i. i. 0.0000220° i. i. 275.75 143.32 yel. pd. wh., cb., 2.071 6.077 5.56 218 d. 455 1550 0.00320° 0.00008910° 0.05100° 0.00217100° AgCN AgNO3 Na 133.89 169.87 22.99 wh., 1.685± col., rhb., 1.744 silv. met, cb. 3.95 4.352 194° 0.9720° −(CN)2, 320 212 97.5 444 d. 880 acetate acetate aluminate amide ammonium phosphate antimonate, metaarsenate arsenate, acid (monobasic) arsenate, acid (dibasic) arsenate, acid (dibasic) arsenite, acid benzoate bicarbonate bifluoride bisulfate bisulfite borate, tetraborate, tetra NaC2H3O2 NaC2H3O2⋅3H2O NaAlO2 NaNH2 NaNH4HPO4⋅4H2O 2NaSbO3⋅7H2O Na3AsO4⋅12H2O NaH2AsO4⋅H2O Na2HAsO4⋅7H2O∗ Na2HAsO4⋅12H2O Na2HAsO3 NaC7H5O2 NaHCO3 NaHF2 NaHSO4 NaHSO3 Na2B4O7 Na2B4O7⋅5H2O 82.03 136.08 81.97 39.01 209.07 511.60 424.07 181.94 312.01 402.09 169.91 144.10 84.01 61.99 120.06 104.06 201.22 291.30 wh., mn., 1.464 wh., mn. amor. olive gn. col., mn. cb. hex., 1.4589 rhb., 1.5535 col., mn., 1.4658 mn., 1.4496 col. col. cr. wh., mn., 1.500 col. cr. col., tri. col., mn., 1.526 1.528 1.45 324 58 1650 210 79 d. col., rhb., 1.461 2.742 1.48 2.367 1.815 borate, tetra- (borax) Na2B4O7⋅10H2O∗ 381.37 wh., mn., 1.4694 1.73 fluoride hydride (silane) oxide, di- (opal) oxide, di- (cristobalite) oxide, di- (lechatelierite) oxide, di- (quartz) oxide, di- (tridymite) Silver bromide (bromyrite) 631.68 128.97 78.10 96.11 28.09 28.09 60.08 1.574 217 d. 688 1420 400 1.759 2.535 1.871 1.72 1.87 86.3 d. 100 125 28 2.20 −CO2, 270 d. >315 d. 741 d., −H2O 75 −10H2O, 200 17.5° bromate bromide bromide NaBrO3 NaBr NaBr⋅2H2O 150.89 102.89 138.92 col., cb. col., cb., 1.6412 col., mn. 3.339 3.20517.5° 2.176 381 755 50.7 carbonate (soda ash) carbonate Na2CO3 Na2CO3⋅H2O 105.99 124.00 2.533 1.55 851 −H2O, 100 carbonate carbonate (sal soda) Na2CO3⋅7H2O Na2CO3⋅10H2O 232.10 286.14 wh. pd., 1.535 wh., rhb., 1.506– 1.509 rhb. or trig. wh., mn., 1.425 1.51 1.46 d. 35.1 ∗Usual commercial form. −3H2O, 120 −7H2O, 100 −12H2O, 100 0.00002220° 1220° d., forms NaOH 46.520° v. s. s. d. 16.7 0.03112.8° 26.717° s. 6115° 5.590.1° v. s. 62.525° 6.90° 3.720° 500° sl. s. 1.30° 2262° (anh.) d. i. 0.00037100° 952100° 170100° v. s. v. s. 100 s. HNO3, al., et. i. al., et.; d. KOH s. HF, h. alk., fused CaCl2 s. HF; i. alk. s. HF; i. alk. s. HF; i. alk. s. HF; i. alk. s. HNO3, h. H2SO4; i. alk. 0.5118° NH4OH; s. KCN, Na2S2O3 s. NH4OH, Na2S2O3; i. al. s. NH4OH, KCN; sl. s. HCl s. NH4OH, KCN, HNO3 s. gly.; v. sl. s. al. i. bz.; d. al. 2.118° al. 7.825° abs. al. i. al. d. al. i. al. sl. s. al., NH4 salts; i. ac. 1.67 al., 5015° gly. v. s. 140.730° sl. s. al. sl. s. al. 2.325°, 8.378° al. i. al. 7.10° s. 76.9100° 16.460° s. 100100° s. 8.7940° 52.3100° (anh.) 20.380° (anh.) 90.9100° 121100° 118.380° (anh.) 48.5104° s. i. al., et. s. gly.; i. al., et. s. 21.50° s. 23830° i. al. 1.30.5 (anh.) 0° 1390 i. i. i. CS2; s. H2SO4 v. s. al.; i. NH3 s. alk.; i. NH4Cl s. alk.; i. NH4Cl s. HNO3 + HF, Ag; sl. s. Pb, Zn; i. HF s. HNO3 + HF, fused alk.; i. HF. s. HF, KOH s. fused alk.; i. a. d. alk. d. conc. H2SO4, al. 27.5 9020° 79.50° (anh.) d. al.; i. NH3 i. al., act. i. al. s. gly.; i. abs. al. i. al. sl. s. al. sl. s. al. (Continued ) 2-21 2-22 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Sodium (Cont.) carbonate, sesqui- (trona) chlorate Formula Na3H(CO3)2⋅2H2O NaClO3 Formula weight Color, crystalline form, and refractive index chloride chromate chromate citrate cyanide dichromate NaCl Na2CrO4 Na2CrO4⋅10H2O 2Na3C6H5O7⋅11H2O NaCN Na2Cr2O7⋅2H2O 58 .44 161 .97 342 .13 714 .31 49 .01 298 .00 wh., mn., 1.5073 wh., cb., or trig., 1.5151 col., cb., 1.5443 yel., rhb. yel., delq., mn. wh ., rhb . wh ., cb ., 1 .452 red, mn ., 1 .6994 ferricyanide ferrocyanide Na3Fe(CN)6⋅H2O Na4Fe(CN)6⋅10H2O 298 .93 484 .06 red, delq . yel ., mn . fluoride (villiaumite) formate hydride NaF NaHCO2 NaH hydrosulfide hydrosulfide hydrosulfite hydroxide hydroxide hypochlorite iodide iodide lactate nitrate (soda niter) nitrite NaSH⋅2H2O NaSH⋅3H2O Na2S2O4⋅2H2O NaOH NaOH⋅3½H2O NaOCl NaI∗ NaI⋅2H2O NaC3H5O3 NaNO3 NaNO2 oxide Na2O perborate perchlorate perchlorate peroxide peroxide phosphate, monobasic phosphate, monobasic phosphate, dibasic phosphate, dibasic phosphate, tribasic phosphate, tribasic phosphate, metaphosphate, pyrophosphate, pyrophosphate (pyrodisodium) phosphate (pyrodisodium) potassium tartrate silicate, metaSodium silicate, metasilicate, orthosilicofluoride stannate sulfate (thenardite) sulfate NaBO3⋅H2O NaClO4 NaClO4⋅H2O Na2O2∗ Na2O2⋅8H2O NaH2PO4⋅H2O∗ NaH2PO4⋅2H2O Na2HPO4⋅7H2O Na2HPO4⋅12H2O Na3PO4 Na3PO4⋅12H2O∗ Na4P4O12 Na4P2O7∗ Na4P2O7⋅10H2O Na2H2P2O7 Na2H2P2O7⋅6H2O NaKC4H4O6⋅4H2O Na2SiO3 Na2SiO3⋅9H2O Na4SiO4 Na2SiF6 Na2SnO3⋅3H2O Na2SO4 Na2SO4 226 .03 106 .44 41 .99 68 .01 24 .00 92 .09 110 .11 210 .14 40 .00 103 .05 74 .44 149 .89 185 .92 112 .06 84 .99 69 .00 61 .98 99 .81 122 .44 140 .46 77 .98 222 .10 137 .99 156 .01 268 .07 358 .14 163 .94 380 .12 407 .85 265 .90 446 .06 221 .94 330 .03 282 .22 122 .06 284 .20 184 .04 188 .06 266 .73 142 .04 142 .04 tet ., 1 .3258 wh ., mn . silv . nd ., 1 .470 col ., delq ., nd . rhb . col . cr . wh ., delq . mn . pa . yel ., in soln . only col ., cb ., 1 .7745 col ., mn . col ., amor . col ., trig ., 1 .5874 pa . yel ., rhb . wh ., delq . wh . pd . rhb ., 1 .4617 hex . yel .-wh . pd . wh ., hex . col ., rhb ., 1 .4852 col ., rhb ., 1 .4629 col ., mn ., 1 .4424 col ., mn ., 1 .4361 wh . wh ., trig ., 1 .4458 col . wh . mn ., 1 .4525 col ., mn ., 1 .510 col ., mn ., 1 .4645 rhb ., 1 .493 col ., rhb ., 1 .520 rhb . col ., hex ., 1 .530 wh ., hex ., 1 .312 hex . tablets col ., rhb ., 1 .477 col ., mn . Specific gravity 2.112 2.49015° 2.163 2.723 1.483 ° 1 .857 23.5 4 2 .5218° Melting point, °C d. 248 800.4 392 19.9 −11H2O, 150 563 .7 −2H2O, 84 .6; 356 (anh .) Boiling point, °C d. 1413 d . 1496 d . 400 1 .458 2 .79 1 .919 0 .92 992 253 d . 800 2 .130 d . 22 d . 318 .4 15 .5 d . 651 3 .6670° 2 .448 2 .257 2 .1680° d . 308 271 2 .27 subl . 2 .02 2 .805 2 .040 1 .91 1 .679 1 .52 2 .53717 .5° 1 .62 2 .476 2 .45 1 .82 1 .862 1 .848 1 .790 2 .679 2 .698 d . 40 482 d . d . 130 d . d . 30 −H2O, 100 60 d . 34 .6 1340 73 .4 616 d . 988 d . d . 220 70 to 80 1088 47 1018 d . d . 140 tr . 100 to mn . tr . 500 to hex . Solubility in 100 parts Cold water 130° 790° 42100° 230100° 0° 1390 1300 d . 380 d . 320 d . 200 −12H2O, 180 −11H2O, 100 −4H2O, 215 −6H2O, 100 100° 35.7 320° v. s. 9125° 4810° 2380° 39.8 126100° ∞ 250100° 8235° 50880° 18 .90° 17 .920° (anh .) 67100° 6398 .5° (anh .) 5100° 160100° 40° 440° d . d . Hot water s . s . 2220° 420° s . 260° 158 .70° v . s . v . s . 730° 72 .10° s . s . d . 347100° v . s . 15856° 302100° v . s . v . s . 180100° 163 .2100° Forms NaOH sl . s . 1700° 20915° s . d . s . d . 710° 91 .10° 18540° 4 .30° 4 .50° 28 .315° s . 2 .260° 5 .40° 4 .50° 6 .90° 260° s . v . s . s . 0 .440° 500° 50° 48 .840° d . 320100° 28450° d . d . 39083° 30840° 2000100° 76 .730° 77100° ∞ s . 4596° 93100° 2140° 3640° 6626° s . d . v . s . s . 2 .45100° 6750° 42100° 42 .5100° Other reagents s. al. sl. s. al.; i. conc. HCl sl . s . al . i . al . s . NH3; sl . s . al . i . al . i . al . v . sl . s . al . sl . s . al .; i . et . i . bz ., CS2, CCl4, NH3; s . molten metal s . al .; d . a . s . al .; d . a . i . al . v . s . al ., et ., gly .; i . act . v . s . al ., act . v . s . NH3 s . al .; i . et . s . NH3; sl . s . gly ., al . 0 .320° et .; 0 .3 abs . al .; 4 .420° m . al .; v . s . NH3 d . al . s . gly ., alk . s . al .; 51 m . al .; 52 act .; i . et . s . al . s . dil . a . i . al . i . al . i . CS2 s . a ., alk . d . a . i . al ., NH3 sl . s . al . i . Na or K salts, al . 2918°, aN NaOH i . al . i . al ., act . i . al . d . HI; s . H2SO4 sulfate sulfate sulfate (Glauber’s salt) sulfide, monosulfide, tetrasulfide, pentasulfite sulfite tartrate thiocyanate thiosulfate thiosulfate (hypo) tungstate tungstate tungstate, parauranate vanadate vanadate, pyroStannic chloride Na2SO4 Na2SO4⋅7H2O Na2SO4⋅10H2O Na2S Na2S4 Na2S5 Na2SO3 Na2SO3⋅7H2O Na2C4H4O6⋅2H2O NaCNS Na2S2O3 Na2S2O3⋅5H2O∗ Na2WO4 Na2WO4⋅2H2O∗ Na6W7O24⋅16H2O Na2UO4 Na3VO4⋅16H2O Na4V2O7 SnCl4 142 .04 268 .15 322 .19 78 .04 174 .24 206 .30 126 .04 252 .15 230 .08 81 .07 158 .11 248 .18 293 .82 329 .85 2097 .05 348 .01 472 .15 305 .84 260 .52 col., hex. tet. col., mn., 1.396 pink or wh., amor. yel., cb. yel. hex. pr., 1.565 mn. rhb. delq., rhb., 1.625± mn. mn. pr., 1.5079 wh., rhb. wh., rhb. wh., tri. yel. col. nd. hex. col., fuming lq. oxide (cassiterite) SnO2 150 .71 wh ., tet ., 1 .9968 sulfate Sn(SO4)2⋅2H2O 346 .87 col ., delq ., hex . Stannous bromide chloride chloride (tin salt) sulfate Strontium 884 1.464 1.856 2.633 154° 1.561 1.818 2.226 866 (anh.) 654 −30.2 7 .0 1127 17° yel ., rhb . wh ., rhb . wh ., tri . wh . cr . silv . met . 2 .6 acetate carbonate (strontianite) chloride chloride hydroxide hydroxide Sr(C2H3O2)2 SrCO3 SrCl2 SrCl2⋅6H2O∗ Sr(OH)2 Sr(OH)2⋅8H2O∗ 205 .71 147 .63 158 .53 266 .62 121 .63 265 .76 wh . cr . wh ., rhb ., 1 .664 wh ., cb ., 1 .6499 wh ., rhb ., 1 .5364 wh ., delq . col ., tet ., 1 .499 2 .099 3 .70 3 .052 1 .93317° 3 .625 1 .90 nitrate nitrate oxide (strontia) Sr(NO3)2∗ Sr(NO3)2⋅4H2O SrO 211 .63 283 .69 103 .62 col ., cb ., 1 .5878 wh ., mn . col ., cb ., 1 .870 2 .986 2 .2 4 .7 SrO2 SrO2⋅8H2O SrSO4 Sr(HSO4)2 NH2SO3H S S8 S8 S2Br2 S2Cl2 SCl2 SCl4 SO2 119 .62 263 .74 183 .68 281 .76 97 .09 32 .07 256 .52 256 .52 223 .94 135 .04 102 .97 173 .88 64 .06 wh . pd . wh . cr . col ., rhb ., 1 .6237 col ., granular wh ., rhb . pa . yel . pd ., 2 .0–2 .9 pa . yel ., mn . pa . yel ., rhb . red, fuming lq . red-yel . lq . dark red fuming lq . yel .-brn . lq . col . gas oxide, tri-(β) Sulfuric acid Sulfuric acid ∗Usual commercial form . SO3 (SO3)2 H2SO4∗ H2SO4⋅H2O 80 .06 160 .13 98 .08 116 .09 col . pr . col ., silky, nd . col ., viscous lq . pr . or lq . d. 287 d. 48.0 692 −2H2O, 100 −16H2O, 300 278 .52 189 .62 225 .65 214 .77 87 .62 oxide, tri-(α) −10H2O, 100 275 251.8 d. −7H2O, 150 1.667 1.685 4.179 3.245 3.98714° SnBr2 SnCl2 SnCl2⋅2H2O∗ SnSO4 Sr peroxide peroxide sulfate (celestite) sulfate, acid Sulfamic acid Sulfur, amorphous Sulfur, monoclinic Sulfur, rhombic Sulfur bromide, monochloride, monochloride, dichloride, tetraoxide, di- 32.4 5 .12 2 .7115 .5° 3 .96 2 .03 124° 2 .046 1 .96 2 .07 2 .635 1 .687 1 .621 1515° lq ., 1 .4340°; 2 .264 (A) lq ., 1 .923; 2 .75 (A) 1 .9720° 1 .834 184° 1 .842 154° 215 .5 246 .8 37 .7 −SO2, 360 800 149760atm . 873 −4H2O, 61 375 −7H2O in dry air 570 114.1 620 623 d . 1150 d . −CO2, 1350 −6H2O, 100 19.420° 44.90° 3615° 15.410° s. s. 13.90° 34.72° 296° 11010° 500° 74.70° 57.580° 880° 8 i. v. s. s. s. 45.360° 202.626° 41234° 57.390° s. s. 28.384° 67.818° 6643° 225100° 23180° 301.860° 97100° 123.5100° d. i. d. i . i . v . s . d . s . 83 .90° 118 .70° 1919° d . d . 269 .815° ∞ 18100° Forms Sr(OH)2 36 .497° 0 .065100° 100 .8100° 19840° 21 .83100° 47 .7100° 36 .90° 0 .001118° 43 .50° 1040° 0 .410° 0 .900° 444 .6 444 .6 444 .6 540 .18mm 138 59 d . > −20 −10 .0 400° 62 .20° Forms Sr(OH)2 0 .00820° 0 .01820° 0 .01130° d . 200° i . i . i . d . d . d . d . 22 .80° 16 .83 44 .6 d . 50 10 .49 8 .62 d . 340 290 Forms H2SO4 ∞ ∞ 2430 d . −8H2O, 100 1580 d . d . 205 d . 120 119 .0 112 .8 −46 −80 −78 −30 −75 .5 d . d. i. al. sl. s. al.; i. et. s. al. s. al. i. al., NH i. al. i. al. v. s. al. s. NH3; v. sl. s. al. sl. s. NH3; i. a., al. s. alk. carb., dil. a. i. al. i. al. s. abs. al., act., NH3; s. ∞ CS2 s . conc . H2SO4; i . alk .; NH4OH, NH3 s . dil . H2SO4, HCl; d . abs . al . s . C6H5N s . alk ., abs . al ., et . s . tart . a ., alk ., al . s . H2SO4 s . al ., a . 0 .2615° m . al . s . a ., NH4 salts, aq . CO2 v . sl . s . act ., abs . al .; i . NH3 s . NH4Cl s . NH4Cl; i . act . 10089° 12420° s . NH3; 0 .012 abs . al . i . HNO3 sl . s . al .; i . et . d . d . 0 .011432° s . al ., NH4Cl; i . act . s . al .; i . NH4OH sl . s . a .; i . dil . H2SO4, al . 1470° H2SO4 sl . s . al ., act .; i . et . sl . s . CS2 s . CS2, al . 240°, 18155° CS2 4070° i . i . i . s . CS2, et ., bz . d . al . 4 .550° s . H2SO4; al ., ac . s . H2SO4 ∞ ∞ s . H2SO4 d . al . d . al . (Continued ) 2-23 2-24 TABLE 2-1 Physical Properties of the Elements and Inorganic Compounds (Continued ) Name Formula Formula weight Color, crystalline form, and refractive index Specific gravity Melting point, °C Boiling point, °C Solubility in 100 parts Cold water Hot water Sulfuric acid Sulfuric acid, pyroSulfuric oxychloride Sulfurous oxybromide oxychloride Tantalum H2SO4⋅2H2O H2S2O7 SO2Cl2 SOBr2 SOCl2 Ta 134 .11 178 .14 134 .97 207 .87 118 .97 180 .95 col. lq. cr . col . lq . or .-yel . lq . yel . fuming lq . bk .-gray, cb . 1.650 04° 1 .920° 1 .667 204° 2 .6818° 1 .631 16 .6 −38.9 35 −54 .1 −50 −104 .5 2850 167 d . 69 .1760mm 6840mm 75 .6 >4100 ∞ d . d . d . d . i . ∞ Tellurium Te 127 .60 met ., hex . (α) 6 .24; (β) 6 .00 452 1390 i . i . Terbium Thallium acetate chloride, monochloride, sesquichloride, trichloride, trisulfate (ic) sulfate (ous) sulfate, acid Thio, cf. sulfo or sulfur Thorium Tb Tl TlC2H3O2 TlCl Tl2Cl3 TlCl3 TlCl3⋅4H2O Tl2(SO4)3⋅7H2O Tl2SO4 TlHSO4 158 .93 204 .38 263 .43 239 .84 515 .13 310 .74 382 .80 823 .06 504 .83 301 .45 blue-wh ., tet . silky nd . wh ., cb . yel ., hex . hex . pl . nd . lf . col ., rhb ., 1 .8671 trimorphous 11 .85 3 .68 7 .00 5 .9 303 .5 110 430 400–500 25 37 −6H2O, 200 632 115 d . 1650 806 d . d . −4H2O, 100 d . d . i . v . s . 0 .210° 0 .2615° v . s . 86 .217° d . 2 .700° d . d . 18 .45100° Th 232 .04 cb . 11 .2 1845 >3000 i . i . oxide, di- (thorianite) sulfate sulfate Thulium Tin ThO2 Th(SO4)2 Th(SO4)2⋅9H2O Tm Sn 264 .04 424 .16 586 .30 168 .93 118 .71 wh ., cb . >2800 4400 mn . pr . 9 .69 4 .22517° 2 .77 silv . met ., tet . 7 .31 231 .85 2260 i . 0 .740° sl . s . i . i . 5 .2250° sl . s . i . i . Tin Sn 118 .71 gray, cb . 5 .750 Stable −163 to +18 2260 i . i . Tin salts, cf. stannic and stannous Titanic acid H2TiO3 97 .88 wh . pd . i . i . i . d . d . s . s . i . s . d . i . i . i . 6 .77 17 .5° i . i . 1 .8100° 1 .9100° Other reagents d . al . d . al . s . ac .; d . al . s . bz ., CS2, CCl4; d . act . s . bz ., chl . s . fused alk ., HF; i . HCl, HNO3, H2SO4 s . H2SO4, HNO3, KCN, KOH, aq . reg .; i . CS2 s . HNO3, H2SO4; i . NH3 v . s . al . sl . s . HCl; i . al ., NH4OH s . al ., et . s . al ., et . s . dil . H2SO4 v . sl . s . dil . H2SO4 −9H2O, 400 >3000 s . HCl, H2SO; sl . s . HNO3; i . HF, alk . s . h . H2SO4; i . alk . s . HCl, H2SO4, dil . HNO3 h . aq KOH s . a ., h . alk . solns . s . alk .; v . sl . s . dil . a .; i . al . s . a . i . CS2, et ., chl . Ti TiCl2 47 .87 118 .77 dark gray, cb . bk ., delq . chloride, trichloride, tetraoxide, di- (anatase) TiCl3 TiCl4∗ TiO2 154 .23 189 .68 79 .87 oxide, di- (brookite) TiO2 4 .26 1640 d . <3000 i . i . s . H2SO4, alk . 19 .3 3370 5900 i . i . 6000 6000 i . i . i . i . i . i . i . sl . s . s . h . conc . KOH; sl . s . NH3, HNO3, aq . reg . s . F2; i . a . s . h . HNO3; sl . s . HCl, H2SO4 s . alk .; i . a . s . HF, alk ., NH3 i . i . s . a ., alk . carb .; i . alk . i . d . i . i . s . a .; i . alk . d . a . s . HNO3, conc . H2SO4 Titanium chloride, di- 4 .50 1800 Unstable in air d . 440 −30 W 183 .84 vl ., delq . col . lq . brn . or bk ., tet ., 2 .534–2 .564 brn . or bk ., rhb ., 2 .586 col . if pure, tet ., 2 .615 gray-bk ., cb . WC W 2C 195 .85 379 .69 gray pd ., cb . iron gray 15 .718° 16 .0618° 2777 2877 oxide, triTungstic acid (tungstite) WO3 H2WO4 231 .84 249 .85 yel ., rhb . yel ., rhb . 2 .24 7 .16 5 .5 Uranic acid H2UO4 304 .04 yel . pd . 5 .92615° Uranium carbide oxide, di- (uraninite) U U2C3 UO2 238 .03 512 .09 270 .03 wh . cr . cr . bk ., rhb . 18 .485 134° 11 .28 10 .9 >2130 −½H2O, 100; 1473 −H2O, 250 to 300 1133 2400 2176 oxide, di- (rutile) Tungsten carbide carbide TiO2 79 .87 79 .87 lq ., 1 .726 3 .84 136 .4 4 .17 3500 i . s . dil . HCl sl . s . alk . oxide (pitchblende) sulfate (ous) Uranyl acetate carbonate (rutherfordine) nitrate sulfate Vanadic acid, metaVanadic acid, pyroVanadium chloride, dichloride, trichloride, tetraoxide, dioxide, trioxide, tetraoxide, pentaoxychloride, monoVanadyl chloride chloride, dichloride, triWater† U3O8 U(SO4)2⋅4H2O UO2(C2H3O2)2⋅2H2O UO2CO3 UO2(NO3)2⋅6H2O UO2SO4⋅3H2O HVO3 H4V2O7 V VCl2 VCl3 VCl4 V2O2 V2O3 V2O4 V2O5 VOCl (VO)2Cl VOCl2 VOCl3 H2O 842 .08 502 .22 424 .15 330 .04 502 .13 420 .14 99 .95 217 .91 50 .94 121 .85 157 .30 192 .75 133 .88 149 .88 165 .88 181 .88 86 .39 169 .33 137 .85 173 .30 18 .02 Water, heavy Xenon D 2O Xe 20 .029 131 .29 olive gn. gn., rhb. yel., rhb. tet. yel., rhb., 1.4967 yel . cr . yel . scales pa . yel ., amor . lt . gray, cb . gn ., hex ., delq . pink, tabular, delq . red lq . lt . gray cr . bk . cr . blue cr . red-yel ., rhb . brn . pd . yel . cr . gn ., delq . yel . lq . col . lq ., 1 .3330020°; hex . solid, 1 .309 col . lq ., 1 .3284420° col . gas Ytterbium Yttrium Zinc acetate acetate bromide carbonate Yb Y Zn Zn(C2H3O2)2 Zn(C2H3O2)2⋅2H2O∗ ZnBr2 ZnCO3 173 .04 88 .91 65 .41 183 .50 219 .53 225 .22 125 .42 dark gray, hex . silv . met ., hex . mn . wh ., mn ., 1 .494 rhb . wh ., trig ., 1 .818 chloride ZnCl2 136 .32 cyanide hydroxide iodide Zn(CN)2 Zn(OH)2 ZnI2 117 .44 99 .42 319 .22 wh ., delq ., 1 .687, uniaxial col ., rhb . col ., rhb . cb . nitrate oxide (zincite) oxide peroxide phosphide silicate Zn(NO3)2⋅6H2O ZnO ZnO ZnO2 Zn3P2 ZnSiO3 297 .51 81 .41 81 .41 97 .41 258 .17 141 .49 sulfate (zincosite) sulfate sulfate sulfate (goslarite) sulfide (α) (wurzite) sulfide (β) (sphalerite) ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O∗ ZnS ZnS 161 .47 179 .49 269 .56 287 .58 97 .47 97 .47 2-25 sulfide (blende) ZnS 97 .47 sulfite ZnSO3⋅2½H2O 190 .51 Zirconium Zr 91 .22 oxide, di- (baddeleyite) ZrO2 123 .22 123 .22 oxide, di- ( free from Hf) ZrO2 ∗Usual commercial form . † Cf. special tables on water and steam, Tables 2-3, 2-4, and 2-5 . note: °F = 9⁄ 5°C + 32 . col ., tet . wh ., hex ., 2 .004 wh ., amor . yel . steel gray, cb . hex . or rhb .; glass, 1 .650 wh ., rhb ., 1 .669 col . mn . rhb ., 1 .4801 wh ., hex ., 2 .356 wh ., cb .; glass (?) 2 .18–2 .25 wh ., granular mn . cb ., pd . ign . easily yel . or brn ., mn ., 2 .19 wh ., mn . 7.31 2.8915° 5.6 2.807 3 .2816 .5° 5 .96 3 .2318° 3 .0018° 1 .81630° 3 .64 4 .87 184° 4 .399 3 .357 184° 2 .824 3 .64 2 .8813° 1 .829 1 .004° (lq .); 0 .9150° (ice) 1 .10720° lq ., 3 .06−109 .1 2 .7−140° 4 .53 (A) d. −4H2O, 300 −2H2O, 110 60.2 d . 100 118 1710 3000 d . −109 ign . 1970 1967 800 148 .5755mm d . 1750 d . in air i. 2311° 9.217° i. 963° d. s. HNO3, H2SO4 s. dil. a. s. al., act. 170.30° 18 .913 .2° i . i . i . s . s . s . d . i . sl . s . i . 0 .820° i . i . d . s . d . ∞60° 23025° v . s . ac ., al ., et .; i . dil ., alk . 4 al .; s . a . s . a ., alk .; i . NH3 s . a ., alk ., NH4OH s . HNO3, H2SO4; i . aq ., alk . s . al ., et . s . abs . al ., et . s . abs . al ., et ., chl ., ac . s . a . s . HNO3, HF, alk . s . a ., alk . s . a ., alk .; i . abs . al . v . s . HNO3 s . HNO3 s . abs . al ., dil . HNO3 s . al ., et ., ∞Br2 ∞ al .; sl . s . et . i . d . d . i . s . i . <−15 0 127 .19 100 3 .82 −140 101 .42 −109 .1 ∞ 24 .20° cc ∞ 7 .350° cc ∞ al .; sl . s . et . 5 .51 7 .140 1 .840 1 .735 4 .2194° 4 .42 1490 419 .4 242 237 394 −CO2, 300 2500 907 subl . in vac . −2H2O, 100 650 sl . d . i . 3025° 4025° 3900° 0 .00115° d . i . 44 .6100° 66 .6100° 670100° 2 .91 254° 283 732 43225° 615100° d . 80 d . 125 446 624 0 .000518° 0 .0005218° 4300° sl . s . 3 .053 ° 4 .666 14.2 4 2 .065 144° 5 .606 5 .47 1 .571 4 .55 134° 3 .52 36 .4 >1800 >1800 expl . 212 >420 1437 v . s . dil . a ., h . KOH s . a ., ac ., alk . 2 .825°, 16679° al . v . s . al . v . s . NH4OH, al ., et . s . a ., alk ., NH4 salts; i . act ., NH3 10012 .5° al .; v . s . et .; i . NH3 s . KCN, NH3, alk .; i . al . s . a ., alk ., NH4OH s . a ., al ., NH3, aq . (NH4)2CO3 v . s . al . s . a ., alk ., NH4Cl; i . NH3 3 .74 154° 3 .28 154° 2 .072 154° 1 .96616 .5° 4 .087 4 .102 254° d . 740 d . 238 −5H2O, 70 tr . 39 1850150atm . tr . 1020 −6H2O, 105 1100 −7H2O, 280 subl . 1185 4 .04 6 .4 5 .49 5 .73 −2½H2O, 100 1700 2700 d . 200 >2900 4300 510100° 324 .5 0 .0004218° 0 .0004218° 0 .0022 i . i . ∞36 .4° 420° s . s . 115 .20° 0 .0006918° i . 61100° 89 .5100° s . 653 .6100° i . i . sl . s . al .; i . act .; NH3 sl . s . al .; i . act .; NH3 v . s . a .; i . ac . s . a . i . 0 .16 i . i . i . i . d . i . i . i . v . s . a .; i . ac . s . H2SO3, NH4OH; i . al . s . HF, aq . reg .; sl . s . a . s . H2SO4, HF s . H2SO4, HF i . NH4OH; d . a . s . dil . a . sl . s . al .; s . gly . 2-26 TABLE 2-2 Physical Properties of Organic Compounds* Abbreviations Used in the Table (A), density referred to air cr., crystalline i-, iso-, containing the group al., ethyl alcohol d., decomposes (CH3)2CHamor., amorphous d-, dextrorotatory i., insoluble aq., aqua, water dl-, dextro-laevorotatory ign., ignites brn., brown et., ethyl ether l-, laevorotatory bz., benzene expl., explodes lf., leaflets c., cubic gn., green lq., liquid cc., cubic centimeter h., hot m-, meta chl., chloroform hex., hexagonal mn., monoclinic col., colorless n-, normal This table of the physical properties includes the organic compounds of most general interest . For the properties of other organic compounds, reference must be made to larger tables in Lange’s Handbook of Chemistry (Handbook Publishers), Handbook of Chemistry and Physics (Chemical Rubber Publishing Co .), Van Nostrand’s Chemical Annual, International Critical Tables (McGraw-Hill), and similar works . The molecular weights are based on the atomic weight values in “Atomic weights of the Elements 2001,” PURE Appl. Chem., 75, 1107, 2003 . The densities are given for the temperature indicated and are usually nd., needles s-, sec-, secondary v. s., very soluble v. sl. s., very slightly soluble o-, ortho silv., silvery wh., white or., orange sl., slightly yel., yellow p-, para subl., sublimes (+), right rotation pd., powder sym., symmetrical >, greater than pet., petroleum ether t-, tertiary <, less than pl., plates tet., tetragonal ∞, infinitely pr., prisms tri., triclinic rhb., rhombic uns., unsymmetrical s., soluble v., very referred to water at 4°C, e.g., 1 .02895/4 a density of 1 .028 at 95°C referred to water at 4°C, the 4 being omitted when it is not clear whether the reference is to water at 4°C or at the temperature indicated by the upper figure . The melting and boiling points given have been selected from available data as probably the most accurate . The solubility is given in grams of the substance in 100 of the solvent . In the case of gases, the solubility is often expressed in some manner as “510 cc .” which indicates that, at 10°C, 5 cc . of the gas are soluble in 100 of the solvent . Name Synonym Formula Formula weight Form and color Abietic acid Acenaphthene Acetal Acet-aldehyde -aldehyde, par-aldehyde ammonia -amide -anilide -phenetidide (o-) (m-) -toluidide (o-) (p-) Acetic acid anhydride nitrile Acetone Acetonyl urea Acetophenone benzoyl hydride Acetyl-chloride -phenylenediamine (-p) Acetylene dichloride (cis) (trans) Aconitic acid Acridine Acrolein ethylene aldehyde Acrylic acid nitrile Adipic acid amide nitrile Adrenaline (1-) (3,4,1) Alanine (α) (dl-) Aldol acetaldol Alizarin Allyl alcohol bromide chloride thiocyanate (i) thiourea Aluminum ethoxide Amino-anthraquinone (α) (β) -azobenzene -benzoic acid (m-) (p-) sylvic acid, abietinic acid naphthylene ethylene acetaldehyde diethylacetal ethanal paraldehyde C20H30O2 C10H6(CH2)2 CH3CH(OC2H5)2 CH3CHO (C2H4O)3 CH3CHOHNH2 CH3CONH2 C6H5NHCOCH3 CH3CONHC6H4OC2H5 CH3CONHC6H4OC2H5 CH3C6H4NHCOCH3 CH3C6H4NHCOCH3 CH3CO2H (CH3CO)2O CH3CN CH3COCH3 <NHCONHCOC>(CH3)2 CH3COC6H5 CH3COCl C2H3ONHC6H4NH2 HC⋮CH CHCl:CHCl CHCl:CHCl C3H3(CO2H)3 C6H4 < (CH)(N) > C6H4 CH2:CH⋅CHO CH2:CH⋅CO2H CH2:CH⋅CN (CH2CH2CO2H)2 (CH2CH2CONH2)2 (CH2CH2CN)2 C6H3(OH)2(CHOHCH2NHCH3) CH3CH(NH2)CO2H CH3CH(OH)CH2COH C6H4(CO)2C6H2(OH)2 CH2:CH⋅CH2OH CH2:CH⋅CH2Br CH2:CH⋅CH2Cl CH2:CH⋅CH2NCS CH2:CH⋅CH2NHCSNH2 Al(OCH2CH3)3 C6H4(CO)2C6H3NH2 C6H4(CO)2C6H3NH2 C6H5⋅N:N⋅C6H4NH2 H2N⋅C6H4CO2H H2N⋅C6H4CO2H 302 .45 154 .21 118 .17 44 .05 132 .16 61 .08 59 .07 135 .16 179 .22 179 .22 149 .19 149 .19 60 .05 102 .09 41 .05 58 .08 128 .13 120 .15 78 .50 150 .18 26 .04 96 .94 96 .94 174 .11 179 .22 56 .06 72 .06 53 .06 146 .14 144 .17 108 .14 183 .20 89 .09 88 .11 240 .21 58 .08 120 .98 76 .52 99 .15 116 .18 162 .16 223 .23 223 .23 197 .24 137 .14 137 .14 lf . rhb ./al . lq . col . lq . col . cr . col . cr . col . cr . rhb ./al . lf ./al . lf ./al . rhb . rhb . or mn . col . lq . col . lq . col . lq . col . lq . tri ./al . lf . col . lq . nd ./aq . col . gas col . lq . col . lq . cr ./aq . rhb ./aq . al . col . lq . col . lq . col . lq . mn . pr . cr . pd . col . oil col . pd . nd ./aq . col . lq . red rhb . col . lq . lq . col . lq . col . oil col . pr . pd . red nd . red nd . yel . mn . nd ./aq . mn . pr . ethanamide antifebrin o-ethoxyacetanilide acetyl-m-phenetidine N-tolylacetamide N-tolylacetamide ethanoic acid, vinegar acid acetyl oxide, acetic oxide methyl cyanide propanone, dimethyl ketone dimethyl hydantoin methyl-phenyl ketone ethanoyl chloride amino-acetanilide (p) ethyne; ethine 1,2-dichloroethene dioform equisetic acid; citridic acid acrylic aldehyde, propenal propenoic acid vinyl cyanide hexandioc acid, adipinic acid tetramethylene 1-suprarenine 2-hydroxybutyraldehyde Anthraquinoic acid propen-1-ol-3,propenyl alcohol 3-bromo-propene-1 3-chloro-propene-1 mustard oil thiosinamide aminodracylic acid Specific gravity 1 .06995/95 0 .82122/4 0 .78318/4 0 .99420/4 1 .159 1 .214 1 .16815 1 .21215 1 .04920/4 1 .08220/4 0 .78320/4 0 .79220/4 1 .03315/15 1 .10520/4 (A) 0 .906 1 .29115/4 1 .26515/4 0 .84120/4 1 .06216/4 0 .81120 1 .36025/4 0 .95119/19 1 .10320/4 0 .85420/4 1 .39820/4 0 .93820/4 1 .01320/4 1 .21920/20 1 .14220/0 1 .5114° Melting point, °C 182 95 −123 .5 10 .5–12 97 81(69 .4) 113–4 79 96–7 110 153 16 .7 −73 −41 −94 .6 175 20 .5 −112 .0 162 −81 .5891 −80 .5 −50 192 d . 110–1 −87 .7 12–13 −82 151–3 226–7 1 d . 207–11 295 d . 289–90 −129 −119 .4 −136 .4 −80 77–8 150–60 256 302 126–7 173–4 187–8 Boiling point, °C 278–9 102 .2 20 .2 124 .4752 100–10 d . 222 305 >250 296 306–7 118 .1 139 .6 81 .6–2 .0 56 .5 subl . 202 .3749 51–2 −84760 60 .3 48 .4 346 52 .5 141–2 78–9 26510 295 subl . >200 8320 430 96 .6 70–1753 44 .6 152 200–510 subl . subl . 225120 Solubility in 100 parts Water Alcohol Ether i . i . 625 ∞ 1213 v . s . s . 0 .56 i . sl . s . 0 .8619 0 .0922 ∞ 12 c . ∞ ∞ s . i . d . s . h . 100 cc .18 0 .3520 0 .6320 3315 sl . s . h . 40 ∞ s . 1 .415 0 .412 v . sl . s . 0 .0320 2217 ∞ 0 .03100 ∞ i . <0 .1 0 .2 30 d . i . i . sl . s . h . v . sl . s . 0 .313 v . s . s . h . ∞ ∞ ∞ v . s . s . 2120 s . s . s . 1025 ∞ ∞ ∞ ∞ s . s . d . v . s . 600 cc .18 ∞ ∞ sl . s . s . s . ∞ v . s . s . chl . ∞ ∞ ∞ sl . s . v . sl . s . 7 25 v . s . 0 .615 s . v . sl . s . v . sl . s . ∞ v . s . ∞ ∞ ∞ ∞ s . i . s . s . s . h . 210 1110 v . sl . s . i . i . s . v . s . ∞ ∞ ∞ ∞ v . sl . s . v . sl . s . s . i . s . 1 .86 8 .26 s . s . ∞ ∞ ∞ ∞ s . s . ∞ v . s . ∞ ∞ v . sl . s . s . s . Amino-diphenylamine (p-) -G-acid (2-)(6-,8-), Na2 salt -mono-potassium salt -sodium salt -J-acid (2-)(5-,7-) -mono-potassium salt -naphthol sulfonic (1-,2-,4-)(α-) (1-,8-,4-) -phenol (o-) (m-) (p-) -toluene sulfonic acid (1-,2-,3-) (1-,4-,2-) (1-,4-,3-) (1-,2-,5-) Amyl acetate (n-) (i-) (s-) (s-) (t-) alcohol (n-) fusel oil, (s-,n-) methyl-propyl carbinol, (prim .-,i-) isobutyl carbinol, (s-,i-) (t-) (d-) -amine (n-) (s-,n-) (i-) (t-) 2-aminophenol 3-aminophenol p-hydroxyaniline common amyl acetate α-Me-Bu-acetate di Et-carbinol acetate pentanol-1 pentanol-2 2-methyl-butanol-4 2-methyl-butanol-3 2-methyl-butanol-2 active amyl alcohol 1-NH2-2-Me-butane 3-amino pentane 3-NH2-2-Me-butane aniline (i-) benzoate (i-) bromide (n-) (i-) (t-) n-butyrate (n-) (i-) (t-) i-butyrate (i-) chloride (n-) (s-) (s-) (i-) (s-,i-) (t-) i-cyanide (i-) formate (n-) (i-) iodide (n-) (i-) (s-,n-) (t-) 1-bromopentane 4-Br-2-Me-butane 2-Br-2-Me-butane 1-chloropentane 2-chloropentane 3-chloropentane 4-Cl-2-Me-butane 3-Cl-2-Me-butane 2-Cl-2-Me-butane 1-Cl-2-Me-butane iso-caproic iso-nitrile 1-iodopentane 4-I-2-Me-butane 2-iodopentane 2-I-2-Me-butane 2-27 H2N⋅C6H4NH⋅C6H5 C10H5(NH2)(SO3Na)2 C10H5(NH2)S2O6HK C10H5(NH2)S2O6HNa C10H5(NH2)(SO3H)2 C10H5(NH2)S2O6HK C10H5OHNH2SO3H½H2O NH2(OH)C10H5SO3H H2N⋅C6H4⋅OH H2N⋅C6H4⋅OH H2N⋅C6H4⋅OH C6H3(CH3)(NH2)SO3H C6H3(CH3)(NH2)SO3H⋅H2O C6H3(CH3)(NH2)SO3H⋅½H2O C6H3(CH3)(NH2)SO3H⋅H2O CH3CO2CH2(CH2)3CH3 CH3CO2CH2CH2CH(CH3)2 CH3CO2CH2CH(CH3)C2H5 CH3CO2CH(CH3)CH2C2H5 CH3CO2CH(C2H5)2 CH3CO2C(CH3)2C2H5 CH3(CH2)3CH2OH C2H5CH2CH(OH)CH3 (CH3)2CHCH2CH2OH (C2H5)2CHOH (CH3)2CHCH(OH)CH3 (CH3)2C(OH)C2H5 (CH3)3CCH2OH C2H5CH(CH3)CH2OH CH3(CH2)4NH2 (C3H7)(CH3)CHNH2 (CH3)2CH(CH2)2NH2 (C2H5)(CH3)2CNH2 C2H5CH(CH3)CH2NH2 (C2H5)2CHNH2 (CH3)2CHCH(CH3)NH2 C6H5NHC5H11 C6H5CO2C5H11 CH3(CH2)3CH2Br (CH3)2CH(CH2)2Br (CH3)2C(Br)C2H5 C2H5CH2CO2(CH2)4CH3 C2H5CH2CO2⋅C5H11 C3H7CO2C(CH3)2C2H5 (CH3)2CHCO2C5H11 CH3(CH2)3CH2Cl C2H5CH2CHClCH3 (C2H5)2CHCl (CH3)2CH(CH2)2Cl (CH3)CHCHClCH3 (CH3)2CClC2H5 (CH3)(C2H5)CHCH2Cl (CH3)2CH(CH2)2NC HCO2CH2(CH2)3CH3 HCO2CH2CH2CH(CH3)2 CH3(CH2)3CH2I (CH3)2CHCH2CH2I C2H5CH2CHICH3 (CH3)2CIC2H5 C2H5CH(CH3)CH2I CH3(CH2)3CH2SH (C2H5)2CHSH (CH3)2CH(CH2)2SH C5H11⋅C6H4OH C2H5CO2(CH2)4CH3 C2H5CO2(CH2)2CH(CH3)2 C2H5CO2C5H11 HOC6H4CO2C5H11 C4H9CO2C5H11 C4H9CO2C5H11 184 .24 347 .28 341 .40 325 .29 303 .31 341 .40 248 .26 239 .25 109 .13 109 .13 109 .13 187 .22 205 .23 196 .22 205 .23 130 .18 130 .18 130 .18 130 .18 130 .18 130 .18 88 .15 88 .15 88 .15 88 .15 88 .15 88 .15 88 .15 88 .15 87 .16 87 .16 87 .16 87 .16 87 .16 87 .16 87 .16 163 .26 192 .25 151 .04 151 .04 151 .04 158 .24 158 .24 158 .24 158 .24 106 .59 106 .59 106 .59 106 .59 106 .59 106 .59 106 .59 97 .16 116 .16 116 .16 198 .05 198 .05 198 .05 198 .05 198 .05 104 .21 104 .21 104 .21 164 .24 144 .21 144 .21 144 .21 208 .25 172 .26 172 .26 nd./aq. al. 67 354 col. nd. pr. lf. nd. mn. nd. tri./aq. col. lq. col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . cr . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . lq . col . lq . lq . col . lq . col . lq . lq . lq . lq . lq . lq . lq . lq . lq . lq . lq . lq . lq . col . lq . lq . cr . lq . col . lq . col . lq . lq . col . lq . col . lq . 173 122–3 184–6 d. subl. subl. d. 0.87920/20 0 .87615/4 0 .88013 0 .9220 0 .87120/4 0 .87419 0 .817 20/20 0 .81020/20 0 .81315/4 0 .815 25/4 0 .81919 0 .809 20/4 20/4 0 .816 0 .76619 0 .749 20/4 0 .75118/4 0 .73125/4 0 .75518 0 .749 20/4 0 .75718 0 .92815/4 0 .99214/14 1 .21820/4 1 .22017/15 1 .21619/0 0 .87115/4 0 .86619/15 0 .86515/0 0 .8760/4 0 .878 20/4 0 .870 20/4 0 .895 21 0 .89320/4 0 .8830 0 .87120/4 0 .88117 .5 0 .9020 0 .882 20/4 1 .51020/4 1 .515 18/4 1 .507 17/4 1 .47119/15 1 .524 20/4 0 .857 20 −H2O, 120 −70.8 −78 .5 −117 .2 −11 .9 52–3 −55 −105 −95 −73 .2 −99 −72 .9 −73 .5 −93 .5 −86 148.4737 142757 141–2 133 .5 133 124 .5 749 137 .9 119 .5 132 .0 115 .6 113–4 102 113–4 128 103–4 91–2 95 77–8 95–6 90–1 83–4 254 .5 261746 129 .7 120745 108765 186 .4 178 .6 164 168 .8 108 .4 96 .7 97 .3 99 .7 758 91753 85 .7 98–9 137–9 132 123 .5 157 .0 147 765 144–5 127 765 148 126767 105 120 265–7 168 .7 160 .2 5816 265 194 173–4 mercaptan (n-) pentanthiol-1 (n-) pentanthiol-3 (i-) 2-Me-butanthiol-4 0 .83520/4 phenol (t-)(p-) pentaphen 93 propionate (n-) 0 .87615/4 −73 .1 (i-) 0 .870 20/4 (act .) 0 .866 20/4 salicylate (n-) 1 .06515 Amyl i-valerate (i) 0 .85820/15 (t-) 0 .86114/0 ∗By N . A . Lange, Ph .D ., Handbook Publishers, Inc ., Sandusky, Ohio . Abridged from table of Physical Constants of Organic Compounds in Lange’s Handbook of Chemistry. sl. s. v. sl. s. 12.820 2.718 10.0 20 3.418 v. s. v. sl. s. 1.7 0 2.6 0 1.10 0.97 11 0.5 20 0.47 311 v. sl. s. 0 .315 v . sl . s . sl . s . sl . s . v . sl . s . 2 .7 22 420 214 5 .5 30 2 .830 sl . s . sl . s . 3 .630 s . ∞ ∞ ∞ ∞ ∞ ∞ i . i . i . 0 .0216 i . 0 .05 50 i . sl . s . i . i . i . i . i . i . i . i . i . v . sl . s . 0 .322 i . i . i . i . i . i . i . i . sl . s . i . 0 .125 v . sl . s . i . v . sl . s . sl . s . s. s. 4.30 s. 40 v. s. sl. s. i. bz. i. i. ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . s . s . ∞ ∞ ∞ s . s . s . ∞ s . s . s . s . s . ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . s . ∞ ∞ ∞ s . s . s . ∞ ∞ s . s . s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ s . (Continued ) 2-28 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Amylene (n-)(α-) (i-) (α-) (-n)(β-) (i-)(β-) Anethole (p-) Anhydroformald-aniline Aniline hydrochloride nitrate sulfate Anisal-acetone (p-) Anisic acid (p-) aldehyde (p-) Anisidine (o-) (m-) (p-) Anisole Anthracene Anthramine (α) (β) Anthranil Anthranilic acid (o-) Anthrapurpurin (1-,2-,7-) Anthraquinone disulfonate Na2 (1-,5-) (1-,8-) (2-,6-) (2-,7-) sulfonate Na (1-) (2-) Anthrarufin (1-,5-) Antipyrene Apiole Arabinose (α)(d- or l-) (dl-) Arachidic acid Arsanilic acid (p-) Asparagine (l-) Aspirin (o-) Atropic acid Auramine Aurine, coralline (4-,4′-) Azo-anisole (2-,2′-) benzene Azoxybenzene Barbituric acid Benzal acetone Benzaldehyde Benzamide Benzanilide Benzene sulfinic acid sulfonic acid sulfonic amide sulfonic chloride Benzidine (4-,4′-) disulfonic acid (2-,2′-) (3-,3′-) Benzil Benzoic acid anhydride nitrile Synonym pentene-1 2-methyl-butene-3 2-methyl-butene-1 pentene-2 2-methyl-butene-2 p-propenyl anisole methylene aniline amino benzene, phenyl amine, cyanol aniline salt, aniline chloride MeO-benzalacetone 2-amino-anisole MeO-aniline(m) 4-amino anisole methyl phenyl ether paranaphthalene, anthracin green oil α-amino-anthracene β-amino-anthracene diphenyleneketone, dihydrodiketoanthracene ρ-anthraquinone disulfonate x-anthraquinone disulfonate 1-ph-2,3-diMepyrazolone-5 1-allyl-2, 5-diMeO-3,4 methylenedioxybenzene eicosanoic acid α-phenyl acrylic acid 4,4′-dimethylaminobenzophenomide diMeO-azobenzene diphenyldiimide malonyl urea Me-cinnamyl ketone artificial almond oil benzol, phenyl hydride, cyclohexatriene benzene sulfonamide benzene sulfonyl chloride dibenzoyl phenyl cyanide Formula Formula weight Form and color Specific gravity Melting point, °C 20 C2H5CH2CH:CH2 (CH3)2CHCH:CH2 (C2H5)(CH3)C:CH2 C2H5CH:CHCH3 (CH3)2C:CHCH3 CH3CH:CH⋅C6H4OCH3 (CH2NC6H5)3 C6H5NH2 70 .13 70 .13 70 .13 70 .13 70 .13 148 .20 315 .41 93 .13 lq. col . lq . col . lq . col . lq . col . lq . lf ./al . pr ./al . col . oil 0.644 0 .63215 0 .667 0/0 0 .650 20/4 0 .66319/4 0 .99120/20 C6H5NH2⋅HCl C6H5NH2⋅HNO3 (C6H5NH2)2⋅H2SO4 CH3OC6H4CH:CHCOCH3 CH3OC6H4CO2H CH3OC6H4CHO CH3OC6H4NH2 CH3OC6H4NH2 CH3OC6H4NH2 CH3OC6H5 C6H4:(CH)2:C6H4 129 .59 156 .14 284 .33 176 .21 152 .15 136 .15 123 .15 123 .15 123 .15 108 .14 178 .23 cr . rhb . lf ./al . lf ./et . mn ./aq . col . oil col . lq . oil pl ./aq . col . lq . col . mn . 1 .222 4 1 .356 4 1 .377 4 C6H4:(CH)2:C6H3NH2 C6H4:(CH)2:C6H3NH2 C6H4:(NH)CO H2NC6H4CO2H C14H5O2(OH)3 C6H4:(CO)2:C6H4 193 .24 193 .24 119 .12 137 .14 256 .21 208 .21 yel ./al . yel ./al . col . oil col . rhb . or . nd ./al . yel . rhb . C14H6O2(SO3Na)2⋅5H2O C14H6O2(SO3Na)2⋅4H2O C14H6O2(SO3Na)2⋅7H2O C14H6O2(SO3Na)2⋅4H2O C14H7O2SO3Na C14H7O2SO3Na C14H6O2(OH)2 C11H12ON2 C12H14O4 502 .38 484 .36 538 .41 484 .36 310 .26 310 .26 240 .21 188 .23 222 .24 yel . lf . yel . pr . col . cr . cr . yel . lf . silv . lf . yel . lf . mn ./aq . col . nd . 1 .088113/4 1 .0220/4 CH2OH(CHOH)3CHO CH2OH(CHOH)3CHO CH3(CH2)18CO2H H2N⋅C6H4 .AsO3H2 HO2C⋅C2H3(NH2)⋅CONH2 CH3CO2⋅C6H4⋅CO2H C6H5C(:CH2)⋅CO2H [(CH3)2NC6H4]2C:NH 150 .13 150 .13 312 .53 217 .05 132 .12 180 .16 148 .16 267 .37 rhb . pr . 1 .585 20/4 col . lf . nd ./aq . rhb . nd ./aq . nd ./aq . col ./al . (HOC6H4)2C:C6H4:O (CH3O⋅C6H4N:)2 C6H5N:N⋅C6H5 (C6H5)2N2O CO:(NHCO)2:CH2⋅2H2O C6H5CH:CHCOCH3 C6H5CHO C6H5CONH2 C6H5CONHC6H5 C6H6 290 .31 242 .27 182 .22 198 .22 164 .12 146 .19 106 .12 121 .14 197 .23 78 .11 red or . pr . or . mn . yel . rhb . col ./aq . pl . col . lq . col . pr . lf ./al . col . lq . C6H5SO2H C6H5SO3H C6H5SO2NH2 C6H5SO2Cl NH2⋅C6H4⋅C6H4⋅NH2 (⋅C6H3(NH2)SO3H)2⋅3H2O (⋅C6H3(NH2)SO3H)2 C6H5CO⋅COC6H5 C6H5CO2H (C6H5CO)2O C6H5CN 142 .18 158 .18 157 .19 176 .62 184 .24 398 .41 344 .36 210 .23 122 .12 226 .23 103 .12 pr ./aq . col . nd . mn ./aq . cr . cr ./aq . pr ./aq . 1 .38415/15 83–4 65–6 156 14 .5 128–9 d . >175 pr . mn . pr . rhb ./et . col . lq . 1 .2315 1 .26615/4 1 .19915/4 1 .00125/6 95 121 .7 42 −12 .9 1 .02220/4 1 .385 4 1 .123 20/4 1 .09815/15 1 .096 20/4 1 .089 55/55 0 .990 22/4 1 .25 27/4 1 .18715/4 1 .438 20/4 1 .54315/4 1 .20320/4 1 .248 20/20 1 .035 20/20 1 .046 20/4 1 .341 1 .314 0 .879 20/4 −135 −139 −124 22 .5 143 −6 .2 Boiling point, °C Solubility in 100 parts Water Alcohol Ether 30–1 20 .5 771 31–2758 36 .4 37–8 235 .3 185 184 .4 i. i . i . v . sl . s . i . v . sl . s . i . 3 .618 ∞ ∞ ∞ ∞ s . s . sl . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ 245 s . s . sl . s . v . s . v . s . ∞ ∞ s . s . s . 1 .520 i . sl . s . i . v . s . v . s . ∞ ∞ s . s . s . 198 d . 190 d . 73–4 184 .2 2 .5 5 .2 <−12 57 .2 −37 .3 217–8 275–80 247–8 225 251 243 154–5 340–2 1815 s . 514 i . 0 .0319 v . sl . s . v . sl . s . v . sl . s . s . h . i . i . 130± 238 <−18 144–5 369 286 subl . d . >215 subl . 462 379–81 i . i . sl . s . h . 0 .35 14 sl . s . h . i . s . sl . s . s . 1110 v . s . h . 0 .0518 sl . s . s . 167 sl . s . v . sl . s . i . i . subl . 319174 294 v . s . sl . s . 3 .920 30 .5 20 0 .5320 0 .8425 i . 100 25 i v . sl . s . i . i . sl . s . 100 s . i . i . i . s . sl . s . s . 280 113(109) 30 159 .5 164 .5 77 232 227–35 135–6 106–7 136 310 d . 153 68 36 d . 245 41–2 −26 130 163 5 .5 328 d . 235 267 d . 297 d . 260–2 179 290 117–910 80 .1 d . > 100 d . 251 .5 400740 348 d . 249 .2 360 190 .7 460 16 .910 i . v . s . h . 3 .128 137 0 .1 c . i . 0 .59° i . s . h . v . s . h . i . c . s . s . 720 v . s . i . i . i . i . i . s . h . i . 0 .3 1 .35 25 i . 0 .07 22 s . s . 4 .220 11 .415 sl . s . s . ∞ 1725 430 s . s . s . ∞ sl . s . sl . s . ∞ v . s . h . v . s . 0 .4316 i . 1 h . 0 .09 25 v . sl . s . i . 0 .217 i . 1100 v . s . v . s . v . s . v . s . 1 h . i . v . s . i . v . s . s . 2 i . v . s . 4615 s . ∞ v . s . 6615 s . ∞ 520 s . 2 .320 s . s . 2-29 Benzoin (dl-) Benzophenone Benzotrichloride Benzoyl-benzoic acid (o-) -chloride -peroxide Benzyl acetate alcohol amine aniline benzoate butyrate chloride ether formate propionate Berberonic acid (2-,4-,5-) Biuret Borneol (dl-) (d- or l-) (iso-) Bornyl acetate (d-) Bromo-aniline (p-) -benzene -camphor (3-)(d-) -diphenyl (p-) -naphthalene (α-) (β-) -phenol (o-) (m-) (p-) -styrene (ω)(1) (2) -toluene (o-) (m-) (p-) Bromoform Butadiene (1-,2-) (1-,3-) Butadienyl acetylene Butane (i-) Butyl acetate (n-) (s-) (i-) (tert-) alcohol (n-) (s-) (i-) (tert-) amine (n-) (s-) (i-) (t-) p-aminophenol (N)(n) (N)(i-) aniline (n-) (i-) arsonic acid (n-) benzoate (n-) (i-) bromide (n-) (s-) (i-) (t-) butyrate (n-)(n-) (n-)(i-) (i-)(i-) caproate carbamate (i-) cellosolve (n-) diphenyl ketone phenyl chloroform phenyl carbinol ω-amino toluene phenyl-benzylamine ω-chlorotoluene dibenzyl ether allophanamide phenyl bromide α-bromocamphor α-naphthyl bromide β-naphthyl bromide o-tolyl bromide tribromo-methane methyl-allene erythrene diethyl trimethyl-methane butanol-1 butanol-2 2-methyl-propanol-1 2-methyl-propanol-2 1-bromo-butane 2-bromo-butane 1-Br-2-Me-propane 2-Br-2-Me-propane 2-BuO-ethanol-1 C6H5CO⋅CHOHC6H5 C6H5COC6H5 C6H5CCl3 C6H5COC6H4CO2H⋅H2O C6H5COCl (C6H5CO)2O2 CH3CO2CH2C6H5 C6H5CH2OH C6H5CH2NH2 C6H5CH2NHC6H5 C6H5CO2CH2C6H5 C2H5CH2CO2CH2C6H5 C6H5CH2Cl (C6H5CH2)2O HCO2CH2C6H5 C2H5CO2CH2C6H5 C5H2N(CO2H)3⋅2H2O NH(CONH2)2 C10H17OH C10H17OH C10H17OH CH3CO2C10H17 BrC6H4NH2 C6H5Br BrC10H15O BrC6H4⋅C6H5 C10H7Br C10H7Br BrC6H4OH BrC6H4OH BrC6H4OH C6H5CH:CHBr C6H5CH:CHBr CH3⋅C6H4Br CH3⋅C6H4Br CH3⋅C6H4Br CHBr3 CH3CH:C:CH2 CH2:CHCH:CH2 CH2:(CH)2:CH⋅C⋮CH CH3CH2CH2CH3 (CH3)2CHCH3 CH3CO2(CH2)2C2H5 CH3CO2CH(CH3)C2H5 CH3CO2CH2CH(CH3)2 CH3CO2C(CH3)3 C2H5CH2CH2OH C2H5CH(OH)CH3 (CH3)2CHCH2OH (CH3)3COH C2H5CH2CH2NH2 C2H5CH(NH2)CH3 (CH3)2CHCH2NH2 (CH3)3CNH2 C4H9NH⋅C6H4⋅OH C4H9NH⋅C6H4⋅OH C4H9NHC6H5 C4H9NHC6H5 C4H9AsO(OH)2 C6H5CO2C4H9 C6H5CO2C4H9 C2H5CH2CH2Br C2H5CH(Br)CH3 (CH3)2CHCH2Br (CH3)3CBr C2H5CH2CO2CH2CH2C2H5 C2H5CH2CO2CH2CH(CH3)2 (CH3)2CHCO2CH2CH(CH3)2 CH3(CH2)4CO2C4H9 NH2CO2CH2CH(CH3)2 C4H9OCH2CH2OH 212 .24 182 .22 195 .47 244 .24 140 .57 242 .23 150 .17 108 .14 107 .15 183 .25 212 .24 178 .23 126 .58 198 .26 136 .15 164 .20 247 .16 103 .08 154 .25 154 .25 154 .25 196 .29 172 .02 157 .01 231 .13 233 .10 207 .07 207 .07 173 .01 173 .01 173 .01 183 .05 183 .05 171 .03 171 .03 171 .03 252 .73 54 .09 54 .09 78 .11 58 .12 58 .12 116 .16 116 .16 116 .16 116 .16 74 .12 74 .12 74 .12 74 .12 73 .14 73 .14 73 .14 73 .14 165 .23 165 .23 149 .23 149 .23 182 .05 178 .23 178 .23 137 .02 137 .02 137 .02 137 .02 144 .21 144 .21 144 .21 172 .26 117 .15 118 .17 mn. col. rhb. col. lq. tri./aq. col. lq. rhb ./et . col . lq . col . lq . lq . mn . pr . nd . col . lq . col . lq . lq . col . lq . lq . tri . nd ./al . col . cr . col . cr . col . cr . rhb ./pet . rhb . col . lq . cr . cr ./al . col . oil lf ./al . col . lq . cr . tet . cr . lq . lq . col . lq . col . lq . cr ./al . col . lq . lq . col . gas col . lq . col . gas col . gas col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . lq . oil col . lf . col . oil col . oil lq . lq . lq . lq . col . lq . col . lq . col . lq . col . lq . col . lf . col . lq . 1.08354 1.38014 1.21220/4 1 .05717 1 .04320/4 0 .98220/4 1 .065 25/25 1 .1220/4 1 .01616/18 1 .100 20/20 1 .03616 1 .08123 1 .03616/17 20/4 1 .011 1 .01120/4 0 .99115 1 .820 1 .495 20/4 1 .449 20/4 1 .48220/4 1 .605 0 1 .55380 1 .588 80 1 .42220/4 1 .427 20/4 1 .42220/4 1 .410 20/4 1 .390 20/4 2 .890 20/4 0 .62120/4 0 .773 20/4 0 .600 0 .600 0 .882 20 0 .865 25/4 0 .87120/4 0 .866 20/4 0 .810 20/4 0 .808 20/4 0 .80517 .5 0 .779 26 0 .739 25/4 0 .724 20/4 0 .73220/20 0 .69818/4 133–7 48.5 −4.75 93(128) −0.5 108 d . −51 .5 −15 .3 37–8 21 238–40 −39 3 .6 243 192–3 d . 210 .5 208–9 212 29 63–4 −30 .6 77–8 90–1 5–6 59 5 .6 32–3 63 .5 7 −7 .5 −28 −39 .8 28 .5 8–9 −108 .9 −135 −145 −76 .3 −98 .9 −79 .9 −114 .7 −108 25 .5 −50 −104 −85 −67 .5 71 79 0 .940 20/4 1 .005 25/25 0 .997 25/25 1 .277 20/4 1 .25125/4 1 .258 25/4 1 .21120/4 0 .87220/20 0 .86318/4 0 .875 0/4 0 .8820/0 0 .95676/4 0 .90320/4 158–9 −22 −112 .4 −112 −118 .5 −16 .2 −80 .7 65 344768 305.4 220.7 197.2 expl . 213 .5 204 .7 184 .5 306750 323–4 i . 179 .4 295–8 202–3747 220–2 subl . 212–3 226–7 156 .2 274 310 281 .1 281–2 194–5 236–7 238 221 10826 181 .8 183 .7 184–5 150 .5 18–9 −4 .41 83–6 −0 .6 −10 125 740 112744 118 95–6760 117 99 .5 107–8 82 .9 77 .8 66772 68–9 45 .2 235720 231–2 249–50 241 .5 101 .6 91 .3 91 .5 73 .3 165 .7736 156 .9 148–9 204 .3 206–7 171 .2 v. sl. s. i. i. sl. s. d. i . i . 417 ∞ i . i . v . s . i . i . i . i . v . sl . s . 1 .30 v . sl . s . v . sl . s . i . i . i . c . i . i . i . i . i . s . 1 .415 i . i . i . i . i . 0 .1 c . i . i . i . i . i . 0 .7 i . 0 .625 i . 915 12 .520 1015 ∞ ∞ ∞ ∞ i . i . i . 0 .0115 s . i . i . 0 .0616 i . 0 .0618 i . i . i . i . i . i . ∞ s. h. 6.515 s. sl. s. 1513 s. d. h. s . h . ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ s . ∞ ∞ v . s . ∞ s . h . s . sl . s . h . s . ∞ s . ∞ i . v . s . v . s . s . v . s . s . 2026 s . s . 620 s . s . v . s . ∞ ∞ s . s . s . ∞ ∞ ∞ s . v . s . ∞ v . s . 34 25 ∞ v . s . ∞ s . v . s . ∞ ∞ ∞25 s . ∞25 ∞ ∞ ∞ s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ v . s . v . s . s . s . ∞ ∞ v . s . v . s . i . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ s . ∞ (Continued ) 2-30 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name chloride (n-) (s-) (i-) (t-) dimethylbenzene (t-)(1-,3-,5-) formate (n-) (s-) (i-) furoate (n-) iodide (n-) (s-) (i-) (t-) lactate (n-) mercaptan (n-) (i-) (t-) methacrylate (n-) (i-) phenol (p-)(t-) propionate (n-) (s-) (i-) stearate (n-) (i-) iso-thiocyanate (n-) (i-) (s-)(d-) (t-) valerate (n-)(n-) (i-)(n-) (i-)(s-) (i-)(i-) Butylene (α-) (β-) Butyraldehyde (n-) (i-) Butyric acid (n-) (i-) amide (n-) (i-) anhydride (n-) (i-) anilide (n-) Caffeic acid (3-,4-) Caffeine Camphene (dl-) (d- or l-) Camphor (d-) Camphoric acid (d-) Cantharidine Capric acid Caproic acid (n-) (i-) Caprylic acid (n-) Carbazole Carbitol Carbon disulfide monoxide suboxide tetrabromide tetrachloride tetrafluoride Carbonyl sulfide Carminic acid Carvacrol (1-,2-,4-) Synonym 1-chloro-butane 2-chloro-butane 1-Cl2-2-Me-propane 2-Cl2-2-Me-propane 1-iodo-butane 2-iodo-butane 1-iodo-2-Me-propane 2-iodo-2-Me-propane butanthiol-1 2-Me-propanthiol-1 butyl mustard oil iso-Bu mustard oil butene-1 butene-2 2-Me-propanol butanoic acid 2-Me-propanoic acid n-butyramide iso-butyramide n-butyranilide decanoic acid hexanoic acid 2-Me-pentanoic-5 acid octanoic acid diphenylenelimine, dibenzopyrrole diethylene glycol mono-Et ether tetrabromomethane tetrachloromethane tetrafluoromethane Formula C2H5CH2CH2Cl C2H5⋅CHCl⋅CH3 (CH3)2CHCH2Cl (CH3)3CCl (CH3)3C⋅C6H3:(CH3)2 HCO2CH2CH2C2H5 HCO2CH(CH3)C2H5 HCO2CH2CH(CH3)2 OC4H3CO2C4H9 C2H5CH2CH2I C2H5CHICH3 (CH3)2CHCH2I (CH3)3CI CH3CH(OH)CO2C4H9 C2H5CH2CH2SH (CH3)2CHCH2SH (CH3)3CSH CH2:C(CH3)CO2C4H9 CH2:C(CH3)CO2C4H9 (CH3)3C⋅C6H4⋅OH C2H5CO2C4H9 C2H5CO2C4H9 C2H5CO2C4H9 CH3(CH2)16CO2C4H9 CH3(CH2)16CO2C4H9 C2H5CH2CH2⋅N:CS (CH3)2CHCH2⋅N:CS C4H9⋅N:CS (CH3)3C⋅N:CS CH3(CH2)3CO2(CH2)3CH3 (CH3)2CHCH2CO2(CH2)3CH3 (CH3)2CHCH2CO2C4H9 C4H9CO2C4H9 C2H5CH:CH2 CH3CH:CHCH3 CH3CH2CH2CHO (CH3)2CHCHO C2H5CH2CO2H (CH3)2CHCO2H C2H5CH2CONH2 (CH3)2CHCONH2 (C2H5CH2CO)2O [(CH3)2CHCO]2O C3H7CONHC6H5 (HO)2C6H3C2H2CO2H C8H10O2N4⋅H2O C10H16 C10H16 C10H16O C8H14(CO2H)2 C10H12O4 CH3(CH2)8CO2H CH3(CH2)4CO2H (CH3)2CH(CH2)2⋅CO2H CH3(CH2)6CO2H (C6H4)2NH C2H5O(CH2)2O(CH2)2OH CS2 CO OC:C:CO CBr4 CCl4 CF4 COS C22H20O13 CH3C6H3(OH)CH(CH3)2 Formula weight 92 .57 92 .57 92 .57 92 .57 162 .27 102 .13 102 .13 102 .13 168 .19 184 .02 184 .02 184 .02 184 .02 146 .18 90 .19 90 .19 90 .19 142 .20 142 .20 150 .22 130 .18 130 .18 130 .18 340 .58 340 .58 115 .20 115 .20 115 .20 115 .20 158 .24 158 .24 158 .24 158 .24 56 .11 56 .11 72 .11 72 .11 88 .11 88 .11 87 .12 87 .12 158 .19 158 .19 163 .22 180 .16 212 .21 136 .23 136 .23 152 .23 200 .23 196 .20 172 .26 116 .16 116 .16 144 .21 167 .21 134 .17 76 .14 28 .01 68 .03 331 .63 153 .82 88 .00 60 .08 492 .39 150 .22 Form and color Specific gravity Melting point, °C Boiling point, °C col. lq. col . lq . col . lq . col . lq . col . lq . lq . lq . lq . col . lq . lq . lq . lq . lq . col . lq . col . lq . lq . lq . lq . lq . nd ./aq . col . lq . col . lq . col . lq . col . lq . wax lq . lq . lq . lq . lq . lq . col . lq . col . lq . col . gas col . gas col . lq . col . lq . col . lq . col . lq . rhb . mn . pl . col . lq . col . lq . mn . pr . yel ./aq . nd ./al . cr . cr . trig . mn . cr . col . nd . oily lq . col . oil col . lf . lf . col . lq . col . lq . col . gas gas col . mn . col . lq . gas col . gas red pd . col . lq . 0.887 20 0 .87120/4 0 .88415 0 .84715 −123.1 −131 −131 .2 −26 .5 77.9763 67 .8767 68 .9 51–2 200–2147 106 .9 97 98 .2 118–2025 129 .9 118–9 120 99 75–66 97–8 88 65–7 155 155 236–8 146 132 .5 136 .8 220–525 0 .9110 0 .88220/4 0 .885 20/4 1 .056 20/4 1 .617 20/4 1 .595 20 1 .606 20/4 1 .370 19/15 0 .968 0 .837 25/4 0 .836 20/4 0 .889 15 .6 0 .889 15 .6 0 .908 112/4 0 .88315 0 .866 20/4 0 .888 0/4 0 .855 25/25 0 .95611 0 .96414/4 0 .943 20/4 0 .91910 0 .87015/4 0 .862 25/4 0 .848 20/4 0 .8740/4 0 .69 20/4 0 .817 0 .79420/4 0 .96420/4 0 .949 20/4 1 .032 1 .013 0 .968 20/20 0 .950 25/4 1 .134 1 .2319 0 .82278 0 .845 50/4 0 .999 9/9 1 .186 0 .889 87 0 .922 20/4 0 .925 20/4 0 .910 20/4 0 .990 20/20 1 .263 20/4 0 .81−195/4 1 .1140 3 .42 1 .595 20/4 1 .24−87 0 .977 20/4 −95 .3 −103 .5 −104 −90 .7 −34 −116 <−79 99 −89 .55 −71 .4 27 .5 25 10 .5 −93 −130 −127 −99 −65 .9 −4 .7 −47 115–6 129–30 −75 −53 .5 92 195–213 237 50 42 .7 178–9 187 212 31 .5 −1 .5 −35 16 244 .8 −108 .6 −207 −107 90 .1(48) −22 .6 −138 .2 d . 136 0 .5 165724 162 159–63 140770 186 168 .8 163–4752 168 .7 −5758 3746 75 .7 64757 163 .5757 154 .5 216 216–20 199 .5 181 .5734 18915 d . subl . 160 159 .6 209 .1759 268–70 202761 207 .7 237 .5 354 .8 201 .9 46 .3 −192 7761 189 .5 76 .8 −128 −50 .2760 238 Solubility in 100 parts Water 0.0718 i . i . i . i . v . sl . s . sl . s . 1 .122 i . i . i . i . i . sl . s . sl . s . v . sl . s . i . i . sl . s . i . i . i . 0 .3 25 i . i . i . i . i . v . sl . s . i . i . i . i . 4 1120 ∞ 20 20 16 .315 v . s . d . d . i . s . h . 2 i . i . 0 .1 0 .612 0 .003 0 .003 1 .120 v . sl . s . 0 .0715 i . ∞ 0 .20 3 .50 cc . d . 0 .0230 0 .0820 sl . s . 8014 cc . s . v . sl . s . Alcohol Ether ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ v . s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ v . s . s . s . ∞ ∞ ∞ s . s . ∞ ∞ ∞ s . s . s . s . s . ∞ ∞ ∞ ∞ v . s . s . s . s . s . ∞ ∞ ∞ ∞ v . s . ∞ ∞ ∞ ∞ s . s . d d s . s . 2 s . s . 12012 s . ∞ ∞ ∞ ∞ sl . s . sl . s . ∞ ∞ s . sl . s . 0 .3 s . s . v . s . s . s . s . s . 0 .9214 v . s . ∞ s . s . s . s . s . sl . s . s . ∞ s . ∞ s . s . ∞ s . s . ∞ s . v . sl . s . ∞ 2-31 Carvacrylamine (2-,1-,4-) Carvone (d-) Cellosolve acetate Cellulose Cetyl acetate alcohol Chloral hydrate Chloranil Chloretone Chloro-acetanilide (p-) -acetic acid -acetone -acetophenone (ω-) -acetyl chloride -aniline (o-) (m-) (p-) -anthraquinone (1-) (2-) -benzaldehyde (o-) (m-) (p-) -benzene -benzoic acid (o-) (m-) (p-) -buta-1,3-diene (2-) (1-) -buta-1,2-diene (4-) -dimethylhydantoin -dinitrobenzene (α)(1-,2-)(4-) (α)(1-,3-)(4-) -diphenyl (o-) (m-) (p-) -hydroquinone -naphthalene (α-) (β-) -nitrobenzene (o-) (m-) (p-) -nitrotoluene (2-,4-) (2-,6-) -phenol (o-) (m-) (p-) -propionic acid (α)(dl-) -toluene (o-) (m-) (p-) Chloroform Chlorophyll (α-) Chloropicrin Cholesterol Chrysene Chrysoidine (2-,4-) Chrysophanic acid Cinchomeronic acid (3-,4-) Cineole, eucalyptole Cinnamic acid (cis-) (trans-) aldehyde Cinnamyl alcohol cinnamate Citraconic acid (cis-) Citral (α) Citric acid Citronellal (d-) Citronellol (d-) Coniine (d-)(2-) H2NC6H3(CH3)C3H7 C10H14O C2H5O(CH2)2OH CH3CO2CH2CH2OC2H5 (C6H10O5)x CH3CO2(CH2)15CH3 CH3(CH2)14CH2OH CCl3⋅CHO CCl3⋅CH(OH)2 OC:(CCl⋅CCl)2:CO Cl3C⋅C(OH)(CH3)2 CH3CONHC6H4CI ClCH2CO2H CH3COCH2Cl C6H5COCH2Cl ClCH2COCl ClC6H4NH2 ClC6H4NH2 ClC6H4NH2 C6H4(CO)2C6H3Cl C6H4(CO)2C6H3Cl ClC6H4CHO ClC6H4CHO ClC6H4CHO C6H5Cl ClC6H4CO2H ClC6H4CO2H ClC6H4CO2H CH2:CCl⋅CH:CH2 CH2:CH⋅CH:CHCl CH2:C:CH⋅CH2Cl —C(CH3)2N(Cl)CON(Cl)CO— ClC6H3(NO2)2 ClC6H3(NO2)2 C6H5⋅C6H4Cl C6H5⋅C6H4Cl C6H5⋅C6H4Cl ClC6H3(OH)2 C10H7Cl C10H7Cl ClC6H4NO2 ClC6H4NO2 ClC6H4NO2 CH3C6H3(NO2)(Cl) CH3C6H3(NO2)(Cl) ClC6H4OH ClC6H4OH ClC6H4OH CH3⋅CHCl⋅CO2H CH3⋅C6H4Cl CH3⋅C6H4Cl CH3⋅C6H4Cl CHCl3 C55H72O5N4Mg Cl3CNO2 C27H45OH⋅H2O C18H12 C6H5⋅N:N⋅C6H3(NH2)2 C14H5(OH)2(CH3)O2 C5H3N(CO2H)2 C10H18O C6H5CH:CHCO2H C6H5CH:CHCO2H C6H5CH:CHCHO C6H5CH:CHCH2OH C8H7CO2C9H9 CH3C(CO2H):CHCO2H C9H15CHO C3H4(OH)(CO2H)3 C9H17⋅CHO C10H20O C3H7⋅C5H10N 149 .23 150 .22 90 .12 132 .16 162 .14 284 .48 242 .44 147 .39 165 .40 245 .88 177 .46 169 .61 94 .50 92 .52 154 .59 112 .94 127 .57 127 .57 127 .57 242 .66 242 .66 140 .57 140 .57 140 .57 112 .56 156 .57 156 .57 156 .57 88 .54 88 .54 88 .54 197 .02 202 .55 202 .55 188 .65 188 .65 188 .65 144 .56 162 .62 162 .62 157 .55 157 .55 157 .55 171 .58 171 .58 128 .56 128 .56 128 .56 108 .52 126 .58 126 .58 126 .58 119 .38 893 .49 164 .38 404 .67 228 .29 212 .25 254 .24 167 .12 154 .25 148 .16 148 .16 132 .16 134 .18 264 .32 130 .10 152 .23 192 .12 154 .25 156 .27 127 .23 oil col. lq. col . lq . col . lq . amor . nd . lf . col . lq . mn . pr . yel ./bz . col . cr . rhb . col . cr . col . lq . rhb . col . lq . lq . lq . rhb . yel . nd . nd ./al . nd . pr . pr . col . lq . mn ./aq . pr . tri . col . lq . col . lq . col . lq . cr ./et . rhb ./et . cr . cr . lf . mn . col . lq . lf ./al . mn . nd . yel ./al . mn . pr . cr . cr . col . lq . nd . nd . col . lq . col . lq . col . lq . col . lq . col . lq . lq . rhb ./al . col . rhb . yel . cr . yel ./al . cr ./HCl col . oil mn . pr . mn . pr . lq . nd . nd . or pr . nd . col . oil cr . col . oil col . oil col . lq . 0.99420 0.96120/4 0 .93120/4 0 .975 20/4 1 .3–1 .4 0 .858 20 0 .818 50/4 1 .505 25/4 1 .619 50/4 1 .385 22 1 .58 20/20 1 .16216 1 .32415 1 .498 20/20 1 .21320/4 1 .216 20/4 1 .42719 1 .298 1 .25015 1 .196 61 1 .107 20/4 1 .544 25/4 1 .496 25/4 1 .54124 0 .958 20/20 0 .965 20/20 0 .99120/20 1 .5 20/20 1 .697 22 1 .194 20/4 1 .26616 1 .305 80/4 1 .34350/4 1 .298 91 1 .256 80 1 .24118/15 1 .268 25 1 .306 20/4 1 .306 9 1 .082 20/4 1 .07220/4 1 .070 20/4 1 .489 20 1 .65123/4 1 .067 20 0 .927 1 .2844 1 .245 1 .110 20/20 1 .040 35/35 1 .08516 .5 1 .617 0 .89017/4 1 .54220/4 0 .85517 .5 0 .84820/4 0 .84717 −16 −70 22–3 49–50 −57 51 .7 290 97 175–6 61 .2 −44 .5 58–9 0 −10 .4 70–1 162 208–9 11 17–8 47 .8 −45 .2 141–2 158 242–3 130 39(36) 53(43) 34 89 77 .5 106 −20 56–7 32 .5 44 .4(24) 83–4 38 .2 37 .5 7(0) 32–3 41–3 <−20 −34 −47 .8 7 .5 −63 .5 d . −64 149–51 253–4 117 .5 195 258–9 d . 1 .5 68 133 −7 .5 33 44 92–3 153 −2 241 230766 135 .1 156 .3 i . 20015 189 .515 97 .6768 d . 98 subl . 167 189 .5 121 245–7 105 210 .5 230767 230–1 subl . 208748 213–4 213748 132 .1 subl . 59 .4 69 88 315 d . 315 d . 267–8 284–5 282 263 sl . d . 259 .3 264751 245 .5753 235 .6 242761 240718 238 175–6 214 217 186 159 .5 161 .6 162 .2 61 .2 i . 112 .3766 subl . 448 subl . subl . d . 176–7 12519 300 252 sl . d . 257 .5 229 d . 204–8 224–5 166–7 v. sl. s. i. ∞ 22 i . i . i . v . s . 47417 i . 0 .8 c . sl . s . v . s . ∞ 0 .11 d . i . i . s . h . i . i . v . sl . s . v . sl . s . s . h . 0 .049 20 0 .20825 0 .04125 0 .00825 v . sl . s . v . sl . s . d . 0 .2125 i . i . i . i . i . v . s . i . i . i . i . i . i . i . 2 .8520 2 .6020 2 .7120 ∞ i . i . i . 0 .8220 s . 0 .1718 0 .2620 i . sl . s . h . i . c . v . sl . s . 1 .915 0 .0418 v . sl . s . sl . s . i . 36025 i . 207 .725 v . sl . s . v . sl . s . 1 .1 s. ∞ ∞ ∞ i . v . sl . s . c . s . ∞ v . s . i . c . 111 s . s . ∞ v . s . d . s . sl . s . h . s. ∞ ∞ ∞ s . ∞ s . i . c . s . v . s . s . ∞ v . s . s . s . s . v . s . v . s . v . s . ∞ s . s . s . ∞ ∞ v . s . v . s . v . s . ∞ s . s . s . ∞ ∞ v . s . h . s . h . v . s . s . v . s . s . v . s . s . h . v . s . h . v . s . h . v . s . ∞ v . s . s . v . s . v . s . s . s . v . s . ∞ s . s . s . ∞ s . s . v . s . ∞ ∞ ∞ ∞ ∞ s . 1 .117 0 .116 s . s . h . sl . s . ∞ s . 18 v . sl . s . s . sl . s . i . ∞ 2420 s . v . s . 4 c . s . ∞ 7615 ∞ ∞ v . s . v . s . ∞ v . s . 33 s . ∞ 215 ∞ ∞ v . s . (Continued ) 2-32 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Coumaric acid (o-) (p-) Coumarin Coumarone Creatine Creatinine Creosol (3-,1-,4-) Cresidine (1-,2-,4-) Cresol (o-) (m-) (p-) Cresyl benzoate (o-) (m-) (p-) Crotonic acid (α-) acid (β-)(cis-) aldehyde (α) Cumene Cumic acid (p-) Cumidine (p-) Cyanamide Cyanic acid Cyanoacetic acid Cyanogen bromide chloride Cyanuric acid Cyclo-butane -heptane -hexane -hexanol -hexanone -hexene -hexyl acetate amine bromide chloride -pentadiene (1-,3-) -pentane -pentanone -propane Cymene (o-) (m-) (p-) Cystine (l-) Dambose Decahydronaphthalene (cis-) (trans-) Decane (n-) Decyl alcohol Dextrin Diacetone alcohol Diamino-benzophenone (4-,4′-) -diphenylamine (4-,4′-) -diphenylmethane (4-,4′-) -diphenylurea (4-,4′-) Diamyl-amine (i-) ether (n-) (i-) Diamyl ketone (i-) phthalate (n-) (i-) tartrate (i-) Dianisidine (o-)(4-,3-)2 Diazo-aminobenzene -aminotoluene (2-,2′-) -methane Formula HOC6H4CH:CHCO2H HOC6H4CH:CHCO2H C9H6O2 C8H6O C4H9N3O2⋅H2O C4H7N3O CH3O⋅C6H3(CH3)OH CH3(NH2)C6H3⋅OCH3 CH3C6H4OH CH3C6H4OH CH3C6H4OH C6H5CO2C6H4CH3 C6H5CO2C6H4CH3 C6H5CO2C6H4CH3 CH3CH:CHCO2H CH3CH:CHCO2H CH3CH:CHCHO C6H5CH(CH3)2 (CH3)2CH⋅C6H4CO2H (CH3)2CH⋅C6H4NH2 H2N⋅CN HOCN or HNCO CH2(CN)CO2H (CN)2 BrCN ClCN C3H3O3N3⋅2H2O CH2 < (CH2)2 > CH2 CH2 < (CH2CH2CH2)2 > CH2 < (CH2CH2)2 > CH2 CH2 < (CH2CH2)2 > CHOH CH2 < (CH2CH2)2 > CO (⋅CH2⋅CH2CH:)2 CH3CO2C6H11 CH2 < (CH2CH2)2 > CHNH2 CH2 < (CH2CH2)2 > CHBr CH2 < (CH2CH2)2 > CHCl CH2 < (CH:CH)2 > CH2 < (CH2CH2)2 > < (CH2CH2)2 > CO < CH2CH2CH2 > CH3⋅C6H4CH(CH3)2 CH3⋅C6H4CH(CH3)2 CH3⋅C6H4CH(CH3)2 [⋅SCH2CH(NH2)CO2H]2 C6H6(OH)6 C10H18 C10H18 CH3(CH2)8CH3 CH3(CH2)8CH2OH (C6H10O5)x (CH3)2C(OH)⋅CH2COCH3 H2NC6H4COC6H4NH2 H2NC6H4NHC6H4NH2 H2NC6H4CH2C6H4NH2 (H2NC6H4NH)2CO [(CH3)2CHCH2CH2]2NH (C2H5CH2CH2CH2)2O [(CH3)2CH(CH2)2]2O [(CH3)2CHCH2CH2]2CO C6H4(CO2C5H11)2 C6H4(CO2C5H11)2 (HOCH⋅CO2C5H11)2 [NH2(OCH3)C6H3⋅]2 C6H5N:N⋅NHC6H5 C7H7N:N⋅NHC7H7 CH2:N2 Formula weight 164 .16 164 .16 146 .14 118 .13 149 .15 113 .12 138 .16 137 .18 108 .14 108 .14 108 .14 212 .24 212 .24 212 .24 86 .09 86 .09 70 .09 120 .19 164 .20 135 .21 42 .04 43 .02 85 .06 52 .03 105 .92 61 .47 165 .10 56 .11 98 .19 84 .16 100 .16 98 .14 82 .14 142 .20 99 .17 163 .06 118 .60 66 .10 70 .13 84 .12 42 .08 134 .22 134 .22 134 .22 240 .30 180 .16 138 .25 138 .25 142 .28 158 .28 162 .14 116 .16 212 .25 199 .25 198 .26 242 .28 157 .30 158 .28 158 .28 170 .29 306 .40 306 .40 290 .35 244 .29 197 .24 225 .29 42 .04 Form and color nd./aq. cr./aq. rhb./et. oil mn./aq. mn. pr. nd ./pet . cr . lq . pr . lq . cr . cr . col . mn . nd . col . lq . col . lq . tri . lq . col . nd . gas col . lq . col . gas nd . gas mn ./aq . col . gas oil col . lq . col . nd . col . oil lq . oil col . lq . col . lq . col . lq . col . lq . col . oil col . oil col . gas col . lq . col . lq . col . lq . pl . mn ./aq . lq . lq . col . lq . col . oil amor . lq . yel . nd . lf ./aq . nd ./aq . cr . col . lq . col . lq . col . lq . yel . oil col . lq . col . lq . lq . col . lf . yel . lf . or . cr . gas Specific gravity 0.93520/4 1.07815/15 1.09220/20 20/4 1 .048 1 .03420/4 1 .03520/4 79 .7 0 .964 1 .03115/4 0 .85320/20 0 .86220/4 1 .1624 0 .953 1 .07348/4 1 .1400 0 .86617 2 .01520/4 1 .2220 1 .7680/4 0 .7030/4 0 .81020/4 0 .77920/4 0 .96220/4 0 .94719/4 0 .81020/4 0 .9850/4 0 .86520/0 1 .32420/20 0 .97718/4 0 .80519/4 0 .74520/4 0 .94820 0 .720−79 0 .87520/4 0 .86220 0 .85720/4 1 .752 0 .89518/4 0 .87220/4 0 .7302 0 .83020/4 1 .038 0 .93125 0 .76721/4 0 .77420/4 0 .77720/4 0 .82125/4 Melting point, °C Boiling point, °C 207–8 206–7 d. 70 <−18 295 260 d. 5.5 93–4 30 .8 10 .9 35–6 subl. 55 71 .5 72 15 .5 −69 −96 .9 116–7 <−20 44–5 −80 65–6 −34 .4 52 −6 .5 >360 −50 −12 6 .5 23 .9 −45 −103 .7 −43 .9 −85 −93 .3 −58 .2 −126 .6 <−25 −73 .5 d . 258–61 253 −51 −32 −29 .7 7 −47 237–9 158 93–4 subl . 310 −44 −69 14 .6 1 .03 1 .06315/4 131 .5 96–8 51 −145 290–1 173–4 221–2765 235 190 .8 202 .8 202 308 314 316 189 170–1 d . 102 .2 152 .5 subl . 225761 14019 −640 1080 .2 −21 61 .3750 12 .5–13 d . 11–12726 118–20 80–1 160–1 155–6 83 .3 174750 134 165714 142 41–2 49–50 129–30 −34749 177 175–6 176–7 31915 193 .3 185 .3 174 .0 232 .9 167 .9 d . 249–5315 188–90 190 173 .4 228 204–611 22540 19516 expl . −23 Solubility in 100 parts Water sl. s. c. s. h. 0.3 c. i. 1.418 8.716 v. sl. s. v . sl . s . 2 .5 0 .5 1 .8 i . i . i . 8 .315 ∞25 18 i . 0 .0225 i . v . s . sl . s . s . 45020 cc . s . 250020 cc . 0 .2717 i . i . i . 3 .620 s . v . sl . s . i . i . i . i . i . i . v . sl . s . i . i . i . i . 0 .0119 212 i . i . i . i . s . ∞ sl . s . h . sl . s . sl . s . c . v . sl . s . sl . s . i . i . i . i . i . i . i . 0 .05 d . Alcohol Ether s. v. s. h. v. s. v. sl. s. v. s. s. s. i. 0.0117 116 ∞ s . ∞30 ∞ ∞36 s . ∞ ∞ s . v . s . s . 230020 cc . s . v . s . 0 .122 v . s . ∞ s . s . v . s . ∞ s . s . ∞ s . s . s . s . i . i . s . s . ∞ s . i . ∞ s . s . s . ∞ s . ∞30 ∞ ∞36 ∞ ∞ s . v . s . s . s . 50020 cc . s . 500020 cc . ∞ s . s . v . s . ∞ s . ∞ ∞ s . s . s . s . i . s . s . ∞ i . ∞ s . s . s . s . ∞ ∞ s . ∞ ∞ ∞ s . s . s . s . s . h . s . v . s . s . 2-33 Dibenzothiazyl-disulfide (2-,2′-) Dibensoyl methane Dibensyl-amine -aniline ketone phthalate (o-) succinate Dibromo-benzene (o-) (m-) (p-) -diphenyl (4-,4′-) Dibutyl-adipate (n-) (i-) -amine (n-) (i-) -p-aminophenol (s-) -aniline (n-) carbonate (n-) (i-) (s-) ether (n-) (i-) (s-) ketone (n-) (i-) malate (l-)(n-) oxalate (n-) phthalate (n-) tartrate (d-)(n-) (d-)(i-) Dichloro-acetic acid -acetone (αα-) -aniline (2-,5-) -anthraquinone (1-,3-) (1-,4-) (1-,5-) (1-,6-) (1-,8-) (2-,3-) (2-,6-) (2-,7-) -benzene (o-) (m-) (p-) -butane (n-)(1-,4-) -diphenyl (4-,4′-) -ethane (1-,2-) -naphthalene (β-)(1-,4-) (γ-)(1-,5-) -nitrobenzene (2-,5-) -pentane (1-,5-) -phenol (2-,4-) Dichloramine T (p-) Dicyandiamide Diethanolamine Diethyl adipate -amine -aminophenol (m-) -aniline sulfonic acid (m-) carbonate diethyl malonate Diethyl dimethyl malonate glutarate ketone malonate -malonic acid -naphthylamine (α-) (β-) oxalate phthalate (o-) sulfate sulfide (C6H4NSC)2S2 (C6H5CO)2CH2 (C6H5CH2)2NH C6H5N(CH2C6H5)2 (C6H5CH2)2CO C6H4(CO2CH2C6H5)2 (⋅CH2CO2CH2C6H5)2 C6H4Br2 C6H4Br2 C6H4Br2 BrC6H4⋅C6H4Br (⋅CH2CH2CO2C4H9)2 (⋅CH2CH2CO2C4H9)2 (C2H5CH2CH2)2NH [(CH3)2CHCH2]2NH (C4H9)2N⋅C6H4OH C6H5N(C4H9)2 CO(OC4H9)2 CO(OC4H9)2 CO(OC4H9)2 (C2H5CH2CH2)2O [(CH3)2CHCH2]2O [C2H5(CH3)CH]2O (C2H5CH2CH2)2CO [(CH3)2CHCH2]2CO C2H4O(CO2C4H9)2 (⋅CO2C4H9)2 C6H4(CO2C4H9)2 (CHOHCO2C4H9)2 (CHOHCO2C4H9)2 Cl2CH⋅CO2H Cl2CHCOCH3 Cl2C6H3NH2 C6H4:(CO)2:C6H2Cl2 C6H4:(CO)2:C6H2Cl2 C6H3Cl:(CO)2:C6H3Cl C6H3Cl:(CO)2:C6H3Cl C6H3Cl:(CO)2:C6H3Cl C6H4:(CO)2:C6H2Cl2 C6H3Cl:(CO)2:C6H3Cl C6H3Cl:(CO)2:C6H3Cl C6H4Cl2 C6H4Cl2 C6H4Cl2 ClCH2(CH2)2CH2Cl ClC6H4⋅C6H4Cl ClCH2⋅CH2Cl C10H6Cl2 C10H6Cl2 Cl2C6H3NO2 ClCH2(CH2)3CH2Cl Cl2C6H3OH CH3C6H4SO2NCl2 H2N⋅C(:NH)⋅NH⋅CN HN(CH2CH2OH)2 (⋅CH2CH2CO2C2H5)2 (C2H5)2NH (C2H5)2N⋅C6H4⋅OH (C2H5)2NC6H5 (C2H5)2NC6H4SO3H OC(OC2H5)2 (C2H5)2C(CO2C2H5)2 (CH3)2C(CO2C2H5)2 CH2(CH2CO2C2H5)2 (C2H5)2CO CH2(CO2C2H5)2 (C2H5)2C(CO2H)2 C10H7N(C2H5)2 C10H7N(C2H5)2 (⋅CO2C2H5)2 C6H4(CO2C2H5)2 O2S(OC2H5)2 (C2H5)2S 332 .49 224 .25 197 .28 273 .37 210 .27 346 .38 298 .33 235 .90 235 .90 235 .90 312 .00 258 .35 258 .35 129 .24 129 .24 221 .34 205 .34 174 .24 174 .24 174 .24 130 .23 130 .23 130 .23 142 .24 142 .24 246 .30 202 .25 278 .34 262 .30 262 .30 128 .94 126 .97 162 .02 277 .10 277 .10 277 .10 277 .10 277 .10 277 .10 277 .10 277 .10 147 .00 147 .00 147 .00 127 .01 223 .10 98 .96 197 .06 197 .06 192 .00 141 .04 163 .00 240 .11 84 .08 105 .14 202 .25 73 .14 165 .23 149 .23 229 .30 118 .13 216 .27 188 .22 188 .22 86 .13 160 .17 160 .17 199 .29 199 .29 146 .14 222 .24 154 .18 90 .19 cr. rhb./al. col. oil pr./al. cr. pr./al. lf./al. col. lq. col. lq. pl./al. mn. pr. col. lq. col . lq . col . lq . col . lq . lq . lq . col . lq . col . lq . col . lq . lq . lq . lq . lq . oil lq . col . lq . col . lq . pr . cr . lq . lq . nd . yel . nd . yel . nd . yel . nd . yel . nd . yel . nd . yel . nd . yel . nd . yel . nd . col . lq . col . lq . col . mn . lq . pr . col . lq . nd ./al . lf ./al . tri ./al . col . lq . nd . cr . mn . pl . pr . col . lq . col . lq . rhb . oil cr . col . lq . col . lq . col . lq . syrup col . lq . col . lq . pr ./aq . col . oil col . oil col . lq . col . lq . col . lq . col . lq . 1.50 1.028 25/25 1.956 20/4 1.952 20/4 2.26118 1.897 0.965 20/4 0 .950 25 0 .768 20/20 0 .74125/4 180 78 −26 70–1 34–5 42–3 45–6 1.8 −6.9 87–8 164–5 −38 −20 −70 0 .924 20/4 0 .91915 0 .769 20/20 0 .76215 0 .756 21 0 .82718/4 0 .805 21/4 1 .038 20/4 0 .986 20/4 1 .045 21 1 .09815 1 .03175/4 1 .560 25/25 1 .23415 1 .305 20/4 1 .288 20/4 1 .458 21 1 .442 0/4 1 .256 20/20 1 .300 76/4 1 .669 22 1 .094 25/4 1 .383 60/25 1 .4014 1 .09720/4 1 .00920/4 0 .712 15/15 0 .934 20/4 0 .975 20/4 0 .985 20/4 0 .994 25/25 1 .025 21 0 .816 19/4 1 .055 20/4 1 .005 1 .026 1 .079 20/4 1 .121 25/25 1 .172 25/4 0 .837 20/4 −98 −5 .9 −29 .6 22–2 .5 73–4 9 .7(−4) 50 208–9 187 .5 251 203–4 202–3 268–70 282 210–11 −17 .6 −24 .8 53 −38 .7 148 −35 .3 67–8 107 54 .6 45 83 207–8 28 −21 −38 .9 78 −34 .4 270 d . −43 −24 −42 −49 .8 125 −40 .6 −25 −99 .5 d. 219–2118 268–71250 >300 330.6 27412 23814 221–2 219755 218.6758 355–60 18314 278–80 159761 139–40 17010 262 .8 207740 190 178–80 142 .4 122 .5 121 187 .7 168 .1 170–118 245 .5 340 200–318 323–5 194 .4 120 251 179 172766 174764 161–3 315–9 83 .7 286–7 740 subl . 266 180–1 209–10 d . 270 748 239–41761 55 .5759 276–80 216 126759 230 196 .7 237 101 .7 198 .9 d . 170–80 285–90 318 186 298–9 210 92–3 754 i. i. i. i. i. v. sl. s. i. i. i. i. i. i. i . ∞ v . sl . s . i . i . i . i . <0 .05 i . i . i . <0 .06 v . sl . s . i . 0 .04 25 i . v . sl . s . ∞ v . sl . s . v . sl . s . i . i . i . i . i . i . i . i . i . i . i . i . 0 .90 i . i . i . i . 0 .45 20 sl . s . 2 .318 ∞ 0 .4380 v . s . s . 1 .412 s . i . i . i . 0 .88 20 4 .7 20 2 .08 20 65 16 i . i . v . sl . s . i . i . 0 .3120 4.420 s. v. s. h. s. s. s. s. s. s. s. 1.6 v. sl. s. h. ∞ s. s. s. s. 7125 ∞ s . ∞ s . ∞ s . ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ v . s . ∞ s . ∞ s . ∞ ∞ s . s . i . v . sl . s . sl . s . ∞ s . s . ∞ v . sl . s . sl . s . sl . s . ∞ s . v . s . ∞ s . v . s . v . sl . s . ∞ v . sl . s . s . v . s . h . s . v . s . 425 ∞ s . v . s . 1 .318 ∞ s . ∞ 0 .0118 v . sl . s . s . ∞ s . s . ∞ ∞ ∞ v . s . ∞ ∞ v . s . ∞ ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ s . ∞ ∞ v . s . ∞ ∞ ∞ ∞ ∞ ∞ s . (Continued ) 2-34 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name tartrate (d-) -toluidine (o-) (m-) (p-) Diethyleneglycol dinitrate Difluorodichloromethane Diglycerol Dihydroxy-dinaphthyl (α-) (-2,-2′,-1,-1′) -diphenyl (4-,4′-) -ethyl formal (β-) -naphthalene (1-,5-) (1-,8-) Dimethoxy-benzene (p-) -diphenylamine (4-,4′-) -ethyl adipate Dimethyl adipate -amine -aminoasobenzene (p-) -aminoethanol -aminophenol (m-) -aniline sulfonic acid (m-) (p-) carbonate ether -formamide fumarate glutarate glyoxime -naphthalene (1-,4-) (2-,3-) -naphthylamine (α-) (β-) oxalate phthalate (o-) sulfate sulfide tartrate (d-) -vinyl-ethenyl carbinol Dinaphthyl (αα-) -methane (αα′-) (β,β′-) Dinitro-anisole (1-)(2-,4-) -benzene (o-) (m-) (p-) sulfonic acid (2-,4-)(1-) -benzoic acid (2-,4-) (3-,5-) -benzophenone (4-,4′-) -diphenyl (4-,4′-) (2-,4′-) -naphthalene (1-,5-) (1-,8-) Dinitro-phenol (2-,3-) (2-,4-) (2-,6-) -salicylic acid (3-,5-) -stilbene (4-,4′-) -toluene (2-,4-) (3-,4-) (3-,5-) Dioxane Dipentene Formula (CHOH⋅CO2C2H5)2 CH3⋅C6H4⋅N(C2H5)2 CH3⋅C6H4⋅N(C2H5)2 CH3⋅C6H4⋅N(C2H5)2 O(CH2CH2ONO2)2 F2CCl2 [(HO)2C3H5]2O (HO⋅C10H6⋅)2 (HO⋅C10H6⋅)2 (HO⋅C6H4⋅)2 CH2(OCH2CH2OH)2 C10H6(OH)2 C10H6(OH)2 (CH3O)2C6H4 HN(C6H4OCH3)2 (CH2)4(CO2C2H4OCH3)2 [(CH2)2CO2CH3]2 (CH3)2NH C6H5N:N⋅C6H4N(CH3)2 (CH3)2NCH2CH2OH (CH3)2NC6H4OH (CH3)2NC6H5 (CH3)2NC6H4SO3H (CH3)2NC6H4SO3H⋅H2O OC(OCH3)2 CH3OCH3 HCON(CH3)2 (:CHCO2CH3)2 (CH2)3(CO2CH3)2 (CH3⋅C:NOH)2 C10H6(CH3)2 C10H6(CH3)2 C10H7N(CH3)2 C10H7N(CH3)2 (⋅CO2CH3)2 C6H4(CO2CH3)2 (CH3O)2SO2 (CH3)2S (CHOH⋅CO2CH3)2 (CH3)2COH⋅C⋮C⋅CH:CH2 C10H7⋅C10H7 (C10H7)2CH2 (C10H7)2CH2 CH3OC6H3(NO2)2 C6H4(NO2)2 C6H4(NO2)2 C6H4(NO2)2 (NO2)2C6H3SO3H⋅3H2O (NO2)2C6H3CO2H (NO2)2C6H3CO2H (NO2C6H4)2CO (NO2C6H4)2 (NO2C6H4)2 C10H6(NO2)2 C10H6(NO2)2 (NO2)2C6H3OH (NO2)2C6H3OH (NO2)2C6H3OH (NO2)2C6H2(OH)CO2H⋅H2O (NO2C6H4CH:)2 (NO2)2C6H3CH3 (NO2)2C6H3CH3 (NO2)2C6H3CH3 O < (CH2⋅CH2)2 > O C10H16 Formula weight 206 .19 163 .26 163 .26 163 .26 196 .12 120 .91 166 .17 286 .32 286 .32 186 .21 136 .15 160 .17 160 .17 138 .16 229 .27 262 .30 174 .19 45 .08 225 .29 89 .14 137 .18 121 .18 201 .24 219 .26 90 .08 46 .07 73 .09 144 .13 160 .17 116 .12 156 .22 156 .22 171 .24 171 .24 118 .09 194 .18 126 .13 62 .13 178 .14 110 .15 254 .33 268 .35 268 .35 198 .13 168 .11 168 .11 168 .11 302 .22 212 .12 212 .12 272 .21 244 .20 244 .20 218 .17 218 .17 184 .11 184 .11 184 .11 246 .13 270 .24 182 .13 182 .13 182 .13 88 .11 136 .23 Form and color Specific gravity Melting point, °C Boiling point, °C lq. lq . lq . lq . lq . gas lq . pl ./al . nd ./al . rhb ./al . lq . pr ./aq . nd . lf . cr . lq . col . lq . col . lq . yel ./al . col . lq . nd . yel . lq . cr . pr . col . lq . gas lq . col . tri . lq . col . cr . lq . lf ./al . col . oil col . cr . col . mn . col . lq . col . oil oil cr . lq . lf ./al . pr ./al . nd ./al . col . mn . col . mn . col . rhb . col . mn . pr . cr ./aq . mn . pr . col . nd . nd ./al . mn . nd . rhb . yel . mn . yel . rhb . yel . rhb . pl ./aq . yel . lf . nd . nd . mn . pr . col . lq . col . lq . 1.204 20/4 17 0 .924 15 .5 1 .377 25/4 1 .486 −30 280 208–9755 231–2 228–9 −11 .3 −155 1 .25 1 .154 25 1 .053 55/55 1 .075 15 .6 1 .063 20/4 0 .680 0/4 0 .887 20/4 0 .956 20/4 1 .070 20/4 0 .94525 1 .08915 .6 1 .016 20/4 1 .042 20 1 .03970/70 1 .14854 1 .18925/25 1 .3520/4 0 .84621/4 1 .32820/4 0 .887 20/4 1 .341 20 1 .5918 1 .575 20/4 1 .625 18 1 .445 1 .474 1 .681 20 1 .683 24 1 .321 71 1 .259 111 1 .277 111 1 .033 20/4 0 .865 18 300 218 270–2 −5 .3 258–60 140 56 103 10–1 −96 116–7 85 2 .5 d . 266 257 0 .5 −138 .5 −58 .3 102 −37 240–6 <−18 104 46 54 −26 .8 −83 .2 61 .5 160 109 92 94–5 117–8 89 .8 173–4 106–8 179–80 204–5 189 233 93 .5 216 170–2 144–5 114–5 63–4 173 d . 210–6 70 60–1 92–3 9 .5–10 .5 −29 .2 220–3010 subl . subl . 264 d . 212 .6 145–502 11518 7 .4 d . 135756 265–8 193 89–90 −23 .7 152 .8 192 13050 264–6 265767 274 .5711 304–5 163 .3 280734 188 .3 37 .3 280 150 240–412 >360 319774 300–2 299777 subl . subl . d . subl . 300 subl . 101 .1 178 Solubility in 100 parts Water sl. s. i . i . i . i . 5 .7 cc .26 s . h . i . i . sl . s . ∞ sl . s . sl . s . h . v . sl . s . i . 5 i . v . s . i . ∞ sl . s . h . i . s . s . h . i . 3700 cc .18 ∞ i . 20 0 .06 i . i . i . i . 6 0 .43 v . sl . s . i . s . 620 i . i . i . sl . s . h . 0 .01 c . 0 .399 0 .18100 s . 1 .8525 s h . i . i . i . i . i . sl . s . 0 .5 c . s . h . s . c . i . 0 .0322 i . sl . s . ∞ i . Alcohol Ether ∞ s . s . ∞ s . s . s . s . i . v . s . v . s . v . s . s . s . v . s . v . s . s . v . s . v . s . v . s . s . s . s . s . s . s . s . s . v . sl . s . ∞ s . v . sl . s . ∞ s . sl . s . sl . s . v . s . v . s . sl . s . s . s . s . s . s . s . ∞ s . 20015 ∞ s . s . h . 0 .8 c . s . 1 .520 1 .921 320 0 .1821 s . s . v . s . s . v . s . v . sl . s . sl . s . 20 1 .5 v . s . h . 0 .2 c . v . s . h . 420 s . h . v . s . v . sl . s . 1 .215 v . s . v . s . h . s . v . s . v . sl . s . 916 s . h . s . s . s . 2-35 Diphenyl -amine carbonate -chloroarsine -ethane ether guanidine -methane phenylenediamine (p-) succinate sulfide sulfone urea (uns .) Diphenylene oxide Dipropyl adipate (n-) -amine (n-) (i-) aniline (n-) carbonate (n-) ether (n-) (i-) ketone (n-) (i-) oxalate (n-) (i-) Disalicylal ethylenediamine Ditolyl guanidine (o-) Divinyl acetylene Docosane (n-) Dodecane (n-) Dulcitol Durene (1-,2-,4-,5-) Elaidic acid Eosine Ephedrine (l-) Epichlorhydrin (α-) Epidichlorohydrin (α-) Erythritol (dl-) tetranitrate Ethane Ethanol-amine formamide Ether Ethyl abietate acetate acetoacetate alcohol -amine hydrochloride aniline sulfonic acid (m-) anisate (p-) anthranilate (o-) benzene benzoate -benzyl-aniline bromide butyrate (n-) (i-) caprate (n-) Ethyl caproate (n-) caprylate (n-) chloride chloroacetate chlorocarbonate cinnamate (trans-) cyanoacetate formate furoate (α) heptoate hypochlorite iodide lactate C6H5⋅C6H5 C6H5NHC6H5 CO(OC6H5)2 (C6H5)2AsCl (C6H5CH2⋅)2 C6H5OC6H5 (C6H5NH)2C:NH (C6H5)2CH2 (C6H5NH)2C6H4 (⋅CH2CO2C6H5)2 (C6H5)2S (C6H5)2SO2 (C6H5)2NCONH2 < (C6H4)2O (⋅CH2CH2CO2C3H7)2 (C2H5CH2)2NH [(CH3)2CH]2NH C6H5N(C3H7)2 CO(OCH2C2H5)2 (C2H5CH2)2O [(CH3)2CH]2O (C2H5CH2)2CO [(CH3)2CH]2CO (CO2CH2C2H5)2 [CO2CH(CH3)2]2 [HOC6H4CH:NCH2⋅]2 (C7H7NH)2C:NH (H2C:CH⋅C⋮)2 CH3(CH2)20CH3 CH3(CH2)10CH3 CH2OH(CHOH)4CH2OH (CH3)4C6H2 C8H17CH:CH(CH2)7CO2H C20H8O5Br4 C6H5CHOHCH(CH3)NHCH3 C2H3O⋅CH2Cl CH2:CCl⋅CH2Cl CH2OH(CHOH)2CH2OH C4H6(ONO2)4 CH3CH3 HOCH2CH2NH2 HCONHCH2CH2OH (CH3CH2)2O C19H29CO2C2H5 CH3CO2C2H5 CH3COCH2CO2C2H5 CH3CH2OH C2H5NH2 C2H5NH2⋅HCl C6H5NHC2H5 C2H5NHC6H4SO3H CH3OC6H4CO2C2H5 NH2C6H4CO2C2H5 C6H5⋅C2H5 C6H5CO2C2H5 C6H5N(C2H5)CH2C6H5 C2H5Br C2H5CH2CO2C2H5 (CH3)2CHCO2C2H5 CH3(CH2)8CO2C2H5 CH3(CH2)4CO2C2H5 CH3(CH2)6CO2C2H5 CH3CH2Cl ClCH2CO2C2H5 ClCO2CH2CH3 C6H5CH:CHCO2C2H5 CH2(CN)CO2C2H5 HCO2CH2CH3 OC4H3CO2C2H5 CH3(CH2)5CO2C2H5 ClOCH2CH3 CH3CH2I CH3CH(OH)CO2C2H5 154 .21 169 .22 214 .22 264 .58 182 .26 170 .21 211 .26 168 .23 260 .33 270 .28 186 .27 218 .27 212 .25 168 .19 230 .30 101 .19 101 .19 177 .29 146 .18 102 .17 102 .17 114 .19 114 .19 174 .19 174 .19 268 .31 239 .32 78 .11 310 .60 170 .33 182 .17 134 .22 282 .46 647 .89 165 .23 92 .52 110 .97 122 .12 302 .11 30 .07 61 .08 89 .09 74 .12 330 .50 88 .11 130 .14 46 .07 45 .08 81 .54 121 .18 201 .24 180 .20 165 .19 106 .17 150 .17 211 .30 108 .97 116 .16 116 .16 200 .32 144 .21 172 .26 64 .51 122 .55 108 .52 176 .21 113 .11 74 .08 140 .14 158 .24 80 .51 155 .97 118 .13 col. mn. col. mn. nd./al. rhb. col. pr. col. rhb. mn ./al . col . pr . cr . lf ./al . col . lq . nd ./aq . rhb . lf ./al . col . lq . col . lq . col . lq . yel . oil col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . cr . cr . lq . cr . lq . mn . mn . lf ./al . col . cr . cr ./et . lq . col . lq . tet . pr . lf ./al . col . gas col . oil lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . mn . lq . nd ./aq . lq . cr . col . lq . col . lq . yel . oil col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lf . col . lq . yel . lq . col . lq . oil 0.992 73/4 1.160 20/20 1.272 14 1.583 40 0.978 50/50 1.073 20 1 .001 26/4 1 .119 15/15 1 .248 25/4 1 .276 20/4 0 .979 0 .739 20/4 0 .722 22 0 .910 20 0 .968 22 0 .744 21/0 0 .725 21/0 0 .822 20/4 0 .806 20/4 1 .038 0/0 1 .34 1 .1020/4 0 .776 20/4 0 .778 44/4 0 .751 20/4 1 .466 15 0 .838 81/4 0 .851 79/4 1 .183 25/25 1 .204 25 1 .451 20/4 −88 0 .546 1 .022 20 1 .169 25 0 .708 25/4 1 .020 20/20 0 .901 20/4 1 .025 20/4 0 .789 20/4 0 .689 15/15 1 .216 0 .963 20/4 1 .103 25/25 1 .117 20/4 0 .867 20/4 1 .052 15/15 1 .034 18 .5 1 .431 20/4 0 .879 20/4 0 .871 20/4 0 .859 28 0 .873 20/20 0 .878 17 0 .917 6/6 1 .159 20/4 1 .138 20/4 1 .049 20/4 1 .062 20/4 0 .923 20/4 1 .117 21/4 0 .872 20/20 1 .013 −6/4 1 .933 20/4 1 .030 25/4 69–70 52.9 80 43–4 52–3 27 147–8 26–7 152 122–3 <−40 128–9 189 86–7 −20 .3 −39 .6 −61 −122 −60 −32 .6 −51 .7 254.9 302 302–6 d. 327 284 259 d . > 170 265 330 296–7 379 287–8 143–510 110–1 83 .5743 245 .4 168 .2 91 69 144 .2 123 .7 213 .5 190 125–6 178–9 44 .5 −9 .6 189 79–80 51–2 40 −25 .6 126 61 −172 10 .5 <−40 −116 .3 −82 .4 −45 −112 −80 .6 108–9 −63 .5 d . 294 7–8 13 −94 .4 −34 .6 −117 .8 −93 .3 −88 .2 −20 −67 .5 −45 −139 −26 −80 .6 12 −22 .5 −79 34 −66 .1 expl . −105 85 224 .515 214 .5 290–53 193–5 288100 255 117756 94 329–31 expl . −88 .6 171757 d . 34 .6 2004 77 .1 180755 78 .4 16 .6 204 269–70 266–8 136 .2 211–2 28510 38 .4 120–1 110–1 244 .6758 165–6736 207–8753 13 144 94–5 271 208753 54760 195766 187–8 36752 72 .4 155 i. 0.0325 i. 0.2 d. i. v. sl. s. v . sl . s . i . i . i . i . sl . s . h . v . sl . s . i . i . s . s . i . v . sl . s . sl . s . 0 .2 0 .43 v . sl . s . d . h . 0 .0328 v . sl . s . i . i . i . 3 .215 i . i . i . 5 <5 i . 60 i . c . 4 .7 cc .20 ∞ ∞ 7 .520 i . 8 .515 1317 ∞ ∞ 24017 i . 2 .1515 i . v . sl . s . 0 .0115 0 .0820 i . 1 .060 0 .6825 sl . s . 0 .00220 i . i . 0 .450 i . d . i . 225 1118 i . 0 .02920 0 .420 ∞ 1020 5619.5 v. s. 20 s. s. 920 v . s . s . h . s . h . s . s . h . s . ∞ s . s . 6.620 s. s. s. v. s. ∞ sl . s . v . s . s . ∞ s . v . s . s . ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . h . s . 4 h . v . s . v . sl . s . s . v . s . s . 500 ∞ ∞ sl . s . c . s . 150 cc . ∞ v . s . v . s . i . s . v . s . s . ∞ ∞ i . s . 1 ∞ ∞ ∞ ∞ v . s . ∞ s . s . ∞ ∞ 18 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ i . ∞ s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ (Continued ) 2-36 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name laurate mercaptan methacrylate naphthylamine (α-) naphthyl ether (α-) nitrate nitrite oleate palmitate pelargonate propionate salicylate (o-) stearate toluate (o-) (m-) toluene sulfonate (p-) toluidine (o-) (p-) urea valerate (n-) (i-) Ethylal Ethylene bromide bromohydrin chlorobromide chlorohydrin diamine oxide Ethylidene diacetate Eugenol (1-,4-,3-) (i-)(1-,3-,4-) Fenchyl alcohol (dl-) (d-)(α-) (i-)(l-) Ferric dimethyl-dithiocarbamate Fluorene Fluorescein Fluoro-dichloromethane -trichloromethane Formaldehyde (m-) (p-) Formamide Formanilide Formic acid Fructose Fuchsin Fulminic acid Fumaric acid (trans-) Furfural Furfuran Furfuryl acetate alcohol butyrate propionate Furoic acid G-acid, K salt (2-)(6-,8-) Na salt (2-)(6-,8-) Galactose (d-)(α-) Gallic acid (3-,4-,5-) Gamma acid (2-,8-,6-) Geraniol Glucose (d-)(α-) (d-)(β-) Glucuronic acid Glutam(in)ic acid (dl-) Formula CH3(CH2)10CO2C2H5 CH3CH2SH CH2:C(CH3)CO2C2H5 C10H7NHC2H5 C10H7OC2H5 C2H5ONO2 C2H5ONO C17H33CO2C2H5 CH3(CH2)14CO2C2H5 CH3(CH2)7CO2C2H5 CH3CH2CO2C2H5 HOC6H4CO2C2H5 CH3(CH2)16CO2C2H5 CH3⋅C6H4CO2C2H5 CH3⋅C6H4CO2C2H5 CH3⋅C6H4SO3C2H5 CH3⋅C6H4NHC2H5 CH3⋅C6H4NHC2H5 C2H5NH⋅CO⋅NH2 CH3(CH2)3CO2C2H5 (CH3)2CH(CH2)CO2C2H5 CH2(OC2H5)2 H2C:CH2 BrCH2⋅CH2Br BrCH2⋅CH2OH ClCH2⋅CH2Br ClCH2⋅CH2OH H2NCH2⋅CH2NH2 < (CH2)2 > O CH3CH(O2CCH3)2 C3H5⋅C6H3(OH)OCH3 C3H5⋅C6H3(OCH3)OH C10H17OH C10H17OH C10H17OH Fe[SSCN(CH3)2]3 (C6H4)2 > CH2 C20H12O5 FCHCl2 Cl3CF HCHO (CH2O)3 (CH2O)x⋅xH2O HCONH2 HCONHC6H5 HCO2H CH2OH(CHOH)3COCH2OH C20H19N3HCl C:NOH HO2CCH:CHCO2H C4H3O⋅CHO C4H4O CH3CO2CH2C4H3O C4H3O⋅CH2OH C3H7CO2CH2⋅C4H3O C2H5CO2CH2⋅C4H3O C4H3O⋅CO2H HOC10H5(SO3K)2 HOC10H5(SO3Na)2 C5H11O5⋅CHO (HO)3C6H2CO2H⋅H2O C10H5(NH2)(OH)SO3H C9H15CH2OH C5H11O5⋅CHO C6H12O6⋅H2O CHO(CHOH)4CO2H [⋅CHNH2(CH2)2⋅](CO2H)2 Formula weight 228 .37 62 .13 114 .14 171 .24 172 .22 91 .07 75 .07 310 .51 284 .48 186 .29 102 .13 166 .17 312 .53 164 .20 164 .20 200 .25 135 .21 135 .21 88 .11 130 .18 130 .18 104 .15 28 .05 187 .86 124 .96 143 .41 80 .51 60 .10 44 .05 146 .14 164 .20 164 .20 154 .25 154 .25 154 .25 416 .49 166 .22 332 .31 102 .92 137 .37 30 .03 90 .08 (30 .03) 45 .04 121 .14 46 .03 180 .16 337 .85 43 .02 116 .07 96 .08 68 .07 140 .14 98 .10 168 .19 154 .16 112 .08 380 .48 348 .26 180 .16 188 .13 239 .25 154 .25 180 .16 198 .17 194 .14 147 .13 Form and color Specific gravity Melting point, °C Boiling point, °C oil lq . col . lq . oil cr . col . lq . lq . oil col . nd . col . lq . col . lq . col . lq . col . cr . lq . lq . pr ./al . lq . lq . nd . col . lq . col . lq . lq . col . gas col . lq . col . lq . lq . col . lq . col . lq . lq . col . lq . oil oil col . cr . col . pr . col . cr . cr . cr ./al . yel . red gas col . lq . gas wh . amor . lq . mn . col . lq . nd ./aq . red 0.868 13/4 0 .839 20/4 0 .913 15 .6 1 .060 20/4 1 .061 20/20 1 .100 25/4 0 .900 15 .5 0 .867 25 0 .858 25/4 0 .866 17 .5 0 .891 20/4 1 .136 15/4 0 .848 36 .3 1 .032 25/25 1 .030 20/20 1 .166 48/4 0 .948 25/4 0 .942 25/4 1 .213 18 0 .877 20 0 .867 20/4 0 .824 25/4 0 .57−102/4 2 .180 20/4 1 .772 20/4 1 .689 19 1 .213 20/4 0 .900 20/20 0 .887 7/4 1 .061 12 1 .070 15/15 1 .091 15/15 0 .935 40 0 .964 20/4 0 .961 −10.7 −121 269 36–7 118 303723 276 .4 87–8 17 216–815 19110 227–8757 99 .1 233–4 20110 227 231750 221 .3 215–6 217 col . pr . lq . col . lq . col . oil oil col . lq . col . lq . mn . pr . cr . cr . pr . mn ./aq . cr . col . lq . rhb . cr . cr . cr ./aq . 1 .203 0/4 1 .4260 1 .494 17 .2 0 .815 −20 1 .1765 1 .139 20/4 1 .147 15/15 1 .220 20/4 1 .669 17 .5 1 .22 20/4 1 .635 1 .159 20/4 0 .937 20/4 1 .118 20/4 1 .129 25/4 1 .053 20/4 1 .109 20/4 5 .5 −102 <−15 24–5 −44 .5 −72 .6 1 .3 33 .4(31) <−10 33–4 <−15 92 −91 .2 −99 .3 −66 .5 −169 10 −16 .6 −69 8 .5 −111 .3 18 .85 10 .3 −10 35 45–7 61–2 d . 100–30 115–6 d . > 290 −127 −92 64 150–60 2 47 8 .6 95–105 d . >200 286–7 −38 .7 133–4 1 .694 4/4 15 0 .883 1 .544 25 1 .562 18/4 1 .460 145 .5 135 89 −103 .9 131 .5 150 .3 106 .7 128 .8 117 .2 13 .5747 168740 253 .5 267 .5 201 201–2 201–2 ign . >150 293–5 14 .5 24 .9 −21 114 .5759 subl . 193 216120 100 .8 290 161 .7760 31–2756 175–7 169 .5752 212–3 195–6 230–2 165 .5 d . 220 <−15 146 150 154 199 d . 230 d . Solubility in 100 parts Water i. 1 .5 i . i . i . 1 .355 v . sl . s . i . i . i . 2 .420 i . i . i . i . i . i . i . v . s . 0 .2425 0 .1720 918 26 cc .0 0 .4380 sl . s . 0 .6980 ∞ ∞ ∞ sl . s . v . sl . s . v . sl . s . sl . s . sl . s . i . v . sl . s . i . v . sl . s . h . i . i . v . s . 2125 20–3018 ∞ sl . s . ∞ v . s . 0 .3 17 0 .7 9 .113 i . i . ∞ v . sl . s . v . sl . s . 3 .615 825 3420 10 .30 113 i . 8217 .5 15415 v . s . 1 .5 20 Alcohol Ether s. s . s . s . s . ∞ ∞ ∞ s . ∞ ∞ ∞ s . ∞ ∞ s . ∞ s . s . s . s . ∞ ∞ ∞ s . ∞ ∞ ∞ s . ∞ ∞ s . 80 ∞ ∞ ∞ 360 cc . ∞ s . i . ∞ ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0 .3 v . s . ∞ ∞ s . s . s . h . s . h . s . ∞ v . s . s . i . ∞ v . s . ∞ 818 s . 5 .8 ∞ s . s . s . s . s . s . 30 s . s . ∞ v . s . s . i . v . sl . s . s . i . 0 .725 ∞ s . s . s . ∞ ∞ s . 0 .640 2815 2 .515 ∞ sl . s . ∞ i . v . sl . s . v . sl . s . Glutaric acid Glycerol acetate (mono-) (di-) nitrate (mono-) (α-) (β-) dinitrate (1-,3-) Glyceryl triacetate tribenzoate tributyrate tricaprate tricaproate tricaprylate trilaurate trimyristate trinitrate trinitrite trioleate tripalmitate tristearate Glycide Glycine, Glycocoll Glycol diacetate dibenzoate dibutyrate dicaprylate diformate dilaurate dinitrate dinitrite dipalmitate dipropionate ether formal formate (mono-) Glycolic acid Guaiacol (o-) Guanidine H-acid, Na salt (1-,8-,3-,6-) Heptacosane (n-) Heptane (n-) (i-) Heptoic acid aldehyde Heptyl acetate (n-) alcohol (n-) mercaptan Hexachloro-benzene -ethane Hexacosane (n-) Hexadecane (n-) Hexaethylbenzene Hexamethylbenzene Hexamethylene-diamine -diisocyanate -glycol tetramine Hexane (n-) (i-) (neo-) 2-37 CH2(CH2CO2H)2 CH2OH⋅CHOH⋅CH2OH C5H10O4 (CH3CO2)2C3H5OH CH2OH⋅CHOH⋅CH2NO3 CH2OH⋅CHNO3⋅CH2OH CHOH(CH2ONO2)2 (CH3CO2)3C3H5 (C6H5CO2)3C3H5 (C2H5CH2CO2)3C3H5 [CH3(CH2)8CO2]3C3H5 [CH3(CH2)4CO2]3C3H5 [CH3(CH2)6CO2]3C3H5 [CH3(CH2)10CO2]3C3H5 [CH3(CH2)12CO2]3C3H5 CH2NO3⋅CHNO3⋅CH2NO3 CH2NO2⋅CHNO2⋅CH2NO2 (C17H33CO2)3C3H5 [CH3(CH2)14CO2]3C3H5 [CH3(CH2)16CO2]3C3H5 C2H3O⋅CH2OH NH2CH2⋅CO2H CH2OH⋅CH2OH (CH3CO2CH2⋅)2 (C6H5CO2CH2⋅)2 (C3H7CO2CH2⋅)2 (C7H15CO2CH2⋅)2 (HCO2CH2⋅)2 (C11H23CO2CH2⋅)2 (O2NO⋅CH2⋅)2 (ONO⋅CH2⋅)2 (C15H31CO2CH2⋅)2 (C2H5CO2CH2⋅)2 (HO⋅CH2CH2)2O < O⋅CH2CH2OCH2 > HCO2CH2CH2OH HOCH2CO2H CH3O⋅C6H4OH NH:C(NH2)2 C10H8O7NS2Na⋅1½H2O CH3(CH2)25CH3 CH3(CH2)5CH3 (CH3)2CH(CH2)3CH3 C3H7⋅CH(CH3)⋅C2H5 (CH3)3C⋅CH2⋅C2H5 [(CH3)2CH]2CH2 (CH3)2C(C2H5)2 (C2H5)3CH (CH3)3C⋅CH(CH3)2 CH3(CH2)5CO2H CH3(CH2)5CHO CH3CO2CH2(CH2)5CH3 CH3(CH2)5CH2OH [(CH3)2CH]2CHOH (C2H5⋅CH2)2CHOH CH3CH(SH)⋅C5H11 C6Cl6 CCl3⋅CCl3 CH3(CH2)24CH3 CH3(CH2)14CH3 C6(C2H5)6 C6(CH3)6 NH2(CH2)6NH2 OCN(CH2)6NCO HO(CH2)6OH (CH2)6N4 CH3(CH2)4CH3 (CH3)2CH(CH2)2CH3 (CH3)3C⋅C2H5 (CH3)2CH⋅CH(CH3)2 (C2H5)2CHCH3 132 .11 92 .09 134 .13 176 .17 137 .09 137 .09 182 .09 218 .20 404 .41 302 .36 554 .84 386 .52 470 .68 639 .00 723 .16 227 .09 179 .09 885 .43 807 .32 891 .48 74 .08 75 .07 62 .07 146 .14 270 .28 202 .25 314 .46 118 .09 426 .67 152 .06 120 .06 538 .89 174 .19 106 .12 74 .08 90 .08 76 .05 124 .14 59 .07 368 .32 380 .73 100 .20 100 .20 100 .20 100 .20 100 .20 100 .20 100 .20 100 .20 130 .18 114 .19 158 .24 116 .20 116 .20 116 .20 132 .27 284 .78 236 .74 366 .71 226 .44 246 .43 162 .27 116 .20 168 .19 118 .17 140 .19 86 .18 86 .18 86 .18 86 .18 86 .18 col. cr. col. lq. col . oil col . lq . col . pr . lf . oil col . lq . nd . col . lq . col . cr . col . lq . col . lq . col . nd . lf . yel . oil yel . lq . col . oil col . nd . col . pr . col . lq . mn . col . lq . col . lq . rhb ./et . col . lq . lq . lq . amor . yel . lq . lq . nd . lq . lq . lq . lq . nd ./aq . pr . col . cr . cr . col . cr . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . lq . mn . rhb . cr . lf . pr ./al . pl ./al . lf . lq . nd ./aq . col . rhb . col . lq . lq . lq . lq . lq . 1.429 15 1.260 50/4 1 .20 20/4 1 .178 15/15 1 .4015 1 .4015 1 .4715 1 .16117/4 1 .228 12 1 .032 20/4 0 .921 40/4 0 .987 20/4 0 .954 20/4 0 .894 60/4 0 .885 60/6 1 .601 15 1 .291 10/16 0 .915 15 0 .866 80/4 0 .862 80/4 1 .114 16/16 1 .161 1 .113 19/4 1 .109 14/4 1 .024 0 97.5 17.9 40 58–9 54 <−30 −78 75–6 <−75 31(25) −25 8 .3(−21) 45–6 56 .5 13 .3(2) −4 65 .1 70 .8(55) 20020 290 158165 175–640 155–60 155–60 146–815 258–9 d . 305–9 16015 150 sl . d . 24018 310–200 .1 166 sl . d . 232–6 d . −15 .6 −31 73–4 197 .4 190 .5 >360 240 22 1 .482 21/2 1 .216 0 52–4 −20 <−15 71–2 1 .045 25 1 .118 20/20 1 .060 20/4 1 .199 15/4 −10 .5 1 .140 15/15 79(63) 28 .3 50 0 .780 60/4 0 .684 20/4 0 .679 20/4 0 .687 20/4 0 .674 20/4 0 .675 20/4 0 .693 20/4 0 .698 20/4 0 .690 20/4 0 .918 20 0 .850 20/ℓ 0 .874 16/16 0 .824 20/4 0 .829 20/4 0 .820 20/4 0 .835 20 2 .044 24 2 .091 20/4 0 .779 57/4 0 .774 20/4 0 .831 130/4 1 .0428 0 .659 20/4 0 .654 20/4 0 .649 20/20 0 .662 20/4 0 .664 20/4 59 .5 −90 .6 −118 .2 −119 .4 −125 −119 .4 −135 .0 −118 .7 −25 −10 −42 −34 −37 228–31 186–7 56 .6 18 .5 130 166 42 42 subl . −94 −153 .7 −98 .2 −129 .8 −118 174 18820 expl . 114 96–8 2600 .1 211–2 244 .8 75–6 180 d . 205 27015 98 .4760 90 .0 91 .8 79 .1 80 .8 86 .0 93 .5 80 .8 221–2 155 191 .5 759 175 756 140 156 174–5 765 309742 186777 26215 287 .5 298 .3 265 204–5 143–420 250 69 60 .2 49 .7 58 .0760 63 .2 63.920 ∞ v . s . s . 7015 7 .1715 i . i . i . i . i . i . i . 0 .1820 d . i . i . i . ∞ 23 c . ∞ 14 .322 i . i . i . v . sl . s . i . 0 .9225 i . i . sl . s . ∞ ∞ ∞ ∞ 1 .715 v . s . 0 .1720 i . 0 .00515 i . i . i . i . i . i . i . 0 .2515 0 .0220 i . 0 .18 25 v . sl . s . i . i . i . 0 .00522 i . i . i . i . v . s . d . s . 8112 0 .01415 i . i . i . i . v. s. ∞ v . s . s . v . s . v . s . v . s . ∞ s . h . s . s . h . s . s . sl . s . c . s . 5020 d . sl . s . 0 .00421 s . h . ∞ 0 .1 c . ∞ ∞ v. s. i . sl . s . sl . s . v . sl . s . sl . s . v . s . ∞ s . s . v . s . s . s . v . s . v . s . ∞ s . v . s . v . s . s . h . ∞ i . 1 .0 ∞ s . v . s . v . s . s . s . d . s . ∞ ∞ v . s . ∞ s . s . ∞ i . 9025 v . s . s . v . s . v . s . sl . s . s . s . s . s . s . s . s . s . ∞ s . ∞ ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . ∞ s . ∞ ∞ s . v . sl . s . h . v . s . v . sl . s . ∞ 0 .7525 0 .20 s . d . s . 3 5033 s . h . v . s . ∞ 825 v . s . sl . s . h . v . sl . s . ∞ s . s . s . s . (Continued ) 2-38 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Hexyl acetate (n-) alcohol (n-) formate (n-) resorcinol (2-,4-) Hippuric acid Histidine (l-) Homophthalic acid (o-) Hydracrylic acid Hydro-cyanic acid -quinone (p-) Hydroxy-benzaldehyde (p-) -benzanilide (o-) -quinoline (2-)(α-) (8-)(o-) Indigo White Indole Indoxyl Iodo-benzene -phenol (p-) Iodoform Ionone (α-) (β-) Irone (β-) Isatin Isoprene Ketene Koch acid (1-)(3-,6-,8-) Lactic acid (dl-) anhydride Lactide (dl-) Lactose Lauric acid Laurone Lauryl alcohol Lead tetraethyl tetramethyl Lepidine (py-4) Leucine (l-) Levulinic acid Limonene (d- or l-) Linalool (d- or l-) Linalyl acetate Linoleic acid Maleic acid anhydride Malic acid (dl-) (d- or l-) Malonic acid Maltose Mandelic acid (dl-) Mannitol (d-) Mannose (d-) Margaric acid Mellitic acid Menthol (l-)(α-) Mercapto-benzothiazole (2-) -thiazoline (2-) Mercuric cyanide fulminate Mesityl oxide Mesitylene (1-,3-,5-) Metanilic acid (m-) Methane Formula CH3CO2(CH2)5CH3 CH3(CH2)4CH2OH (CH3)2CH⋅C(CH3)2OH (CH3)2COH⋅CH2C2H5 HCO2CH2(CH2)4CH3 CH3(CH2)5C6H3(OH)2 C6H5CONHCH2CO2H C6H9O2N3 HO2C⋅C6H4⋅CH2CO2H HOCH2CH2CO2H HCN C6H4(OH)2 HO⋅C6H4⋅CHO HO⋅C6H4⋅CONHC6H5 C9H6N⋅OH C9H6N⋅OH [C6H4(CO)(NH)C:]2 C16H12O2N2 C8H7N C8H6NOH C6H5I IC6H4OH HCI3 C10H16:CHCOCH3 C10H16:CHCOCH3 C14H22O C6H4 < (CO)(N) > COH CH2:CH⋅C(CH3):CH2 H2C:CO C10H4(NH2)S3O9HNa2 CH3CH(OH)CO2H C6H10O5 C6H8O4 C12H22O11⋅H2O CH3(CH2)10CO2H [CH3(CH2)10]2CO CH3(CH2)10CH2OH Pb(CH2CH3)4 Pb(CH3)4 C9H6N⋅CH3 (CH3)2CHCH2CH(NH2)CO2H CH3CO(CH2)2CO2H C10H16 C10H17OH CH3CO2C10H17 C17H31CO2H HO2C⋅CH:CH⋅CO2H < (⋅CHCO)2 > O HO2CCH2CH(OH)CO2H HO2CCH2CH(OH)CO2H H2C(CO2H)2 C12H22O11⋅H2O C6H5CH(OH)CO2H CH2OH(CHOH)4CH2OH CH2OH(CHOH)4CHO CH3(CH2)15CO2H C6(CO2H)6 C10H19OH < C6H4N:C(SH)S > < CH2N:C(SH)SCH2 > Hg(CN)2 Hg(ONC)2⋅½H2O (CH3)2C:CHCOCH3 C6H3(CH3)3 H2NC6H4SO3H CH4 Formula weight 144 .21 102 .17 102 .17 102 .17 130 .18 194 .27 179 .17 155 .15 180 .16 90 .08 27 .03 110 .11 122 .12 213 .23 145 .16 145 .16 262 .26 264 .28 117 .15 133 .15 204 .01 220 .01 393 .73 192 .30 192 .30 206 .32 147 .13 68 .12 42 .04 427 .34 90 .08 162 .14 144 .13 360 .31 200 .32 338 .61 186 .33 323 .44 267 .34 143 .19 131 .17 116 .12 136 .23 154 .25 196 .29 280 .45 116 .07 98 .06 134 .09 134 .09 104 .06 360 .31 152 .15 182 .17 180 .16 270 .45 342 .17 156 .27 167 .25 119 .21 252 .62 293 .63 98 .14 120 .19 173 .19 16 .04 Form and color Specific gravity col. lq. col. lq. lq . lq . lq . col . nd . rhb . lf ./aq . cr ./aq . syrup lq . cr . nd ./aq . pr ./al . pr ./al . pr . cr . gray lf ./aq . yel . pr . col . lq . nd ./aq . yel . hex . col . oil col . oil col . oil yel . red col . lq . col . gas cr . hyg . yel . oil tri ./al . col . rhb . col . nd . pl . lf . col . lq . col . lq . lq . cr . lf . lq . col . oil col . lq . yel . oil mn . cr . col . cr . col . cr . col . tri . col . nd . rhb ./aq . col . rhb . rhb . col . pl . nd ./al . col . cr . nd . cr . cr . cr ./aq . lq . col . lq . col . nd . gas 0.890 0/0 0.820 20/20 0 .821 20/0 0 .809 20/4 0 .898 0 1 .371 20/4 0 .697 18 1 .332 15 1 .129 130 1 .35 1 .824 25/4 1 .857 112 4 .008 17 0 .930 20 0 .944 20 0 .939 20 Melting point, °C −51.6 −14 −107 68–70 187–8 d . 287 175–80 −12 170 .3 116–7 135 199–200 75–6 390–2 52 85 −28 .5 93–4 119 0 .681 20/4 200–1 −120 −151 1 .249 15/4 16 .8 10/4 0 .862 1 .525 20 0 .869 50/4 0 .809 69/4 0 .831 24/4 1 .659 18/4 1 .995 20/4 1 .086 20 1 .29318 1 .140 20/20 0 .842 20/4 0 .868 20 0 .895 20 0 .903 18/4 1 .609 1 .5 1 .601 20/4 1 .595 20/4 1 .631 15 1 .540 17 1 .300 20/4 1 .489 20/4 1 .539 20/4 0 .853 60 15/15 0 .890 1 .4220/4 1 .50 4 .003 22 4 .4 0 .858 20/4 0 .865 20/4 0 .415 −164 124 .5 202 48(44) 69–70 24 −136 −27 .5 9–10 295 33 .5 −96 .9 −9 .5 130 .5 57–60 128–9 99–100 130–5 d . d . 118 .1 166 132 60–1 286–8 42–3 179 106 d . 320 expl . −59 −45(−52) d . −182 .6 Boiling point, °C 169.2 157.2 120–1 123762 153 .6 1797 d . d . 25–6 285730 subl . d . subl . 266 .6752 subl . 253–4 110 188 .6 d . subl . 136 .117 14018 14416 subl . 34 −56 12214 d . 250 255757 d . 225100 255–9 152291 110760 261–3 subl . 245–6 177 198–200 220762 d . 229–3016 135 d . 202 150 d . 140 d . d . 290–53 227100 d . 212 d . 130750 164 .8 −161 .4 Solubility in 100 parts Water i. 0.620 v . sl . s . v . sl . s . 0 .05 0 .420 s . s . h . ∞ 615 1 .3831 v . sl . s . h . s . h . v . sl . s . c . i . i . s . h . s . 0 .03420 sl . s . 0 .0125 sl . s . sl . s . v . sl . s . s . h . i . d . 7 .220 ∞ v . sl . s . v . sl . s . 1710 i . i . i . i . i . sl . s . 2 .218 v . s . i . v . sl . s . v . sl . s . i . 7925 16 .380 14426 v . s . 13816 10825 1620 1314 24817 i . v . s . 0 .04 c . i . 1 .660 12 .515 0 .0712 320 i . 215 0 .420 cc . Alcohol Ether v. s. ∞ ∞ ∞ ∞ v . s . s . h . v . sl . s . v . s . v. s. ∞ ∞ ∞ ∞ s . 0 .2518 i . sl . s . ∞ v . s . ∞ v . s . s . v . s . s . i . s . s . h . s . s . v . s . 1 .517 ∞ ∞ v . s . v . s . h . ∞ d . s . v . s . sl . s . i . s . s . s . ∞ v . s . 13 .625 ∞ ∞ v . s . sl . s . ∞ s . ∞ s . v . sl . s . c . i . s . i . c . s . sl . s . ∞ ∞ ∞ s . v . s . ∞ s . ∞ ∞ 7030 v . s . ∞ ∞ ∞ ∞ 825 v . s . v . s . 4225 v . sl . s . c . s . 0 .0114 v . sl . s . 3228 v . s . v . s . s . v . s . 8 .415 815 i . s . i . i . v . s . s . ∞ s . v . sl . s . 4720 cc . i . s . s . ∞ ∞ ∞ v . s . sl . s . ∞ ∞ v . sl . s . 10410 cc . 2-39 Methoxy-methoxyethanol Methyl acetate acrylic acid (α-) alcohol -amine -amine hydrochloride aniline anthracene (α-) (β-) anthranilate (o-) anthraquinone (2-) benzoate benzylaniline bromide butyrate (n-) (i-) caprate caproate (n-) caprylate cellosolve chloride chloroacetate chloroformate cinnamate cyclohexane ethyl carbonate ethyl ketone ethyl oxalate formate furoate glucamine glycolate heptoate hypochlorite iodide lactate laurate mercaptan methacrylate myristate naphthalene (α-) (β-) nitrate nitrite nonyl ketone (n-) oleate orange palmitate phosphine propionate propyl ketone (n-) salicylate (o-) stearate toluate (o-) (m-) (p-) Methyl toluidine (o-) (m-) (p-) valerate (n-) (i-) vinyl ketone Methylal Methylene-bis-(phenyl-4-isocyanate) bromide chloride dianiline iodide Michler’s hydrol (p-,p′-) ketone Morphine Mucic acid CH3(OCH2)2CH2OH CH3CO2CH3 CH2:C(CH3)CO2H CH3OH CH3NH2 CH3NH2⋅HCl C6H5NHCH3 C6H4:(CH)2:C6H3CH3 C6H4:(CH)2:C6H3CH3 NH2C6H4CO2CH3 C6H4:(CO)2:C6H3CH3 C6H5CO2CH3 C6H5N(CH3)CH2C6H5 CH3Br CH3(CH2)2CO2CH3 (CH3)2CHCO2CH3 CH3(CH2)8CO2CH3 CH3(CH2)4CO2CH3 CH3(CH2)6CO2CH3 CH3OCH2CH2OH CH3Cl ClCH2CO2CH3 ClCO2CH3 C6H5CH:CHCO2CH3 CH2 < (CH2CH2)2 > CHCH3 CH3O⋅CO⋅OC2H5 CH3 .CO⋅C2H5 CH3OCO⋅CO2C2H5 HCO2CH3 C4H3O⋅CO2CH3 CH2OH(CHOH)4CH2NHCH3 HOCH2CO2CH3 CH3(CH2)5CO2CH3 ClOCH3 CH3I CH3CH(OH)CO2CH3 CH3(CH2)10CO2CH3 CH3SH CH2:C(CH3)CO2CH3 CH3(CH2)12CO2CH3 C10H7CH3 C10H7CH3 CH3ONO2 CH3ONO CH3(CH2)8COCH3 C17H33CO2CH3 (CH3)2NC6H4N2C6H4SO3Na CH3(CH2)14CO2CH3 CH3PH2 CH3CH2CO2CH3 CH3COCH2CH2CH3 HO⋅C6H4CO2CH3 CH3(CH2)16CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4CO2CH3 CH3⋅C6H4NHCH3 CH3⋅C6H4NHCH3 CH3⋅C6H4NHCH3 CH3(CH2)3CO2CH3 (CH3)2CHCH2CO2CH3 CH3COCH:CH2 HCH(OCH3)2 (OCN⋅C6H4)2CH2 CH2Br2 CH2Cl2 (C6H5NH)2CH2 CH2I2 [(CH3)2NC6H4]2CHOH [(CH3)2NC6H4]2CO C17H19O3N⋅H2O (⋅CHOHCHOHCO2H)2 106 .12 74 .08 86 .09 32 .04 31 .06 67 .52 107 .15 192 .26 192 .26 151 .16 222 .24 136 .15 197 .28 94 .94 102 .13 102 .13 186 .29 130 .18 158 .24 76 .09 50 .49 108 .52 94 .50 162 .19 98 .19 104 .10 72 .11 132 .11 60 .05 126 .11 195 .21 90 .08 144 .21 66 .49 141 .94 104 .10 214 .34 48 .11 100 .12 242 .40 142 .20 142 .20 77 .04 61 .04 170 .29 296 .49 327 .33 270 .45 48 .02 88 .11 86 .13 152 .15 298 .50 150 .17 150 .17 150 .17 121 .18 121 .18 121 .18 116 .16 116 .16 70 .09 76 .09 250 .25 173 .83 84 .93 198 .26 267 .84 270 .37 268 .35 303 .35 210 .14 lq. col . lq . pr . col . lq . col . gas pl ./al . lq . lf ./al . col . lf . col . lq . col . nd . col . lq . lq . gas col . lq . col . lq . lq . col . lq . col . lq . col . lq . gas col . lq . col . lq . cr . col . lq . lq . col . lq . lq . lq . col . lq . lq . lq . gas col . lq . lq . lq . gas lq . cr ./al . oil mn . lq . gas col . oil oil red pd . col . cr . gas col . lq . col . lq . col . lq . col . cr . col . lq . col . lq . cr . lq . lq . lq . lq . col . lq . lq . col . lq . lq . col . lq . col . lq . cr . col . lq . gn . lf ./al . pr ./al . pd . 1.038 25 0 .924 20/4 1 .015 20/4 0 .792 20/4 0 .699 −11 1 .23 0 .989 20/4 1 .047 99 .4 1 .181 0/4 1 .168 19/4 1 .087 25/25 1 .732 0/0 0 .898 20/4 0 .891 20/4 0 .904 0/0 0 .887 18 0 .965 20/4 0 .952 0 1 .236 20/4 1 .236 15 1 .042 36/0 0 .769 20/4 1 .002 27 0 .805 20/4 1 .156 0/0 0 .974 20/4 1 .179 21/4 <−70 −98 .7 15–16 −97–8 −92 .5 226–8 −57 86 207 24 176–7 −12 .5 9 .2 −93 <−95 −84 .7 −18 −40 −97 .7 −32 .7 33 .4 −126 .3 −14 .5 −85 .9 −99 .8 18 1 .168 0 .881 15/4 2 .279 20/4 1 .090 19 0 .896 0 0 .950 15 .6 1 .025 14/4 0 .994 40/4 1 .203 25 0 .991 15 0 .828 20/20 0 .879 18 −64 .4 5 −121 −48 18–9 −19 35–6 expl . 13 .5 30–1 20/4 0 .915 0 .812 15/15 1 .182 25/25 1 .073 15 1 .066 15 0 .973 15 0 .935 55/4 0 .895 15/4 0 .881 20/4 0 .836 20/4 0 .866 15/4 1 .222 30 2 .495 20/4 1 .336 20/4 3 .325 20/4 1 .317 −87 .5 −77 .8 −8 .3 38–9 <−50 33–4 −91 −104 .8 −52 .8 −96 .7 65 5 .7 96–7 174 254 d . 206–14 167.5 57 .1 161–3 64 .7 −6 .7 758 23015 195 .5 135 .5 15 subl . 198–9 305–6 4 .5 758 102 .3 92 .6 223–4 149 .5 192–4 124–5 −24 130740 71–2 263 101 109 .2 79 .6 173 .7 32 181 .3 151 .2 172–3 12726 42 .4 144 .8 14818 5 .8752 100 .3 295715 244 .6 241–2 65 −12 228 190–110 19615 −14759 79 .7 102 222 .2 21515 213 215 217 206–7 206–7 211761 127 .3 116 .7764 81 42–3 210–213 98 .5756 40–1 208–9 d . 180 d . >360 d . ∞ 3322 s . h . ∞ v . s . v . s . 0 .0125 i . i . sl . s . i . 0 .0230 i . v . sl . s . 1 .7 v . sl . s . i . i . i . ∞ 28016 cc . v . sl . s . d . i . i . i . 3510 i . 3020 i . ∞ ∞ ∞ v . s . 23 h . s . ∞ ∞ ∞ i . ∞ v . sl . s . s . s . ∞ s . s . ∞ ∞ ∞ ∞ ∞ ∞ v . s . ∞ ∞ v . s . s . ∞ ∞ v . s . ∞ ∞ v . sl . s . s . s . ∞ s . s . ∞ ∞ ∞ ∞ ∞ ∞ v . s . ∞ ∞ v . s . s . ∞ ∞ v . s . ∞ s . ∞ s . v . s . v . s . v . s . v . s . s . s . s . ∞ v . s . v . s . s . s . s . ∞ s . sl . s . ∞ ∞ ∞ s . ∞ s . ∞ ∞ ∞ s . ∞ v . s . ∞ ∞ ∞ ∞ ∞ v . s . ∞ ∞ ∞ ∞ ∞ ∞ d . ∞ ∞ s . ∞ s . h . sl . s . sl . s . i . ∞ ∞ i . 1 .815 ∞ i . s . i . i . i . i . sl . s . i . i . 0 .2 c . i . i . 0 .520 v . sl . s . 0 .0730 i . i . i . i . i . i . i . v . sl . s . v . sl . s . >85 33 d . 1 .170 220 i . 1 .420 i . i . 0 .0220 0 .3314 ∞ ∞ s . ∞ s . v . sl . s . s . i . (Continued ) 2-40 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Mustard gas Myricyl alcohol Myristic acid Myristyl alcohol Naphthalene disulfonic acid (1-,5-) (1-,6-) sulfonic acid (α-) (β-) Naphthasultam (1-,8-) disulfonate Na (1-,8-) (2-,4-) Naphthoic acid (α-) (β-) Naphthol (α-) (β-) sulfonic acid (α-)(1-,2-) (β-)(2-,6-) Naphthyl acetate (α-) (β-) amine (α-) (β-) amine hydrochloride (α-) (β-) amine sulfonic acid (1-,4-) (1-,5-) (1-,7-) (1-,8-) (2-,5-) (2-,6-) (2-,7-) isocyanate (α-) Nicotine Nicotinic acid (3-) (i-)(4-) Nitro-acetanilide (p-) -acetophenone (m-) -aminoanisole (4-,1-,2-) (5-,1-,2-) (3-,1-,4-) -aminophenol (4-,2-,1-) -aniline (o-) (m-) (p-) -anisole (o-) (p-) -anthraquinone (α-) -anthraquinone sulfonic acid (1-,5-) -benzal chloride (m-) -benzaldehyde (m-) Nitro-benzene -benzidine (2-) -benzoic acid (o-) (m-) (p-) -benzyl alcohol (m-) -benzyl bromide (p-) -chlorotoluene (1-,2-,6-) -cresol (1-,3-,4-) -cymene (1-,2-,4-) -dimethylaniline (o-) (m-) (p-) -diphenyl (o-) (p-) -diphenylamine (o-) -guanidine Formula (ClCH2⋅CH2)2S C31H63OH(?) CH3(CH2)12CO2H CH3(CH2)12CH2OH C10H8 C10H6(SO3H)2 C10H6(SO3H)2 C10H7SO3H⋅2H2O C10H7SO3H⋅H2O C10H7O2NS C10H5O8NS3Na2⋅2H2O C10H4O8NS3Na3⋅8½H2O C10H7CO2H C10H7CO2H C10H7OH C10H7OH HO⋅C10H6SO3H HO⋅C10H6SO3H CH3CO2C10H7 CH3CO2C10H7 C10H7NH2 C10H7NH2 C10H7NH2⋅HCl C10H7NH2⋅HCl NH2⋅C10H6⋅SO3H NH2⋅C10H6⋅SO3H⋅H2O NH2⋅C10H6⋅SO3H⋅H2O NH2⋅C10H6⋅SO3H⋅H2O NH2⋅C10H6⋅SO3H NH2⋅C10H6⋅.SO3H⋅H2O NH2⋅C10H6⋅SO3H⋅H2O C10H7N:CO C10H14N2 C5H4NCO2H C5H4NCO2H CH3CONHC6H4NO2 CH3COC6H4NO2 NO2⋅C6H3(OCH3)NH2 NO2⋅C6H3(OCH3)NH2 NO2⋅C6H3(OCH3)NH2 NO2⋅C6H3(NH2)OH NO2⋅C6H4NH2 NO2⋅C6H4NH2 NO2⋅C6H4NH2 CH3OC6H4NO2 CH3OC6H4NO2 C6H4:(CO)2:C6H3NO2 NO2⋅C14H6O2⋅SO3H NO2⋅C6H4⋅CHCl2 NO2⋅C6H4CHO C6H5NO2 NH2C6H4C6H3(NH2)NO2 NO2⋅C6H4⋅CO2H NO2⋅C6H4⋅CO2H NO2⋅C6H4⋅CO2H NO2⋅C6H4⋅CH2OH NO2⋅C6H4CH2Br CH3⋅C6H3(NO2)Cl CH3⋅C6H3(NO2)OH CH3⋅C6H3(NO2)CH(CH3)2 NO2⋅C6N4N(CH3)2 NO2⋅C6H4N(CH3)2 NO2⋅C6H4N(CH3)2 C6H5⋅C6H4NO2 C6H5⋅C6H4NO2 C6H5⋅NH⋅C6H4NO2 H2NC(NH)NHNO2 Formula weight 159 .08 452 .84 228 .37 214 .39 128 .17 288 .30 288 .30 244 .26 226 .25 205 .23 445 .35 584 .43 172 .18 172 .18 144 .17 144 .17 224 .23 224 .23 186 .21 186 .21 143 .19 143 .19 179 .65 179 .65 223 .25 241 .26 241 .26 241 .26 223 .25 241 .26 241 .26 169 .18 162 .23 123 .11 123 .11 180 .16 165 .15 168 .15 168 .15 168 .15 154 .12 138 .12 138 .12 138 .12 153 .14 153 .14 253 .21 333 .27 206 .03 151 .12 123 .11 229 .23 167 .12 167 .12 167 .12 153 .14 216 .03 171 .58 153 .14 179 .22 166 .18 166 .18 166 .18 199 .21 199 .21 214 .22 104 .07 Form and color Specific gravity Melting point, °C Boiling point, °C oil cr. col. lf. cr. pl./al. lf. cr. cr. cr. nd. cr. lf. nd. mn. mn. mn. pl./aq. lf. nd./al. nd./al. rhb. lf./aq. nd. lf. nd. cr. cr. cr. cr. cr. cr. col. lq. oil nd ./al . nd ./aq . rhb . nd . red nd . yel . nd . red or . pr . yel . rhb . yel . rhb . yel . mn . col . cr . pr ./al . nd . yel . cr . mn . nd ./aq . yel . lq . red nd . tri ./aq . mn . yel . mn . cr . nd ./al . cr . yel . oil yel . oil red mn . yel . nd . rhb . nd ./al . or . cr . nd ./aq . 1.275 20/4 0.777 95 0.853 70/4 0.824 38/4 1.145 20/4 13–4 88 57–8 38 80.2 d. d. 125 90 125 177–8 217 1.077 100/4 1.224 4 1.217 4 1.123 25/25 1.061 98/4 160–1 184 96 122–3 >250 125 46–9 69–70 50 111–2 250.5100 16715 217.9 300 >300 278–80 285–6 300.8 306.1 subl. d. 1.18 1.009 20/4 1 .207 156 1 .211 156 15 1 .442 1 .43 1 .437 14 1 .254 20/4 1 .233 20 1 .205 18/4 1 .575 4/4 1 .494 4/4 1 .550 22/4 89/4 1 .240 1 .067 20/4 1 .179 20/4 1 .313 17 1 .44 <−80 235 .2 317 215–6 80–1 118 139–40 123 142–3 71 .5 114 146–7 9 .4 54 230 65 58 5 .7 143 147 .5 140–1 240–2 27 99–100 37 .5 32 60–1 163–4 37 113–4 75–6 246–7 269–70 246730 subl . d . 202 284 .1 306 .4 331 .7 272–3 274 2707 16423 210 .9 subl . 175–803 238 12522 15215 151–380 280–5 320 340 Solubility in 100 parts Water 0.0725 i. i. <0.02 0.00325 10220 16420 v. s. 7730 s. h. v. s. v. s. v. sl. s. h. 0.00725 sl. s. h. 0.07425 v. s. h. v. s. sl. s. h. i. 0.17 c. v. s. h. 3.820 v. s. 0.2100 sl. s. 0.4625 0.42100 0.08 0.38100 0.28100 d. s. s . h . s . h . s . h . i . i . sl . s . sl . s . c . s . h . 0 .1120 0 .0819 0 .1730 0 .0630 i . s . i . 1 .95112 0 .1920 sl . s . h . 0 .6520 0 .24165 0 .0215 Alcohol Ether s. v. sl. s. v. s. sl. s. 9.520 s. s. v. s. s. v. s. v. s. s. v. s. i. i. sl. s. sl. s. s. sl. s. s. h. s. v. s. v. s. v. s. s. s. v. s. s. s. v. s. i. s. s. v. s. v. s. i. s. s. v. s. s. s. i. s. ∞ s . h . sl . s . h . s . s . s . s. ∞ v . sl . s . v . sl . s . s . s . v . s . v . s . 7 .120 5 .820 ∞ v . s . sl . s . i . v . s . h . v . s . h . v . s . s . v . s . v . s . 7 .920 6 .120 ∞ v . s . v . sl . s . i . v . s . v . s . ∞ 2811 3112 0 .910 2211 2510 2 .218 219 v . s . i . i . v . sl . s . i . v . sl . s . i . i . i . i . v . s . v . s . v . s . s . s . h . s . sl . s . c . v . s . s . 9100 sl . s . v . sl . s . v . s . v . s . 2-41 -naphthalene (α-) (β-) -phenol (o-) (m-) (p-) -phenol sulfonic acid (1-,4-,2-) (1-,2-,4-) -phthalic acid (3-) (4-) -toluene (o-) (m-) (p-) -toluene sulfonic acid (1-,4-,2-) -toluidine (4-,1-,2-) (3-,1-,4-) Nitron Nitroso-dimethylaniline (p-) -naphthol (β-)(1-) Nonadecane (n-) Nonane (n-) Octadecane (n-) Octane (n-) (iso-) Octyl acetate (n-) (sec-) alcohol (n-) (sec-) Octylene (n-) Oleic acid Orcinol (1-,3-,5-) Oxalic acid Palmitic acid Pelargonic acid Penta-chloroethane -decane (n-) -erythritol Pentandiol Pentane (n-) (i-) (neo-) Phenacetin Phenanthrene Phenetidine (o-) (p-) Phenetole Phenol -phthalein -sulfonic acid (o-) Phenyl acetaldehyde acetic acid -acetylene aniline (o-) (p-) Phenyl-ethyl alcohol -glycine -hydrazine -hydrazine sulfonic acid (p-) isocyanate -methylpyrazolone (3-)(N-) -mustard oil naphthalene (α-) (β-) naphthylamine (α-) (β-) phenol (o-) (p-) propyl alcohol (γ-) quinoline (2-)(α-) (8-)(0-) salicylate, salol stearate urethane C10H7NO2 C10H7NO2 NO2⋅C6H4⋅OH NO2⋅C6H4⋅OH NO2⋅C6H4⋅OH HO⋅C6H3(NO2)SO3H⋅3H2O HO⋅C6H3(NO2)SO3H⋅3H2O NO2⋅C6H3(CO2H)2 NO2⋅C6H3(CO2H)2 CH3⋅C6H4NO2 CH3⋅C6H4NO2 CH3⋅C6H4NO2 CH3⋅C6H3(NO2)SO3H⋅2H2O NO2⋅C6H3(CH3)NH2 NO2⋅C6H3(CH3)NH2 C20H16N4 ON⋅C6H4N(CH3)2 ON⋅C10H6OH CH3(CH2)17CH3 CH3(CH2)7CH3 CH3(CH2)16CH3 CH3(CH2)6CH3 (CH3)3CCH2CH(CH3)2 CH3CO2CH2(CH2)6CH3 CH3CO2CH(CH3)C6H13 CH3(CH2)6CH2OH CH3(CH2)5CH(OH)CH3 CH3(CH2)5CH:CH2 C8H17CH:CH(CH2)7CO2H (HO)2C6H3⋅CH3 HO2C⋅CO2H⋅2H2O CH3(CH2)14CO2H CH3(CH2)7CO2H CHCl2⋅CCl3 CH3(CH2)13CH3 C(CH2OH)4 HOCH2(CH2)3CH2OH CH3(CH2)3CH3 (CH3)2CHCH2CH3 (CH3)2C(CH3)2 C2H5OC6H4NHCOCH3 < (C6H4CH)2 > C2H5O⋅C6H4⋅NH2 C2H5O⋅C6H4⋅NH2 C2H5O⋅C6H5 C6H5OH C20H14O4 HO⋅C6H4SO3H⋅¾H2O C6H5CH2CHO C6H5CH2CO2H C6H5C:CH C6H5⋅C6H4⋅NH2 C6H5⋅C6H4⋅NH2 C6H5CH2CH2OH C6H5NHCH2CO2H C6H5NH⋅NH2 H2NNHC6H4SO3H C6H5N:CO C4H5ON2⋅C6H5 C6H5N:CS C10H7⋅C6H5 C10H7⋅C6H5 C10H7NHC6H5 C10H7NHC6H5 C6H5⋅C6H4OH C6H5⋅C6H4OH C6H5(CH2)3OH C6H5⋅C9H6N C6H5⋅C9H6N HO⋅C6H4CO2C6H5 CH3(CH2)16CO2C6H5 C6H5NHCO2C2H5 173 .17 173 .17 139 .11 139 .11 139 .11 273 .22 273 .22 211 .13 211 .13 137 .14 137 .14 137 .14 253 .23 152 .15 152 .15 312 .37 150 .18 173 .17 268 .52 128 .26 254 .49 114 .23 114 .23 172 .26 172 .26 130 .23 130 .23 112 .21 282 .46 124 .14 126 .07 256 .42 158 .24 202 .29 212 .41 136 .15 104 .15 72 .15 72 .15 72 .15 179 .22 178 .23 137 .18 137 .18 122 .16 94 .11 318 .32 187 .69 120 .15 136 .15 102 .13 169 .22 169 .22 122 .16 151 .16 108 .14 188 .20 119 .12 174 .20 135 .19 204 .27 204 .27 219 .28 219 .28 170 .21 170 .21 136 .19 205 .25 205 .25 214 .22 360 .57 165 .19 yel./al. col./al. yel. mn. col. mn. yel. pr. nd. nd./aq. yel./aq. yel. cr. yel. lq. lq . rhb . pl ./aq . yel . mn . red mn . yel . lf . gn . tri . brn . pr . cr . col . lq . cr . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . nd . pr ./bz . col . mn . col . pl . col . oil col . lq . col . lq . cr . lq . col . lq . col . lq . col . lq . col . mn . pl ./al . oil lq . col . lq . col . nd . col . rhb . cr . lq . lf . col . lq . cr . lf . col . oil cr . yel . oil cr ./al . lq . pr ./aq . col . lq . waxy lf ./al . pr ./al . rhb . nd . nd . oil nd . lq . rhb ./al . cr . pl ./al . 1.223 62 45 1.295 1.485 20 1.479 20 20/4 1.163 1 .160 18/4 1 .139 55/55 1 .365 15 1 .312 17 0 .777 32/4 0 .718 20/4 0 .775 28/4 0 .703 20/4 0 .692 20/4 0 .885 0/4 0 .863 14/4 0 .827 20/4 0 .822 20/4 0 .721 18/4 0 .854 78/4 1 .290 4 1 .653 19/4 0 .849 70/4 0 .906 20/4 1 .671 25/4 0 .770 20/4 0 .994 20/4 0 .630 18/4 0 .621 19 0 .613 20/4 1 .179 25 1 .061 15 0 .967 20/4 1 .071 25/4 1 .299 25/4 1 .025 20 1 .081 80/4 0 .930 20/4 1 .023 18/4 1 .097 23/4 1 .096 20/4 1 .138 15/15 1 .17 1 .18 1 .008 20/4 1 .250 20/4 1 .106 30/4 59–60 79 44–5 96–7 113–4 d. 110 51.5 222 164–5 −4.1 15–16 51 .9 130 105–7 116–7 189–90 d . 86–7 109 .5 32 −53 .7 28 −56 .5 −107 .4 −38 .5 −16 −38 .6 14 107–8 101 .5 63–4 12 .5 −22 10 262 −129 .7 −160 .0 −20 134–5 99–100 <−21 3–4 −30 .2 42–3 261–2 50 d . 76–7 −43 45–6 50–2 127 19 .6 286 128 −21 45 102 .5 62 107–8 56–7 164–5 <−18 86 42–3 52 52–3 304 16515 214.5 19470 subl. 222.3 230–1 237 .7 330 150 .5759 317 125 .7 99 .3760 210 195 194–5 179–80 126 285–6100 287–90 subl . 271 .5100 253–4 162 270 .5 27630 239 .4 36 .3 27 .95 9 .5 d . 340 228–9 254–5 172 181 .4 193–4 265 .5 142–3 299760 302 219–21750 243 .5 166769 19117 219–20 336–7 345–6 335258 399 .5 275 305–8 235–7 363 283187 172–312 26715 237–8 i. i. 1.08100 1.3520 1.625 v. s. v. s. 2.0525 v. s. 0.0780 0 .0580 0 .0480 47 .728 v . sl . s . sl . s . h . i . i . 0 .120 i . i . i . 0 .00216 i . i . i . 0 .05425 0 .09625 i . i . v . s . s . i . v . sl . s . 0 .0520 i . 5 .615 ∞ 0 .03616 i . i . 0 .720 i . i . i . i . 8 .215 0 .220 v . s . v . sl . s . 1 .6620 i . v . sl . s . s . h . 1 .620 s . sl . s . h . 0 .612 d . 120 i . i . i . 0 .0860 0 .460 i . i . sl . s . sl . s . sl . s . 0 .01525 i . i . c . s. v. s. v. s. v. s. v. s. v. s. v. s. v. s. h. v. s. ∞ ∞ 8 .615 v . s . s . s . s . h . s . 2 .418 sl . s . sl . s . sl . s . sl . s . sl . s . s . s . ∞ ∞ ∞ ∞ v . s . s . 920 s . ∞ v . s . v . sl . s . s. v. s. v. s. s. v. s. sl. s. sl. s. s. ∞ ∞ 80 .815 v . s . s . v . sl . s . s . s . s . s . s . s . s . s . ∞ ∞ ∞ ∞ v . s . 1 .3 s . s . ∞ v . s . i . ∞ ∞ s . 40 h . 10 h . s . s . ∞ ∞ 1025 v . s . ∞ v . s . ∞ s . s . s . s . ∞ sl . s . d . v . s . h . s . v . s . sl . s . s . v . s . h . s . s . ∞ s . h . s . v . s . ∞ ∞ s . 1 .625 v . s . s . s . ∞ ∞ 5 .9 c . s . s . ∞ v . s . ∞ s . s . ∞ sl . s . ∞ v . s . v . sl . s . s . v . s . sl . s . s . v . s . h . s . s . ∞ s . s . s . (Continued ) 2-42 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Phenylene-diamine (o-) (m-) (p-) Phloroglucinol (1-,3-,5-) Phorone Phosgene Phthalic acid (o-) (m-)(iso-) anhydride (o-) nitrile (o-) Phthalide Phthalimide (o-) Picoline (α-) (β-) (γ-) Picramic acid (1-,2-,4-,6-) Picric acid (2-,4-,6-) Picryl chloride (2-,4-,6-) Pinacol Pinacoline Pinene (α-)(dl-) hydrochloride Pinol (dl-) Piperidine carboxylic acid (α-)(dl-) Piperidinium pentamethylene dithiocarbamate Propane Propionic acid aldehyde anhydride Propyl acetate (n-) (i-) alcohol (n-) (i-) amine (n-) (i-) aniline (n-) benzoate (n-) (i-) bromide (n-) (i-) n-butyrate (n-) i-butyrate (n-) n-butyrate (i-) i-butyrate (i-) chloride (n-) (i-) Propyl formate (n-) (i-) furoate (n-) lactate (n-) (i-) mercaptan (n-) (i-) propionate (n-) (i-) thiocyanate (i-) n-valerate (n-) i-valerate (n-) i-valerate (i-) Propylene bromide chlorohydrin chloride glycol oxide Protocatechuic acid (3-,4-) Formula C6H4(NH2)2 C6H4(NH2)2 C6H4(NH2)2 C6H3(OH)3⋅2H2O [(CH3)2C:CH]2CO OCCl2 C6H4(CO2H)2 C6H4(CO2H)2 C6H4 < (CO)2 > O C6H4(CN)2 C6H4(CH2)(CO) > O C6H4 < (CO)2 > NH C5H4N⋅CH3 C5H4N⋅CH3 C5H4N⋅CH3 HO⋅C6H2(NH2)(NO2)2 HO⋅C6H2(NO2)3 ClC6H2(NO2)3 [(CH3)2C⋅OH]2 CH3COC(CH3)3 C10H16 C10H17Cl C10H16O CH2 < (CH2CH2)2 > NH HO2C⋅CH < (CH2CH2)2 > NH (CH2)5CS2H⋅HN(CH2)5 CH3CH2CH3 CH3CH2CO2H CH3CH2CHO (CH3CH2CO)2O CH3CO2CH2CH2CH3 CH3CO2CH(CH3)2 CH3CH2CH2OH (CH3)2CHOH CH3CH2CH2NH2 (CH3)2CHNH2 C6H5NHCH2CH2CH3 C6H5CO2CH2CH2CH3 C6H5CO2CH(CH3)2 CH3CH2CH2Br (CH3)2CHBr C2H5CH2CO2CH2C2H5 (CH3)2CHCO2CH2C2H5 C2H5CH2CO2CH(CH3)2 (CH3)2CHCO2CH(CH3)2 CH3CH2CH2Cl (CH3)2CHCl HCO2CH2CH2CH3 HCO2CH(CH3)2 C4H3O⋅CO2C3H7 CH3CH(OH)CO2CH2C2H5 CH3CH(OH)CO2CH(CH3)2 CH3CH2CH2SH (CH3)2CHSH C2H5CO2CH2C2H5 C2H5CO2CH(CH3)2 (CH3)2CH⋅CNS CH3(CH2)3CO2CH2C2H5 (CH3)2CHCH2CO2C3H7 (CH3)2CHCH2CO2C3H7 CH3CH:CH2 CH3CHBrCH2Br CH3CHClCH2OH CH3CHClCH2Cl CH3CH(OH)CH2OH CH3(CHCH2)O (HO)2C6H3CO2H⋅H2O Formula weight Form and color 108 .14 108 .14 108 .14 162 .14 138 .21 98 .92 166 .13 166 .13 148 .12 128 .13 134 .13 147 .13 93 .13 93 .13 93 .13 199 .12 229 .10 247 .55 118 .17 100 .16 136 .23 172 .69 152 .23 85 .15 129 .16 232 .43 44 .10 74 .08 58 .08 130 .14 102 .13 102 .13 60 .10 60 .10 59 .11 59 .11 135 .21 164 .20 164 .20 122 .99 122 .99 130 .18 130 .18 130 .18 130 .18 78 .54 78 .54 88 .11 88 .11 154 .16 132 .16 132 .16 76 .16 76 .16 116 .16 116 .16 101 .17 144 .21 144 .21 144 .21 42 .08 201 .89 94 .54 112 .99 76 .09 58 .08 172 .14 lf./aq. rhb. mn. rhb. yel. pr. gas mn./aq. nd./aq. rhb. cr. nd./aq. cr./et. col. lq. col . lq . lq . red nd . yel . rhb . yel . mn . col . nd . col . lq . col . lq . lf . lq . lq . cr . cr . gas col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . col . lq . lq . lq . col . lq . col . lq . lq . lq . col . lq . col . lq . gas col . lq . col . lq . col . lq . col . oil col . lq . nd ./aq . Specific gravity 1.139 15/15 0.885 20/4 1.392 19/4 1.593 20/4 1.527 4 1.164 99/4 0.950 15/4 0 .961 15/4 0 .957 15/4 1 .763 20/4 1 .797 20 0 .967 15 0 .800 16 0 .878 20/4 0 .953 20/20 0 .860 20/4 1 .13 0 .585 −45/4 0 .992 20/4 0 .807 20/4 1 .012 20/4 0 .886 20/4 0 .874 20/20 0 .804 20/4 0 .78920/4 0 .718 20/20 0 .694 15/4 0 .949 18 1 .021 25/25 1 .010 25/25 1 .353 20/4 1 .310 20/4 0 .879 15 0 .884 0/4 0 .865 18 0 .869 0/4 0 .890 20/4 0 .859 20 0 .901 20/4 0 .873 20/4 1 .075 26/4 0 .836 25/4 0 .809 25/4 0 .883 20/4 0 .893 0 0 .963 20 0 .874 15 0 .863 20/4 0 .854 17 0 .609 −47/4 1 .933 20/4 1 .103 20 1 .159 20/20 1 .040 19 .4 0 .831 20/20 1 .542 4/4 Melting point, °C Boiling point, °C 103–4 62.8 140 117 28 −104 208 330 130.8 141 73(65) 238 −70 256–8 284–7 267 subl. 197.2743 8.2756 d. subl. 284.5 169 121 .8 83 43(38) −52 .5 −55 131–2 −9 264 175 −187 .1 −22 −81 −45 −92 .5 −73 .4 −127 −85 .8 −83 −101 −51 .6 −109 .9 −89 −95 .2 −122 .8 −117 −92 .9 −112 −130 .7 −76 −70 .7 −185 −55 .5 <−70 199 d . 290 subl. 128.8 143 .5 143 .1 expl . d . 171–2789 106 .2 154–6 207–8 183–4 106 −42 .2 141 .1 49 .5740 168 .8780 101 .6 88 .4 97 .8 82 .5 49–50761 33–4 222 231 218 .5 70 .8 60 142 .7 134–5 128 120 .8 46 .4 36 .5 81 .3 68–71751 211 122–3150 167 .5 67–8 58–60 122–3 109–11750 152–3754 67 .5 155 .9 142756 −48749 141 .6 133–4 96 .8 188–9 35 Solubility in 100 parts Water 73381 35.125 669107 1.1325 0.150 v. sl. s. 0.7025 0.2100 v. sl. s. sl. s. c. v. sl. s. 0.0425 v. s. ∞ ∞ 0 .1422 1 .2320 0 .01815 sl . s . c . 2 .515 v . sl . s . i . Alcohol Ether v. s. v. s. s. v. s. s. v. s. s. s. v. s. s. 1218 s. s. 0.6815 s. 5 ∞ ∞ ∞ s . 620 4 .817 v . s . s . s . 33 s . ∞ sl. s. s. h. ∞ ∞ ∞ sl . s . 113 717 v . s . s . ∞ s . s . ∞ s . 628 6 .518 cc . ∞ 2020 d . 1 .616 320 ∞ ∞ ∞ ∞ i . i . i . 0 .2520 0 .3220 0 .1717 v . sl . s . v . sl . s . v . sl . s . 0 .2720 0 .3120 12 .222 2 .122 v . sl . s . s . s . v . sl . s . v . sl . s . 0 .5625 0 .625 i . i . i . s . ∞ ∞ d . ∞ ∞ ∞ ∞ ∞ ∞ v . s . s . s . ∞ ∞ ∞ v . s . ∞ ∞ ∞ ∞ ∞ ∞ s . s . s . s . ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ s . s . s . ∞ ∞ ∞ ∞ ∞ ∞ 44 .6 cc . 0 .2520 s . 0 .2720 ∞ 3320 1 .8214 1200 cc . s . s . v . s . ∞ ∞ v . s . v . s . s . v . s . 8 ∞ s . ∞ ∞ ∞ ∞ ∞ ∞ v . s . s . s . ∞ ∞ ∞ 2-43 Pulegol (iso-)(d-) Pulegone Pyrazole Pyrazoline Pyrazolone Pyrene Pyridazine Pyridine Pyrocatechol (o-) Pyrogallol (1-,2-,3-) Pyrone Pyrrole Pyrrolidine Pyrroline Pyruvic acid Quercitrin Quinaldine (py-2) Quinoline (iso-) -diol (1-,3-) Quinone (p-) R-acid Ca salt (2-)(3-,6-) K salt Na salt Raffinose Resorcinol (m-) Retene Rhamnose (β-) Ricinoleic acid Rosaniline Rosolic acid Saccharin Safrole (1-,3-,4-) (iso-)(1-,3-,4-) Salicylic acid (o-) aldehyde (o-) Saligenin Schaeffer’s salt, Ca K Na Semicarbazide hydrochloride Skatole (3-) Sodium methylate Sorbitol Sorbose (d- or l-) Starch Stearic acid amide Styrene Suberic acid Succinic acid Sucrose Sulfanilic acid (p-) Sylvestrene (d-) Tartaric acid (meso-) (racemic) (d- or l-) Tartronic acid Terephthalic acid (p-) Terpin hydrate (cis-) Terpineol (α-)(d- or l-) (dl-) Terpinyl acetate (α-)(dl-) Tetrabromo-ethane (sym) (uns) Tetrachloro-ethane (sym) (uns) -ethylene Tetracosane (n-) Tetradecane (n-) Tetraethyl-thiuram disulfide C10H17OH C10H16O —NH⋅N:CH⋅CH:CH— —NH⋅N:CH⋅CH2CH2— —NH⋅CO⋅CH2CH:N— C16H10 N2 < (CHCH)2 > CH < (CHCH)2 > N C6H4(OH)2 C6H3(OH)3 CO < (CHCH)2 > O < (CH:CH)2 > NH < (CH2⋅CH2)2 > NH < (CH⋅CH2)2 > NH CH3COCO2H C21H20O11⋅2H2O CH3⋅C9H6N C9H7N C9H7N —C6H4CH:C(OH)N:C(OH)— CO < (CHCH)2 > CO HOC10H5(SO3)2Ca HOC10H5(SO3K)2 HOC10H5(SO3Na)2 C18H32O16⋅5H2O C6H4(OH)2 C18H18 CH3(CHOH)4CHO⋅H2O C17H32(OH)CO2H C20H21ON3 C20H16O3 C6H4(CO)(SO2) > NH CH2:CHCH2⋅C6H3:O2CH2 CH3⋅CH:CH⋅C6H3:O2CH2 HO⋅C6H4⋅CO2H HO⋅C6H4⋅CHO HO⋅C6H4⋅CH2OH (HOC10H6SO3)2Ca⋅5H2O HOC10H6SO3K HOC10H6SO3Na NH2⋅CO⋅NH⋅NH2 NH2⋅CO⋅NH⋅NH3Cl CH3⋅C8H6N CH3ONa [CH2OH(CHOH)2]2 C6H12O6 (C6H10O5)x CH3(CH2)16CO2H CH3(CH2)16CONH2 C6H5CH:CH2 HO2C(CH2)6CO2H HO2C(CH2)2CO2H C12H22O11 H2N⋅C6H4⋅SO3H C10H16 (CHOHCO2H)2 (CHOHCO2H)2⋅H2O (CHOHCO2H)2 CH(OH)(CO2H)2⋅½H2O C6H4(CO2H)2 C10H20O2⋅H2O C10H18O C10H18O CH3CO2⋅C10H17 Br2CH⋅CHBr2 Br3C⋅CH2Br Cl2CH⋅CHCl2 Cl3C⋅CH2Cl Cl2C:CCl2 CH3(CH2)22CH3 CH3(CH2)12CH3 [(C2H5)2NCS]2S2 154 .25 152 .23 68 .08 70 .09 84 .08 202 .25 80 .09 79 .10 110 .11 126 .11 96 .08 67 .09 71 .12 69 .11 88 .06 484 .41 143 .19 129 .16 129 .16 161 .16 108 .09 342 .36 380 .48 348 .26 594 .51 110 .11 234 .34 182 .17 298 .46 319 .40 304 .34 183 .18 162 .19 162 .19 138 .12 122 .12 124 .14 576 .60 262 .32 246 .21 75 .07 111 .53 131 .17 54 .02 182 .17 180 .16 162 .14 284 .48 283 .49 104 .15 174 .19 118 .09 342 .30 173 .19 136 .23 150 .09 168 .10 150 .09 129 .07 166 .13 190 .28 154 .25 154 .25 196 .29 345 .65 345 .65 167 .85 167 .85 165 .83 338 .65 198 .39 296 .54 col. lq. col. lq. nd ./et . lq . nd . yel . pr . lq . col . lq . nd ./aq . nd . cr . lq . lq . lq . col . lq . yel . nd . lq . lq . pl . cr . yel . mn . cr . cr . cr . cr ./aq . col . rhb . lf ./al . col . mn . lq . col . nd . red lf . mn . col . mn . col . lq . mn . col . oil rhb ./aq . cr . cr . cr . pr ./al . pr . lf . pd . cr . rhb . amor . mn . col . cr . col . lq . nd ./aq . col . mn . col . mn . col . cr . lq . cr . tri . mn . pr ./aq . cr . rhb . col . cr . col . cr . lq . col . lq . col . lq . col . lq . lq . col . lq . cr . col . lq . cr . 0.911 20/4 0.932 20/20 70 1 .277 0/4 1 .107 20/4 0 .982 20/4 1 .344 4 1 .453 4 1 .190 40 .3 0 .948 20/4 0 .852 22 .5 0 .910 20/4 1 .267 20/4 1 .059 20/4 1 .095 20 1 .099 21/4 1 .318 20/4 1 .465 0 1 .272 15 1 .1316 1 .47120/4 0 .954 16 1 .100 20/4 1 .122 20/4 1 .443 20/4 1 .153 25/4 1 .161 25 1 .654 15 1 .5021 0 .847 69 .3 0 .903 20/4 1 .266 25/4 1 .572 25/4 1 .588 15 0 .863 20/4 1 .737 1 .697 20/4 1 .760 20/4 1 .510 0 .935 15 0 .935 20/20 0 .966 20/4 2 .964 20/4 2 .875 20/4 1 .600 20/4 1 .588 20/4 1 .624 15/4 0 .779 51/4 0 .765 20/4 1 .17 165 149–50 −8 −42 104–5 133–4 32 .5 13 .6 182–5 −1 −15 24 .6 237 115 .7 119 110 .7 98–9 126 4–5 186 d . 308–10 d . 225–8 11 .2 6–7 159 −7 86–7 96 173 d . 95 d . 300 110–2 165 d . 70–1 108–9 −31 140–4 189–90 170–86 d . d . > 280 86–9 10 224754 186–8 144 subl . d . >360 208 115–6 240–5 309 215–7 131 87–8 90–1 165 244–5750 237 .1747 240 .5763 subl . d . 130 276 .5 390–4 226–810 subl . 233–4 252–3 21120 196 .5 subl . 265–6755 291110 25112 145–6 279100 235 d . 176–7 159–60 205–6 168–70 d . 155–8 subl . 117 38–40 35 < −50 −1 .0 0 −36 −19 51 .1 5 .5 70 d . subl . d . 219–21 218–9752 220 d . 15154 10413 146 .3 129–30 120 .8 324 252 .5 v. sl. s. i. s . ∞ s . i . ∞ ∞ 45 .120 40 13 v . sl . s . i . ∞ v . s . ∞ 0 .04 20 v . sl . s . 6 sl . s . v . sl . s . sl . s . h . 30 .6 25 29 .5 25 25 .2 25 14 .3 20 14712 i . 60 .8 21 i . v . sl . s . 0 .1225 0 .4 25 i . i . 0 .223 1 .7 86 6 .615 4 .7620 3 .4625 6 .2925 v . s . v . s . 0 .05 c . d . v . s . 5517 i . 0 .0325 i . v . sl . s . 0 .1416 6 .820 1790 0 .810 12015 20 .620 13920 v . s . 0 .001 c . 0 .415 i . i . i . i . 20 0 .29 i . 0 .0220 i . i . ∞ s . ∞ v . s . 3 h . s . ∞ v . s . s . s . s . ∞ ∞ ∞ s . ∞ s . 0 .120 v . s . 69 h . ∞ s . sl . s . v . sl . s . v . s . s . s . v . s . s . v . s . s . ∞ ∞ ∞ sl . s . s . ∞ s . s . ∞ sl . s . v . s . h . 3 .1 c . s . ∞ 4915 ∞ v . s . v . s . v . s . h . i . ∞ i . sl . s . 1 .05 c . ∞ ∞ 5115 ∞ v . s . v . s . sl . s . s . i . i . s . v . s . h . sl . s . i . 220 s . h . ∞ s . 9 .915 0 .9 v . sl . s . i . 6g s . h: ∞ 0 .815 1 .215 i . v . sl . s . 20 2515 v . s . sl . s . h . 1015 v . s . v . s . 20 ∞ s . ∞ ∞ ∞ v . s . 0 .09 0 .415 i . i . 115 v . s . v . s . ∞ ∞ ∞ ∞ s . v . s . (Continued ) 2-44 TABLE 2-2 Physical Properties of Organic Compounds (Continued ) Name Tetrafluoro-ethylene Tetrahydro-furan -furfuryl alcohol -pyran Tetralin Tetramethyl-thiuram disulfide Tetryl (2-,4-,6-) Theobromine Thio-acetic acid -aniline (4-,4′-) -carbanilide -naphthol (β-) -phenol -salicylic acid (o-) -urea Thiophene Thymol (5-,2-,1-) Tolidine (0-)(3-,3′-,4-,4′-) Toluene sulfonic acid (o-) (p-) sulfonic amide (p-) sulfonic chloride (p-) Toluic acid (o-) (m-) (p-) Toluidine (o-) (m-) (p-) hydrochloride (o-) sulfonic acid (1-,2-,3-) Toluylenediamine (1-,2-,4-) Tolylene diisocyanate (1-,2-,4-) Trehalose Triamylamine (n-) (i-) Tributyl-amine (n-) phosphite Trichloro-acetic acid -benzene (s-)(1-,3-,5-) -ethane (1-,1-,1-) -ethylene -phenol Tricosane (n-) Tricresyl phosphate (o-) Tridecane (n-) Triethanol amine Triethyl-amine -benzene (1-,3-,5-) (1-,2-,4-) borate citrate Triethylene glycol Trifluoro-chloromethane -chloroethylene -trichloroethane Trimethoxybutane (1-,3-,3-) Trimethylamine Trimethylene bromide chloride glycol Formula Formula weight F2C:CF2 —CH2(CH2)2CH2⋅O— C4H7O⋅CH2OH —CH2(CH2)3CH2⋅O— —C6H4CH2(CH2)2CH2— [(CH3)2NCS]2S2 (NO2)3C6H2⋅N(CH3)NO2 C7H8O2N4 CH3⋅CO⋅SH (NH2⋅C6H4)2S (C6H5⋅NH)2CS C10H7⋅SH C6H5⋅SH HS⋅C6H4⋅CO2H NH2⋅CS⋅NH2 < (CH:CH)2 > S (CH3)(C3H7)C6H3OH [CH3(NH2)C6H3]2 C6H5⋅CH3 CH3⋅C6H4SO3H⋅2H2O CH3⋅C6H4SO3H⋅H2O CH3⋅C6H4SO2NH2 CH3⋅C6H4⋅SO2Cl CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅CO2H CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH2 CH3⋅C6H4⋅NH3Cl CH3(NH2)C6H3SO3H CH3⋅C6H3(NH2)2 CH3⋅C6H3(NCO)2 C12H22O11⋅2H2O [CH3(CH2)3CH2]3N [(CH3)2CH(CH2)2]3N [CH3(CH2)2CH2]3N [CH3(CH2)3O]3P Cl3C⋅CO2H C6H3Cl3 Cl3C⋅CH3 Cl2C:CHCl Cl3C6H2OH CH3(CH2)21CH3 OP(OC6H4CH3)3 CH3(CH2)11CH3 (HOCH2CH2)3N (CH3CH2)3N (C2H5)3C6H3 (C2H5)3C6H3 B(OCH2CH3)3 HOC3H4(CO2C2H5)3 (⋅CH2OCH2CH2OH)2 CF3Cl F2C:CFCl Cl2CF⋅CClF2 CH2(OCH3)CH2C(OCH3)2CH3 (CH3)3N BrCH2CH2CH2Br ClCH2CH2CH2Cl HOCH2CH2CH2OH 100 .02 72 .11 102 .13 86 .13 132 .20 240 .43 287 .14 180 .16 76 .12 216 .30 228 .31 160 .24 110 .18 154 .19 76 .12 84 .14 150 .22 212 .29 92 .14 208 .23 190 .22 171 .22 190 .65 136 .15 136 .15 136 .15 107 .15 107 .15 107 .15 143 .61 187 .22 122 .17 174 .16 378 .33 227 .43 227 .43 185 .35 250 .31 163 .39 181 .45 133 .40 131 .39 197 .45 324 .63 368 .36 184 .36 149 .19 101 .19 162 .27 162 .27 145 .99 276 .28 150 .17 104 .46 116 .47 187 .38 148 .20 59 .11 201 .89 112 .99 76 .09 Form and color Specific gravity Melting point, °C Boiling point, °C gas col. lq. col. lq. lq . col . lq . cr . yel . mn . rhb . yel . lq . nd ./aq . rhb ./al . cr ./al . col . lq . yel . nd . rhb ./al . col . lq . cr . lf . col . lq . cr . mn . mn . tri . cr ./aq . pr ./aq . cr ./aq . col . lq . col . lq . cr . mn . pr . cr . rhb . lq . rhb ./al . lq . col . lq . col . lq . lq . cr . nd . lq . col . lq . nd . lf . lq . col . lq . col . lq . col . oil lq . lq . lq . oil col . lq . gas gas lq . lq . gas lq . lq . oil 1.58−78 0.88821/4 1.05020/4 0 .88120/4 0 .97318/4 1 .29 1 .5719 −142.5 −65 −76.3 65–6 177–8743 88 206764 1 .07410 24 1 .3 −31 155–6 130 .5 330 < −17 108 154 81 23/4 1 .074 1 .40520/4 1 .07015/4 0 .97225/25 20/4 0 .866 1 .062115/4 1 .054112/4 20/4 0 .999 0 .98920/4 1 .04620/4 164 180–2 −30 51 .5 128–9 −95 d . 104–5 137 69 104–5 110–1 179–80 −16 .3 −31 .5 44–5 218–20 99 1 .2328 expl . 93 d . 286–8 168–9 subl . d . 84 232752 110 .8 128 .80 146–70 134 .510 259751 263 274–5 199 .7 203 .3 200 .3 242 283–5 134 .520 97 20/4 0 .786 0 .77820/20 0 .92520/4 1 .61746/15 1 .32526/4 1 .46620/20 1 .49075/4 0 .77948/4 0 .75720/4 1 .12620/20 0 .72920/20 0 .86120/4 0 .88217/4 0 .86420/20 1 .13720/4 1 .12520/20 1 .726−130 1 .57620/4 0 .932 0 .662 −5 1 .987 15/4 1 .201 15 1 .060 20/4 58 63 .5 −73 68–9 47 .7 −6 .2 20–1 −114 .8 −5 −182 −157 .5 −35 −124 −34 .4 240–5 235 216 .5761 122–312 195 .5754 208 .5764 74 .1 87 .2 246 23415 234 277–9150 89 .4 215 217–8755 120 294 290 −80 −27 .9 47 .6 63–525 3 .5 167 .5 123–5 214 Solubility in 100 parts Water 0.0130 s. ∞ s . i . i . i . 0 .0615 s . sl . s . h . i . v . sl . s . v . sl . s . sl . s . h . 9 .213 i . 0 .0919 v . sl . s . 0 .0516 v . s . v . s . 0 .29 i . 2 .17100 1 .6100 1 .3100 1 .525 sl . s . 0 .7421 s . 0 .9711 s . h . d . s . h . i . i . i . i . 12025 i . i . 0 .125 0 .0925 i . i . i . ∞ ∞ > 190 i . i . d . i . ∞ d . i . d . 4119 0 .1730 0 .2725 ∞ Alcohol Ether s. ∞ s. ∞ s . s . s . h . 0 .06 c . ∞ s . v . s . v . s . v . s . s . s . s . v . s . s . s . s . s . 7 .45 s . v . s . v . s . v . s . ∞ ∞ v . s . sl . s . s . 0 .03 h . ∞ s . v . s . v . s . ∞ s . d . sl . s . h . sl . s . v . s . s . ∞ s . v . s . v . s . ∞ ∞ v . s . s . i . s . ∞ s . sl . s . ∞ ∞ v . s . s . v . s . ∞ ∞ s . s . v . s . sl . s . ∞ s . s . ∞ ∞ ∞ v . sl . s . ∞ ∞ s . s . s . ∞ s . s . s . ∞ ∞ v . s . Trinitro-benzene (1-,3-,5-) -benzoic acid (2-,4-,6-) -tert-butylxylene -naphthalene (α-)(1-,3-,5-) (β-)(1-,3-,8-) (γ-)(1-,4-,5-) -phenol (2-,3-,6-) -toluene (β-)(2-,3-,4-) (γ-)(2-,4-,5-) (α-)(2-,4-,6-) Trional Triphenyl-arsine carbinol guanidine (α-) methane methyl phosphate Tripropylamine (n-) Undecane (n-) Urea nitrate Uric acid Valeric acid (n-) (i-) aldehyde (n-) (i-) amide (n-) (i-) Vanillic acid (3-,4-,1-) alcohol (3-,4-,1-) hyl-thiuram disulfide Vanillin (3-,4-,1-) Veratrole (o-) Vinyl acetate (poly-) acetic acid acetylene alcohol (poly-) chloride propionate Xylene (o-) (m-) (p-) sulfonic acid (1-,4-,2-) Xylidine (1:2)(3-) (1:2)(4-) (1:3)(2-) (1:3)(4-) (1:3)(5-) (1:4)(2-) Xylose (l-)(+) Xylylene dichloride (p-) Zinc diethyl dimethyl dimethyl-dithiocarbamate note: °F = 9⁄5°C + 32 . C6H3(NO2)3 (NO2)3C6H2CO2H (NO2)3C6(CH3)2C4H9 C10H5(NO2)3 C10H5(NO2)3 C10H5(NO2)3 (NO2)3C6H2OH CH3C6H2(NO2)3 CH3C6H2(NO2)3 CH3C6H3(NO2)3 (C2H5SO2C2H4)2 (C6H5)3As (C6H5)3COH C6H5N:C(NHC6H5)2 (C6H5)3CH (C6H5)3C . . . OP(OC6H5)3 (CH3CH2CH2)3N CH3(CH2)9CH3 H2N⋅CO⋅NH2 CO(NH2)2⋅HNO3 C5H4O3N4 C2H5CH2CH2CO2H (CH3)2CHCH2CO2H C2H5CH2CH2CHO (CH3)2CHCH2CHO C2H5CH2CH2CONH2 (CH3)2CHCH2CONH2 CH3O(OH)C6H3CO2H CH3O(OH)C6H3CH2OH [(C2H5)2NCS]2S2 CH3O(OH)C6H3CHO C6H4(OCH3)2 CH3CO2CH:CH2 (CH3CO2CH:CH2)x CH2:CH⋅CH2CO2H CH2:CH⋅C:CH CH2:CHOH (CH2:CHOH)x CH2:CHCl C2H5CO2CH:CH2 C6H4(CH3)2 C6H4(CH3)2 C6H4(CH3)2 (CH3)2C6H3SO3H⋅2H2O (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 (CH3)2C6H3NH2 CH2OH(CHOH)3CHO C6H4(CH2Cl)2 Zn(CH2CH3)2 Zn(CH3)2 Zn[S2CN(CH3)2]2 213 .10 257 .11 297 .26 263 .16 263 .16 263 .16 229 .10 227 .13 227 .13 227 .13 242 .36 306 .23 260 .33 287 .36 244 .33 243 .32 326 .28 143 .27 156 .31 60 .06 123 .07 168 .11 102 .13 102 .13 86 .13 86 .13 101 .15 101 .15 168 .15 154 .16 296 .54 152 .15 138 .16 86 .09 (86 .09) 86 .09 52 .07 44 .05 (44 .05) 62 .50 100 .12 106 .17 106 .17 106 .17 222 .26 121 .18 121 .18 121 .18 121 .18 121 .18 121 .18 150 .13 175 .06 123 .53 95 .48 305 .84 col. rhb. rhb./aq. nd./al. rhb. cr./al. yel. cr. nd. cr. yel. pl. cr./al. pl./al. pl. cr. rhb./al. cr. col. cr. pr./al. col. lq. col . lq . col . pr . col . mn . cr . col . lq . col . lq . lq . col . lq . mn . pl . mn . nd ./aq . mn ./aq . cr . mn . cr . col . lq . col . lq . gas gas lq . col . lq . col . lq . col . lq . col . lf . lq . pr . lq . lq . oil oil nd . mn . col . lq . col . lq . 1.688 20/4 1.620 20/4 1.620 20/4 1.654 1.199 85/4 1.306 1.188 20/4 1.13 1.014 99/4 1.206 58/4 0.757 20/4 0 .741 20/4 1 .335 20/4 1 .893 20 0 .939 20/4 0 .931 20/20 0 .819 11 0 .803 17 1 .023 0 .965 20/4 1 .17 1 .056 1 .091 15/15 0 .932 20/4 1 .1920 1 .013 15/15 0 .705 1 .5 1 .320 0 .908 25/25 20/4 0 .881 0 .867 17/4 0 .861 20/4 0 .991 15 1 .076 17 .5 0 .980 15 0 .978 20/4 0 .972 20/4 0 .979 21/4 1 .535 0 1 .417 0 1 .182 18 1 .386 11 2 .0040/4 121 210–20 d. 110 122–3 218–9 148–9 117–8 112 104 80.8 76 59–60 162.5 144–5 93.4 145–7 49–50 −93.5 −25 .6 132 .7 152 d . d . −34 .5 −37 .6 −92 −51 106 135–7 207 115 70 81–2 22 .5 < −60 100–25 −39 d . >200 −160 −25 −47 .4 13 .2 86 < −15 49–50 15 .5 153–4 100 .5 −28 −40 248–50 d. expl. expl. expl. d. >360 >360 d. 359754 d. 24511 156.5 194 .5 d . 187 176 103 .4 92 .5 232 subl . d . 285 207 .1 72–3 163 5 .5 −12 93–5 144 139 .3 138 .5 1490 .1 223 224–6 216–7 213–4 221–2 215789 240–5 d . 118 46 0.0315 2.0524 i. i. 0.02100 i. s. h. i. i. 0.0120 0.315 i. i. i. i. i. i. v. sl. s. i . 10017 v . s . h . 0 .06 h . 3 .316 4 .220 v . sl . s . sl . s . v . s . s . 0 .1214 v . s . h . i . 114 v . sl . s . 220 i . s . 0 .670 .6 s . sl . s . v . sl . s . i . i . i . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . v . sl . s . 11720 i . d . d . i . 1.918 1.518 sl. s. s. 0.0523 0.1119 v. s. sl. s. c. s. h. 1.522 50 s. v. s. 40 v. s. h. sl. s. h. 15525 ∞ ∞ 2020 s . i . ∞ ∞ s . s . v . s . s . v . s . v . s . s. i . ∞ ∞ s . s . v . s . s . v . s . v . s . v . s . s . ∞ v . s . s . ∞ ∞ ∞ s . v . s . s . s . s . ∞ ∞ v . s . s . s . v . sl . s . s . d . d . i . v . sl . s . 0.1315 0.419 v. s. s. v. s. 533 6.615 v. s. v. s. v. s. v. s. ∞ ∞ sl . s . 2-45 2-46 PHYSICAL AnD CHEMICAL DATA VAPOR PRESSURES VAPOR PRESSURES OF PURE SUBSTAnCES TABLE 2-3 Vapor Pressure of Water Ice from 0 to -40çC Vapor pressure t, °C 0 −0 .5 −1 .0 −1 .5 −2 .0 −2 .5 −3 .0 −3 .5 −4 .0 −4 .5 −5 .0 −5 .5 −6 .0 −6 .5 −7 .0 −7 .5 −8 .0 −8 .5 −9 .0 −9 .5 −10 .0 −10 .5 −11 .0 −11 .5 −12 .0 −12 .5 −13 .0 Vapor pressure Vapor pressure mmHg kPa t, °C mmHg kPa t, °C mmHg kPa 4 .584 4 .399 4 .220 4 .049 3 .883 3 .724 3 .571 3 .423 3 .281 3 .145 3 .013 2 .887 2 .766 2 .649 2 .537 2 .429 2 .325 2 .225 2 .130 2 .038 1 .949 1 .865 1 .783 1 .705 1 .630 1 .558 1 .489 0 .6112 0 .5865 0 .5627 0 .5398 0 .5177 0 .4965 0 .4761 0 .4564 0 .4375 0 .4193 0 .4018 0 .3849 0 .3687 0 .3532 0 .3382 0 .3238 0 .3100 0 .2967 0 .2839 0 .2717 0 .2599 0 .2486 0 .2377 0 .2273 0 .2173 0 .2077 0 .1985 −13 .5 −14 .0 −14 .5 −15 .0 −15 .5 −16 .0 −16 .5 −17 .0 −17 .5 −18 .0 −18 .5 −19 .0 −19 .5 −20 .0 −20 .5 −21 .0 −21 .5 −22 .0 −22 .5 −23 .0 −23 .5 −24 .0 −24 .5 −25 .0 −25 .5 −26 .0 −26 .5 1 .423 1 .359 1 .298 1 .240 1 .184 1 .130 1 .079 1 .029 0 .9822 0 .9370 0 .8937 0 .8522 0 .8125 0 .7745 0 .7381 0 .7034 0 .6701 0 .6383 0 .6078 0 .5787 0 .5509 0 .5243 0 .4989 0 .4747 0 .4515 0 .4294 0 .4083 0 .1897 0 .1812 0 .1731 0 .1653 0 .1578 0 .1507 0 .1438 0 .1372 0 .1310 0 .1249 0 .1191 0 .1136 0 .1083 0 .1033 0 .09841 0 .09377 0 .08934 0 .08510 0 .08104 0 .07716 0 .07345 0 .06991 0 .06652 0 .06329 0 .06020 0 .05725 0 .05443 −27 .0 −27 .5 −28 .0 −28 .5 −29 .0 −29 .5 −30 .0 −30 .5 −31 .0 −31 .5 −32 .0 −32 .5 −33 .0 −33 .5 −34 .0 −34 .5 −35 .0 −35 .5 −36 .0 −36 .5 −37 .0 −37 .5 −38 .0 −38 .5 −39 .0 −39 .5 −40 .0 0 .3881 0 .3688 0 .3505 0 .3330 0 .3162 0 .3003 0 .2851 0 .2706 0 .2568 0 .2437 0 .2311 0 .2192 0 .2078 0 .1970 0 .1867 0 .1769 0 .1676 0 .1587 0 .1503 0 .1423 0 .1347 0 .1274 0 .1206 0 .1140 0 .1078 0 .1019 0 .0963 0 .05174 0 .04918 0 .04673 0 .04439 0 .04216 0 .04004 0 .03801 0 .03608 0 .03424 0 .03249 0 .03082 0 .02923 0 .02771 0 .02627 0 .02490 0 .02359 0 .02235 0 .02116 0 .02004 0 .01897 0 .01796 0 .01699 0 .01607 0 .01520 0 .01437 0 .01359 0 .01284 source: Formulation of Wagner, Saul, and Pruss, J. Phys. Chem. Ref. Data, 23, 515 (1994), implemented in Harvey, Peskin, and Klein, NIST/ASME Steam Properties, NIST Standard Reference Database 10, Version 2 .2, National Institute of Standards and Technology, Gaithersburg, Md ., 2000 . This source provides data down to 190 K (−83 .15°C) . A formula extending to 110 K may be found in Murphy and Koop, Q. J. R. Meteorol. Soc., 131, 1539 (2005) . TABLE 2-4 Vapor Pressure of Supercooled Liquid Water from 0 to -40çC* Vapor pressure Vapor pressure Vapor pressure t, °C mmHg kPa t, °C mmHg kPa t, °C mmHg kPa 0 −0.5 −1.0 −1.5 −2.0 −2.5 −3.0 −3.5 −4.0 −4.5 −5.0 −5.5 −6.0 −6.5 −7.0 −7.5 −8.0 −8.5 −9.0 −9.5 −10.0 −10.5 −11.0 −11.5 −12.0 −12.5 −13.0 4.584 4.421 4.262 4.108 3.959 3.816 3.676 3.542 3.411 3.285 3.163 3.046 2.932 2.822 2.715 2.612 2.513 2.417 2.324 2.235 2.149 2.065 1.985 1.907 1.832 1.760 1.690 0.6112 0.5894 0.5682 0.5477 0.5279 0.5087 0.4901 0.4722 0.4548 0.4380 0.4218 0.4061 0.3909 0.3762 0.3620 0.3483 0.3351 0.3223 0.3099 0.2980 0.2865 0.2753 0.2646 0.2542 0.2442 0.2346 0.2253 −13.5 −14.0 −14.5 −15.0 −15.5 −16.0 −16.5 −17.0 −17.5 −18.0 −18.5 −19.0 −19.5 −20.0 −20.5 −21.0 −21.5 −22.0 −22.5 −23.0 −23.5 −24.0 −24.5 −25.0 −25.5 −26.0 −26.5 1.623 1.558 1.495 1.435 1.377 1.321 1.267 1.215 1.165 1.117 1.070 1.026 0.9827 0.9414 0.9016 0.8633 0.8265 0.7911 0.7571 0.7244 0.6930 0.6628 0.6337 0.6059 0.5791 0.5534 0.5288 0.2163 0.2077 0.1993 0.1913 0.1836 0.1761 0.1689 0.1620 0.1553 0.1489 0.1427 0.1367 0.1310 0.1255 0.1202 0.1151 0.1102 0.1055 0.1009 0.0965 0.0923 0.08836 0.08449 0.08078 0.07721 0.07379 0.07050 −27.0 −27.5 −28.0 −28.5 −29.0 −29.5 −30.0 −30.5 −31.0 −31.5 −32.0 −32.5 −33.0 −33.5 −34.0 −34.5 −35.0 −35.5 −36.0 −36.5 −37.0 −37.5 −38.0 −38.5 −39.0 −39.5 −40.0 0.5051 0.4824 0.4606 0.4397 0.4197 0.4005 0.3820 0.3644 0.3475 0.3313 0.3158 0.3009 0.2867 0.2731 0.2600 0.2476 0.2356 0.2242 0.2133 0.2029 0.1929 0.1834 0.1743 0.1656 0.1573 0.1494 0.1419 0.06734 0.06431 0.06141 0.05862 0.05595 0.05339 0.05094 0.04858 0.04633 0.04417 0.04210 0.04012 0.03822 0.03640 0.03467 0.03300 0.03141 0.02989 0.02844 0.02705 0.02572 0.02445 0.02324 0.02208 0.02098 0.01992 0.01891 ∗source: Murphy and Koop, Q. J. R. Meteorol. Soc., 131, 1552 (2005) . The formula in the reference extends down to 123 K (−150 .15°C), although in practice pure liquid water cannot be supercooled below about 235 K . Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32 . To convert millimeters of mercury to pounds-force per square inch, multiply by 0 .01934 . To convert cubic feet to cubic meters, multiply by 0 .02832 . To convert bars to pounds-force per square inch, multiply by 14 .504 . To convert bars to kilopascals, multiply by 1 × 102 . Additional References Additional vapor-pressure data may be found in major thermodynamic property databases, such as those produced by the AIChE’s DIPPR program (aiche .org/dippr), NIST’s Thermodynamics Research Center (trc .nist .gov), the Dortmund Databank (ddbst .de), and the Physical Property Data Service (ppds .co .uk) . Additional sources include the NIST Chemistry Webbook (webbook .nist .gov/chemistry/); Boublik, T ., V . Fried, and E . Hala, The Vapor Pressures of Pure Substances, 2d ed ., Elsevier, Amsterdam, 1984; Bruce Poling, JohnPrausnitz, and John O’Connell, The Properties of Gases and Liquids, 5th ed ., McGraw-Hill, New York, 2001; Vapor Pressure of Chemicals (subvolumes A, B, and C), vol . IV/20 in Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology—New Series, Springer-Verlag, Berlin, 1999–2001 . The most recent work on water may be found at The International Association for the Properties of Water and Steam website http:// iapws .org . TABLE 2-5 Vapor Pressure (MPa) of Liquid Water from 0 to 100çC t, °C 0 .01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Pvp, MPa t, °C Pvp, MPa t, °C Pvp, MPa 0 .00061165 0 .00065709 0 .00070599 0 .00075808 0 .00081355 0 .00087258 0 .00093536 0 .0010021 0 .0010730 0 .0011483 0 .0012282 0 .0013130 0 .0014028 0 .0014981 0 .0015990 0 .0017058 0 .0018188 0 .0019384 0 .0020647 0 .0021983 0 .0023393 0 .0024882 0 .0026453 0 .0028111 0 .0029858 0 .0031699 0 .0033639 0 .0035681 0 .0037831 0 .0040092 0 .0042470 0 .0044969 0 .0047596 0 .0050354 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 0 .0053251 0 .0056290 0 .0059479 0 .0062823 0 .0066328 0 .0070002 0 .0073849 0 .0077878 0 .0082096 0 .0086508 0 .0091124 0 .0095950 0 .010099 0 .010627 0 .011177 0 .011752 0 .012352 0 .012978 0 .013631 0 .014312 0 .015022 0 .015762 0 .016533 0 .017336 0 .018171 0 .019041 0 .019946 0 .020888 0 .021867 0 .022885 0 .023943 0 .025042 0 .026183 0 .027368 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 0 .028599 0 .029876 0 .031201 0 .032575 0 .034000 0 .035478 0 .037009 0 .038595 0 .040239 0 .041941 0 .043703 0 .045527 0 .047414 0 .049367 0 .051387 0 .053476 0 .055635 0 .057867 0 .060173 0 .062556 0 .065017 0 .067558 0 .070182 0 .072890 0 .075684 0 .078568 0 .081541 0 .084608 0 .087771 0 .091030 0 .094390 0 .097852 0 .10142 From E . W . Lemmon, M . O . McLinden, and D . G . Friend, “ Thermophysical Properties of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds . P . J . Linstrom and W . G . Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg, Md . (http://webbook .nist .gov) and Wagner, W ., and A ., Pruss, “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002 . The website mentioned above allows users to generate their own tables of thermodynamic properties . The user can select the units as well as the temperatures and/or pressures for which properties are to be generated . The results can then be copied into spreadsheets or other files . VAPOR PRESSURES TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family Name Cmpd. no. Formula Paraffins Methane Ethane Propane Butane Pentane Hexane Heptane Octane Nonane Decane Undecane Dodecane Tridecane Tetradecane Pentadecane Hexadecane Heptadecane Octadecane Nonadecane Eicosane 2-Methylpropane 2-Methylbutane 2,3-Dimethylbutane 2-Methylpentane 2,3-Dimethylpentane 2,2,3,3-Tetramethylbutane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane Cyclopropane Cyclobutane Cyclopentane Cyclohexane Methylcyclopentane Ethylcyclopentane Methylcyclohexane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Ethylcyclohexane 193 125 295 31 279 171 160 265 256 74 336 123 327 319 277 169 158 263 254 124 236 202 107 234 114 323 332 333 71 64 69 65 217 134 213 108 109 110 133 CH4 C2H6 C 3H 8 C4H10 C5H12 C6H14 C7H16 C8H18 C9H20 C10H22 C11H24 C12H26 C13H28 C14H30 C15H32 C16H34 C17H36 C18H38 C19H40 C20H42 C4H10 C5H12 C6H14 C6H14 C7H16 C8H18 C8H18 C8H18 C 3H 6 C 4H 8 C5H10 C6H12 C6H12 C7H14 C7H14 C8H16 C8H16 C8H16 C8H16 135 305 36 37 38 70 285 68 177 166 271 260 77 238 205 206 218 219 298 294 29 30 201 C 2H 4 C 3H 6 C4H8 C4H8 C4H8 C5H8 C5H10 C6H10 C6H12 C7H14 C8H16 C9H18 C10H20 C4H8 C5H10 C5H10 C6H10 C6H10 C9H14 C3H4 C4H6 C4H6 C5H8 7 43 288 289 178 180 181 168 C2H2 C4H6 C5H8 C5H8 C6H10 C6H10 C6H10 C7H12 Olefins Ethylene Propylene 1-Butene cis-2-Butene trans-2-Butene Cyclopentene 1-Pentene Cyclohexene 1-Hexene 1-Heptene 1-Octene 1-Nonene 1-Decene 2-Methyl propene 2-Methyl-1-butene 2-Methyl-2-butene 1-Methylcyclopentene 3-Methylcyclopentene Propenylcyclohexene Propadiene 1,2-Butadiene 1,3-Butadiene 3-Methyl-1,2-butadiene Acetylenes Acetylene 1-Butyne 1-Pentyne 2-Pentyne 3-Hexyne 1-Hexyne 2-Hexyne 1-Heptyne Name Cmpd. no. Formula Acetylenes 1-Octyne 1-Nonyne 1-Decyne Methyl acetylene Vinyl acetylene Dimethyl acetylene 2-Methyl -1-butene-3-yne 3-Methyl-1-butyne 273 262 79 197 339 105 207 210 C8H14 C9H16 C10H18 C3H4 C4H4 C4H6 C5H6 C5H8 16 325 312 129 343 344 345 243 62 304 330 331 246 321 40 24 290 318 C6H6 C7H8 C8H8 C8H10 C8H10 C8H10 C8H10 C9H10 C9H12 C9H12 C9H12 C9H12 C10H8 C10H12 C10H14 C12H10 C14H10 C18H14 153 1 299 44 278 170 159 264 255 73 CH2O C2H4O C3H6O C4H8O C5H10O C6H12O C7H14O C8H16O C9H18O C10H20O 8 5 222 229 283 284 310 67 144 175 176 226 102 164 165 269 270 20 C3H4O C3H6O C4H8O C5H10O C5H10O C5H10O C6H4O2 C6H10O C6H12O C6H12O C6H12O C6H12O C7H14O C7H14O C7H14O C8H16O C8H16O C13H10O 156 324 320 322 C4H4O C4H4S C4H8O C4H8S 14 25 52 80 149 Ar Br2 Cl2 D2 F2 Aromatics Benzene Toluene Styrene Ethylbenzene m-Xylene o-Xylene p-Xylene alpha-Methyl styrene Cumene Propylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Naphthalene 1,2,3,4-Tetrahydronaphthalene Butylbenzene Biphenyl Phenanthrene o-Terphenyl Aldehydes Formaldehyde Acetaldehyde Propionaldehyde Butyraldehyde Pentanal Hexanal Heptanal Octanal Nonanal Decanal Ketones Acrolein Acetone Methylethyl ketone Methylisopropyl ketone 2-Pentanone 3-Pentanone Quinone Cyclohexanone Ethylisopropyl ketone 2-Hexanone 3-Hexanone Methylisobutyl ketone Diisopropyl ketone 3-Heptanone 2-Heptanone 2-Octanone 3-Octanone Benzophenone Heterocyclics Furan Thiophene Tetrahydrofuran Tetrahydrothiophene Elements Argon Bromine Chlorine Deuterium Fluorine (Continued ) 2-47 2-48 PHYSICAL AnD CHEMICAL DATA TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family (Continued ) Name Cmpd. no. Formula Elements Hydrogen Helium-4 Nitrogen Neon Oxygen 183 157 249 247 275 H2 He N2 Ne O2 194 126 296 297 34 35 281 282 66 173 174 162 163 267 268 258 259 76 337 237 204 21 214 215 216 137 309 32 33 CH4O C2H6O C3H8O C3H8O C4H10O C4H10O C5H12O C5H12O C6H12O C6H14O C6H14O C7H16O C7H16O C8H18O C8H18O C9H20O C9H20O C10H22O C11H24O C4H10O C5H12O C7H8O C7H14O C7H14O C7H14O C2H6O2 C3H8O2 C4H10O2 C4H10O2 291 59 60 61 C6H6O C7H8O C7H8O C7H8O 112 245 221 120 95 240 228 103 208 225 244 147 143 104 101 235 13 84 142 22 121 C2H6O C3H6O C3H8O C4H8O2 C4H10O C4H10O C4H10O C4H10O2 C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O2 C6H14O C6H14O C7H8O C8H18O C8H18O C9H12O C12H10O 155 274 3 9 191 300 CH2O2 C2H2O4 C2H4O2 C3H4O2 C3H4O4 C3H6O2 Alcohols Methanol Ethanol 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol 2-Pentanol Cyclohexanol 1-Hexanol 2-Hexanol 1-Heptanol 2-Heptanol 1-Octanol 2-Octanol 1-Nonanol 2-Nonanol 1-Decanol 1-Undecanol 2-Methyl-2-propanol 3-Methyl-1-butanol Benzyl alcohol 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Ethylene glycol 1,2-Propylene glycol 1,2-Butanediol 1,3-Butanediol Phenols Phenol m-Cresol o-Cresol p-Cresol Ethers Dimethyl ether Methyl vinyl ether Methylethyl ether 1,4-Dioxane Diethyl ether Methylpropyl ether Methylisopropyl ether 1,1-Dimethoxyethane Methylbutyl ether Methylisobutyl ether Methyl tert-butyl ether Ethylpropyl ether Ethylisopropyl ether 1,2-Dimethoxypropane Di-isopropyl ether Methyl pentyl ether Anisole Dibutyl ether Ethylhexyl ether Benzyl ethyl ether Diphenyl ether Acids Formic acid Oxalic acid Acetic acid Acrylic acid Malonic acid Propionic acid Name Cmpd. no. Formula Methacrylic acid Acetic anhydride Succinic acid Butyric acid Isobutyric acid 2-Methylbutanoic acid Pentanoic acid 2-Ethyl butanoic acid Hexanoic acid Benzoic acid Heptanoic acid Phthalic anhydride Terephthalic acid 2-Ethyl hexanoic acid Octanoic acid 2-Methyloctanoic acid Nonanoic acid Decanoic acid 192 4 313 45 189 203 280 131 172 18 161 293 317 141 266 233 257 75 C4H6O2 C4H6O3 C4H6O4 C4H8O2 C4H8O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C7H6O2 C7H14O2 C8H4O3 C8H6O4 C8H16O2 C8H16O2 C9H18O2 C9H18O2 C10H20O2 224 140 196 198 338 127 239 306 232 146 211 302 39 132 200 130 115 119 C2H4O2 C3H6O2 C3H6O2 C4H6O2 C4H6O2 C4H8O2 C4H8O2 C4H8O2 C5H8O2 C5H10O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C8H8O2 C9H10O2 C10H10O4 C10H10O4 199 138 106 128 136 190 303 329 94 93 100 122 328 CH5N C2H5N C2H7N C2H7N C2H8N2 C3H9N C3H9N C3H9N C4H11N C4H11NO2 C6H15N C6H15N C6H15N 154 2 113 195 15 CH3NO C2H5NO C3H7NO C3H7NO C7H7NO 6 63 10 301 46 19 C2H3N C2N2 C3H3N C3H5N C4H7N C7H5N 251 248 CH3NO2 C2H5NO2 Acids Esters Methyl formate Ethyl formate Methyl acetate Methyl acrylate Vinyl acetate Ethyl acetate Methyl propionate Propyl formate Methyl methacrylate Ethyl propionate Methyl butyrate Propyl acetate Butyl acetate Ethyl butyrate Methyl benzoate Ethyl benzoate Dimethyl phthalate Dimethyl terephthalate Amines Methyl amine Ethyleneimine Dimethyl amine Ethyl amine Ethylenediamine Isopropyl amine Propyl amine Trimethyl amine Diethyl amine Diethanol amine Di-isopropyl amine Dipropyl amine Triethyl amine Amides Formamide Acetamide N,N-Dimethyl formamide N-Methyl acetamide Benzamide Nitriles Acetonitrile Cyanogen Acrylonitrile Propionitrile Butyronitrile Benzonitrile Nitro Compounds Nitromethane Nitroethane VAPOR PRESSURES 2-49 TABLE 2-6 Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Sorted by Chemical Family (Continued ) Name Cmpd. no. Formula 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene 334 335 C6H3N3O6 C7H5N3O6 227 292 C2H3NO C7H5NO 231 145 308 307 41 42 287 286 17 72 179 23 167 272 261 78 CH4S C2H6S C3H8S C3H8S C4H10S C4H10S C5H12S C5H12S C6H6S C6H12S C6H14S C7H8S C7H16S C8H18S C9H20S C10H22S 117 111 223 96 230 241 209 C2H6S C2H6S2 C3H8S C4H10S C4H10S C4H10S C5H12S 50 51 55 83 90 99 28 56 152 340 326 81 82 88 CCl4 CF4 CHCl3 CH2Br2 CH2Cl2 CH2F2 CH3Br CH3Cl CH3F C2H3Cl C2H3Cl3 C2H4Br2 C2H4Br2 C2H4Cl2 Isocyanates Methyl isocyanate Phenyl isocyanate Mercaptans Methyl mercaptan Ethyl mercaptan Propyl mercaptan 2-Propyl mercaptan Butyl mercaptan sec-Butyl mercaptan Pentyl mercaptan 2-Pentyl mercaptan Benzenethiol Cyclohexyl mercaptan Hexyl mercaptan Benzyl mercaptan Heptyl mercaptan Octyl mercaptan Nonyl mercaptan Decyl mercaptan Sulfides Dimethyl sulfide Dimethyl disulfide Methylethyl sulfide Diethyl sulfide Methylisopropyl sulfide Methylpropyl sulfide Methylbutyl sulfide Cmpd. no. Formula 1,2-Dichloroethane 1,1-Difluoroethane 1,2-Difluoroethane Bromoethane Chloroethane Fluoroethane 1,1-Dichloropropane 1,2-Dichloropropane 1-Chloropropane 2-Chloropropane m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene Bromobenzene Chlorobenzene Fluorobenzene 89 97 98 27 54 151 91 92 57 58 85 86 87 26 53 150 C2H4Cl2 C2H4F2 C2H4F2 C2H5Br C2H5Cl C2H5F C3H6Cl2 C3H6Cl2 C3H7Cl C3H7Cl C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H5Br C6H5Cl C6H5F 242 212 220 341 148 116 311 CH6Si CH5ClSi CH4Cl2Si C2H3Cl3Si C2H5Cl3Si C2H8Si F4Si 186 49 47 48 250 315 184 185 187 188 12 182 253 252 314 276 316 CHN CO CO2 CS2 F3N F6S HBr HCl HF H2S H3N H4N2 NO N2 O O2 S O3 O3 S 11 139 118 342 Mixture C2H4O C2H6OS H2O Silanes Methylsilane Methylchlorosilane Methyldichlorosilane Vinyl trichlorosilane Ethyltrichlorosilane Dimethylsilane Silicon tetrafluoride Light Gases Halogenated Hydrocarbons Carbon tetrachloride Carbon tetrafluoride Chloroform Dibromomethane Dichloromethane Difluoromethane Bromomethane Chloromethane Fluoromethane Vinyl chloride 1,1,2-Trichloroethane 1,1-Dibromoethane 1,2-Dibromoethane 1,1-Dichloroethane Name Halogenated Hydrocarbons Nitro Compounds Hydrogen cyanide Carbon monoxide Carbon dioxide Carbon disulfide Nitrogen trifluoride Sulfur hexafluoride Hydrogen bromide Hydrogen chloride Hydrogen fluoride Hydrogen sulfide Ammonia Hydrazine Nitric oxide Nitrous oxide Sulfur dioxide Ozone Sulfur trioxide Others Air Ethylene oxide Dimethyl sulfoxide Water 2-50 PHYSICAL AnD CHEMICAL DATA TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 Formula No. Name Ar Br2 CCl4 CF4 CHCl3 CHN CH2Br2 CH2Cl2 CH2F2 CH2O CH2O2 CH3Br CH3Cl CH3F CH3NO CH3NO2 CH4 CH4Cl2Si CH4O CH4S CH5ClSi CH5N CH6Si CO CO2 CS2 C2H2 C2H2O4 C2H3Cl C2H3Cl3 C2H3Cl3Si C2H3N C2H3NO C2H4 C2H4Br2 C2H4Br2 C2H4Cl2 C2H4Cl2 C2H4F2 C2H4F2 C2H4O C2H4O C2H4O2 C2H4O2 C2H5Br C2H5Cl C2H5Cl3Si C2H5F C2H5N C2H5NO C2H5NO2 C2H6 C2H6O C2H6O C2H6O2 C2H6OS C2H6S C2H6S C2H6S2 C2H7N C2H7N C2H8N2 C2H8Si C2N2 C3H3N C3H4 C3H4 C3H4O C3H4O2 C3H4O4 C3H5N C3H6 C3H6 C3H6Cl2 11 14 25 50 51 55 186 83 90 99 153 155 28 56 152 154 251 193 220 194 231 212 199 242 49 47 48 7 274 340 326 341 6 227 135 81 82 88 89 97 98 1 139 3 224 27 54 148 151 138 2 248 125 112 126 137 118 117 145 111 106 128 136 116 63 10 197 294 8 9 191 301 71 305 91 Air Argon Bromine Carbon tetrachloride Carbon tetrafluoride Chloroform Hydrogen cyanide Dibromomethane Dichloromethane Difluoromethane Formaldehyde Formic acid Bromomethane Chloromethane Fluoromethane Formamide Nitromethane Methane Methyldichlorosilane Methanol Methyl mercaptan Methylchlorosilane Methyl amine Methylsilane Carbon monoxide Carbon dioxide Carbon disulfide Acetylene Oxalic acid Vinyl chloride 1,1,2-Trichloroethane Vinyl trichlorosilane Acetonitrile Methyl Isocyanate Ethylene 1,1-Dibromoethane 1,2-Dibromoethane 1,1-Dichloroethane 1,2-Dichloroethane 1,1-Difluoroethane 1,2-Difluoroethane Acetaldehyde Ethylene oxide Acetic acid Methyl formate Bromoethane Chloroethane Ethyltrichlorosilane Fluoroethane Ethyleneimine Acetamide Nitroethane Ethane Dimethyl ether Ethanol Ethylene glycol Dimethyl sulfoxide Dimethyl sulfide Ethyl mercaptan Dimethyl disulfide Dimethyl amine Ethyl amine Ethylenediamine Dimethylsilane Cyanogen Acrylonitrile Methyl acetylene Propadiene Acrolein Acrylic acid Malonic acid Propionitrile Cyclopropane Propylene 1,1-Dichloropropane Formula No. Name C3H6Cl2 C3H6O C3H6O C3H6O C3H6O2 C3H6O2 C3H6O2 C3H7Cl C3H7Cl C3H7NO C3H7NO C3H8 C3H8O C3H8O C3H8O C3H8O2 C3H8S C3H8S C3H8S C3H9N C3H9N C3H9N C4H4 C4H4O C4H4S C4H6 C4H6 C4H6 C4H6 C4H6O2 C4H6O2 C4H6O2 C4H6O3 C4H6O4 C4H7N C4H8 C4H8 C4H8 C4H8 C4H8 C4H8O C4H8O C4H8O C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8O2 C4H8S C4H10 C4H10 C4H10O C4H10O C4H10O C4H10O C4H10O C4H10O C4H10O2 C4H10O2 C4H10O2 C4H10S C4H10S C4H10S C4H10S C4H10S C4H11N C4H11NO2 C5H6 C5H8 C5H8 C5H8 C5H8 C5H8 C5H8O2 92 5 245 299 140 196 300 57 58 113 195 295 221 296 297 309 223 308 307 190 303 329 339 156 324 29 30 43 105 192 198 338 4 313 46 36 37 38 64 238 44 222 320 45 120 127 189 239 306 322 31 236 34 35 95 237 240 228 32 33 103 41 42 96 230 241 94 93 207 70 201 210 288 289 232 1,2-Dichloropropane Acetone Methyl vinyl ether Propionaldehyde Ethyl formate Methyl acetate Propionic acid 1-Chloropropane 2-Chloropropane N,N-Dimethyl formamide N-Methyl acetamide Propane Methylethyl ether 1-Propanol 2-Propanol 1,2-Propylene glycol Methylethyl sulfide Propyl mercaptan 2-Propyl mercaptan Isopropyl amine Propyl amine Trimethyl amine Vinyl acetylene Furan Thiophene 1,2-Butadiene 1,3-Butadiene 1-Butyne Dimethyl acetylene Methacrylic acid Methyl acrylate Vinyl acetate Acetic anhydride Succinic acid Butyronitrile 1-Butene cis-2-Butene trans-2-Butene Cyclobutane 2-Methyl propene Butyraldehyde Methylethyl ketone Tetrahydrofuran Butyric acid 1,4-Dioxane Ethyl acetate Isobutyric acid Methyl propionate Propyl formate Tetrahydrothiophene Butane 2-Methylpropane 1-Butanol 2-Butanol Diethyl ether 2-Methyl-2-propanol Methylpropyl ether Methylisopropyl ether 1,2-Butanediol 1,3-Butanediol 1,1-Dimethoxyethane Butyl mercaptan sec-Butyl mercaptan Diethyl sulfide Methylisopropyl sulfide Methylpropyl sulfide Diethyl amine Diethanol amine 2-Methyl-1-butene-3-yne Cyclopentene 3-Methyl-1,2-butadiene 3-Methyl-1-butyne 1-Pentyne 2-Pentyne Methyl methacrylate VAPOR PRESSURES 2-51 TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 (Continued ) Formula No. Name C5H10 C5H10 C5H10 C5H10 C5H10O C5H10O C5H10O C5H10O C5H10O2 C5H10O2 C5H10O2 C5H10O2 C5H10O2 C5H12 C5H12 C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O C5H12O2 C5H12S C5H12S C5H12S C6H3N3O6 C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H4O2 C6H5Br C6H5Cl C6H5F C6H6 C6H6O C6H6S C6H10 C6H10 C6H10 C6H10 C6H10 C6H10 C6H10O C6H12 C6H12 C6H12 C6H12O C6H12O C6H12O C6H12O C6H12O C6H12O C6H12O2 C6H12O2 C6H12O2 C6H12O2 C6H12S C6H14 C6H14 C6H14 C6H14O C6H14O C6H14O C6H14O C6H14S C6H15N C6H15N C6H15N C7H5N C7H5N3O6 C7H5NO C7H6O2 C7H7NO 69 205 206 285 229 278 283 284 146 203 211 280 302 202 279 143 147 204 208 225 244 281 282 104 209 286 287 334 85 86 87 310 26 53 150 16 291 17 218 68 178 180 181 219 67 65 177 217 66 144 170 175 176 226 39 131 132 172 72 107 171 234 101 173 174 235 179 100 122 328 19 335 292 18 15 Cyclopentane 2-Methyl-1-butene 2-Methyl-2-butene 1-Pentene Methylisopropyl ketone Pentanal 2-Pentanone 3-Pentanone Ethyl propionate 2-Methylbutanoic acid Methyl butyrate Pentanoic acid Propyl acetate 2-Methylbutane Pentane Ethylisopropyl ether Ethylpropyl ether 3-Methyl-1-butanol Methylbutyl ether Methylisobutyl ether Methyl tert-butyl ether 1-Pentanol 2-Pentanol 1,2-Dimethoxypropane Methylbutyl sulfide 2-Pentyl mercaptan Pentyl mercaptan 1,3,5-Trinitrobenzene m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene Quinone Bromobenzene Chlorobenzene Fluorobenzene Benzene Phenol Benzenethiol 1-Methylcyclopentene Cyclohexene 3-Hexyne 1-Hexyne 2-Hexyne 3-Methylcyclopentene Cyclohexanone Cyclohexane 1-Hexene Methylcyclopentane Cyclohexanol Ethylisopropyl ketone Hexanal 2-Hexanone 3-Hexanone Methylisobutyl ketone Butyl acetate 2-Ethyl butanoic acid Ethyl butyrate Hexanoic acid Cyclohexyl mercaptan 2,3-Dimethylbutane Hexane 2-Methylpentane Di-isopropyl ether 1-Hexanol 2-Hexanol Methyl pentyl ether Hexyl mercaptan Di-isopropyl amine Dipropyl amine Triethyl amine Benzonitrile 2,4,6-Trinitrotoluene Phenyl isocyanate Benzoic acid Benzamide Formula C7H8 C7H8O C7H8O C7H8O C7H8O C7H8O C7H8S C7H12 C7H14 C7H14 C7H14 C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O C7H14O2 C7H16 C7H16 C7H16O C7H16O C7H16S C8H4O3 C8H6O4 C8H8 C8H8O2 C8H10 C8H10 C8H10 C8H10 C8H14 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16O C8H16O C8H16O C8H16O2 C8H16O2 C8H18 C8H18 C8H18 C8H18 C8H18O C8H18O C8H18O C8H18O C8H18S C9H10 C9H10O2 C9H12 C9H12 C9H12 C9H12 C9H12O C9H14 C9H16 C9H18 C9H18O C9H18O2 C9H18O2 C9H20 C9H20O C9H20O C9H20S C10H8 C10H10O4 C10H10O4 C10H12 C10H14 C10H18 No. Name 325 13 21 59 60 61 23 168 134 166 213 102 159 164 165 214 215 216 161 114 160 162 163 167 293 317 312 200 129 343 344 345 273 108 109 110 133 271 264 269 270 141 266 265 323 332 333 84 142 267 268 272 243 130 62 304 330 331 22 298 262 260 255 233 257 256 258 259 261 246 115 119 321 40 79 Toluene Anisole Benzyl alcohol m-Cresol o-Cresol p-Cresol Benzyl mercaptan 1-Heptyne Ethylcyclopentane 1-Heptene Methylcyclohexane Di-isopropyl ketone Heptanal 3-Heptanone 2-Heptanone 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Heptanoic acid 2,3-Dimethylpentane Heptane 1-Heptanol 2-Heptanol Heptyl mercaptan Phthalic anhydride Terephthalic acid Styrene Methyl benzoate Ethylbenzene m-Xylene o-Xylene p-Xylene 1-Octyne 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Ethylcyclohexane 1-Octene Octanal 2-Octanone 3-Octanone 2-Ethyl hexanoic acid Octanoic acid Octane 2,2,3,3-Tetramethylbutane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane Dibutyl ether Ethylhexyl ether 1-Octanol 2-Octanol Octyl mercaptan alpha-Methyl styrene Ethyl benzoate Cumene Propylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene Benzyl ethyl ether Propenylcyclohexene 1-Nonyne 1-Nonene Nonanal 2-Methyloctanoic acid Nonanoic acid Nonane 1-Nonanol 2-Nonanol Nonyl mercaptan Naphthalene Dimethyl phthalate Dimethyl terephthalate 1,2,3,4-Tetrahydronaphthalene Butylbenzene 1-Decyne (Continued ) 2-52 PHYSICAL AnD CHEMICAL DATA TABLE 2-7 Formula Index of Substances in Tables 2-8, 2-22, 2-32, 2-69, 2-72, 2-74, 2-75, 2-95, 2-106, 2-139, 2-140, 2-146, and 2-148 (Continued ) Formula No. Name Formula No. Name C10H20 C10H20O C10H20O2 C10H22 C10H22O C10H22S C11H24 C11H24O C12H10 C12H10O C12H26 C13H10O C13H28 C14H10 C14H30 C15H32 C16H34 C17H36 C18H14 C18H38 C19H40 C20H42 Cl2 77 73 75 74 76 78 336 337 24 121 123 20 327 290 319 277 169 158 318 263 254 124 52 1-Decene Decanal Decanoic acid Decane 1-Decanol Decyl mercaptan Undecane 1-Undecanol Biphenyl Diphenyl ether Dodecane Benzophenone Tridecane Phenanthrene Tetradecane Pentadecane Hexadecane Heptadecane o-Terphenyl Octadecane Nonadecane Eicosane Chlorine D2 F2 F3N F4Si F6S HBr HCl HF H2 H2O H2S H3N H4N2 He NO N2 N2O Ne O2 O2S O3 O3S 80 149 250 311 315 184 185 187 183 342 188 12 182 157 253 249 252 247 275 314 276 316 Deuterium Fluorine Nitrogen trifluoride Silicon tetrafluoride Sulfur hexafluoride Hydrogen bromide Hydrogen chloride Hydrogen fluoride Hydrogen Water Hydrogen sulfide Ammonia Hydrazine Helium-4 Nitric oxide Nitrogen Nitrous oxide Neon Oxygen Sulfur dioxide Ozone Sulfur trioxide TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K Cmpd. no.∗ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O CAS C1 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 52.9107 125.8 1 53.27 67.1818 69.006 46.735 39.63 138.4 46.745 57.3157 21.662 90.483 128.06 42.127 85.474 83.107 77.765 88.513 55.0403 88.404 100.68 68.541 118.02 77.314 108.26 63.749 57.3242 44.7643 39.714 75.572 66.343 103.28 123.22 106.29483 122.552 51.836 72.541 71.704 122.82 101.22 65.382 60.649 77.004 51.648 78.1171 60.6576 47.0169 67.114 45.698 78.441 61.89 71.334 54.144 44.677 146.43 44.555 58.3592 46.854 95.403 210.88 C2 −4643.14 −12,376 −6304.5 −7463.47 −5599.6 −5126.18 −2552.2 −7122.7 −6587.1 −5662.2 −692.39 −4669.7 −9307.7 −1093.1 −11,932 −6486.2 −8455.1 −11,829 −7363.83 −11,769 −11,059 −7886.2 −10,527 −9910.4 −6592 −7130.2 −4931.2 −3907.8 −3769.9 −4621.9 −4363.2 −11,548 −12,620 −9866.35511 −10,236.2 −4019.2 −4691.2 −4563.1 −9253.2 −9255.4 −6262.4 −5785.9 −5054.5 −5301.36 −8924.37 −6404.32 −2839 −4820.4 −1076.6 −6128.1 −2296.3 −3855 −6244.4 −4026 −7792.3 −3521.3 −5111.33 −4445.5 −10,581 −13,928 C3 −4.50683 −14.589 −4.2985 −6.24388 −7.0985 −3.54064 −2.78 −19.638 −3.2208 −5.06221 −0.39208 −11.607 −16.693 −4.1425 −8.3348 −9.2194 −7.7404 −8.6826 −4.50612 −8.9014 −10.709 −6.5804 −13.91 −7.5079 −14.16 −5.879 −5.2244 −3.4016 −2.6407 −8.5323 −7.046 −10.925 −13.986 −11.6553 −14.125 −4.5229 −7.9776 −7.9053 −14.99 −11.538 −6.2585 −5.6113 −8.5665 −4.2559 −7.59929 −5.49286 −3.86388 −7.5303 −4.8814 −8.5766 −7.086 −8.5171 −4.5343 −3.371 −20.614 −3.4258 −5.35261 −3.6533 −10.004 −29.483 C4 2.70E-17 5.0824E-06 8.89E-18 6.86E-18 6.2237E-06 1.40E-17 2.39E-16 0.026447 5.2253E-07 1.51E-17 0.0047574 0.017194 0.014919 0.000057254 1.29E-18 6.9844E-06 4.31E-18 2.32E-19 1.95E-18 1.93E-18 3.06E-18 2.4285E-06 6.4794E-06 2.24E-18 0.016043 5.21E-18 3.08E-17 2.95E-17 6.94E-18 0.000012269 9.4509E-06 4.26E-18 0.000003926 1.08E-17 2.36E-17 4.88E-17 0.000010368 0.000011319 0.00001047 5.9208E-06 1.49E-17 1.59E-17 0.000010161 1.14E-17 7.39E-18 1.13E-17 2.81E-16 0.0091695 0.000075673 6.8465E-06 0.000034687 0.012378 4.70E-18 2.27E-17 0.024578 5.63E-17 2.47E-17 1.33E-17 4.30E-18 0.025182 C5 Tmin, K P at Tmin 6 2 6 6 2 6 6 1 2 6 1 1 1 2 6 2 6 6 6 6 6 2 2 6 1 6 6 6 6 2 2 6 2 6 6 6 2 2 2 2 6 6 2 6 6 6 6 1 2 2 2 1 6 6 1 6 6 6 6 1 149.78 353.33 289.81 200.15 178.45 229.32 192.4 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.2 265.85 242.43 154.25 179.44 136.95 164.25 134.86 220 196.15 183.85 158.45 87.8 134.26 167.62 199.65 185.3 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.11 68.15 250.33 89.56 172.12 227.95 136.75 207.15 175.45 150.35 155.97 285.39 304.19 5.15E-01 3.36E+02 1.28E+03 4.10E-02 2.79E+00 1.71E+02 1.27E+05 1.03E+01 2.57E+02 2.47E+00 5.64E+03 6.11E+03 2.45E+00 6.87E+04 3.55E+02 4.76E+03 7.68E+00 7.96E+02 5.40E+00 1.49E+00 1.88E-01 2.31E+01 2.98E-01 9.42E+01 5.85E+03 7.84E+00 3.80E-01 2.07E+02 4.47E-01 6.92E+01 6.74E-01 2.93E-04 3.74E-07 2.91E-04 1.24E-06 6.94E-07 2.72E-01 7.45E+01 8.17E-02 1.54E-04 2.35E-03 3.40E-05 1.18E+00 6.97E-01 1.03E+01 9.41E-04 5.18E+05 1.49E+00 1.54E+04 1.12E+03 1.08E+02 1.37E+03 8.45E+00 2.61E-01 5.25E+01 8.84E+02 8.47E-02 9.08E-01 5.86E+00 6.53E+01 Tmax, K 466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15 632.35 460.35 536.4 416.25 503.15 489 705.85 697.55 P at Tmax 5.570E+06 6.569E+06 5.739E+06 4.000E+06 4.709E+06 4.850E+06 6.106E+06 5.020E+06 5.661E+06 4.660E+06 3.793E+06 1.130E+07 4.273E+06 4.896E+06 5.047E+06 4.875E+06 4.728E+06 4.469E+06 4.215E+06 3.357E+06 4.372E+06 3.113E+06 4.074E+06 3.407E+06 1.028E+07 4.520E+06 5.565E+06 6.929E+06 4.361E+06 4.303E+06 3.770E+06 5.202E+06 4.033E+06 4.414E+06 4.190E+06 4.021E+06 4.238E+06 4.100E+06 3.087E+06 2.882E+06 3.973E+06 4.060E+06 4.599E+06 4.410E+06 4.060E+06 3.880E+06 7.384E+06 8.041E+06 3.494E+06 4.544E+06 3.742E+06 7.793E+06 4.529E+06 5.267E+06 5.554E+06 6.759E+06 4.425E+06 4.510E+06 4.522E+06 5.058E+06 2-53 (Continued ) 2-54 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗ Name 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di-sopropyl amine Di-sopropyl ether Di-sopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Formula C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 CAS 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 C1 C2 C3 118.53 102.81 39.0596 85.899 51.087 189.19 85.424 88.184 66.341 67.952 40.608 85.146 93.5742 112.73 126.405 156.23933 68.401 91.91 142.94 18.947 62.711 43.751 86.295 72.227 53.187 77.105 88.31 66.611 92.355 101.6 83.495 65.955 106.38 49.314 136.9 46.705 73.491 84.625 69.132 462.84 41.631 50.868 53.637 62.097 66.592 71.738 77.161 81.184 78.952 78.429 81.045 44.704 82.762 78.335 72.517 63.08 84.39 56.273 66.1795 44.494 −11,957 −8674.6 −3473.98 −4884.4 −5226.4 −14,337 −7944.4 −6624.9 −5198.5 −5187.5 −3179.6 −7843.7 −10,403.8 −9749.6 −14,864.6 −15,212.33492 −7776.9 −10,565 −11,119 −154.47 −6503.5 −5587.7 −7010.3 −7537.6 −6827.5 −8111.1 −8463.4 −5493.1 −6920.4 −6541.6 −6661.4 −6015.6 −13,714 −4949 −6954.3 −5177.4 −4385.9 −5217.4 −3847.7 −18,227 −4668.7 −6036.5 −5251.2 −6174.9 −4999.8 −5302 −5691.1 −6927 −7075.4 −6882.1 −6941.3 −3525.6 −7955.5 −6348.7 −10,415 −4062.3 −5740.6 −7620.6 −9870.41 −5406.7 −13.293 −11.922 −2.48683 −10.883 −4.2278 −24.148 −9.2862 −10.059 −6.8103 −7.0785 −2.8937 −9.2982 −9.79483 −13.245 −13.9067 −18.42393 −6.4637 −9.5957 −17.818 −0.57226 −5.7669 −3.0891 −9.5972 −7.0596 −4.3233 −7.8886 −9.6308 −6.7301 −10.651 −12.247 −9.2386 −6.5509 −11.06 −3.9256 −19.254 −3.5985 −8.1851 −9.871 −7.5868 −73.734 −2.8551 −4.066 −4.5649 −5.715 −6.8387 −7.3324 −8.501 −8.8498 −8.4344 −8.4129 −8.777 −3.4444 −8.8038 −8.5105 −6.755 −6.425 −9.6454 −4.6279 −5.85599 −3.1287 C4 8.70E-18 7.0048E-06 2.86E-17 0.014934 9.76E-18 0.00001074 4.9957E-06 8.2566E-06 0.000006193 6.8165E-06 5.61E-17 5.1788E-06 4.57E-18 7.1266E-06 2.51E-18 8.50E-18 6.38E-18 5.70E-18 0.00001102 0.038899 1.0427E-06 8.2664E-07 6.7794E-06 9.14E-18 2.31E-18 2.7267E-06 4.5833E-06 5.3579E-06 9.1426E-06 0.000012311 6.7652E-06 4.3172E-06 3.26E-18 9.20E-18 0.024508 1.7147E-06 0.000012978 0.00001305 0.000015065 0.092794 0.00063693 1.1326E-06 1.68E-17 1.23E-17 6.6793E-06 6.42E-17 8.0325E-06 0.000005458 4.5035E-06 4.9831E-06 5.5501E-06 5.46E-17 4.2431E-06 6.4311E-06 1.3269E-06 1.51E-16 0.000010073 4.3819E-07 1.47E-18 2.89E-18 C5 Tmin, K P at Tmin 6 2 6 1 6 2 2 2 2 2 6 2 6 2 6 6 6 6 2 1 2 2 2 6 6 2 2 2 2 2 2 2 6 6 1 2 2 2 2 1 1 2 6 6 2 6 2 2 2 2 2 6 2 2 2 6 2 2 6 6 307.93 177.14 245.25 182.48 279.69 296.6 242 169.67 179.28 138.13 145.59 189.64 285 243.51 304.55 280.05 206.89 247.56 229.15 18.73 210.15 282.85 220.6 175.3 248.39 256.15 326.14 176.19 237.49 178.01 192.5 172.71 301.15 223.35 156.85 169.2 154.56 179.6 136.95 176.85 187.65 204.81 159.95 226.1 240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 212.72 160 274.18 122.93 174.88 291.67 413.79 284.95 3.45E+01 4.71E-04 7.44E+04 1.80E+02 5.36E+03 7.65E+01 6.80E+00 1.04E-01 9.07E+00 1.28E-02 7.80E+01 8.24E-03 5.51E+00 1.39E+00 1.45E-01 1.50E-01 2.59E-02 2.59E-02 1.60E-01 1.72E+04 2.64E+00 7.53E+02 2.13E+01 7.14E-04 6.41E+00 6.49E+00 1.23E+03 2.21E+00 2.37E+02 5.93E+00 1.72E+00 8.25E-02 1.02E-01 3.74E+02 3.95E-01 9.93E-02 6.45E+01 1.17E+02 5.43E+01 4.47E-03 6.86E+00 8.21E-01 9.45E-02 4.50E+01 6.12E+03 7.56E+01 1.52E-02 6.06E+01 6.41E+00 8.04E-02 2.07E-01 3.05E+00 1.95E-01 1.26E-02 3.72E-02 4.15E-01 7.86E+00 5.02E+01 1.15E+03 2.53E+03 Tmax, K 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.26 523.1 500.05 576 507.8 543 473.2 437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587 P at Tmax 5.151E+06 3.226E+06 5.924E+06 4.991E+06 4.093E+06 4.265E+06 3.989E+06 4.392E+06 4.513E+06 4.799E+06 5.494E+06 3.970E+06 2.600E+06 2.091E+06 2.280E+06 2.308E+06 2.223E+06 2.130E+06 2.363E+06 1.663E+06 6.034E+06 5.375E+06 7.170E+06 2.459E+06 4.070E+06 4.074E+06 4.070E+06 5.106E+06 5.318E+06 6.093E+06 4.239E+06 4.232E+06 4.260E+06 3.674E+06 3.641E+06 3.961E+06 4.507E+06 4.372E+06 5.761E+06 3.199E+06 2.869E+06 3.017E+06 3.773E+06 3.447E+06 4.870E+06 5.258E+06 3.130E+06 2.939E+06 2.939E+06 2.938E+06 5.363E+06 5.274E+06 4.365E+06 2.882E+06 2.779E+06 3.561E+06 5.533E+06 5.648E+06 2.759E+06 5.158E+06 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 59.969 54 137.47 203.66 51.857 73.304 66.824 81.56 89.063 52.923 90.464 57.661 80.208 88.671 53.963 73.51 84.09 66.51 91.944 73.833 122.364 77.523 57.723 57.459 65.551 105.64 86.898 61.6271 42.393 51.915 38.593 41.2744 49.3632 100.3 43.8066 74.738 11.533 156.95 55.3058 87.829 112.372 147.41 153.088 78.463 75.494 65.922 79.858 59.083 156.06 58.7734 104.65 98.3767 135.42149 122.695 107.44 73.155 51.9766 47.091 68.467 133.2 123.71 76.858 12.69 −8585.5 −6018.5 −11,976 −19,441 −2598.7 −7122.3 −6227.6 −5596.9 −7733.7 −7531.7 −10,243 −6346.5 −7203.2 −7012.7 −2443 −7572.7 −10,411 −6019.2 −5293.4 −5817 −13,308.8 −7978.8 −5236.9 −6356.8 −5027.4 −8007 −6646.4 −6095.88 −1103.3 −5439 −3123.34 −2676.65 −3847.87 −10,763 −5131.03 −5417 −8.99 −15,557 −6694.68 −6996.4 −12,660.1 −13,466 −12,618.7 −8077.2 −7896.5 −6189 −8501.8 −6031.8 −15,015 −6529.3 −6995.5 −11,394 −12,288.40621 −10,870 −8528.6 −7242.9 −5104.66 −5104 −7390.5 −7492.9 −7639 −7245.2 −94.896 −5.1538 −4.4981 −16.698 −25.525 −5.1283 −7.1424 −6.41 −9.0779 −9.917 −4.2347 −9.2836 −5.032 −8.6023 −10.045 −5.5643 −7.1435 −8.1976 −6.3332 −11.682 −7.809 −13.5709 −7.7757 −5.2136 −4.9545 −6.6853 −12.477 −9.5758 −5.69714 −4.1203 −4.2896 −2.53014 −3.03914 −4.09834 −10.946 −3.18777 −8.0636 0.6724 −18.966 −4.64122 −9.8802 −12.147 −17.353 −18.7479 −7.9062 −7.5047 −6.3629 −8.1043 −5.3072 −18.941 −5.17151 −12.702 −10.2239 −15.73191 −14.192 −12.679 −7.2569 −4.34844 −3.6371 −6.5456 −18.405 −16.451 −8.22 1.1125 2.00E-18 9.97E-18 8.0906E-06 8.8382E-06 0.000014913 2.8853E-06 1.79E-17 0.000008792 0.000005986 1.1835E-06 5.26E-18 8.25E-18 4.5901E-06 7.4578E-06 0.000019079 1.21E-17 1.65E-18 1.04E-17 0.014902 0.00000632 6.42E-18 1.01E-17 2.30E-17 5.20E-18 6.3208E-06 0.000009 5.96E-17 1.06E-17 0.000057815 8.75E-18 5.30E-17 2.45E-16 4.64E-17 3.8503E-06 2.37819E-06 0.00000747 0.2743 6.4559E-06 5.28E-18 7.2099E-06 4.39E-18 1.13E-17 7.45073E-06 8.05E-18 8.91E-18 2.01E-17 8.15E-18 1.44E-17 6.8172E-06 6.95E-18 0.000012381 3.29E-18 1.27E-17 0.000003871 8.4606E-06 1.27E-17 1.17E-17 0.00051621 7.76E-18 0.022062 0.016495 0.0061557 0.00032915 6 6 2 2 2 2 6 2 2 2 6 6 2 2 2 6 6 6 1 2 6 6 6 6 2 2 6 6 2 6 6 6 6 2 2 2 1 2 6 2 6 6 2 6 6 6 6 6 2 6 2 6 6 2 2 6 6 1 6 1 1 1 2 300.03 210.15 263.57 309.58 90.35 159.05 189.6 192.15 178.2 238.45 258.15 175.15 161.84 134.71 104 284.29 260.15 195.2 160.65 193.55 155.15 180 140 204.15 125.26 199.25 145.65 167.55 53.48 230.94 129.95 131.35 155.15 275.6 281.45 187.55 1.76 295.13 229.8 182.57 265.83 239.15 220 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95 7.09E+00 3.69E+00 6.15E-01 9.26E-03 1.13E+00 4.96E-04 1.43E+00 1.52E+02 3.91E-03 1.69E-01 4.63E-01 1.04E-02 3.57E-04 3.71E-06 1.26E+02 6.78E+02 2.19E-01 9.71E+00 7.79E+00 1.81E+01 1.44E-14 7.60E-04 4.31E-03 9.70E-01 1.14E-03 7.80E-01 1.61E-03 1.96E-02 2.53E+02 1.51E+02 9.43E+00 4.34E+02 4.89E+01 1.04E+00 2.41E+03 5.00E+01 1.46E+03 4.65E-02 2.56E+00 1.83E-01 4.66E-02 1.95E-02 6.55E-03 2.30E+00 3.54E+00 1.86E-03 3.05E-01 8.15E-01 9.23E-02 1.86E+00 9.02E-01 3.17E-01 2.25E-02 7.46E-02 1.45E+00 2.22E+00 5.16E-04 2.20E-01 1.31E-02 3.92E-04 5.40E-01 4.08E+02 7.21E+03 766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620 540.2 677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19 3.097E+06 3.111E+06 1.822E+06 1.175E+06 4.852E+06 6.109E+06 3.850E+06 5.594E+06 3.590E+06 3.203E+06 3.403E+06 2.935E+06 3.041E+06 3.412E+06 5.032E+06 6.290E+06 8.257E+06 6.850E+06 7.255E+06 4.708E+06 2.780E+06 2.460E+06 3.414E+06 3.293E+06 5.492E+06 3.336E+06 3.372E+06 3.321E+06 5.167E+06 4.544E+06 4.980E+06 5.875E+06 6.590E+06 7.751E+06 5.810E+06 5.550E+06 2.284E+05 1.344E+06 3.160E+06 2.719E+06 3.042E+06 3.013E+06 3.000E+06 2.919E+06 2.946E+06 2.921E+06 2.772E+06 3.209E+06 1.411E+06 3.460E+06 3.045E+06 3.309E+06 3.446E+06 3.323E+06 3.286E+06 3.322E+06 3.210E+06 3.540E+06 3.079E+06 3.635E+06 3.530E+06 1.473E+07 1.315E+06 2-55 (Continued ) 2-56 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗ 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 Name Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl-1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane Formula BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si CAS 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 C1 29.315 104.27 36.75 59.544 85.584 110.38 136.66 119.172 109.53 39.205 82.718 79.128 61.267 50.242 107.69 75.206 84.828 66.575 71.308 85.383 117.074 93.131 83.927 95.453 60.164 96.344 69.459 71.87 95.984 92.684 134.63 125.1 54.179 55.368 52.732 52.601 79.788 78.586 72.698 79.07 77.184 57.984 80.503 57.612 53.867 45.242 52.82 54.15 107.36 105.7 53.579 61.907 108.43 172.27 78.01 70.717 67.942 83.711 37.205 C2 −2424.5 −3731.2 −3927.1 −4143.8 −3839.9 −10,540 −7201.5 −15,688.8 −10,410 −1324.4 −6904.5 −9523.9 −5618.6 −3811.9 −7027.2 −5082.8 −9334.7 −5213.4 −4976 −9575.4 −10,743.2 −5525.4 −5640.5 −5448.8 −5621.7 −7856.3 −5250 −6885.7 −5401.7 −7080.8 −10,682 −10,288 −7477.2 −5149.8 −5286.9 −5120.3 −5420 −5176.3 −6143.6 −6114.1 −5606.1 −5339.6 −7421.8 −5197.9 −4701 −5324.4 −5437.7 −4337.7 −8085.3 −12,458 −5041.2 −6188.9 −5039.9 −11,589 −4634.1 −6439.7 −5419.1 −6786.9 −2590.3 C3 −1.1354 −15.047 −2.1245 −6.1764 −11.199 −12.262 −18.934 −12.6757 −12.289 −3.4366 −8.8622 −7.7355 −5.6473 −4.2526 −13.916 −8.0919 −8.7063 −6.7693 −7.7169 −8.6164 −13.1654 −11.852 −9.6453 −12.384 −5.53 −11.058 −7.1125 −7.0944 −11.829 −10.695 −16.511 −15.157 −4.22 −5.0136 −4.4509 −4.4554 −9.0702 −8.7501 −7.5779 −8.631 −8.392 −5.2362 −8.379 −5.1269 −4.7052 −3.2551 −4.442 −4.8127 −12.72 −11.234 −4.6404 −5.706 −15.012 −22.113 −8.9575 −6.9845 −6.8067 −9.2526 −2.5993 C4 2.38E-18 0.03134 3.89E-17 0.000014161 0.018848 1.43E-17 0.022255 1.55E-18 0.000003199 0.000031019 7.4664E-06 3.16E-18 2.11E-17 6.53E-17 0.015185 0.000008113 6.17E-18 4.8106E-06 8.7271E-06 5.61E-18 1.17E-17 0.014205 0.000011121 0.015643 1.86E-17 0.000007308 7.93E-17 1.49E-17 0.000018092 8.1366E-06 8.4427E-06 0.000010918 3.52E-18 0.000003222 1.09E-17 1.33E-17 0.000011489 9.1727E-06 5.6476E-06 6.5333E-06 7.8468E-06 2.08E-17 1.81E-17 2.17E-17 2.88E-17 3.04E-18 9.51E-18 4.50E-17 8.3307E-06 4.46E-18 1.94E-17 1.18E-17 0.022725 0.000013703 0.000013413 2.01E-17 4.78E-17 6.6666E-06 6.0508E-06 C5 Tmin, K P at Tmin 6 1 6 2 1 6 1 6 2 2 2 6 6 6 1 2 6 2 2 6 6 1 2 1 6 2 6 6 2 2 2 2 6 2 6 6 2 2 2 2 2 6 6 6 6 6 6 6 2 6 6 6 1 2 2 6 6 2 2 185.15 158.97 259.83 189.79 187.68 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 193 155.95 135.58 139.39 160.15 157.48 175.3 183.45 187.35 139.05 146.58 299.15 280.15 269.15 130.73 146.62 168.54 182.55 160 186.48 167.23 174.15 188 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240 119.55 176 113.54 298.97 132.81 185.65 133.97 160.17 116.34 2.95E+04 1.35E+04 1.87E+04 3.37E+02 2.29E+04 7.82E-02 7.73E+00 9.97E+01 5.86E+01 1.17E+04 1.11E-01 2.86E+01 1.02E+00 4.15E+02 4.07E+00 1.77E+02 1.81E+00 7.28E-01 1.21E-04 6.94E-05 1.14E-08 2.05E-02 1.94E-02 2.92E+00 2.99E-02 4.61E-03 4.36E+01 1.34E-01 4.12E-01 1.52E-04 2.57E+02 4.56E+01 1.62E+01 2.25E-04 3.98E-03 5.37E-01 2.58E+01 7.85E+00 1.39E+00 2.25E-01 6.88E+00 8.70E+00 6.99E-02 7.28E+03 3.32E-03 2.95E-01 1.80E-01 3.15E+00 1.91E+01 4.19E-04 2.07E-05 6.33E-02 1.21E-02 5.88E+03 6.45E-01 6.34E-01 2.90E-03 4.26E-03 1.43E+01 Tmax, K 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.56 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5 442 572.1 686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5 P at Tmax 8.463E+06 8.356E+06 5.353E+06 6.487E+06 8.999E+06 3.683E+06 4.540E+06 6.097E+06 4.812E+06 4.590E+06 8.145E+06 4.997E+06 4.695E+06 5.619E+06 4.277E+06 7.414E+06 3.589E+06 3.831E+06 3.366E+06 3.886E+06 3.933E+06 3.465E+06 3.394E+06 4.469E+06 3.377E+06 3.464E+06 4.199E+06 3.480E+06 4.170E+06 3.486E+06 3.994E+06 3.807E+06 3.767E+06 3.759E+06 4.130E+06 4.129E+06 3.964E+06 4.433E+06 4.120E+06 4.261E+06 5.983E+06 3.416E+06 3.272E+06 5.480E+06 3.764E+06 3.792E+06 4.022E+06 7.231E+06 3.674E+06 2.545E+06 3.044E+06 3.041E+06 3.630E+06 3.957E+06 4.004E+06 4.028E+06 3.802E+06 3.972E+06 4.702E+06 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2 O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 56.485 57.1299 51.085 62.964 29.755 75.632 58.282 68.149 57.278 96.512 72.974 182.54 80.3832 109.35 123.374 162.854 213.069 63.313 106.2 114.77 157.68 74.0298 96.084 116.477 144.11083 185.828 63.775 72.382 74.936 78.368 64.612 107.476 51.245 40.067 135.57 28.3041 78.741 93.2079 114.74801 116.828 84.635 44.286 46.994 58.985 67.309 82.805 137.29 72.958 95.444 86.779 126.5 57.069 59.078 84.66416 110.717 64.268 50.8769 54.552 59.9958 115.16 58.398 91.379 43.905 −6954.2 −5200.7 −4271 −8137.5 −271.06 −7202.3 −1084.1 −2257.9 −6089 −4045 −2650 −17,897 −9096.15 −9030.4 −14,215.3 −15,204.55331 −16,246 −7040.4 −10,982 −9430.8 −16,093 −8302.12 −7900.2 −13,300.4 −13,667.15667 −14,520.2 −7711.3 −8054.8 −7155.9 −8855.4 −6802.5 −12,833.4 −1200.2 −2204.8 −13,478 −4657.56 −5420.3 −10,470.5 −10,643.3 −10,453 −7078.4 −5415.1 −4289.5 −6193.1 −6880.8 −5683.8 −7447.1 −10,943 −10,113 −8101.8 −12,551 −3682.7 −3492.6 −8307.24422 −9040 −7298.9 −4931 −7149.4 −6006.16 −8433.9 −5312.7 −8276.8 −3097.8 −4.7889 −5.13976 −4.307 −5.6317 −2.6081 −7.6464 −8.3144 −8.9118 −4.9821 −12.277 −8.261 −22.498 −8.03581 −12.882 −13.5607 −19.42436 −27.6195 −5.8055 −11.696 −13.631 −18.954 −7.19776 −11.003 −12.6746 −16.82611 −23.6236 −5.7359 −7.0002 −7.5843 −7.8202 −6.0261 −11.3837 −6.4361 −2.9351 −16.022 −0.732149 −8.8253 −9.61345 −12.85754 −13.1768 −9.3 −3.0913 −3.7345 −5.2746 −6.4449 −9.4301 −19.01 −6.7902 −10.09 −9.5303 −15.002 −5.5662 −6.0669 −8.57673 −12.676 −5.9109 −4.16673 −4.2769 −5.46004 −13.934 −5.2876 −10.176 −3.4425 2.78E-18 1.65E-17 3.05E-17 2.27E-18 0.000527 1.83E-17 0.044127 0.023233 1.22E-17 0.00002886 9.70E-15 7.4008E-06 4.71E-18 7.8544E-06 3.17E-18 1.07E-17 1.31827E-05 7.58E-18 8.90E-18 8.1918E-06 5.9272E-06 5.31E-18 7.1802E-06 3.98E-18 9.37E-18 1.08854E-05 3.09E-18 5.83E-18 1.71E-17 5.66E-18 1.10E-17 1.34E-18 0.028405 7.75E-16 5.6136E-06 –8.31E-18 9.6171E-06 5.62E-18 1.25E-17 1.07E-17 6.2702E-06 1.86E-18 2.54E-17 7.40E-18 1.01E-17 0.000010767 0.021415 1.09E-18 6.76E-18 6.1367E-06 7.7521E-06 6.5133E-06 0.000010919 7.51E-18 0.000005538 4.85E-18 1.67E-17 1.18E-18 1.70E-17 0.000010346 1.9913E-06 0.000005624 1.00E-16 6 6 6 6 2 6 1 1 6 2 6 2 6 2 6 6 2 6 6 2 2 6 2 6 6 2 6 6 6 6 6 6 1 6 2 6 2 6 6 6 2 6 6 6 6 2 1 6 6 2 2 2 2 6 2 6 6 6 6 2 2 2 6 249.95 164.55 151.15 353.43 24.56 183.63 63.15 66.46 244.6 182.3 109.5 305.04 267.3 219.66 285.55 268.15 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.36 80.15 283.07 191.59 143.42 239.15 195.56 200 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 146.95 185.26 199 165 252.45 180.37 178.15 188.36 173.55 87.89 9.23E+00 4.94E-01 3.37E+00 9.91E+02 4.38E+04 3.18E-02 1.25E+04 1.86E-01 1.47E+02 8.69E+04 2.20E+04 1.59E-02 4.25E+00 4.31E-01 4.58E-02 8.58E-02 3.85E-03 2.04E-02 1.47E-01 4.50E-01 3.39E-02 3.49E+00 2.11E+00 2.76E-01 9.60E-02 3.79E-02 4.68E+00 7.84E+00 2.98E-03 3.05E-02 1.04E-01 1.97E+04 1.48E+02 7.35E-01 1.29E-01 1.16E+00 6.86E-02 3.97E-02 5.47E-04 5.24E-03 7.52E-01 7.34E+01 3.71E-05 1.77E-03 2.01E-01 2.40E+00 2.05E-01 2.93E+01 1.88E+02 4.33E+00 7.90E+02 1.82E+01 1.68E-04 4.27E-07 1.69E-02 2.48E-02 7.54E-01 1.31E+01 1.89E-01 1.71E-02 1.30E+01 1.81E-04 1.17E-03 654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26 652.3 629.8 632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85 3.341E+06 3.286E+06 4.583E+06 4.069E+06 2.665E+06 5.159E+06 3.391E+06 4.500E+06 6.309E+06 7.278E+06 6.516E+06 1.208E+06 2.680E+06 2.305E+06 2.513E+06 2.528E+06 2.540E+06 2.427E+06 2.330E+06 2.619E+06 1.255E+06 2.960E+06 2.467E+06 2.779E+06 2.781E+06 2.749E+06 2.647E+06 2.705E+06 2.663E+06 2.523E+06 2.880E+06 8.203E+06 5.021E+06 5.566E+06 1.474E+06 3.845E+06 3.364E+06 3.630E+06 3.897E+06 3.699E+06 3.706E+06 3.699E+06 3.562E+06 3.537E+06 3.473E+06 4.170E+06 4.020E+06 2.902E+06 6.058E+06 4.063E+06 4.734E+06 5.218E+06 4.213E+06 5.169E+06 4.771E+06 3.130E+06 5.040E+06 4.608E+06 4.260E+06 3.366E+06 4.738E+06 3.202E+06 4.599E+06 2-57 (Continued ) 2-58 TABLE 2-8 Vapor Pressure of Inorganic and Organic Liquids, ln P = C1 + C2/T + C3 ln T + C4 T C5, P in Pa, T in K (Continued ) Cmpd. no.∗ Name 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene Formula C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 CAS 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 C1 C2 104.08 60.43 62.165 212.8 48.651 272.85 105.93 165.977 47.365 29.16 180.99 124.004 110.52 140.47 54.898 137.23 75.881 57.963 93.193 76.945 54.153 137.45 56.55 134.68 78.341 85.301 84.912 83.105 506.33 302 131 182.57122 57.406 55.682 91.432 54.571 73.649 85.099 90.405 88.72 −7535.9 −5276.9 −5624 −15,420 −7289.5 −9548.9 −8685.9 −19,914.4 −4084.5 −2383.6 −12,060 −17,894.4 −14,045 −13,231 −5305.4 −10,620 −6910.6 −5901.5 −7001.5 −6729.8 −6041.8 −12,549 −5681.9 −6055.8 −8019.8 −8215.9 −6722.2 −6903.7 −37,483 −24,324 −11,143 −17,112.47062 −5702.8 −4439.3 −5141.7 −5561.5 −7258.2 −7615.9 −7955.2 −7741.2 C3 −12.348 −5.6572 −5.8595 −28.109 −3.4453 −40.089 −12.42 −18.9344 −3.6469 −1.1342 −22.839 −13.156 −11.861 −16.859 −4.7627 −17.908 −7.9499 −5.2048 −10.738 −8.179 −4.5383 −16.543 −4.9815 −19.415 −8.1458 −9.2166 −9.5157 −9.1858 −69.22 −40.13 −15.855 −22.1251 −5.0307 −5.0136 −10.981 −4.712 −7.3037 −9.3072 −10.086 −9.8693 C5 Tmin, K P at Tmin 0.000009602 2.60E-17 2.06E-17 0.000021564 1.01E-18 6.37E-15 7.5583E-06 1.91E-18 1.80E-17 2 6 6 2 6 6 2 6 6 7.24E-17 1.18E-18 2.21E-18 6.5877E-06 1.43E-17 0.014506 4.4315E-06 9.13E-18 8.2308E-06 5.3017E-06 4.98E-18 7.1275E-06 1.24E-17 0.028619 3.8971E-06 4.7979E-06 7.2244E-06 6.4703E-06 0.000027381 0.000017403 8.1871E-06 1.13E-17 1.10E-17 1.97E-17 0.000014318 1.07E-17 4.1653E-06 5.5643E-06 5.9594E-06 0.000006077 6 6 6 2 6 1 2 6 2 2 6 2 6 1 2 2 2 2 2 2 2 6 6 6 2 6 2 2 2 2 180.25 142.61 159.95 213.15 388.85 186.35 242.54 460.85 197.67 223.15 289.95 700.15 329.35 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.5 267.76 158.45 156.08 247.79 229.33 165.78 172.22 398.4 354 247.57 288.45 180.35 173.15 119.36 178.35 273.16 225.3 247.98 286.41 2.11E-01 9.73E-03 6.51E-02 9.29E-05 1.17E+04 2.21E+05 1.06E+01 7.78E+02 1.67E+03 2.30E+05 2.09E+04 2.42E+05 4.14E-01 2.53E-01 1.96E-01 1.33E-01 1.54E-02 8.69E+04 1.86E+02 4.75E-02 4.47E+01 2.51E-01 1.06E-02 9.92E+00 3.71E+00 6.93E-01 1.71E-02 1.68E-02 8.50E+00 9.36E-01 4.08E-01 1.25E-01 7.06E-01 6.69E+01 1.92E-02 3.54E-01 6.11E+02 3.18E+00 2.18E+01 5.76E+02 C4 Tmax, K 538 517 536.6 626 683 259 636 838 430.75 318.69 490.85 883.6 857 693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 647.1 617 630.3 616.2 P at Tmax 4.031E+06 4.752E+06 4.627E+06 6.041E+06 5.925E+06 3.748E+06 3.823E+06 5.001E+06 7.860E+06 3.771E+06 8.192E+06 3.487E+06 2.974E+06 1.569E+06 5.203E+06 3.624E+06 5.117E+06 2.871E+06 5.702E+06 4.080E+06 4.447E+06 1.679E+06 3.037E+06 4.102E+06 3.447E+06 3.211E+06 2.550E+06 2.812E+06 3.410E+06 3.019E+06 1.949E+06 2.119E+06 3.930E+06 4.887E+06 5.749E+06 3.058E+06 2.193E+07 3.528E+06 3.741E+06 3.501E+06 Vapor pressure Ps is calculated by Ps = exp(C1 + C2/T + C3 ln(T) + C4T C5) where Ps is in Pa and T is in K. ∗All substances and their numbers are listed by chemical family in Table 2-6 and by formula in Table 2-7. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. VAPOR PRESSURES TABLE 2-9 2-59 Vapor Pressures of Inorganic Compounds, up to 1 atm* Compound Pressure, mmHg 1 Name Aluminum borohydride bromide chloride fluoride iodide oxide Ammonia heavy Ammonium bromide carbamate chloride cyanide hydrogen sulfide iodide Antimony tribromide trichloride pentachloride triiodide trioxide Argon Arsenic Arsenic tribromide trichloride trifluoride pentafluoride trioxide Arsine Barium Beryllium borohydride bromide chloride iodide Bismuth tribromide trichloride Diborane hydrobromide Borine carbonyl triamine Boron hydrides dihydrodecaborane dihydrodiborane dihydropentaborane tetrahydropentaborane tetrahydrotetraborane Boron tribromide trichloride trifluoride Bromine pentafluoride Cadmium chloride fluoride iodide oxide Calcium Carbon (graphite) dioxide disulfide monoxide oxyselenide oxysulfide selenosulfide subsulfide tetrabromide tetrachloride tetrafluoride Cesium bromide chloride fluoride iodide 5 10 20 Formula Al Al(BH4)3 AlBr3 Al2Cl6 AlF3 AlI3 Al2O3 NH3 ND3 NH4Br N2H6CO2 NH4Cl NH4CN NH4HS NH4I Sb SbBr3 SbCl3 SbCl5 SbI3 Sb4O6 A As AsBr3 AsCl3 AsF3 AsF5 As2O3 AsH3 Ba Be(BH4)2 BeBr2 BeCl2 BeI2 Bi BiBr3 BiCl3 B2H5Br BH3CO B3N3H6 B10H14 B2H6 B5H9 B5H11 B4H10 BBr3 BCl3 BF3 Br2 BrF5 Cd CdCl2 CdF2 CdI2 CdO Ca C CO2 CS2 CO COSe COS CSeS C3S2 CBr4 CCl4 CF4 Cs CsBr CsCl CsF CsI 40 60 100 200 400 760 Melting point, °C 1749 −3.9 176.1 152.0 1422 294.5 2665 −68.4 −67.4 320.0 26.7 271.5 −0.5 0.0 331.8 1223 203.5 143.3 114.1 303.5 957 −200.5 518 145.2 70.9 13.2 −84.3 332.5 −98.0 1301 58.6 405 411 411 1271 360 343 −29.0 −95.3 +4.0 1844 +11.2 199.8 161.8 1457 322.0 2766 −57.0 −57.0 345.3 37.2 293.2 +9.6 +10.5 355.8 1288 225.7 165.9 1947 28.1 227.0 171.6 1496 354.0 2874 −45.4 −45.4 370.8 48.0 316.5 20.5 21.8 381.0 1364 250.2 192.2 2056 45.9 256.3 180.2 1537 385.5 2977 −33.6 −33.4 396.0 58.3 337.8 31.7 33.3 404.9 1440 275.0 219.0 660 −64. 97. 192.4 1040 333.8 1085 −195.6 548 167.7 89.2 26.7 −75.5 370.0 −87.2 1403 69.0 427 435 435 1319 392 372 −15.4 −85.5 18.5 368.5 1242 −190.6 579 193.6 109.7 41.4 −64.0 412.2 −75.2 1518 79.7 451 461 461 1370 425 405 0.0 −74.8 34.3 401.0 1425 −185.6 610 220.0 130.4 56.3 −52.8 457.2 −62.1 1638 90.0 474 487 487 1420 461 441 +16.3 −64.0 50.6 142.3 −120.9 +9.6 20.1 −28.1 33.5 −32.4 −123.0 +9.3 −4.5 611 797 1486 640 1341 1207 4373 −100.2 −5.1 −205.7 −61.7 −85.9 28.3 109.9 119.7 23.0 −150.7 509 1072 1069 1025 1055 163.8 −111.2 24.6 34.8 −14.0 50.3 −18.9 −115.9 24.3 +9.9 658 847 1561 688 1409 1288 4516 −93.0 +10.4 −201.3 −49.8 −75.0 45.7 130.8 139.7 38.3 −143.6 561 1140 1139 1092 1124 −99.6 40.8 51.2 +0.8 70.0 −3.6 −108.3 41.0 25.7 711 908 1651 742 1484 1388 4660 −85.7 28.0 −196.3 −35.6 −62.7 65.2 −86.5 58.1 67.0 16.1 91.7 +12.7 −100.7 58.2 40.4 765 967 1751 796 1559 1487 4827 −78.2 46.5 −191.3 −21.9 −49.9 85.6 163.5 57.8 −135.5 624 1221 1217 1170 1200 189.5 76.7 −127.7 690 1300 1300 1251 1280 Temperature, °C 1284 81.3 100.0 1238 178.0 2148 −109.1 1421 −52.2 103.8 116.4 1298 207.7 2306 −97.5 1487 −42.9 118.0 123.8 1324 225.8 2385 −91.9 1555 −32.5 134.0 131.8 1350 244.2 2465 −85.8 1635 −20.9 150.6 139.9 1378 265.0 2549 −79.2 198.3 −26.1 160.4 −50.6 −51.1 210.9 886 93.9 49.2 22.7 163.6 574 −218.2 372 41.8 −11.4 234.5 −10.4 193.8 −35.7 −36.0 247.0 984 126.0 71.4 48.6 203.8 626 −213.9 416 70.6 +11.7 252.0 −2.9 209.8 −28.6 −28.7 263.5 1033 142.7 85.2 61.8 223.5 666 −210.9 437 85.2 +23.5 270.6 +5.3 226.1 −20.9 −20.8 282.8 1084 158.3 100.6 75.8 244.8 729 −207.9 459 101.3 36.0 −117.9 212.5 −142.6 −108.0 242.6 −130.8 984 19.8 325 328 322 1099 261 242 −75.3 −127.3 −45.0 −103.1 259.7 −124.7 1049 28.1 342 346 341 1136 282 264 −66.3 −121.1 −35.3 −98.0 279.2 −117.7 1120 36.8 361 365 361 1177 305 287 −56.4 −114.1 −25.0 290.0 14.0 245.0 −12.6 −12.3 302.8 1141 177.4 117.8 91.0 267.8 812 −204.9 483 118.7 50.0 −2.5 −92.4 299.2 −110.2 1195 46.2 379 384 382 1217 327 311 −45.4 −106.6 −13.2 1684 −13.4 161.7 145.4 1398 277.8 2599 −74.3 −74.0 303.8 19.6 256.2 −7.4 −7.0 316.0 1176 188.1 128.3 101.0 282.5 873 −202.9 498 130.0 58.7 +4.2 −88.5 310.3 −104.8 1240 51.7 390 395 394 1240 340 324 −38.2 −101.9 −5.8 3586 −134.3 −73.8 −222.0 −117.1 −132.4 −47.3 14.0 80.8 −149.5 −40.4 −29.9 −73.1 −20.4 −75.2 −145.4 −32.8 −51.0 455 618 1231 481 1100 926 3828 −124.4 −54.3 −217.2 −102.3 −119.8 −26.5 41.2 90.2 −144.3 −30.7 −19.9 −64.3 −10.1 −66.9 −141.3 −25.0 −41.9 484 656 1286 512 1149 983 3946 −119.5 −44.7 −215.0 −95.0 −113.3 −16.0 54.9 100.0 −138.5 −20.0 −9.2 −54.8 +1.5 −57.9 −136.4 −16.8 −32.0 516 695 1344 546 1200 1046 4069 −114.4 −34.3 −212.8 −86.3 −106.0 −4.4 69.3 −50.0 −184.6 279 748 744 712 738 −30.0 −174.1 341 838 837 798 828 −19.6 −169.3 375 887 884 844 873 −8.2 −164.3 409 938 934 893 923 117.4 −131.6 −8.0 +2.7 −44.3 14.0 −47.8 −131.0 −8.0 −21.0 553 736 1400 584 1257 1111 4196 −108.6 −22.5 −210.0 −76.4 −98.3 +8.6 85.6 96.3 +4.3 −158.8 449 993 989 947 976 127.8 −127.2 −0.4 10.2 −37.4 22.1 −41.2 −127.6 −0.6 −14.0 578 762 1436 608 1295 1152 4273 −104.8 −15.3 −208.1 −70.2 −93.0 17.0 96.0 106.3 12.3 −155.4 474 1026 1023 980 1009 +1.0 289 291 283 1021 −93.3 −139.2 −63.0 60.0 −159.7 −50.2 −90.9 −41.4 −91.5 −154.6 −48.7 −69.3 394 1112 416 1000 ∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947). 2050 −77.7 −74.0 520 36 630.5 96.6 73.4 2.8 167 656 −189.2 814 −18 −5.9 −79.8 312.8 −116.3 850 123 490 405 488 271 218 230 −104.2 −137.0 −58.2 99.6 −169 −47.0 −119.9 −45 −107 −126.8 −7.3 −61.4 320.9 568 520 385 851 −57.5 −110.8 −205.0 −138.8 −75.2 +0.4 90.1 −22.6 −183.7 28.5 636 646 683 621 (Continued ) 2-60 PHYSICAL AnD CHEMICAL DATA TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Compound Pressure, mmHg 1 Name Chlorine fluoride trifluoride monoxide dioxide heptoxide Chlorosulfonic acid Chromium carbonyl oxychloride Cobalt chloride nitrosyl tricarbonyl Columbium fluoride Copper Cuprous bromide chloride iodide Cyanogen bromide chloride fluoride Deuterium cyanide Fluorine oxide Germanium bromide chloride hydride Trichlorogermane Tetramethylgermane Digermane Trigermane Gold Helium para-Hydrogen Hydrogen bromide chloride cyanide fluoride iodide oxide (water) sulfide disulfide selenide telluride Iodine heptafluoride Iron pentacarbonyl Ferric chloride Ferrous chloride Krypton Lead bromide chloride fluoride iodide oxide sulfide Lithium bromide chloride fluoride iodide Magnesium chloride Manganese chloride Mercury Mercuric bromide chloride iodide Molybdenum hexafluoride oxide 5 10 20 Formula Cl2 ClF ClF3 Cl2O ClO2 Cl2O7 HSO3Cl Cr Cr(CO)6 CrO2Cl2 CoCl2 Co(CO)3NO CbF5 Cu Cu2Br2 Cu2Cl2 Cu2I2 C2N2 CNBr CNCl CNF DCN F2 F2O GeBr4 GeCl4 GeH4 GeHCl3 Ge(CH3)4 Ge2H6 Ge3H8 Au He H2 HBr HCl HCN H2F2 HI H2O H2S HSSH H2Se H2Te I2 IF7 Fe Fe(CO)5 Fe2Cl6 FeCl2 Kr Pb PbBr2 PbCl2 PbF2 PbI2 PbO PbS Li LiBr LiCl LiF LiI Mg MgCl2 Mn MnCl2 Hg HgBr2 HgCl2 HgI2 Mo MoF6 MoO3 40 60 100 200 400 760 Melting point, °C −71.7 −120.8 −34.7 −39.4 −29.4 29.1 105.3 2139 108.0 58.0 843 29.0 148.5 2207 951 960 907 −51.8 22.6 −24.9 −97.0 −17.5 −202.7 −165.8 113.2 27.5 −120.3 26.5 −6.3 −20.3 47.9 2521 −270.3 −257.9 −97.7 −114.0 −17.8 −28.2 −72.1 51.6 −91.6 22.0 −74.2 −45.7 116.5 −31.9 2360 50.3 272.5 842 −171.8 1421 745 784 1080 701 1265 1108 1097 1076 1129 1425 993 909 1142 1792 960 261.7 237.8 237.0 261.8 4109 −8.0 955 −60.2 −114.4 −20.7 −26.5 −17.8 44.6 120.0 2243 121.8 75.2 904 44.4 172.2 2325 1052 1077 1018 −42.6 33.8 −14.1 −89.2 −5.4 −198.3 −159.0 135.4 44.4 −111.2 41.6 +8.8 −4.7 67.0 2657 −269.8 −256.3 −88.1 −105.2 −5.3 −13.2 −60.3 66.5 −82.3 35.3 −65.2 −32.4 137.3 −20.7 2475 68.0 285.0 897 −165.9 1519 796 833 1144 750 1330 1160 1178 1147 1203 1503 1049 967 1223 1900 1028 290.7 262.7 256.5 291.0 4322 +4.1 1014 −47.3 −107.0 −4.9 −12.5 −4.0 62.2 136.1 2361 137.2 95.2 974 62.0 198.0 2465 1189 1249 1158 −33.0 46.0 −2.3 −80.5 +10.0 −193.2 −151.9 161.6 63.8 −100.2 58.3 26.0 +13.3 88.6 2807 −269.3 −254.5 −78.0 −95.3 +10.2 +2.5 −48.3 83.0 −71.8 49.6 −53.6 −17.2 159.8 −8.3 2605 86.1 298.0 961 −159.0 1630 856 893 1219 807 1402 1221 1273 1226 1290 1591 1110 1034 1316 2029 1108 323.0 290.0 275.5 324.2 4553 17.2 1082 −33.8 −100.5 +11.5 +2.2 +11.1 78.8 151.0 2482 151.0 117.1 1050 80.0 225.0 2595 1355 1490 1336 −21.0 61.5 +13.1 −72.6 26.2 −187.9 −144.6 189.0 84.0 −88.9 75.0 44.0 31.5 110.8 2966 −268.6 −252.5 −66.5 −84.8 25.9 19.7 −35.1 100.0 −60.4 64.0 −41.1 −2.0 183.0 +4.0 2735 105.0 319.0 1026 −152.0 1744 914 954 1293 872 1472 1281 1372 1310 1382 1681 1171 1107 1418 2151 1190 357.0 319.0 304.0 354.0 4804 36.0 1151 −100.7 −145 −83 −116 −59 −91 −80 1615 Temperature, °C −118.0 −98.5 −106.7 −143.4 −80.4 −81.6 −45.3 32.0 1616 36.0 −18.4 −23.8 53.5 1768 58.0 +3.2 1628 572 546 −95.8 −35.7 −76.7 −134.4 −68.9 −223.0 −196.1 −45.0 −163.0 −41.3 −73.2 −88.7 −36.9 1869 −271.7 −263.3 −138.8 −150.8 −71.0 −123.3 −17.3 −134.3 −43.2 −115.3 −96.4 38.7 −87.0 1787 194.0 −199.3 973 513 547 479 943 852 723 748 783 1047 723 621 778 1292 126.2 136.5 136.2 157.5 3102 −65.5 734 1795 666 645 610 −83.2 −18.3 −61.4 −123.8 −54.0 −216.9 −186.6 43.3 −24.9 −151.0 −22.3 −54.6 −69.8 −12.8 2059 −271.5 −261.9 −127.4 −140.7 −55.3 −74.7 −109.6 +1.2 −122.4 −24.4 −103.4 −82.4 62.2 −70.7 1957 −6.5 221.8 −191.3 1099 578 615 861 540 1039 928 838 840 880 1156 802 702 877 1434 736 164.8 165.3 166.0 189.2 3393 −49.0 785 −101.6 −139.0 −71.8 −73.1 −59.0 −13.2 64.0 1845 68.3 13.8 −93.3 −134.3 −62.3 −64.3 −51.2 −2.1 75.3 1928 79.5 25.7 86.3 1879 718 702 656 −76.8 −10.0 −53.8 −118.5 −46.7 −214.1 −182.3 56.8 −15.0 −145.3 −13.0 −45.2 −60.1 −0.9 2154 −271.3 −261.3 −121.8 −135.6 −47.7 −65.8 −102.3 11.2 −116.3 −15.2 −97.9 −75.4 73.2 −63.0 2039 +4.6 235.5 700 −187.2 1162 610 648 904 571 1085 975 881 888 932 1211 841 743 930 1505 778 184.0 179.8 180.2 204.5 3535 −40.8 814 −1.3 103.0 1970 777 766 716 −70.1 −1.0 −46.1 −112.8 −38.8 −211.0 −177.8 71.8 −4.1 −139.2 −3.0 −35.0 −49.9 +11.8 2256 −271.1 −260.4 −115.4 −130.0 −39.7 −56.0 −94.5 22.1 −109.7 −5.1 −91.8 −67.8 84.7 −54.5 2128 16.7 246.0 737 −182.9 1234 646 684 950 605 1134 1005 940 939 987 1270 883 789 988 1583 825 204.6 194.3 195.8 220.0 3690 −32.0 851 −84.5 −128.8 −51.3 −54.3 −42.8 +10.3 87.6 2013 91.2 38.5 770 +11.0 121.5 2067 844 838 786 −62.7 +8.6 −37.5 −106.4 −30.1 −207.7 −173.0 88.1 +8.0 −131.6 +8.8 −23.4 −38.2 26.3 2363 −270.7 −259.6 −108.3 −123.8 −30.9 −45.0 −85.6 34.0 −102.3 +6.0 −84.7 −59.1 97.5 −45.3 2224 30.3 256.8 779 −178.4 1309 686 725 1003 644 1189 1048 1003 994 1045 1333 927 838 1050 1666 879 228.8 211.5 212.5 238.2 3859 −22.1 892 −79.0 −125.3 −44.1 −48.0 −37.2 +18.2 95.2 2067 98.3 46.7 801 18.5 133.2 2127 887 886 836 −57.9 14.7 −32.1 −102.3 −24.7 −205.6 −170.0 98.8 16.2 −126.7 16.2 −16.2 −30.7 35.5 2431 −270.6 −258.9 −103.8 −119.6 −25.1 −37.9 −79.8 41.5 −97.9 12.8 −80.2 −53.7 105.4 −39.4 2283 39.1 263.7 805 −175.7 1358 711 750 1036 668 1222 1074 1042 1028 1081 1372 955 868 1088 1720 913 242.0 221.0 222.2 249.0 3964 −16.2 917 735 −11 75.5 1083 504 422 605 −34.4 58 −6.5 −12 −223 −223.9 26.1 −49.5 −165 −71.1 −88 −109 −105.6 1063 −259.1 −87.0 −114.3 −13.2 −83.7 −50.9 0.0 −85.5 −89.7 −64 −49.0 112.9 5.5 1535 −21 304 −156.7 327.5 373 501 855 402 890 1114 186 547 614 870 446 651 712 1260 650 −38.9 237 277 259 2622 17 795 VAPOR PRESSURES TABLE 2-9 2-61 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Compound Pressure, mmHg 1 Name Neon Nickel carbonyl chloride Nitrogen Nitric oxide Nitrogen dioxide Nitrogen pentoxide Nitrous oxide Nitrosyl chloride fluoride Osmium tetroxide (yellow) (white) Oxygen Ozone Phosgene Phosphorus (yellow) (violet) tribromide trichloride pentachloride Phosphine Phosphonium bromide chloride iodide Phosphorus trioxide pentoxide oxychloride thiobromide thiochloride Platinum Potassium bromide chloride fluoride hydroxide iodide Radon Rhenium heptoxide Rubidium bromide chloride fluoride iodide Selenium dioxide hexafluoride oxychloride tetrachloride Silicon dioxide tetrachloride tetrafluoride Trichlorofluorosilane Iodosilane Diiodosilane Disiloxan Trisilane Trisilazane Tetrasilane Octachlorotrisilane Hexachlorodisiloxane Hexachlorodisilane Tribromosilane Trichlorosilane Trifluorosilane Dibromosilane Difluorosilane Monobromosilane Monochlorosilane Monofluorosilane Tribromofluorosilane Dichlorodifluorosilane Trifluorobromosilane 5 10 20 Formula Ne Ni Ni(CO)4 NiCl2 N2 NO NO2 N2O5 N2O NOCl NOF OsO4 OsO4 O2 O3 COCl2 P P PBr3 PCl3 PCl5 PH3 PH4Br PH4Cl PH4I P4O6 P4O10 POCl3 PSBr3 PSCl3 Pt K KBr KCl KF KOH KI Rn Re2O7 Rb RbBr RbCl RbF RbI Se SeO2 SeF6 SeOCl2 SeCl4 Si SiO2 SiCl4 SiF4 SiFCl3 SiH3I SiH2I2 (SiH3)2O Si3H8 (SiH3)3N Si4H10 Si3Cl3 (SiCl3)2O Si2Cl6 SiHBr3 SiHCl3 SiHF3 SiH2Br2 SiH2F2 SiH3Br SiH3Cl SiH3F SiFBr3 SiF2Cl2 SiF3Br 40 60 100 200 400 760 Melting point, °C −251.0 2364 −6.0 866 −209.7 −166.0 −14.7 7.4 −110.3 −46.3 −88.8 71.5 71.5 −198.8 −141.0 −35.6 197.3 349 103.6 21.0 117.0 −118.8 7.4 −52.0 29.3 108.3 510 47.4 126.3 63.8 3714 586 1137 1164 1245 1064 1080 −99.0 289.0 514 1114 1133 1168 1072 554 258.0 −73.9 118.0 147.5 2083 1969 +5.4 −113.3 −33.2 −4.4 79.4 −55.9 +1.6 −1.1 47.4 146.0 75.4 85.4 51.6 −16.4 −118.7 14.1 −107.3 −42.3 −68.5 −122.4 28.6 −70.3 −249.7 2473 +8.8 904 −205.6 −162.3 −5.0 15.6 −103.6 −34.0 −79.2 89.5 89.5 −194.0 −132.6 −22.3 222.7 370 125.2 37.6 131.3 −109.4 17.6 −44.0 39.9 129.0 532 65.0 141.8 82.0 3923 643 1212 1239 1323 1142 1152 −87.7 307.0 563 1186 1207 1239 1141 594 277.0 −64.8 134.6 161.0 2151 2053 21.0 −170.2 −19.3 +10.7 101.8 −43.5 17.8 +14.0 63.6 166.2 92.5 102.2 70.2 −1.8 −111.3 31.6 −98.3 −28.6 −57.0 −115.2 45.7 −58.0 −69.8 −248.1 2603 25.8 945 −200.9 −156.8 +8.0 24.4 −96.2 −20.3 −68.2 109.3 109.3 −188.8 −122.5 −7.6 251.0 391 149.7 56.9 147.2 −98.3 28.0 −35.4 51.6 150.3 556 84.3 157.8 102.3 4169 708 1297 1322 1411 1233 1238 −75.0 336.0 620 1267 1294 1322 1223 637 297.7 −55.2 151.7 176.4 2220 2141 38.4 −100.7 −4.0 27.9 125.5 −29.3 35.5 31.0 81.7 189.5 113.6 120.6 90.2 +14.5 −102.8 50.7 −87.6 −13.3 −44.5 −106.8 64.6 −45.0 −55.9 −246.0 2732 42.5 987 −195.8 −151.7 21.0 32.4 −85.5 −6.4 −56.0 130.0 130.0 −183.1 −111.1 +8.3 280.0 417 175.3 74.2 162.0 −87.5 38.3 −27.0 62.3 173.1 591 105.1 175.0 124.0 4407 774 1383 1407 1502 1327 1324 −61.8 362.4 679 1352 1381 1408 1304 680 317.0 −45.8 168.0 191.5 2287 2227 56.8 −94.8 +12.2 45.4 149.5 −15.4 53.1 48.7 100.0 211.4 135.6 139.0 111.8 31.8 −95.0 70.5 −77.8 +2.4 −30.4 −98.0 83.8 −31.8 −41.7 −248.7 1452 −25 1001 −210.0 −161 −9.3 30 −90.9 −64.5 −134 56 42 −218.7 −251 −104 44.1 590 −40 −111.8 Temperature, °C −257.3 1810 −255.5 1979 −254.6 2057 −253.7 2143 671 −226.1 −184.5 −55.6 −36.8 −143.4 731 −221.3 −180.6 −42.7 −23.0 −133.4 759 −219.1 −178.2 −36.7 −16.7 −128.7 789 −216.8 −175.3 −30.4 −10.0 −124.0 −132.0 3.2 −5.6 −219.1 −180.4 −92.9 76.6 237 7.8 −51.6 55.5 −120.3 22.0 +15.6 −213.4 −168.6 −77.0 111.2 271 34.4 −31.5 74.0 −114.3 31.3 26.0 −210.6 −163.2 −69.3 128.0 287 47.8 −21.3 83.2 −107.8 41.0 37.4 −207.5 −157.2 −60.3 146.2 306 62.4 −10.2 92.5 −43.7 −91.0 −25.2 384 −28.5 −79.6 −9.0 39.7 424 50.0 −18.3 2730 341 795 821 885 719 745 −144.2 212.5 297 781 792 921 748 356 157.0 −118.6 34.8 74.0 1724 72.4 +4.6 3007 408 892 919 988 814 840 −132.4 237.5 358 876 887 982 839 413 187.7 −105.2 59.8 96.3 1835 −63.4 −144.0 −92.6 −44.1 −134.8 −76.4 −53.0 3.8 −95.8 −49.7 −49.9 −6.2 74.7 17.8 27.4 −8.0 −62.6 −142.7 −40.0 −136.0 −85.7 −104.3 −145.5 −25.4 −110.5 −21.2 −74.0 −1.1 53.0 442 2.0 83.6 16.1 3146 443 940 968 1039 863 887 −126.3 248.0 389 923 937 1016 884 442 202.5 −98.9 71.9 107.4 1888 1732 −34.4 −130.4 −68.3 −47.7 18.0 −88.2 −40.0 −40.4 +4.3 89.3 29.4 38.8 +3.4 −53.4 −138.2 −29.4 −130.4 −77.3 −97.7 −141.2 −15.1 −102.9 −13.3 −68.0 +7.3 67.8 462 13.6 95.5 29.0 3302 483 994 1020 1096 918 938 −119.2 261.0 422 975 990 1052 935 473 217.5 −92.3 84.2 118.1 1942 1798 −24.0 −125.9 −59.0 −33.4 34.1 −79.8 −29.0 −30.0 15.8 104.2 41.5 51.5 16.0 −43.8 −132.9 −18.0 −124.3 −68.3 −90.1 −136.3 −3.7 −94.5 −112.5 −68.9 −68.7 −27.7 46.3 −5.0 +4.0 −30.5 −80.7 −152.0 −60.9 −146.7 −117.8 −153.0 −46.1 −124.7 −252.6 2234 −23.0 821 −214.0 −171.7 −23.9 −2.9 −118.3 −60.2 −100.3 51.7 50.5 −204.1 −150.7 −50.3 166.7 323 79.0 +2.3 102.5 −129.4 −5.0 −61.5 16.1 84.0 481 27.3 108.0 42.7 3469 524 1050 1078 1156 976 995 −111.3 272.0 459 1031 1047 1096 991 506 234.1 −84.7 98.0 130.1 2000 1867 −12.1 −120.8 −48.8 −21.8 52.6 −70.4 −16.9 −18.5 28.4 121.5 55.2 65.3 30.0 −32.9 −127.3 −5.2 −117.6 −57.8 −81.8 −130.8 +9.2 −85.0 −251.9 2289 −15.9 840 −212.3 −168.9 −19.9 +1.8 −114.9 −54.2 −95.7 59.4 59.4 −201.9 −146.7 −44.0 179.8 334 89.8 10.2 108.3 −125.0 +0.3 −57.3 21.9 94.2 493 35.8 116.0 51.8 3574 550 1087 1115 1193 1013 1030 −106.2 280.0 482 1066 1084 1123 1026 527 244.6 −80.0 106.5 137.8 2036 1911 −4.8 −117.5 −42.2 −14.3 64.0 −64.2 −9.0 −11.0 36.6 132.0 63.8 73.9 39.2 −25.8 −123.7 +3.2 −113.3 −51.1 −76.0 −127.2 17.4 −78.6 −132.5 −28.5 22.5 569 2 38 −36.2 1755 62.3 730 790 880 380 723 −71 296 38.5 682 715 760 642 217 340 −34.7 8.5 1420 1710 −68.8 −90 −120.8 −57.0 −1.0 −144.2 −117.2 −105.7 −93.6 −33.2 −1.2 −73.5 −126.6 −131.4 −70.2 −93.9 −82.5 −139.7 −70.5 (Continued ) 2-62 PHYSICAL AnD CHEMICAL DATA TABLE 2-9 Vapor Pressures of Inorganic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Trifluorochlorosilane Hexafluorodisilane Dichlorofluorobromosilane Dibromochlorofluorosilane Silane Disilane Silver chloride iodide Sodium bromide chloride cyanide fluoride hydroxide iodide Strontium Strontium oxide Sulfur monochloride hexafluoride Sulfuryl chloride Sulfur dioxide trioxide (α) trioxide (β) trioxide (γ) Tellurium chloride fluoride Thallium Thallous bromide chloride iodide Thionyl bromide Thionyl chloride Tin Stannic bromide Stannous chloride Stannic chloride iodide hydride Tin tetramethyl trimethyl-ethyl trimethyl-propyl Titanium chloride Tungsten Tungsten hexafluoride Uranium hexafluoride Vanadyl trichloride Xenon Zinc chloride fluoride diethyl Zirconium bromide chloride iodide 1 5 10 20 Formula SiF3Cl Si2F6 SiFCl2Br SiFClBr2 SiH4 Si2H6 Ag AgCl AgI Na NaBr NaCl NaCN NaF NaOH NaI Sr SrO S S2Cl2 SF6 SO2Cl2 SO2 SO3 SO3 SO3 Te TeCl4 TeF6 Tl TlBr TlCl TlI SOBr2 SOCl2 Sn SnBr4 SnCl2 SnCl4 SnI4 SnH4 Sn(CH3)4 Sn(CH3)3⋅C2H5 Sn(CH3)3⋅C3H7 TiCl4 W WF6 UF6 VOCl3 Xe Zn ZnCl2 ZnF2 Zn(C2H5)2 ZrBr4 ZrCl4 ZrI4 40 100 200 400 760 Melting point, °C −108.2 −46.7 −29.0 −4.7 −146.3 −66.4 1795 1242 1152 662 1099 1169 1156 1403 1057 1039 1057 −101.7 −41.7 −19.5 +6.3 −140.5 −57.5 1865 1297 1210 701 1148 1220 1214 1455 1111 1083 1111 −91.7 −34.2 −3.2 23.0 −131.6 −44.6 1971 1379 1297 758 1220 1296 1302 1531 1192 1150 1192 −81.0 −26.4 +15.4 43.0 −122.0 −29.0 2090 1467 1400 823 1304 1379 1401 1617 1286 1225 1285 −70.0 −18.9 35.4 59.5 −111.5 −14.3 2212 1564 1506 892 1392 1465 1497 1704 1378 1304 1384 305.5 63.2 −96.8 +7.2 −54.6 +4.0 8.0 21.4 789 287 −73.8 1143 621 612 631 68.3 10.4 1903 116.2 467 43.5 234.2 −96.6 11.7 38.4 57.5 58.0 5007 −27.5 10.4 49.8 −137.7 700 584 1207 47.2 289 268 355 327.2 75.3 −90.9 17.8 −46.9 10.5 14.3 28.0 838 304 −67.9 1196 653 645 663 80.6 21.4 1968 131.0 493 54.7 254.2 −89.2 22.8 50.0 69.8 71.0 5168 −20.3 18.2 62.5 −132.8 736 610 1254 59.1 301 279 369 359.7 93.5 −82.3 33.7 −35.4 20.5 23.7 35.8 910 330 −57.3 1274 703 694 712 99.0 37.9 2063 152.8 533 72.0 283.5 −78.0 39.8 67.3 88.0 90.5 5403 −10.0 30.0 82.0 −125.4 788 648 1329 77.0 318 295 389 399.6 115.4 −72.6 51.3 −23.0 32.6 32.6 44.0 997 360 −48.2 1364 759 748 763 119.2 56.5 2169 177.7 577 92.1 315.5 −65.2 58.5 87.6 109.6 112.7 5666 +1.2 42.7 103.5 −117.1 844 689 1417 97.3 337 312 409 444.6 138.0 −63.5 69.2 −10.0 44.8 44.8 51.6 1087 392 −38.6 1457 819 807 823 139.5 75.4 2270 204.7 623 113.0 348.0 −52.3 78.0 108.8 131.7 136.0 5927 17.3 55.7 127.2 −108.0 907 732 1497 118.0 357 331 431 −142 −18.6 −112.3 −99.3 −185 −132.6 960.5 455 552 97.5 755 800 564 992 318 651 800 2430 112.8 −80 −50.2 −54.1 −73.2 16.8 32.3 62.1 452 224 −37.8 3035 460 430 440 −52.2 −104.5 231.9 31.0 246.8 −30.2 144.5 −149.9 60 Temperature, °C −144.0 −81.0 −86.5 −65.2 −179.3 −114.8 1357 912 820 439 806 865 817 1077 739 767 2068 183.8 −7.4 −132.7 −95.5 −39.0 −34.0 −15.3 520 −111.3 825 440 −6.7 −52.9 1492 316 −22.7 −140.0 −51.3 −30.0 −12.0 −13.9 3990 −71.4 −38.8 −23.2 −168.5 487 428 970 −22.4 207 190 264 −133.0 −68.8 −68.4 −45.5 −168.6 −99.3 1500 1019 927 511 903 967 928 1186 843 857 847 2198 223.0 +15.7 −120.6 −35.1 −83.0 −23.7 −19.2 −2.0 605 −98.8 931 490 487 502 +18.4 −32.4 1634 58.3 366 −1.0 156.0 −125.8 −31.0 −7.6 +10.7 +9.4 4337 −56.5 −22.0 +0.2 −158.2 558 481 1055 0.0 237 217 297 −127.0 −63.1 −59.0 −35.6 −163.0 −91.4 1575 1074 983 549 952 1017 983 1240 897 903 898 2262 243.8 27.5 −114.7 −24.8 −76.8 −16.5 −12.3 +4.3 650 233 −92.4 983 522 517 531 31.0 −21.9 1703 72.7 391 +10.0 175.8 −118.5 −20.6 +3.8 21.8 21.3 4507 −49.2 −13.8 12.2 −152.8 593 508 1086 +11.7 250 230 311 −120.5 −57.0 −48.8 −24.5 −156.9 −82.7 1658 1134 1045 589 1005 1072 1046 1300 953 952 953 2333 264.7 40.0 −108.4 −13.4 −69.7 −9.1 −4.9 11.1 697 253 −86.0 1040 559 550 567 44.1 −10.5 1777 88.1 420 22.0 196.2 −111.2 −9.3 16.1 34.0 34.2 4690 −41.5 −5.2 26.6 −147.1 632 536 1129 24.2 266 243 329 −112.8 −50.6 −37.0 −12.0 −150.3 −72.8 1743 1200 1111 633 1063 1131 1115 1363 1017 1005 1018 2410 288.3 54.1 −101.5 −1.0 −60.5 −1.0 +3.2 17.9 753 273 −78.4 1103 598 589 607 58.8 +2.2 1855 105.5 450 35.2 218.8 −102.3 +3.5 30.0 48.5 48.4 4886 −33.0 +4.4 40.0 −141.2 673 566 1175 38.0 281 259 344 −30 3370 −0.5 69.2 −111.6 419.4 365 872 −28 450 437 499 VAPOR PRESSURES 2-63 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm* Pressure, mmHg Compound 1 Name Formula Acenaphthalene Acetal Acetaldehyde Acetamide Acetanilide Acetic acid anhydride Acetone Acetonitrile Acetophenone Acetyl chloride Acetylene Acridine Acrolein (2-propenal) Acrylic acid Adipic acid Allene (propadiene) Allyl alcohol (propen-1-ol-3) chloride (3-chloropropene) isopropyl ether isothiocyanate n-propyl ether 4-Allylveratrole iso-Amyl acetate n-Amyl alcohol iso-Amyl alcohol sec-Amyl alcohol (2-pentanol) tert-Amyl alcohol sec-Amylbenzene iso-Amyl benzoate bromide (1-bromo-3-methylbutane) n-butyrate formate iodide (1-iodo-3-methylbutane) isobutyrate Amyl isopropionate iso-Amyl isovalerate n-Amyl levulinate iso-Amyl levulinate nitrate 4-tert-Amylphenol Anethole Angelonitrile Aniline 2-Anilinoethanol Anisaldehyde o-Anisidine (2-methoxyaniline) Anthracene Anthraquinone Azelaic acid Azelaldehyde Azobenzene Benzal chloride (α,α-Dichlorotoluene) Benzaldehyde Benzanthrone Benzene Benzenesulfonylchloride Benzil Benzoic acid anhydride Benzoin Benzonitrile Benzophenone Benzotrichloride (α,α,α-Trichlorotoluene) Benzotrifluoride (α,α,α-Trifluorotoluene) Benzoyl bromide chloride nitrile Benzyl acetate alcohol C12H10 C6H14O2 C2H4O C2H5NO C8H9NO C2H4O2 C4H6O3 C3H6O C2H3N C8H8O C2H3OCl C2H2 C13H9N C3H4O C3H4O2 C6H10O4 C3H4 C3H6O C3H5Cl C6H12O C4H5NS C6H12O C11H14O2 C7H14O2 C5H12O C5H12O C5H12O C5H12O C11H16 C12H16O2 C5H11Br C9H18O2 C6H12O2 C5H11I C9H18O2 C8H16O2 C10H20O2 C10H18O3 C10H18O3 C5H11NO3 C11H16O C10H12O C5H7N C6H7N C8H11NO C8H8O2 C7H9NO C14H10 C14H8O2 C9H16O4 C9H18O C12H10N2 C7H6Cl2 C7H6O C17H10O C6H6 C6H5ClO2S C14H10O2 C7H6O2 C14H10O3 C14H12O2 C7H5N C13H10O C7H5Cl3 C7H5F3 C7H5BrO C7H5ClO C8H5NO C9H10O2 C7H8O 5 10 20 114.8 −2.3 −65.1 92.0 146.6 +6.3 24.8 −40.5 −26.6 64.0 −35.0 −133.0 165.8 −46.0 27.3 191.0 −108.0 +0.2 −52.0 −23.1 +25.3 −18.2 113.9 +23.7 34.7 30.9 22.1 +7.2 55.8 104.5 +2.1 47.1 +5.4 +21.9 40.1 33.7 54.4 110.0 104.0 28.8 109.8 91.6 +15.0 57.9 134.3 102.6 88.0 173.5 219.4 210.4 58.4 135.7 64.0 50.1 274.5 −19.6 96.5 165.2 119.5 180.0 170.2 55.3 141.7 73.7 −10.3 75.4 59.1 71.7 73.4 80.8 131.2 +8.0 −56.8 105.0 162.0 17.5 36.0 −31.1 −16.3 78.0 −27.6 −128.2 184.0 −36.7 39.0 205.5 −101.0 10.5 −42.9 −12.9 38.3 −7.9 127.0 35.2 44.9 40.8 32.2 17.2 69.2 121.6 13.6 59.9 17.1 34.1 52.8 46.3 68.6 124.0 118.8 40.3 125.5 106.0 28.0 69.4 149.6 117.8 101.7 187.2 234.2 225.5 71.6 151.5 78.7 62.0 297.2 −11.5 112.0 183.0 132.1 198.0 188.1 69.2 157.6 87.6 −0.4 89.8 73.0 85.5 87.6 92.6 148.7 19.6 −47.8 120.0 180.0 29.9 48.3 −20.8 −5.0 92.4 −19.6 −122.8 203.5 −26.3 52.0 222.0 −93.4 21.7 −32.8 −1.8 52.1 +3.7 142.8 47.8 55.8 51.7 42.6 27.9 83.8 139.7 26.1 74.0 30.0 47.6 66.6 60.0 83.8 139.7 134.4 53.5 142.3 121.8 41.0 82.0 165.7 133.5 116.1 201.9 248.3 242.4 85.0 168.3 94.3 75.0 322.5 −2.6 129.0 202.8 146.7 218.0 207.0 83.4 175.8 102.7 12.2 105.4 87.6 100.2 102.3 105.8 40 60 100 200 400 760 197.5 50.1 −22.6 158.0 227.2 63.0 82.2 +7.7 27.0 133.6 +3.2 −107.9 256.0 +2.5 86.1 265.0 −72.5 50.0 −4.5 29.0 89.5 35.8 183.7 83.2 85.8 80.7 70.7 55.3 124.1 186.8 60.4 113.1 65.4 84.4 104.4 97.6 125.1 180.5 177.0 88.6 189.0 164.2 77.5 119.9 209.5 176.7 155.2 250.0 285.0 286.5 123.0 216.0 138.3 112.5 390.0 26.1 174.5 255.8 186.2 270.4 258.0 123.5 224.4 144.3 45.3 147.7 128.0 141.0 144.0 141.7 222.1 66.3 −10.0 178.3 250.5 80.0 100.0 22.7 43.7 154.2 16.1 −100.3 284.0 17.5 103.3 287.8 −61.3 64.5 10.4 44.3 108.0 52.6 204.0 101.3 102.0 95.8 85.7 69.7 145.2 210.2 78.7 133.2 83.2 103.8 124.2 117.3 146.1 203.1 198.1 106.7 213.0 186.1 96.3 140.1 230.6 199.0 175.3 279.0 314.6 309.6 142.1 240.0 160.7 131.7 426.5 42.2 198.0 283.5 205.8 299.1 284.4 144.1 249.8 165.6 62.5 169.2 149.5 161.3 165.5 160.0 250.0 84.0 +4.9 200.0 277.0 99.0 119.8 39.5 62.5 178.0 32.0 −92.0 314.3 34.5 122.0 312.5 −48.5 80.2 27.5 61.7 129.8 71.4 226.2 121.5 119.8 113.7 102.3 85.7 168.0 235.8 99.4 155.3 102.7 125.8 146.0 138.4 169.5 227.4 222.7 126.5 239.5 210.5 117.7 161.9 254.5 223.0 197.3 310.2 346.2 332.8 163.4 266.1 187.0 154.1 277.5 102.2 20.2 222.0 303.8 118.1 139.6 56.5 81.8 202.4 50.8 −84.0 346.0 52.5 141.0 337.5 −35.0 96.6 44.6 79.5 150.7 90.5 248.0 142.0 137.8 130.6 119.7 101.7 193.0 262.0 120.4 178.6 123.3 148.2 168.8 160.2 194.0 253.2 247.9 147.5 266.0 235.3 140.0 184.4 279.6 248.0 218.5 342.0 379.9 356.5 185.0 293.0 214.0 179.0 60.6 224.0 314.3 227.0 328.8 313.5 166.7 276.8 189.2 82.0 193.7 172.8 185.0 189.0 183.0 80.1 251.5 347.0 249.2 360.0 343.0 190.6 305.4 213.5 102.2 218.5 197.2 208.0 213.5 204.7 Temperature, °C −23.0 −81.5 65.0 114.0 −17.2 1.7 −59.4 −47.0 37.1 −50.0 −142.9 129.4 −64.5 +3.5 159.5 −120.6 −20.0 −70.0 −43.7 −2.0 −39.0 85.0 0.0 +13.6 +10.0 +1.5 −12.9 29.0 72.0 −20.4 21.2 −17.5 −2.5 14.8 +8.5 27.0 81.3 75.6 +5.2 62.6 −8.0 34.8 104.0 73.2 61.0 145.0 190.0 178.3 33.3 103.5 35.4 26.2 225.0 −36.7 65.9 128.4 96.0 143.8 135.6 28.2 108.2 45.8 −32.0 47.0 32.1 44.5 45.0 58.0 168.2 31.9 −37.8 135.8 199.6 43.0 62.1 −9.4 +7.7 109.4 −10.4 −116.7 224.2 −15.0 66.2 240.5 −85.2 33.4 −21.2 +10.9 67.4 16.4 158.3 62.1 68.0 63.4 54.1 38.8 100.0 158.3 39.8 90.0 44.0 62.3 81.8 75.5 100.6 155.8 151.7 67.6 160.3 139.3 55.8 96.7 183.7 150.5 132.0 217.5 264.3 260.0 100.2 187.9 112.1 90.1 350.0 +7.6 147.7 224.5 162.6 239.8 227.6 99.6 195.7 119.8 25.7 122.6 103.8 116.6 119.6 119.8 181.2 39.8 −31.4 145.8 211.8 51.7 70.8 −2.0 15.9 119.8 −4.5 −112.8 238.7 −7.5 75.0 251.0 −78.8 40.3 −14.1 18.7 76.2 25.0 169.6 71.0 75.5 71.0 61.5 46.0 110.4 171.4 48.7 99.8 53.3 71.9 91.7 85.2 110.3 165.2 162.6 76.3 172.6 149.8 65.2 106.0 194.0 161.7 142.1 231.8 273.3 271.8 110.0 199.8 123.4 99.6 368.8 15.4 158.2 238.2 172.8 252.7 241.7 109.8 208.2 130.0 34.0 133.4 114.7 127.0 129.8 129.3 Melting point, °C 95 −123.5 81 113.5 16.7 −73 −94.6 −41 20.5 −112.0 −81.5 110.5 −87.7 14 152 −136 −129 −136.4 −80 −117.2 −11.9 93 22.5 −6.2 2.5 5.2 217.5 286 106.5 68 −16.1 −26 174 +5.5 14.5 95 121.7 42 132 −12.9 48.5 −21.2 −29.3 0 −0.5 33.5 −51.5 −15.3 ∗Compiled from the extended tables published by D. R. Stull in Ind. Eng. Chem., 39, 517 (1947). For information on fuels see Hibbard, N.A.C.A. Research Mem. E56I21, 1956. For methane see Johnson (ed.), WADD-TR-60-56, 1960. (Continued ) 2-64 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Benzylamine Benzyl bromide (α-bromotoluene) chloride (α-chlorotoluene) cinnamate Benzyldichlorosilane Benzyl ethyl ether phenyl ether isothiocyanate Biphenyl 1-Biphenyloxy-2,3-epoxypropane d-Bornyl acetate Bornyl n-butyrate formate isobutyrate propionate Brassidic acid Bromoacetic acid 4-Bromoanisole Bromobenzene 4-Bromobiphenyl 1-Bromo-2-butanol 1-Bromo-2-butanone cis-1-Bromo-1-butene trans-1-Bromo-1-butene 2-Bromo-1-butene cis-2-Bromo-2-butene trans-2-Bromo-2-butene 1,4-Bromochlorobenzene 1-Bromo-1-chloroethane 1-Bromo-2-chloroethane 2-Bromo-4,6-dichlorophenol 1-Bromo-4-ethyl benzene (2-Bromoethyl)-benzene 2-Bromoethyl 2-chloroethyl ether (2-Bromoethyl)-cyclohexane 1-Bromoethylene Bromoform (tribromomethane) 1-Bromonaphthalene 2-Bromo-4-phenylphenol 3-Bromopyridine 2-Bromotoluene 3-Bromotoluene 4-Bromotoluene 3-Bromo-2,4,6-trichlorophenol 2-Bromo-1,4-xylene 1,2-Butadiene (methyl allene) 1,3-Butadiene n-Butane iso-Butane (2-methylpropane) 1,3-Butanediol 1,2,3-Butanetriol 1-Butene cis-2-Butene trans-2-Butene 3-Butenenitrile iso-Butyl acetate n-Butyl acrylate alcohol iso-Butyl alcohol sec-Butyl alcohol tert-Butyl alcohol iso-Butyl amine n-Butylbenzene iso-Butylbenzene sec-Butylbenzene tert-Butylbenzene iso-Butyl benzoate n-Butyl bromide (1-bromobutane) iso-Butyl n-butyrate carbamate Butyl carbitol (diethylene glycol butyl ether) n-Butyl chloride (1-chlorobutane) iso-Butyl chloride 1 5 10 20 29.0 32.2 22.0 173.8 45.3 26.0 95.4 79.5 70.6 135.3 46.9 74.0 47.0 70.0 64.6 209.6 54.7 48.8 +2.9 98.0 23.7 +6.2 −44.0 −38.4 −47.3 −39.0 −45.0 32.0 −36.0 −28.8 84.0 30.4 48.0 36.5 38.7 −95.4 70.0 54.8 59.6 47.8 206.3 70.2 52.0 127.7 107.8 101.8 169.9 75.7 103.4 74.8 99.8 93.7 241.7 81.6 77.8 27.8 133.7 45.4 30.0 −23.2 −17.0 −27.0 −17.9 −24.1 59.5 −18.0 −7.0 115.6 42.5 76.2 63.2 66.6 −77.8 22.0 117.5 135.4 42.0 49.7 50.8 47.5 146.2 65.0 −72.7 −87.6 −85.7 −94.1 67.5 132.0 −89.4 −81.1 −84.0 +2.9 +1.4 +23.5 +20.0 +11.6 +7.2 −3.0 −31.0 48.8 40.5 44.2 39.0 93.6 −11.2 30.0 83.7 95.7 67.7 73.4 60.8 221.5 83.2 65.0 144.0 121.8 117.0 187.2 90.2 118.0 89.3 114.0 108.0 256.0 94.1 91.9 40.0 150.6 55.8 41.8 −12.8 −6.4 −16.8 −7.2 −13.8 72.7 −9.4 +4.1 130.8 74.0 90.5 76.3 80.5 −68.8 34.0 133.6 152.3 55.2 62.3 64.0 61.1 163.2 78.8 −64.2 −79.7 −77.8 −86.4 85.3 146.0 −81.6 −73.4 −76.3 14.1 12.8 35.5 30.2 21.7 16.9 +5.5 −21.0 62.0 53.7 57.0 51.7 108.6 −0.3 42.2 96.4 107.8 81.8 88.3 75.0 239.3 96.7 79.6 160.7 137.0 134.2 205.8 106.0 133.8 104.0 130.0 123.7 272.9 108.2 107.8 53.8 169.8 67.2 54.2 −1.4 +5.4 −5.3 +4.6 −2.4 87.8 0.0 16.0 147.7 90.2 105.8 90.8 95.8 −58.8 48.0 150.2 171.8 69.1 76.0 78.1 75.2 181.8 94.0 −54.9 −71.0 −68.9 −77.9 100.0 161.0 −73.0 −64.6 −67.5 26.6 25.5 48.6 41.5 32.4 27.3 14.3 −10.3 76.3 67.8 70.6 65.6 124.2 +11.6 56.1 110.1 120.5 97.3 104.8 90.7 255.8 111.8 95.4 180.1 153.0 152.5 226.3 123.7 150.7 121.2 147.2 140.4 290.0 124.0 125.0 68.6 190.8 79.5 68.2 +11.5 18.4 +7.2 17.7 +10.5 103.8 +10.4 29.7 165.8 108.5 123.2 106.6 113.0 −48.1 63.6 170.2 193.8 84.1 91.0 93.9 91.8 200.5 110.6 −44.3 −61.3 −59.1 −68.4 117.4 178.0 −63.4 −54.7 −57.6 40.0 39.2 63.4 53.4 44.1 38.1 24.5 +1.3 92.4 83.3 86.2 80.8 141.8 24.8 71.7 125.3 135.5 C4H9Cl C4H9Cl −49.0 −53.8 −28.9 −34.3 −18.6 −24.5 −7.4 −13.8 +5.0 −1.9 60 100 200 400 760 107.3 115.6 100.5 267.0 121.3 105.5 192.6 163.8 165.2 239.7 135.7 161.8 131.7 157.6 151.2 301.5 133.8 136.0 78.1 204.5 87.0 77.3 19.8 27.2 15.4 26.2 18.7 114.8 17.0 38.0 177.6 121.0 133.8 116.4 123.7 −41.2 73.4 183.5 207.0 94.1 100.0 104.1 102.3 213.0 121.6 −37.5 −55.1 −52.8 −62.4 127.5 188.0 −57.2 −48.4 −51.3 48.8 48.0 72.6 60.3 51.7 45.2 31.0 8.8 102.6 93.3 96.0 90.6 152.0 33.4 81.3 134.6 146.0 120.0 129.8 114.2 281.5 133.5 118.9 209.2 177.7 180.7 255.0 149.8 176.4 145.8 172.2 165.7 316.2 146.3 150.1 90.8 221.8 97.6 89.2 30.8 38.1 26.3 37.5 29.9 128.0 28.0 49.5 193.2 135.5 148.2 129.8 138.0 −31.9 85.9 198.8 224.5 107.8 112.0 117.8 116.4 229.3 135.7 −28.3 −46.8 −44.2 −54.1 141.2 202.5 −48.9 −39.8 −42.7 60.2 59.7 85.1 70.1 61.5 54.1 39.8 18.8 116.2 107.0 109.5 103.8 166.4 44.7 94.0 147.2 159.8 140.0 150.8 134.0 303.8 152.0 139.6 233.2 198.0 204.2 280.4 172.0 198.0 166.4 194.2 187.5 336.8 165.8 172.7 110.1 248.2 112.1 107.0 47.8 55.7 42.8 54.5 46.5 149.5 44.7 66.8 216.5 156.5 169.8 150.0 160.0 −17.2 106.1 224.2 251.0 127.7 133.6 138.0 137.4 253.0 156.4 −14.2 −33.9 −31.2 −41.5 161.0 222.0 −36.2 −26.8 −29.7 78.0 77.6 104.0 84.3 75.9 67.9 52.7 32.0 136.9 127.2 128.8 123.7 188.2 62.0 113.9 165.7 181.2 161.3 175.2 155.8 326.7 173.0 161.5 259.8 220.4 229.4 309.8 197.5 222.2 190.2 218.2 211.2 359.6 186.7 197.5 132.3 277.7 128.3 126.3 66.8 75.0 61.9 74.0 66.0 172.6 63.4 86.0 242.0 182.0 194.0 172.3 186.2 −1.1 127.9 252.0 280.2 150.0 157.3 160.0 160.2 278.0 181.0 +1.8 −19.3 −16.3 −27.1 183.8 243.5 −21.7 −12.0 −14.8 98.0 97.5 125.2 100.8 91.4 83.9 68.0 50.7 159.2 149.6 150.3 145.8 212.8 81.7 135.7 186.0 205.0 184.5 198.5 179.4 350.0 194.3 185.0 287.0 243.0 254.9 340.0 223.0 247.0 214.0 243.0 235.0 382.5 208.0 223.0 156.2 310.0 145.0 147.0 86.2 94.7 81.0 93.9 85.5 196.9 82.7 106.7 268.0 206.0 219.0 195.8 213.0 +15.8 150.5 281.1 311.0 173.4 181.8 183.7 184.5 305.8 206.7 18.5 −4.5 −0.5 −11.7 206.5 264.0 −6.3 +3.7 +0.9 119.0 118.0 147.4 117.5 108.0 99.5 82.9 68.6 183.1 172.8 173.5 168.5 237.0 101.6 156.9 206.5 231.2 13.0 +5.9 24.0 16.0 40.0 32.0 58.8 50.0 77.8 68.9 Temperature, °C Formula C7H9N C7H7Br C7H7Cl C16H14O2 C7H8Cl2Si C9H12O C13H12O C8H7NS C12H10 C15H14O2 C12H20O2 C14H24O2 C11H18O2 C14H24O2 C13H22O2 C22H42O2 C2H3BrO2 C7H7BrO C6H5Br C12H9Br C4H9BrO C4H7BrO C4H7Br C4H7Br C4H7Br C4H7Br C4H7Br C6H4BrCl C2H4BrCl C2H4BrCl C6H3BrCl2O C8H9Br C8H9Br C4H8BrClO C8H15Br C2H3Br CHBr3 C10H7Br C12H9BrO C5H4BrN C7H7Br C7H7Br C7H7Br C6H2BrCl3O C8H9Br C 4H 6 C 4H 6 C4H10 C4H10 C4H10O2 C4H10O3 C4H8 C4H8 C4H8 C4H5N C6H12O2 C7H12O2 C4H10O C4H10O C4H10O C4H10O C4H11N C10H14 C10H14 C10H14 C10H14 C11H14O2 C4H9Br C8H16O2 C5H11NO2 C8H18O3 40 84.2 100.0 16.8 24.4 14.8 10.3 112.4 37.5 −89.0 −102.8 −101.5 −109.2 22.2 102.0 −104.8 −96.4 −99.4 −19.6 −21.2 −0.5 −1.2 −9.0 −12.2 −20.4 −50.0 22.7 14.1 18.6 13.0 64.0 −33.0 +4.6 Melting point, °C −4 −39 39 69.5 29 61.5 49.5 12.5 −30.7 90.5 −100.3 −133.4 −111.2 −114.6 16.6 −16.6 68 −45.0 −138 8.5 5.5 95 −28 39.8 28.5 +9.5 −108.9 −135 −145 77 −130 −138.9 −105.4 −98.9 −64.6 −79.9 −108 −114.7 25.3 −85.0 −88.0 −51.5 −75.5 −58 −112.4 65 −123.1 −131.2 VAPOR PRESSURES 2-65 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Formula sec-Butyl chloride (2-Chlorobutane) tert-Butyl chloride sec-Butyl chloroacetate 2-tert-Butyl-4-cresol 4-tert-Butyl-2-cresol iso-Butyl dichloroacetate 2,3-Butylene glycol (2,3-butanediol) 2-Butyl-2-ethylbutane-1,3-diol 2-tert-Butyl-4-ethylphenol n-Butyl formate iso-Butyl formate sec-Butyl formate sec-Butyl glycolate iso-Butyl iodide (1-iodo-2-methylpropane) isobutyrate isovalerate levulinate naphthylketone (1-isovaleronaphthone) 2-sec-Butylphenol 2-tert-Butylphenol 4-iso-Butylphenol 4-sec-Butylphenol 4-tert-Butylphenol 2-(4-tert-Butylphenoxy)ethyl acetate 4-tert-Butylphenyl dichlorophosphate C4H9Cl C4H9Cl C6H11ClO2 C11H16O C11H16O C6H10Cl2O2 C4H10O2 C10H22O2 C12H15O C5H10O2 C5H10O2 C5H10O2 C6H12O3 C4H9I C8H16O2 C9H18O2 C9H16O3 C15H16O C10H14O C10H14O C10H14O C10H14O C10H14O C14H20O3 C10H13Cl2 O2P C11H14O C7H14O2 C12H18O C12H18O C12H18O C12H18O C4H8O2 C4H8O2 C4H7N C11H14O C10H16 C10H16O2 C10H16O C10H19N C10H20O C10H20O2 C6H12O2 C6H12O2 C6H10O2 C6H11N C8H18O C8H16O C8H16O2 C8H15N C12H9N CO2 CS2 CO COSe COS CBr4 CCl4 CF4 C10H14O C10H14O C10H12O2 C2HCl3O C2H3Cl3O2 C6Cl4O2 C2H3ClO2 C4H4Cl2O3 C6H6ClN C6H6ClN C6H6ClN C6H5Cl tert-Butyl phenyl ketone (pivalophenone) iso-Butyl propionate 4-tert-Butyl-2,5-xylenol 4-tert-Butyl-2,6-xylenol 6-tert-Butyl-2,4-xylenol 6-tert-Butyl-3,4-xylenol Butyric acid iso-Butyric acid Butyronitrile iso-Valerophenone Camphene Campholenic acid d-Camphor Camphylamine Capraldehyde Capric acid n-Caproic acid iso-Caproic acid iso-Caprolactone Capronitrile Capryl alcohol (2-octanol) Caprylaldehyde Caprylic acid (octanoic acid) Caprylonitrile Carbazole Carbon dioxide disulfide monoxide oxyselenide (carbonyl selenide) oxysulfide (carbonyl sulfide) tetrabromide tetrachloride tetrafluoride Carvacrol Carvone Chavibetol Chloral (trichloroacetaldehyde) hydrate (trichloroacetaldehyde hydrate) Chloranil Chloroacetic acid anhydride 2-Chloroaniline 3-Chloroaniline 4-Chloroaniline Chlorobenzene 2-Chlorobenzotrichloride (2-α,α,α-tetrachlorotoluene) C7H4Cl4 1 5 10 20 −60.2 −39.8 −29.2 −17.7 17.0 70.0 74.3 28.6 44.0 94.1 76.3 −26.4 −32.7 −34.4 28.3 −17.0 +4.1 16.0 65.0 136.0 57.4 56.6 72.1 71.4 70.0 118.0 96.0 41.8 98.0 103.7 54.3 68.4 122.6 106.2 −4.7 −11.4 −13.3 53.6 +5.8 28.0 41.2 92.1 167.9 86.0 84.2 100.9 100.5 99.2 150.0 129.6 54.6 112.0 118.0 67.5 80.3 136.8 121.0 +6.1 −0.8 −3.1 66.0 17.0 39.9 53.8 105.9 184.0 100.8 98.1 115.5 114.8 114.0 165.8 146.0 57.8 −2.3 88.2 74.0 70.3 83.9 25.5 14.7 −20.0 58.3 85.7 +20.9 119.8 103.9 100.2 113.6 49.8 39.3 +2.1 87.0 97.6 41.5 45.3 51.9 125.0 71.4 66.2 38.3 9.2 32.8 73.4 92.3 43.0 40 60 Melting point, °C 100 200 400 760 31.5 +14.6 124.1 187.8 197.8 139.2 145.6 212.0 200.3 67.9 60.0 56.8 135.5 81.0 106.3 124.8 181.8 269.7 179.7 173.8 192.1 194.3 191.5 250.3 240.0 50.0 32.6 146.0 210.0 221.8 160.0 164.0 233.5 223.8 86.2 79.0 75.2 155.6 100.3 126.3 146.4 205.5 294.0 203.8 196.3 214.7 217.6 214.0 277.6 268.2 68.0 51.0 167.8 232.6 247.0 183.0 182.0 255.0 247.8 106.0 98.2 93.6 177.5 120.4 147.5 168.7 229.9 320.0 228.0 219.5 237.0 242.1 238.0 304.4 299.0 Temperature, °C 68.2 127.2 134.0 81.4 93.4 151.2 137.0 18.0 +11.0 +8.4 79.8 29.8 52.4 67.7 120.2 201.6 116.1 113.0 130.3 130.3 129.5 183.3 164.0 −5.0 −19.0 83.6 143.9 150.8 96.7 107.8 167.8 154.0 31.6 24.1 21.3 94.2 42.8 67.2 82.7 136.2 219.7 133.4 129.2 147.2 147.8 146.0 201.5 184.3 +3.4 −11.4 93.0 153.7 161.7 106.6 116.3 178.0 165.4 39.8 32.4 29.6 104.0 51.8 75.9 92.4 147.0 231.5 143.9 140.0 157.0 157.9 156.0 212.8 197.2 14.2 −1.0 105.5 167.0 176.2 119.8 127.8 191.9 179.0 51.0 43.4 40.2 116.4 63.5 88.0 105.2 160.2 246.7 157.3 153.5 171.2 172.4 170.2 228.0 214.3 125.7 68.6 74.0 78.8 142.0 89.5 83.0 66.4 34.6 57.6 92.0 114.1 67.6 99.0 32.3 135.0 119.0 115.0 127.0 61.5 51.2 13.4 101.4 47.2 139.8 82.3 83.7 92.0 152.2 99.5 94.0 80.3 47.5 70.0 101.2 124.0 80.4 114.3 44.8 151.0 135.0 131.0 143.0 74.0 64.0 25.7 116.8 60.4 153.9 97.5 97.6 106.3 165.0 111.8 107.0 95.7 61.7 83.3 110.2 136.4 94.6 130.4 58.5 169.8 152.2 148.5 159.7 88.0 77.8 38.4 133.8 75.7 170.0 114.0 112.5 122.2 179.9 125.0 120.4 112.3 76.9 98.0 120.0 150.6 110.6 −134.3 −73.8 −222.0 −117.1 −132.4 −124.4 −54.3 −217.2 −102.3 −119.8 −119.5 −44.7 −215.0 −95.0 −113.3 −114.4 −34.3 −212.8 −86.3 −106.0 −50.0 −184.6 70.0 57.4 83.6 −37.8 −9.8 −30.0 −174.1 98.4 86.1 113.3 −16.0 +10.0 −19.6 −169.3 113.2 100.4 127.0 −5.0 19.5 −8.2 −164.3 127.9 116.1 143.2 +7.2 29.2 −108.6 −22.5 −210.0 −76.4 −98.3 96.3 +4.3 −158.8 145.2 133.0 159.8 20.2 39.7 140.8 67.6 180.3 163.6 158.2 170.0 96.5 86.3 47.3 144.6 85.0 180.0 124.0 122.0 132.0 189.8 133.3 129.6 123.2 86.8 107.4 126.0 160.0 121.2 248.2 −104.8 −15.3 −208.1 −70.2 −93.0 106.3 12.3 −155.4 155.3 143.8 170.7 29.1 46.2 154.0 79.5 195.0 176.0 172.0 184.0 108.0 98.0 59.0 158.0 97.9 193.7 138.0 134.6 145.3 200.0 144.0 141.4 137.2 99.8 119.8 133.9 172.2 134.8 265.0 −100.2 −5.1 −205.7 −61.7 −85.9 119.7 23.0 −150.7 169.7 157.3 185.5 40.2 55.0 70.7 43.0 67.2 46.3 63.5 59.3 −13.0 89.3 68.3 94.1 72.3 89.8 87.9 +10.6 97.8 81.0 108.0 84.8 102.0 102.1 22.2 106.4 94.2 122.4 99.2 116.7 117.8 35.3 116.1 109.2 138.2 115.6 133.6 135.0 49.7 122.0 118.3 148.0 125.7 144.1 145.8 58.3 129.5 130.7 159.8 139.5 158.0 159.9 70.7 140.3 149.0 177.8 160.0 179.5 182.3 89.4 151.3 169.0 197.0 183.7 203.5 206.6 110.0 162.6 189.5 217.0 208.8 228.5 230.5 132.2 290 61.2 46 0 −10.4 70.5 −45.2 69.0 101.8 117.9 135.8 155.0 167.8 185.0 208.0 233.0 262.1 28.7 175.0 197.7 220.0 97.0 116.4 136.8 217.5 241.3 265.3 196.0 217.8 239.8 192.3 214.2 236.5 204.5 226.7 249.5 125.5 144.5 163.5 115.8 134.5 154.5 76.7 96.8 117.5 180.1 204.2 228.0 117.5 138.7 160.5 212.7 234.0 256.0 157.9 182.0 209.2 153.0 173.8 195.0 164.8 186.3 208.5 217.1 240.3 268.4 160.8 181.0 202.0 158.3 181.0 207.7 157.8 182.1 207.0 119.7 141.0 163.7 138.0 157.5 178.5 145.4 156.5 168.5 190.3 213.9 237.5 155.2 179.5 204.5 292.5 323.0 354.8 −93.0 −85.7 −78.2 +10.4 28.0 46.5 −201.3 −196.3 −191.3 −49.8 −35.6 −21.9 −75.0 −62.7 −49.9 139.7 163.5 189.5 38.3 57.8 76.7 −143.6 −135.5 −127.7 191.2 213.8 237.0 179.6 203.5 227.5 206.8 229.8 254.0 57.8 77.5 97.7 68.0 82.1 96.2 −131.3 −26.5 22.5 −95.3 −90.7 −80.7 99 −71 −74 −47 50 178.5 31.5 −1.5 −35 −38.6 16 244.8 −57.5 −110.8 −205.0 −138.8 90.1 −22.6 −183.7 +0.5 −57 51.7 (Continued ) 2-66 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 2-Chlorobenzotrifluoride (2-chloro-α,α,α-trifluorotoluene) 2-Chlorobiphenyl 4-Chlorobiphenyl α-Chlorocrotonic acid Chlorodifluoromethane Chlorodimethylphenylsilane 1-Chloro-2-ethoxybenzene 2-(2-Chloroethoxy) ethanol bis-2-Chloroethyl acetacetal 1-Chloro-2-ethylbenzene 1-Chloro-3-ethylbenzene 1-Chloro-4-ethylbenzene 2-Chloroethyl chloroacetate 2-Chloroethyl 2-chloroisopropyl ether 2-Chloroethyl 2-chloropropyl ether 2-Chloroethyl α-methylbenzyl ether Chloroform (trichloromethane) 1-Chloronaphthalene 4-Chlorophenethyl alcohol 2-Chlorophenol 3-Chlorophenol 4-Chlorophenol 2-Chloro-3-phenylphenol 2-Chloro-6-phenylphenol Chloropicrin (trichloronitromethane) 1-Chloropropene 2-Chloropyridine 3-Chlorostyrene 4-Chlorostyrene 1-Chlorotetradecane 2-Chlorotoluene 3-Chlorotoluene 4-Chlorotoluene Chlorotriethylsilane 1-Chloro-1,2,2-trifluoroethylene Chlorotrifluoromethane Chlorotrimethylsilane trans-Cinnamic acid Cinnamyl alcohol Cinnamylaldehyde Citraconic anhydride cis-α-Citral d-Citronellal Citronellic acid Citronellol Citronellyl acetate Coumarin o-Cresol (2-cresol; 2-methylphenol) m-Cresol (3-cresol; 3-methylphenol) p-Cresol (4-cresol; 4-methylphenol) cis-Crotonic acid trans-Crotonic acid cis-Crotononitrile trans-Crotononitrile Cumene 4-Cumidene Cuminal Cuminyl alcohol 2-Cyano-2-n-butyl acetate Cyanogen bromide chloride iodide Cyclobutane Cyclobutene Cyclohexane Cyclohexaneethanol Cyclohexanol Cyclohexanone 2-Cyclohexyl-4,6-dinitrophenol Cyclopentane Cyclopropane Cymene 1 5 10 20 60 100 200 400 760 88.3 197.0 212.5 155.9 −76.4 124.7 141.8 139.5 150.7 110.0 113.6 116.0 140.0 115.8 125.6 164.8 10.4 180.4 188.1 106.0 143.0 150.0 237.0 237.1 53.8 −15.1 104.6 121.2 122.0 215.5 94.7 96.3 96.6 82.3 −66.7 −111.7 +6.0 232.4 177.8 177.7 145.4 160.0 140.1 195.4 159.8 161.0 216.5 127.4 138.0 140.0 116.3 128.0 50.1 62.8 88.1 158.0 160.0 176.2 133.8 −51.8 22.6 −24.9 97.6 −32.8 −41.2 25.5 142.7 103.7 90.4 229.0 −1.3 −70.0 110.8 108.3 219.6 237.8 173.8 −65.8 145.5 162.0 157.2 169.8 130.2 133.8 137.0 159.8 135.7 146.3 186.3 25.9 204.2 210.0 126.4 164.8 172.0 261.3 261.6 71.8 +1.3 125.0 142.2 143.5 240.3 115.0 116.6 117.1 101.6 −55.0 −102.5 21.9 253.3 199.8 199.3 165.8 181.8 160.0 214.5 179.8 178.8 240.0 146.7 157.3 157.3 133.9 146.0 68.0 81.1 107.3 180.0 182.8 197.9 152.2 −42.6 33.8 −14.1 111.5 −18.9 −27.8 42.0 161.7 121.7 110.3 248.7 +13.8 −59.1 131.4 130.0 243.8 264.5 193.2 −53.6 168.6 185.5 176.5 190.5 152.2 156.7 159.8 182.2 156.5 169.8 210.8 42.7 230.8 234.5 149.8 188.7 196.0 289.4 289.5 91.8 18.0 147.7 165.7 166.0 267.5 137.1 139.7 139.8 123.6 −41.7 −92.7 39.4 276.7 224.6 222.4 189.8 205.0 183.8 236.6 201.0 197.8 264.7 168.4 179.0 179.4 152.2 165.5 88.0 101.5 129.2 203.2 206.7 221.7 173.4 −33.0 46.0 −2.3 126.1 −3.4 −12.2 60.8 183.5 141.4 132.5 269.8 31.0 −46.9 153.5 152.2 267.5 292.9 212.0 −40.8 193.5 208.0 196.0 212.6 177.6 181.1 184.3 205.0 180.0 194.1 235.0 61.3 259.3 259.3 174.5 214.0 220.0 317.5 317.0 111.9 37.0 170.2 190.0 191.0 296.0 159.3 162.3 162.3 146.3 −27.9 −81.2 57.9 300.0 250.0 246.0 213.5 228.0 206.5 257.0 221.5 217.0 291.0 190.8 202.8 201.8 171.9 185.0 108.0 122.8 152.4 227.0 232.0 246.6 195.2 −21.0 61.5 +13.1 141.1 +12.9 +2.4 80.7 205.4 161.0 155.6 291.5 49.3 −33.5 177.2 Temperature, °C Formula C7H4ClF3 C12H9Cl C12H9Cl C4H5ClO2 CHClF2 C8H11ClSi C8H9ClO C4H9ClO2 C6H12Cl2O2 C8H9Cl C8H9Cl C8H9Cl C4H6Cl2O2 C5H10Cl2O C5H10Cl2O C10H13ClO CHCl3 C10H7Cl C8H9ClO C6H5ClO C6H5ClO C6H5ClO C12H9ClO C12H9ClO CCl3NO2 C3H5Cl C5H4ClN C8H7Cl C8H7Cl C14H29Cl C7H7Cl C7H7Cl C7H7Cl C6H15ClSi C2ClF3 CClF3 C3H9ClSi C9H8O2 C9H10O C9H8O C5H4O3 C10H16O C10H18O C10H18O2 C10H20O C12H22O2 C9H6O2 C7H8O C7H8O C7H8O C4H6O2 C4H6O2 C4H5N C4H5N C9H12 C9H13N C10H12O C10H14O C7H11NO2 C2N2 CBrN CClN CIN C4H8 C4H6 C6H12 C8H16O C6H12O C6H10O C12H14N2O5 C5H10 C3H6 C10H14 40 0.0 89.3 96.4 70.0 −122.8 29.8 45.8 53.0 56.2 17.2 18.6 19.2 46.0 24.7 29.8 62.3 −58.0 80.6 84.0 12.1 44.2 49.8 118.0 119.8 −25.5 −81.3 13.3 25.3 28.0 98.5 +5.4 +4.8 +5.5 −4.9 −116.0 −149.5 −62.8 127.5 72.6 76.1 47.1 61.7 44.0 99.5 66.4 74.7 106.0 38.2 52.0 53.0 33.5 24.7 109.8 129.8 95.6 −110.2 56.7 72.8 78.3 83.7 43.0 45.2 46.4 72.1 50.1 56.5 91.4 −39.1 104.8 114.3 38.2 72.0 78.2 152.2 153.7 −3.3 −63.4 38.8 51.3 54.5 131.8 30.6 30.3 31.0 +19.8 −102.5 −139.2 −43.6 157.8 102.5 105.8 74.8 90.0 71.4 127.3 93.6 100.2 137.8 64.0 76.0 76.5 57.4 −29.0 −19.5 +2.9 60.0 58.0 74.2 42.0 −95.8 −35.7 −76.7 25.2 −92.0 −99.1 −45.3 50.4 21.0 +1.4 132.8 −68.0 −116.8 17.3 −7.1 +3.5 26.8 88.2 87.3 103.7 68.7 −83.2 −18.3 −61.4 47.2 −76.0 −83.4 −25.4 77.2 44.0 26.4 161.8 −49.6 −104.2 43.9 37.1 134.7 146.0 108.0 −103.7 70.0 86.5 90.7 97.6 56.1 58.1 60.0 86.0 63.0 70.0 106.0 −29.7 118.6 129.0 51.2 86.1 92.2 169.7 170.7 +7.8 −54.1 51.7 65.2 67.5 148.2 43.2 43.2 43.8 32.0 −95.9 −134.1 −34.0 173.0 117.8 120.0 88.9 103.9 84.8 141.4 107.0 113.0 153.4 76.7 87.8 88.6 69.0 80.0 +4.0 15.0 38.3 102.2 102.0 118.0 82.0 −76.8 −10.0 −53.8 57.7 −67.9 −75.4 −15.9 90.0 56.0 38.7 175.9 −40.4 −97.5 57.0 50.6 151.2 164.0 121.2 −96.5 84.7 101.5 104.1 112.2 70.3 73.0 75.5 100.0 77.2 84.8 121.8 −19.0 134.4 145.0 65.9 101.7 108.1 186.7 189.8 20.0 −44.0 65.8 80.0 82.0 166.2 56.9 57.4 57.8 45.5 −88.2 −128.5 −23.2 189.5 133.7 135.7 103.8 119.4 99.8 155.6 121.5 126.0 170.0 90.5 101.4 102.3 82.0 93.0 16.4 27.8 51.5 117.8 117.9 133.8 96.2 −70.1 −1.0 −46.1 68.6 −58.7 −66.6 −5.0 104.0 68.8 52.5 191.2 −30.1 −90.3 71.1 65.9 169.9 183.8 135.6 −88.6 101.2 117.8 118.4 127.8 86.2 89.2 91.8 116.0 92.4 101.5 139.6 −7.1 153.2 162.0 82.0 118.0 125.0 207.4 208.2 33.8 −32.7 81.7 96.5 98.0 187.0 72.0 73.0 73.5 60.2 −79.7 −121.9 −11.4 207.1 151.0 152.2 120.3 135.9 116.1 171.9 137.2 140.5 189.0 105.8 116.0 117.7 96.0 107.8 30.0 41.8 66.1 134.2 135.2 150.3 111.8 −62.7 +8.6 −37.5 80.3 −48.4 −56.4 +6.7 119.8 83.0 67.8 206.7 −18.6 −82.3 87.0 75.4 182.1 196.0 144.4 −83.4 111.5 127.8 127.5 138.0 96.4 99.6 102.0 126.2 102.2 111.8 150.0 +0.5 165.6 173.5 92.0 129.4 136.1 219.6 220.0 42.3 −25.1 91.6 107.2 108.5 199.8 81.8 83.2 83.3 69.5 −74.1 −117.3 −4.0 217.8 162.0 163.7 131.3 146.3 126.2 182.1 147.2 149.7 200.5 115.5 125.8 127.0 104.5 116.7 38.5 50.9 75.4 145.0 146.0 161.7 121.5 −57.9 14.7 −32.1 88.0 −41.8 −50.0 14.7 129.8 91.8 77.5 216.0 −11.3 −77.0 97.2 Melting point, °C −6.0 34 75.5 −160 −80.2 −53.3 −62.6 −63.5 −20 7 32.5 42 +6 −64 −99.0 −15.0 +0.9 +7.3 −157.5 133 33 −7.5 70 30.8 10.9 35.5 15.5 72 −96.0 −34.4 58 −6.5 −50 +6.6 23.9 −45.0 −93.7 −126.6 −68.2 VAPOR PRESSURES 2-67 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name cis-Decalin trans-Decalin Decane Decan-2-one 1-Decene Decyl alcohol Decyltrimethylsilane Dehydroacetic acid Desoxybenzoin Diacetamide Diacetylene (1,3-butadiyne) Diallyldichlorosilane Diallyl sulfide Diisoamyl ether oxalate sulfide Dibenzylamine Dibenzyl ketone (1,3-diphenyl2-propanone) 1,4-Dibromobenzene 1,2-Dibromobutane dl-2,3-Dibromobutane meso-2,3-Dibromobutane 1,2-Dibromodecane Di(2-bromoethyl) ether α,β-Dibromomaleic anhydride 1,2-Dibromo-2-methylpropane 1,3-Dibromo-2-methylpropane 1,2-Dibromopentane 1,2-Dibromopropane 1,3-Dibromopropane 2,3-Dibromopropene 2,3-Dibromo-1-propanol Diisobutylamine 2,6-Ditert-butyl-4-cresol 4,6-Ditert-butyl-2-cresol 4,6-Ditert-butyl-3-cresol 2,6-Ditert-butyl-4-ethylphenol 4,6-Ditert-butyl-3-ethylphenol Diisobutyl oxalate 2,4-Ditert-butylphenol Dibutyl phthalate sulfide Diisobutyl d-tartrate Dicarvacryl-mono-(6-chloro-2-xenyl) phosphate Dicarvacryl-2-tolyl phosphate Dichloroacetic acid 1,2-Dichlorobenzene 1,3-Dichlorobenzene 1,4-Dichlorobenzene 1,2-Dichlorobutane 2,3-Dichlorobutane 1,2-Dichloro-1,2-difluoroethylene Dichlorodifluoromethane Dichlorodiphenyl silane Dichlorodiisopropyl ether Di(2-chloroethoxy) methane Dichloroethoxymethylsilane 1,2-Dichloro-3-ethylbenzene 1,2-Dichloro-4-ethylbenzene 1,4-Dichloro-2-ethylbenzene cis-1,2-Dichloroethylene trans-1,2-Dichloro ethylene Di(2-chloroethyl) ether Dichlorofluoromethane 1,5-Dichlorohexamethyltrisiloxane Dichloromethylphenylsilane 1,1-Dichloro-2-methylpropane 1,2-Dichloro-2-methylpropane 1,3-Dichloro-2-methylpropane 2,4-Dichlorophenol 2,6-Dichlorophenol 1 5 10 20 40 C10H18 C10H18 C10H22 C10H20O C10H20 C10H22O C13H30Si C8H8O4 C14H12O C4H7NO2 C4H2 C6H10Cl2Si C6H10S C10H22O C12H22O4 C10H22S C14H15N C15H14O 22.5 −0.8 16.5 44.2 14.7 69.5 67.4 91.7 123.3 70.0 −82.5 +9.5 −9.5 18.6 85.4 43.0 118.3 125.5 50.1 +30.6 42.3 71.9 40.3 97.3 96.4 122.0 156.2 95.0 −68.0 34.8 +14.4 44.3 116.0 73.0 149.8 159.8 64.2 47.2 55.7 85.8 53.7 111.3 111.0 137.3 173.5 108.0 −61.2 47.4 26.6 57.0 131.4 87.6 165.6 177.6 79.8 65.3 69.8 100.7 67.8 125.8 126.5 153.0 192.0 122.6 −53.8 61.3 39.7 70.7 147.7 102.7 182.2 195.7 97.2 85.7 85.5 117.1 83.3 142.1 144.0 171.0 212.0 138.2 −45.9 76.4 54.2 86.3 165.7 120.0 200.2 216.6 C6H4Br2 C4H8Br2 C4H8Br2 C4H8Br2 C10H20Br2 C4H8Br2O C4H2Br2O3 C4H8Br2 C4H8Br2 C5H10Br2 C3H6Br2 C3H6Br2 C3H4Br2 C3H6Br2O C8H19N C15H24O C15H24O C15H24O C16H26O C16H26O C10H18O4 C14H22O C16H22O4 C8H18S C12H22O6 C32H34ClO4P 61.0 7.5 +5.0 +1.5 95.7 47.7 50.0 −28.8 14.0 19.8 −7.0 +9.7 −6.0 57.0 −5.1 85.8 86.2 103.7 89.1 111.5 63.2 84.5 148.2 +21.7 117.8 204.2 79.3 33.2 30.0 26.6 123.6 75.3 78.0 −3.0 40.0 45.4 +17.3 35.4 +17.9 84.5 +18.4 116.2 117.3 135.2 121.4 142.6 91.2 115.4 182.1 51.8 151.8 234.5 87.7 46.1 41.6 39.3 137.3 88.5 92.0 +10.5 53.0 58.0 29.4 48.0 30.0 98.2 30.6 131.0 132.4 150.0 137.0 157.4 105.3 130.0 198.2 66.4 169.0 249.3 103.6 60.0 56.4 53.2 151.0 103.6 106.7 25.7 67.5 72.0 42.3 62.1 43.2 113.5 43.7 147.0 149.0 167.0 154.0 174.0 120.3 146.0 216.2 80.5 188.0 264.5 C27H33O4P C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C4H8Cl2 C4H8Cl2 C2Cl2F2 CCl2F2 C12H10Cl2Si C6H12Cl2O C5H10Cl2O2 C8H8Cl2OSi C8H8Cl2 C8H8Cl2 C8H8Cl2 C2H2Cl2 C2H2Cl2 C4H8Cl2O CHCl2F C6H18Cl2 O2Si3 C7H8Cl2Si C4H8Cl2 C4H8Cl2 C4H8Cl2 C6H4Cl2O C6H4Cl2O 180.2 44.0 20.0 12.1 209.3 69.8 46.0 39.0 −23.6 −25.2 −82.0 −118.5 109.6 29.6 53.0 −33.8 46.0 47.0 38.5 −58.4 −65.4 23.5 −91.3 26.0 −0.3 −3.0 −65.6 −104.6 142.4 55.2 80.4 −12.1 75.0 77.2 68.0 −39.2 −47.2 49.3 −75.5 52.0 221.8 82.6 59.1 52.0 54.8 +11.5 +8.5 −57.3 −97.8 158.0 68.2 94.0 −1.3 90.0 92.3 83.2 −29.9 −38.0 62.0 −67.5 65.1 35.7 −31.0 −25.8 −3.0 53.0 59.5 63.5 −8.4 −4.2 +20.6 80.0 87.6 77.4 +2.6 +6.7 32.0 92.8 101.0 60 Melting point, °C 100 200 400 760 108.0 98.4 95.5 127.8 93.5 152.0 154.3 181.5 224.5 148.0 −41.0 86.3 63.7 96.0 177.0 130.6 212.2 229.4 123.2 114.6 108.6 142.0 106.5 165.8 169.5 197.5 241.3 160.6 −34.0 99.7 75.8 109.6 192.2 145.3 227.3 246.6 145.4 136.2 128.4 163.2 126.7 186.2 191.0 219.5 265.2 180.8 −20.9 119.4 94.8 129.0 215.0 166.4 249.8 272.3 169.9 160.1 150.6 186.7 149.2 208.8 215.5 244.5 293.0 202.0 −6.1 142.0 116.1 150.3 240.0 191.0 274.3 301.7 194.6 186.7 174.1 211.0 172.0 231.0 240.0 269.0 321.0 223.0 +9.7 165.3 138.6 173.4 265.0 216.0 300.0 330.5 120.8 76.0 72.0 68.0 167.4 119.8 123.5 42.3 83.5 87.4 57.2 77.8 57.8 129.8 57.8 164.1 167.4 185.3 172.1 192.3 137.5 164.3 235.8 96.0 208.5 280.5 131.6 86.0 82.0 78.0 177.5 130.0 133.8 53.7 93.7 97.4 66.4 87.8 67.0 140.0 67.0 175.2 179.0 196.1 183.9 204.4 147.8 175.8 247.8 105.8 221.6 290.7 146.5 99.8 95.3 91.7 190.2 144.0 147.7 68.8 107.4 110.1 78.7 101.3 79.5 153.0 79.2 190.0 194.0 211.0 198.0 218.0 161.8 190.0 263.7 118.6 239.5 304.9 168.5 120.2 115.7 111.8 209.6 165.0 168.0 92.1 117.8 130.2 97.8 121.7 98.0 173.8 97.6 212.8 217.5 233.0 220.0 241.7 183.5 212.5 287.0 138.0 264.7 323.8 192.5 143.5 138.0 134.2 229.8 188.0 192.0 119.8 150.6 151.8 118.5 144.1 119.5 196.0 118.0 237.6 243.4 257.1 244.0 264.6 205.8 237.0 313.5 159.0 294.0 342.0 218.6 166.3 160.5 157.3 250.4 212.5 215.0 149.0 174.6 175.0 141.6 167.5 141.2 219.0 139.5 262.5 269.3 282.0 268.6 290.0 229.5 260.8 340.0 182.0 324.0 361.0 237.0 96.3 73.4 66.2 69.2 24.5 21.2 −48.3 −90.1 176.0 82.2 109.5 +11.3 105.9 109.6 99.8 −19.4 −28.0 76.0 −58.6 79.0 251.5 111.8 89.4 82.0 84.8 37.7 35.0 −38.2 −81.6 195.5 97.3 125.5 24.4 123.8 127.5 118.0 −7.9 −17.0 91.5 −48.8 94.8 260.3 121.5 99.5 92.2 95.2 47.8 43.9 −31.8 −76.1 207.5 106.9 135.8 32.6 135.0 139.0 129.0 −0.5 −10.0 101.5 −42.6 105.0 272.5 134.0 112.9 105.0 108.4 60.2 56.0 −23.0 −68.6 223.8 119.7 149.6 44.1 149.8 153.3 144.0 +9.5 −0.2 114.5 −33.9 118.2 290.0 152.3 133.4 125.9 128.3 79.7 74.0 −10.0 −57.0 248.0 139.0 170.0 61.0 172.0 176.0 166.2 24.6 +14.3 134.0 −20.9 138.3 309.8 173.7 155.8 149.0 150.2 100.8 94.2 +5.0 −43.9 275.5 159.8 192.0 80.3 197.0 201.7 191.5 41.0 30.8 155.4 −6.2 160.2 330.0 194.4 179.0 173.0 173.9 123.5 116.0 20.9 −29.8 304.0 182.7 215.0 100.6 222.1 226.6 216.3 59.0 47.8 178.5 +8.9 184.0 92.4 14.6 18.7 44.8 107.7 115.5 109.5 28.2 32.0 58.6 123.4 131.6 120.0 37.0 40.2 67.5 133.5 141.8 134.2 48.2 51.7 78.8 146.0 154.6 155.5 65.8 68.9 96.1 165.2 175.5 180.2 85.4 87.8 115.4 187.5 197.7 205.5 106.0 108.0 135.0 210.0 220.0 Temperature, °C Formula −43.3 −30.7 −29.7 +3.5 +7 60 78.5 −34.9 −83 −26 34.5 87.5 −64.5 −34.5 −70.3 −55.5 −34.4 −70 −79.7 73.5 9.7 −17.6 −24.2 53.0 −80.4 −112 −40.8 −76.4 −61.2 −80.5 −50.0 −135 −53.0 45.0 (Continued ) 2-68 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name α,α-Dichlorophenylacetonitrile Dichlorophenylarsine 1,2-Dichloropropane 2,3-Dichlorostyrene 2,4-Dichlorostyrene 2,5-Dichlorostyrene 2,6-Dichlorostyrene 3,4-Dichlorostyrene 3,5-Dichlorostyrene 1,2-Dichlorotetraethylbenzene 1,4-Dichlorotetraethylbenzene 1,2-Dichloro-1,1,2,2-tetrafluoroethane Dichloro-4-tolylsilane 3,4-Dichloro-α,α,α-trifluorotoluene Dicyclopentadiene Diethoxydimethylsilane Diethoxydiphenylsilane Diethyl adipate Diethylamine N-Diethylaniline Diethyl arsanilate 1,2-Diethylbenzene 1,3-Diethylbenzene 1,4-Diethylbenzene Diethyl carbonate cis-Diethyl citraconate Diethyl dioxosuccinate Diethylene glycol Diethyleneglycol-bis-chloroacetate Diethylene glycol dimethyl ether Di(2-methoxyethyl) ether glycol ethyl ether Diethyl ether ethylmalonate fumarate glutarate Diethylhexadecylamine Diethyl itaconate ketone (3-pentanone) malate maleate malonate mesaconate oxalate phthalate sebacate 2,5-Diethylstyrene Diethyl succinate isosuccinate sulfate sulfide sulfite d-Diethyl tartrate dl-Diethyl tartrate 3,5-Diethyltoluene Diethylzinc 1-Dihydrocarvone Dihydrocitronellol 1,4-Dihydroxyanthraquinone Dimethylacetylene (2-butyne) Dimethylamine N,N-Dimethylaniline Dimethyl arsanilate Di(α-methylbenzyl) ether 2,2-Dimethylbutane 2,3-Dimethylbutane Dimethyl citraconate 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane trans-1,3-Dimethylcyclohexane cis-1,3-Dimethylcyclohexane cis-1,4-Dimethylcyclohexane trans-1,4-Dimethylcyclohexane 1 5 10 20 40 C8H5Cl2N C6H5AsCl2 C3H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C8H6Cl2 C14H20Cl2 C14H20Cl2 C2Cl2F4 C7H8Cl2Si C7H3Cl2F3 C10H8 C6H16O2Si C16H20O2Si C10H18O4 C4H11N C10H15N C10H16As NO3 C10H14 C10H14 C10H14 C5H10O3 C9H14O4 C8H10O6 C4H10O3 C8H12Cl2O5 56.0 61.8 −38.5 61.0 53.5 55.5 47.8 57.2 53.5 105.6 91.7 −95.4 46.2 11.0 −19.1 111.5 74.0 84.0 100.0 −17.0 90.1 82.2 83.9 75.7 86.0 82.2 138.7 126.1 −80.0 71.7 38.3 34.1 +2.4 142.8 106.6 49.7 78.0 98.1 116.0 −6.1 104.6 97.4 98.2 90.0 100.4 97.4 155.0 143.8 −72.3 84.2 52.2 47.6 13.3 157.6 123.0 −33.0 91.9 113.8 133.1 +6.0 120.5 111.8 114.0 105.5 116.2 111.8 172.5 162.0 −63.5 97.8 67.3 62.0 25.3 174.3 138.3 −22.6 107.2 130.0 151.0 19.4 137.8 129.2 131.0 122.4 133.7 129.2 192.2 183.2 −53.7 113.2 84.0 77.9 38.0 193.2 154.6 −11.3 123.6 38.0 22.3 20.7 20.7 −10.1 59.8 70.0 91.8 148.3 62.6 48.7 46.8 47.1 +12.3 88.3 98.0 120.0 180.0 74.8 62.0 59.9 60.3 23.8 103.0 112.0 133.8 195.8 88.0 76.4 74.5 74.7 36.0 118.2 126.8 148.0 212.0 C6H14O3 C6H14O3 C4H10O C9H16O4 C8H12O4 C9H16O4 C20H43N C9H14O4 C5H10O C8H14O5 C8H12O4 C7H12O4 C9H14O4 C6H10O4 C12H14O4 C14H26O4 C12H16 C8H14O4 C8H14O4 C4H10O4S C4H10S C4H10O3S C8H14O6 C8H14O6 C11H16 C4H10Zn C10H16O C10H22O C14H8O4 C4H6 C2H7N C8H11N C8H12AsNO3 C16H18O C6H14 C6H14 C7H10O4 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16 C8H16 13.0 45.3 −74.3 50.8 53.2 65.6 139.8 51.3 −12.7 80.7 57.3 40.0 62.8 47.4 108.8 125.3 49.7 54.6 39.8 47.0 −39.6 10.0 102.0 100.0 34.0 −22.4 46.6 68.0 196.7 −73.0 −87.7 29.5 15.0 96.7 −69.3 −63.6 50.8 −24.4 −15.9 −21.1 −19.4 −22.7 −20.0 −24.3 37.6 72.0 −56.9 77.8 81.2 94.7 175.8 80.2 +7.5 110.4 85.6 67.5 91.0 71.8 140.7 156.2 78.4 83.0 66.7 74.0 −18.6 34.2 133.0 131.7 61.5 0.0 75.5 91.7 239.8 −57.9 −72.2 56.3 39.6 128.3 −50.7 −44.5 78.2 −1.4 +7.3 +1.7 +3.4 0.0 +3.2 −1.7 50.0 85.8 −48.1 91.6 95.3 109.7 194.0 95.2 17.2 125.3 100.0 81.3 105.3 83.8 156.0 172.1 92.6 96.6 80.0 87.7 −8.0 46.4 148.0 147.2 75.3 +11.7 90.0 103.0 259.8 −50.5 −64.6 70.0 51.8 144.0 −41.5 −34.9 91.8 +10.3 18.4 13.0 14.9 +11.2 14.5 +10.1 63.0 100.3 −38.5 106.0 110.2 125.4 213.5 111.0 27.9 141.2 115.3 95.9 120.3 96.8 173.6 189.8 108.5 111.7 94.7 102.1 +3.5 59.7 164.2 163.8 90.2 24.2 106.0 115.0 282.0 −42.5 −56.0 84.8 65.0 160.3 −31.1 −24.1 106.5 23.0 31.1 25.6 27.4 23.6 27.1 22.6 60 100 200 400 760 141.0 163.2 28.0 149.0 140.0 142.0 133.3 144.6 140.0 204.8 195.8 −47.5 122.6 95.0 88.0 46.3 205.0 165.8 −4.0 133.8 154.5 178.9 39.4 163.5 153.8 155.8 147.6 158.2 153.8 220.7 212.0 −39.1 135.5 109.2 101.7 57.6 220.0 179.0 +6.0 147.3 176.2 202.8 57.0 185.7 176.0 178.0 169.0 181.5 176.0 245.6 238.5 −26.3 153.5 129.0 121.8 74.2 243.8 198.2 21.0 168.2 199.5 228.8 76.0 210.0 200.0 202.5 193.5 205.7 200.0 272.8 265.8 −12.0 175.2 150.5 144.2 93.2 259.7 219.1 38.0 192.4 223.5 256.5 96.8 235.0 225.0 227.0 217.0 230.0 225.0 302.0 296.5 +3.5 196.3 172.8 166.6 113.5 296.0 240.0 55.5 215.5 102.6 92.5 90.4 91.1 49.5 135.7 143.8 164.3 229.0 111.8 102.6 100.7 101.3 57.9 146.2 153.7 174.0 239.5 123.8 116.2 114.4 115.3 69.7 160.0 167.7 187.5 252.0 141.9 136.7 134.8 136.1 86.5 182.3 188.0 207.0 271.5 161.0 159.0 156.9 159.0 105.8 206.5 210.8 226.5 291.8 181.0 183.5 181.1 183.8 125.8 230.3 233.5 244.8 313.0 77.5 116.7 27.7 122.4 126.7 142.8 235.0 128.2 39.4 157.8 131.8 113.3 137.3 110.6 192.1 207.5 125.8 127.8 111.0 118.0 16.1 74.2 182.3 181.7 107.0 38.0 123.7 127.6 307.4 −33.9 −46.7 101.6 79.7 179.6 −19.5 −12.4 122.6 37.3 45.3 39.7 41.4 37.5 41.1 36.5 86.8 126.8 −21.8 132.4 137.7 153.2 248.5 139.9 46.7 169.0 142.4 123.0 147.9 119.7 204.1 218.4 136.8 138.2 121.4 128.6 24.2 83.8 194.0 193.2 117.7 47.2 134.7 136.7 323.3 −27.8 −40.7 111.9 88.6 191.5 −12.1 −4.9 132.7 45.7 54.4 48.7 50.4 46.4 50.1 45.4 99.5 140.3 −11.5 146.0 151.1 167.8 265.5 154.3 56.2 183.9 156.0 136.2 161.6 130.8 219.5 234.4 151.0 151.1 134.8 142.5 35.0 96.3 208.5 208.0 131.7 59.1 149.7 145.9 344.5 −18.8 −32.6 125.8 101.0 206.8 −2.0 +5.4 145.8 57.9 66.8 61.0 62.5 58.5 62.3 57.6 118.0 159.0 +2.2 166.0 172.2 189.5 292.8 177.5 70.6 205.3 177.8 155.5 183.2 147.9 243.0 255.8 173.2 171.7 155.1 162.5 51.3 115.8 230.4 230.0 152.4 77.0 171.8 160.2 377.8 −5.0 −20.4 146.5 119.8 229.7 +13.4 21.1 165.8 76.2 85.6 79.6 81.0 76.9 80.8 76.0 138.5 180.3 17.9 188.7 195.8 212.8 324.6 203.1 86.3 229.5 201.7 176.8 205.8 166.2 267.5 280.3 198.0 193.8 177.7 185.5 69.7 137.0 254.8 254.3 176.5 97.3 197.0 176.8 413.0 +10.6 −7.1 169.2 140.3 254.8 31.0 39.0 188.0 97.2 107.0 100.9 102.1 97.8 101.9 97.0 159.8 201.9 34.6 211.5 218.5 237.0 355.0 227.9 102.7 253.4 225.0 198.9 229.0 185.7 294.0 305.5 223.0 216.5 201.3 209.5 88.0 159.0 280.0 280.0 200.7 118.0 223.0 193.5 450.0 27.2 +7.4 193.1 160.5 281.0 49.7 58.0 210.5 119.5 129.7 123.4 124.4 120.1 124.3 119.3 Temperature, °C Formula Melting point, °C −94 −12.1 32.9 −21 −38.9 −34.4 −31.4 −83.9 −43.2 −43 −116.3 +0.6 −42 −49.8 −40.6 1.3 −20.8 −25.0 −99.5 17 −28 194 −32.5 −96 +2.5 −99.8 −128.2 −34 −50.0 −88.0 −92.0 −76.2 −87.4 −36.9 VAPOR PRESSURES 2-69 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Dimethyl ether 2,2-Dimethylhexane 2,3-Dimethylhexane 2,4-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 3,4-Dimethylhexane Dimethyl itaconate 1-Dimethyl malate Dimethyl maleate malonate trans-Dimethyl mesaconate 2,7-Dimethyloctane Dimethyl oxalate 2,2-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,3-Dimethylphenol (2,3-xylenol) 2,4-Dimethylphenol (2,4-xylenol) 2,5-Dimethylphenol (2,5-xylenol) 3,4-Dimethylphenol (3,4-xylenol) 3,5-Dimethylphenol (3,5-xylenol) Dimethylphenylsilane Dimethyl phthalate 3,5-Dimethyl-1,2-pyrone 4,6-Dimethylresorcinol Dimethyl sebacate 2,4-Dimethylstyrene 2,5-Dimethylstyrene α,α-Dimethylsuccinic anhydride Dimethyl sulfide d-Dimethyl tartrate dl-Dimethyl tartrate N,N-Dimethyl-2-toluidine N,N-Dimethyl-4-toluidine Di(nitrosomethyl) amine Diosphenol 1,4-Dioxane Dipentene Diphenylamine Diphenyl carbinol (benzhydrol) chlorophosphate disulfide 1,2-Diphenylethane (dibenzyl) Diphenyl ether 1,1-Diphenylethylene trans-Diphenylethylene 1,1-Diphenylhydrazine Diphenylmethane Diphenyl sulfide Diphenyl-2-tolyl thiophosphate 1,2-Dipropoxyethane 1,2-Diisopropylbenzene 1,3-Diisopropylbenzene Dipropylene glycol Dipropyleneglycol monobutyl ether isopropyl ether Di-n-propyl ether Diisopropyl ether Di-n-propyl ketone (4-heptanone) Di-n-propyl oxalate Diisopropyl oxalate Di-n-propyl succinate Di-n-propyl d-tartrate Diisopropyl d-tartrate Divinyl acetylene (1,5-hexadiene-3-yne) 1,3-Divinylbenzene Docosane n-Dodecane 1-Dodecene n-Dodecyl alcohol Dodecylamine Dodecyltrimethylsilane Elaidic acid 1 5 10 20 40 −101.1 −7.9 −1.1 −5.3 −5.5 −4.4 +0.2 94.0 104.0 73.0 59.8 74.0 30.5 44.0 −28.7 −20.8 −27.4 −25.0 83.8 78.0 78.0 93.8 89.2 30.3 131.8 107.6 76.8 139.8 61.9 55.9 88.1 −58.0 133.2 131.8 54.1 74.3 27.8 95.4 −12.8 40.4 141.7 145.0 160.5 164.0 119.8 97.8 119.6 145.8 159.3 107.4 129.0 179.8 −10.3 67.8 62.3 102.1 92.0 72.8 −22.3 −37.4 44.4 80.2 69.0 107.6 147.7 133.7 −24.4 60.0 195.4 75.8 74.0 120.2 111.8 122.1 206.7 −93.3 +3.1 +9.9 +5.2 +5.3 +6.1 11.3 106.6 118.3 86.4 72.0 87.8 42.3 56.0 −18.7 −10.3 −17.1 −14.4 97.6 91.3 91.3 107.7 102.4 42.6 147.6 122.0 90.7 156.2 75.8 69.0 102.0 −49.2 148.2 147.5 66.2 86.7 40.0 109.0 −1.2 53.8 157.0 162.0 182.0 180.0 136.0 114.0 135.0 161.0 176.1 122.8 145.0 201.6 +5.0 81.8 76.0 116.2 106.0 86.2 −11.8 −27.4 55.0 93.9 81.9 122.2 163.5 148.2 −14.0 73.8 213.0 90.0 87.8 134.7 127.8 137.7 223.5 −85.2 15.0 22.1 17.2 17.2 18.2 23.5 119.7 133.8 101.3 85.0 102.1 55.8 69.4 −7.5 +1.1 −5.9 −2.9 112.0 105.0 105.0 122.0 117.0 56.2 164.0 136.4 105.8 175.8 90.8 84.0 116.3 −39.4 164.3 164.0 80.2 100.0 53.7 124.0 +12.0 68.2 175.2 180.9 203.8 197.0 153.7 130.8 151.8 179.8 194.0 139.8 162.0 215.5 22.3 96.8 91.2 131.3 120.4 100.8 0.0 −16.7 66.2 108.6 95.6 138.0 180.4 164.0 −2.8 88.7 233.5 104.6 102.4 150.0 141.6 153.8 242.3 −76.2 28.2 35.6 30.5 30.4 31.7 37.1 133.7 150.1 117.2 100.0 118.0 71.2 83.6 +5.0 13.9 +6.5 +9.9 129.2 121.5 121.5 138.0 133.3 71.4 182.8 152.7 122.5 196.0 107.7 100.2 132.3 −28.4 182.4 182.4 95.0 116.3 68.2 141.2 25.2 84.3 194.3 200.0 227.9 214.8 173.7 150.0 170.8 199.0 213.5 157.8 182.8 230.6 42.3 114.0 107.9 147.4 136.3 117.0 +13.2 −4.5 78.1 124.6 110.5 154.8 199.7 181.8 +10.0 105.5 254.5 121.7 118.6 167.2 157.4 172.1 260.8 Melting point, °C 100 200 400 760 −62.7 48.2 56.0 50.6 50.5 52.5 57.7 153.7 175.1 140.4 121.9 141.5 93.9 104.8 23.9 33.3 25.4 29.3 152.2 143.0 143.0 161.0 156.0 94.2 210.0 177.5 147.3 222.6 132.3 124.7 155.3 −12.0 208.8 209.5 118.1 140.3 90.3 165.6 45.1 108.3 222.8 227.5 265.0 241.3 202.8 178.8 198.6 227.4 242.5 186.3 211.8 252.5 74.2 138.7 132.3 169.9 159.8 140.3 33.0 13.7 96.0 148.1 132.6 180.3 227.0 207.3 29.5 130.0 286.0 146.2 142.3 192.0 182.1 199.5 288.0 −50.9 65.7 73.8 68.1 68.0 70.0 75.6 171.0 196.3 160.0 140.0 161.0 114.0 123.3 40.3 50.1 41.8 46.2 173.0 161.5 161.5 181.5 176.2 114.2 232.7 198.0 167.8 245.0 153.2 145.6 175.8 +2.6 230.5 232.3 138.3 161.6 110.0 186.2 62.3 128.2 247.5 250.0 299.5 262.6 227.8 203.3 222.8 251.7 267.2 210.7 236.8 270.3 103.8 159.8 153.7 189.9 180.0 160.0 50.3 30.0 111.2 168.0 151.2 202.5 250.1 228.2 46.0 151.4 314.2 167.2 162.2 213.0 203.0 222.0 312.4 −37.8 85.6 94.1 88.2 87.9 90.4 96.0 189.8 219.5 182.2 159.8 183.5 136.0 143.3 59.2 69.4 60.6 65.5 196.0 184.2 184.2 203.6 197.8 136.4 257.8 221.0 192.0 269.6 177.5 168.7 197.5 18.7 255.0 257.4 161.5 185.4 131.3 209.5 81.8 150.5 274.1 275.6 337.2 285.8 255.0 230.7 249.8 278.3 294.0 237.5 263.9 290.0 140.0 184.3 177.6 210.5 203.8 183.1 69.5 48.2 127.3 190.3 171.8 226.5 275.6 251.8 64.4 175.2 343.5 191.0 185.5 235.7 225.0 248.0 337.0 −23.7 106.8 115.6 109.4 109.1 112.0 117.7 208.0 242.6 205.0 180.7 206.0 159.7 163.3 79.2 89.8 80.5 86.1 218.0 211.5 211.5 225.2 219.5 159.3 283.7 245.0 215.0 293.5 202.0 193.0 219.5 36.0 280.0 282.0 184.8 209.5 153.0 232.0 101.1 174.6 302.0 301.0 378.0 310.0 284.0 258.5 277.0 306.5 322.2 264.5 292.5 310.0 180.0 209.0 202.0 231.8 227.0 205.6 89.5 67.5 143.7 213.5 193.5 250.8 303.0 275.0 84.0 199.5 376.0 216.2 208.0 259.0 248.0 273.0 362.0 Temperature, °C Formula C2H6O −115.7 −29.7 C8H18 −23.0 C8H18 C8H18 −26.9 −26.7 C8H18 −25.8 C8H18 C8H18 −22.1 69.3 C7H10O4 75.4 C6H10O5 C6H8O4 45.7 35.0 C5H8O4 46.8 C7H10O4 C10H22 +6.3 20.0 C4H6O4 −49.0 C7H16 C7H16 −42.0 −48.0 C7H16 −45.9 C7H16 C8H10O 56.0 51.8 C8H10O 51.8 C8H10O C8H10O 66.2 62.0 C8H10O +5.3 C8H12Si C10H10O4 100.3 78.6 C7H8O2 49.0 C8H10O2 C12H22O4 104.0 34.2 C10H12 29.0 C10H12 C6H8O3 61.4 −75.6 C2H6S 102.1 C6H10O6 C6H10O6 100.4 28.8 C9H13N 50.1 C9H13N C2H5N3O2 +3.2 66.7 C10H16O2 −35.8 C4H8O2 C10H16 14.0 108.3 C12H11N 110.0 C13H12O C12H10ClPO3 121.5 131.6 C12H10S2 86.8 C14H14 C12H10O 66.1 87.4 C14H12 113.2 C14H12 C12H12N2 126.0 76.0 C13H12 96.1 C12H10S C18H17O3PS 159.7 −38.8 C8H18O2 40.0 C12H18 C12H18 34.7 73.8 C6H14O3 64.7 C10H22O3 C9H20O3 46.0 −43.3 C6H14O −57.0 C6H14O C7H14O 23.0 53.4 C8H14O4 43.2 C8H14O4 C10H18O4 77.5 115.6 C10H18O6 103.7 C10H18O6 C6H6 −45.1 32.7 C10H10 157.8 C22H46 C12H26 47.8 47.2 C12H24 91.0 C12H26O C12H27N 82.8 91.2 C15H34Si 171.3 C18H34O2 60 −70.4 36.7 44.2 39.0 38.9 40.4 45.8 142.6 160.4 127.1 109.7 127.8 80.8 92.8 13.0 22.1 14.5 18.1 139.5 131.0 131.0 148.0 143.5 81.3 194.0 163.8 133.2 208.0 118.0 110.7 142.4 −21.4 193.8 193.8 105.2 126.4 77.7 151.3 33.8 94.6 206.9 212.0 244.2 226.2 186.0 162.0 183.4 211.5 225.9 170.2 194.8 240.4 55.8 124.3 118.2 156.5 146.3 126.8 21.6 +3.4 85.8 134.8 120.0 166.0 211.7 192.6 18.1 116.0 268.3 132.1 128.5 177.8 168.0 184.2 273.0 −138.5 −90.7 38 −62 −52.8 −123.7 −135 −119.5 −135.0 75 25.5 74.5 62.5 68 51.5 38 −83.2 61.5 89 −61 10 52.9 68.5 61 51.5 27 124 44 26.5 −105 −122 −60 −32.6 −66.9 44.5 −9.6 −31.5 24 51.5 (Continued ) 2-70 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Epichlorohydrin 1,2-Epoxy-2-methylpropane Erucic acid Estragole (p-methoxy allyl benzene) Ethane Ethoxydimethylphenylsilane Ethoxytrimethylsilane Ethoxytriphenylsilane Ethyl acetate acetoacetate Ethylacetylene (1-butyne) Ethyl acrylate α-Ethylacrylic acid α-Ethylacrylonitrile Ethyl alcohol (ethanol) Ethylamine 4-Ethylaniline N-Ethylaniline 2-Ethylanisole 3-Ethylanisole 4-Ethylanisole Ethylbenzene Ethyl benzoate benzoylacetate bromide α-bromoisobutyrate n-butyrate isobutyrate Ethylcamphoronic anhydride Ethyl isocaproate carbamate carbanilate Ethylcetylamine Ethyl chloride chloroacetate chloroglyoxylate α-chloropropionate trans-cinnamate 3-Ethylcumene 4-Ethylcumene Ethyl cyanoacetate Ethylcyclohexane Ethylcyclopentane Ethyl dichloroacetate N,N-diethyloxamate N-Ethyldiphenylamine Ethylene Ethylene-bis-(chloroacetate) Ethylene chlorohydrin (2-chloroethanol) diamine (1,2-ethanediamine) dibromide (1,2-dibromethane) dichloride (1,2-dichloroethane) glycol (1,2-ethanediol) glycol diethyl ether (1,2-diethoxyethane) glycol dimethyl ether (1,2-dimethoxyethane) glycol monomethyl ether (2-methoxyethanol) oxide Ethyl α-ethylacetoacetate fluoride formate 2-furoate glycolate 3-Ethylhexane 2-Ethylhexyl acrylate Ethylidene chloride (1,1-dichloroethane) fluoride (1,1-difluoroethane) Ethyl iodide Ethyl l-leucinate Ethyl levulinate Ethyl mercaptan (ethanethiol) Ethyl methylcarbamate Ethyl methyl ether 1 5 10 20 −16.5 −69.0 206.7 52.6 −159.5 36.3 −50.9 167.0 −43.4 28.5 −92.5 −29.5 47.0 −29.0 −31.3 −82.3 52.0 38.5 29.7 33.7 33.5 −9.8 44.0 107.6 −74.3 10.6 −18.4 −24.3 118.2 11.0 107.8 133.2 −89.8 +1.0 −5.1 +6.6 87.6 28.3 31.5 67.8 −14.5 −32.2 9.6 76.0 98.3 −168.3 112.0 −4.0 −11.0 −27.0 −44.5 53.0 −33.5 +5.6 −50.0 239.7 80.0 −148.5 63.1 −31.0 198.2 −23.5 54.0 −76.7 −8.7 70.7 −6.4 −12.0 −66.4 80.0 66.4 55.9 60.3 60.2 +13.9 72.0 136.4 −56.4 35.8 +4.0 −2.4 149.8 35.8 65.8 131.8 168.2 −73.9 25.4 +18.0 30.2 108.5 55.5 58.4 93.5 +9.2 −10.8 34.0 106.3 130.2 −158.3 142.4 +19.0 +10.5 +4.7 −24.0 79.7 −10.2 16.6 −40.3 254.5 93.7 −142.9 76.2 −20.7 213.5 −13.5 67.3 −68.7 +2.0 82.0 +5.0 −2.3 −58.3 93.8 80.6 69.0 73.9 73.9 25.9 86.0 150.3 −47.5 48.0 15.3 +8.4 165.0 48.0 77.8 143.7 186.0 −65.8 37.5 29.9 41.9 134.0 68.8 72.0 106.0 20.6 −0.1 46.3 121.7 146.0 −153.2 158.0 30.3 21.5 18.6 −13.6 92.1 +1.6 29.0 −29.5 270.6 108.4 −136.7 91.0 −9.8 230.0 −3.0 81.1 −59.9 13.0 94.4 17.7 +8.0 −48.6 109.0 96.0 83.1 88.5 88.5 38.6 101.4 166.8 −37.8 61.8 27.8 20.6 181.8 61.7 91.0 155.5 205.5 −56.8 50.4 42.0 54.3 150.3 83.6 86.7 119.8 33.4 +11.7 59.5 137.7 162.8 −147.6 173.5 42.5 33.0 32.7 −2.4 105.8 14.7 42.0 −17.3 289.1 124.6 −129.8 107.2 +3.7 247.0 +9.1 96.2 −50.0 26.0 108.1 31.8 19.0 −39.8 125.7 113.2 98.8 104.8 104.7 52.8 118.2 181.8 −26.7 77.0 41.5 33.8 199.8 76.3 105.6 168.8 226.5 −47.0 65.2 56.0 68.2 169.2 99.9 103.3 133.8 47.6 25.0 74.0 154.4 182.0 −141.3 191.0 56.0 45.8 48.0 +10.0 120.0 29.7 50.6 −9.7 300.2 135.2 −125.4 127.5 11.5 258.3 16.6 106.0 −43.4 33.5 116.7 40.6 26.0 −33.4 136.0 123.6 109.0 115.5 115.4 61.8 129.0 191.9 −19.5 86.7 50.1 42.3 211.5 85.8 114.8 177.3 239.8 −40.6 74.0 65.2 77.3 181.2 110.2 113.8 142.1 56.7 33.4 83.6 166.0 193.7 −137.3 201.8 64.1 53.8 57.9 18.1 129.5 39.0 62.0 +1.2 314.4 148.5 −119.3 131.4 22.1 273.5 27.0 118.5 −34.9 44.5 127.5 53.0 34.9 −25.1 149.8 137.3 122.3 129.2 128.4 74.1 143.2 205.0 −10.0 99.8 62.0 53.5 226.6 98.4 126.2 187.9 256.8 −32.0 86.0 76.6 89.3 196.0 124.3 127.2 152.8 69.0 45.0 96.1 180.3 209.8 −131.8 215.0 75.0 62.5 70.4 29.4 141.8 51.8 C4H10O2 −48.0 −26.2 −15.3 −3.0 +10.7 19.7 31.8 50.0 70.8 93.0 C3H8O2 −13.5 +10.2 22.0 34.3 47.8 56.4 68.0 85.3 104.3 124.4 −89.7 40.5 −117.0 −60.5 37.6 14.3 −20.0 50.0 −60.7 −112.5 −54.4 27.8 47.3 −76.7 26.5 −91.0 −73.8 67.3 −103.8 −42.2 63.8 38.8 +2.1 77.7 −41.9 −98.4 −34.3 57.3 74.0 −59.1 51.0 −75.6 −65.7 80.2 −97.7 −33.0 77.1 50.5 12.8 91.8 −32.3 −91.7 −24.3 72.1 87.3 −50.2 63.2 −67.8 −56.6 94.6 −90.0 −22.7 91.5 63.9 25.0 106.3 −21.9 −84.1 −13.1 88.0 101.8 −40.7 76.1 −59.1 −46.9 110.3 −81.8 −11.5 107.5 78.1 38.5 123.7 −10.2 −75.8 −0.9 106.0 117.7 −29.8 91.0 −49.4 −40.7 120.6 −76.4 −4.3 117.5 87.6 47.1 134.0 −2.9 −70.4 +7.2 117.8 127.6 −22.4 100.0 −43.3 −32.1 133.8 −69.3 −5.4 130.4 99.8 58.9 147.9 +7.2 −63.2 18.0 131.8 141.3 −13.0 112.0 −34.8 −19.5 153.2 −58.0 20.0 150.1 117.8 76.7 168.2 22.4 −52.0 34.1 149.8 160.2 +1.5 130.0 −22.0 −4.9 175.6 −45.5 37.1 172.5 138.0 97.0 192.2 39.8 −39.5 52.3 167.3 183.0 17.7 149.8 −7.8 +10.7 198.0 −32.0 54.3 195.0 158.2 118.5 216.0 57.4 −26.5 72.4 184.0 206.2 35.0 170.0 +7.5 C2H4O C8H14O3 C2H5F C3H6O2 C7H8O3 C4H8O3 C8H18 C11H20O2 C2H4Cl2 C2H4F2 C2H5I C8H17NO2 C7H12O3 C2H6S C4H9NO2 C3H8O 60 100 200 400 760 Temperature, °C Formula C3H5ClO C4H8O C22H42O2 C10H12O C2H6 C10H16OSi C5H14OSi C20H20OSi C4H8O2 C6H10O3 C4H6 C5H8O2 C5H8O2 C5H7N C2H6O C2H7N C8H11N C8H11N C9H12O C9H12O C9H12O C8H10 C9H10O2 C11H12O3 C2H5Br C6H11BrO2 C6H12O2 C6H12O2 C11H16O5 C8H16O2 C3H7NO2 C9H11NO2 C18H39N C2H5Cl C4H7ClO2 C4H5ClO3 C5H9ClO2 C11H12O2 C11H16 C11H16 C5H7NO2 C8H16 C7H14 C4H6Cl2O2 C8H15NO3 C14H15N C2H4 C6H8Cl2O4 C2H5ClO C2H8N2 C2H4Br2 C2H4Cl2 C2H6O2 C6H14O2 40 79.3 98.0 117.9 17.5 36.0 55.5 336.5 358.8 381.5 168.7 192.0 215.0 −110.2 −99.7 −88.6 151.5 175.0 199.5 38.1 56.3 75.7 295.0 319.5 344.0 42.0 59.3 77.1 138.0 158.2 180.8 −21.6 −6.9 +8.7 61.5 80.0 99.5 144.0 160.7 179.2 71.6 92.2 114.0 48.4 63.5 78.4 −12.3 +2.0 16.6 170.6 194.2 217.4 156.9 180.8 204.0 142.1 164.2 187.1 149.7 172.8 196.5 149.2 172.3 196.5 92.7 113.8 136.2 164.8 188.4 213.4 223.8 244.7 265.0 +4.5 21.0 38.4 119.7 141.2 163.6 79.8 100.0 121.0 71.0 90.0 110.0 248.5 272.8 298.0 117.8 139.2 160.4 144.2 164.0 184.0 203.8 220.0 237.0 283.3 313.0 342.0 −18.6 −3.9 +12.3 103.8 123.8 144.2 94.5 114.7 135.0 107.2 126.2 146.5 219.3 245.0 271.0 145.4 168.2 193.0 148.3 171.8 195.8 169.8 187.8 206.0 87.8 109.1 131.8 62.4 82.3 103.4 115.2 135.9 156.5 202.8 226.5 252.0 233.0 258.8 286.0 −123.4 −113.9 −103.7 237.3 259.5 283.5 91.8 110.0 128.8 81.0 99.0 117.2 89.8 110.1 131.5 45.7 64.0 82.4 158.5 178.5 197.3 71.8 94.1 119.5 Melting point, °C −25.6 33.5 −183.2 −82.4 −45 −130 −71.2 −112 −80.6 −4 −63.5 −94.9 −34.6 −117.8 −93.3 −88.2 49 52.5 −139 −26 12 −111.3 −138.6 −169 −69 8.5 10 −35.3 −15.6 −111.3 −79 34 −96.7 −117 −105 −121 VAPOR PRESSURES 2-71 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 1-Ethylnaphthalene Ethyl α-naphthyl ketone (1-propionaphthone) Ethyl 3-nitrobenzoate 3-Ethylpentane 4-Ethylphenetole 2-Ethylphenol 3-Ethylphenol 4-Ethylphenol Ethyl phenyl ether (phenetole) Ethyl propionate Ethyl propyl ether Ethyl salicylate 3-Ethylstyrene 4-Ethylstyrene Ethylisothiocyanate 2-Ethyltoluene 3-Ethyltoluene 4-Ethyltoluene Ethyl trichloroacetate Ethyltrimethylsilane Ethyltrimethyltin Ethyl isovalerate 2-Ethyl-1,4-xylene 4-Ethyl-1,3-xylene 5-Ethyl-1,3-xylene Eugenol iso-Eugenol Eugenyl acetate Fencholic acid d-Fenchone dl-Fenchyl alcohol Fluorene Fluorobenzene 2-Fluorotoluene 3-Fluorotoluene 4-Fluorotoluene Formaldehyde Formamide Formic acid trans-Fumaryl chloride Furfural (2-furaldehyde) Furfuryl alcohol Geraniol Geranyl acetate Geranyl n-butyrate Geranyl isobutyrate Geranyl formate Glutaric acid Glutaric anhydride Glutaronitrile Glutaryl chloride Glycerol Glycerol dichlorohydrin (1,3-dichloro-2-propanol) Glycol diacetate Glycolide (1,4-dioxane-2,6-dione) Guaicol (2-methoxyphenol) Heneicosane Heptacosane Heptadecane Heptaldehyde (enanthaldehyde) n-Heptane Heptanoic acid (enanthic acid) 1-Heptanol Heptanoyl chloride (enanthyl chloride) 2-Heptene Heptylbenzene Heptyl cyanide (enanthonitrile) Hexachlorobenzene Hexachloroethane Hexacosane Hexadecane 1-Hexadecene n-Hexadecyl alcohol (cetyl alcohol) 1 100 200 400 760 Melting point, °C 164.1 180.0 204.6 230.8 258.1 −27 206.9 192.6 17.5 119.8 117.9 130.0 131.3 86.6 27.2 −12.0 136.7 99.2 97.3 50.8 76.4 73.3 73.6 85.5 −9.0 30.0 55.2 96.0 97.2 92.6 155.8 167.0 183.0 171.8 99.5 110.8 185.2 +11.5 34.7 37.0 37.8 −70.6 137.5 24.0 79.5 82.1 95.7 141.8 150.0 170.1 164.0 136.2 226.3 185.5 176.4 128.3 198.0 93.0 218.2 205.0 25.7 129.8 127.9 139.8 141.7 95.4 35.1 −4.0 147.6 109.6 107.6 59.8 86.0 82.9 83.2 94.4 −1.2 38.4 64.0 106.2 107.4 103.0 167.3 178.2 194.0 181.5 109.8 120.2 197.8 19.6 43.7 45.8 46.5 −65.0 147.0 32.4 89.0 91.5 104.0 151.5 160.3 180.2 174.0 147.2 235.5 196.2 189.5 139.1 208.0 102.0 233.5 220.3 36.9 143.5 141.8 152.0 154.2 108.4 45.2 +6.8 161.5 123.2 121.5 71.9 99.0 95.9 96.3 107.4 +9.2 50.0 75.9 120.0 121.2 116.5 182.2 194.0 209.7 194.0 123.6 132.3 214.7 30.4 55.3 57.5 58.1 −57.3 157.5 43.8 101.0 103.4 115.9 165.3 175.2 193.8 187.7 160.7 247.0 212.5 205.5 151.8 220.1 114.8 255.5 244.6 53.8 163.2 161.6 171.8 175.0 127.9 61.7 23.3 183.7 144.0 142.0 90.0 119.0 115.5 116.1 125.8 25.0 67.3 93.8 140.2 141.8 137.4 204.7 217.2 232.5 215.0 144.0 150.0 240.3 47.2 73.0 75.4 76.0 −46.0 175.5 61.4 120.0 121.8 133.1 185.6 196.3 214.0 207.6 182.6 265.0 236.5 230.0 172.4 240.0 133.3 280.2 270.6 73.0 185.7 184.5 193.3 197.4 149.8 79.8 41.6 207.0 167.2 165.0 110.1 141.4 137.8 136.4 146.0 42.8 87.6 114.0 163.1 164.4 159.6 228.3 242.3 257.4 237.8 166.8 173.2 268.6 65.7 92.8 95.4 96.1 −33.0 193.5 80.3 140.0 141.8 151.8 207.8 219.8 235.0 228.5 205.8 283.5 261.0 257.3 195.3 263.0 153.5 306.0 298.0 93.5 208.0 207.5 214.0 219.0 172.0 99.1 61.7 231.5 191.5 189.0 131.0 165.1 161.3 162.0 167.0 62.0 108.8 134.3 186.9 188.4 183.7 253.5 267.5 282.0 264.1 191.0 201.0 295.0 84.7 114.0 116.0 117.0 −19.5 210.5 100.6 160.0 161.8 170.0 230.0 243.3 257.4 251.0 230.0 303.0 287.0 286.2 217.0 290.0 174.3 106.1 148.6 121.6 243.4 305.7 195.8 66.3 22.3 139.5 99.8 86.4 21.5 144.0 92.6 206.0 102.3 295.2 181.3 178.8 219.8 115.8 158.2 131.0 255.3 318.3 207.3 74.0 30.6 148.5 108.0 93.5 30.0 154.8 103.0 219.0 112.0 307.8 193.2 190.8 234.3 128.0 173.2 144.0 272.0 333.5 223.0 84.0 41.8 160.0 119.5 102.7 41.3 170.2 116.8 235.5 124.2 323.2 208.5 205.3 251.7 147.8 194.0 162.7 296.5 359.4 247.8 102.0 58.7 179.5 136.6 116.3 58.6 193.3 137.7 258.5 143.1 348.4 231.7 226.8 280.2 168.3 217.0 184.1 323.8 385.0 274.5 125.5 78.0 199.6 155.6 130.7 78.1 217.8 160.0 283.5 163.8 374.6 258.3 250.0 312.7 190.5 240.0 205.0 350.5 410.6 303.0 155.0 98.4 221.5 175.8 145.0 98.5 244.0 184.6 309.4 185.6 399.8 287.5 274.0 344.0 5 10 20 70.0 101.4 116.8 133.8 152.0 C13H12O C9H9NO4 C7H16 C10H14O C8H10O C8H10O C8H10O C8H10O C5H10O2 C5H12O C9H10O3 C10H12 C10H12 C3H5NS C9H12 C9H12 C9H12 C4H5Cl3O2 C5H14Si C5H14Sn C7H14O2 C10H14 C10H14 C10H14 C10H12O2 C10H12O2 C12H14O3 C10H16O2 C10H16O C10H18O C13H10 C6H5F C7H7F C7H7F C7H7F CH2O CH3NO CH2O2 C4H2Cl2O2 C5H4O2 C5H6O2 C10H18O C12H20O2 C14H24O2 C14H24O2 C11H18O2 C5H8O4 C5H6O3 C5H6N2 C5H6Cl2O2 C3H8O3 C3H6Cl2O 124.0 108.1 −37.8 48.5 46.2 60.0 59.3 18.1 −28.0 −64.3 61.2 28.3 26.0 −13.2 9.4 7.2 7.6 20.7 −60.6 −30.0 −6.1 25.7 26.3 22.1 78.4 86.3 101.6 101.7 28.0 45.8 −43.4 −24.2 −22.4 −21.8 155.5 140.2 −17.0 75.7 73.4 86.8 86.5 43.7 −7.2 −45.0 90.0 55.0 52.7 +10.6 34.8 32.3 32.7 45.5 −41.4 −7.6 +17.0 52.0 53.0 48.8 108.1 117.0 132.3 128.7 54.7 70.3 129.3 −22.8 −2.2 −0.3 +0.3 70.5 −20.0 +15.0 18.5 31.8 69.2 73.5 96.8 90.9 61.8 155.5 100.8 91.3 56.1 125.5 28.0 96.3 −5.0 38.5 42.6 56.0 96.8 102.7 125.2 119.6 90.3 183.8 133.3 123.7 84.0 153.8 52.2 171.0 155.0 −6.8 89.5 87.0 100.2 100.2 56.4 +3.4 −35.0 104.2 68.3 66.3 22.8 47.6 44.7 44.9 57.7 −31.8 +3.8 28.7 65.6 66.4 62.1 123.0 132.4 148.0 142.3 68.3 82.1 146.0 −12.4 +8.9 +11.0 11.8 −88.0 109.5 +2.1 51.8 54.8 68.0 110.0 117.9 139.0 133.0 104.3 196.0 149.5 140.0 97.8 167.2 64.7 188.1 173.6 +4.7 103.8 101.5 114.5 115.0 70.3 14.3 −24.0 119.3 82.8 80.8 36.1 61.2 58.2 58.5 70.6 −21.0 16.1 41.3 79.8 80.6 76.5 138.7 149.0 164.2 155.8 83.0 95.6 164.2 −1.2 21.4 23.4 24.0 −79.6 122.5 10.3 65.0 67.8 81.0 125.6 133.0 153.8 147.9 119.8 210.5 166.0 156.5 112.3 182.2 78.0 C6H10O4 C4H4O4 C7H8O2 C21H44 C27H56 C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H13ClO C7H14 C13H20 C7H13N C6Cl6 C2Cl6 C26H54 C16H34 C16H32 C16H34O 38.3 64.1 103.0 79.1 188.0 248.6 145.2 32.7 −12.7 101.3 64.3 54.6 −14.1 94.6 47.8 149.3 49.8 240.0 135.2 131.7 158.3 77.1 116.6 92.0 205.4 266.8 160.0 43.0 −2.1 113.2 74.7 64.6 −3.5 110.0 61.6 166.4 73.5 257.4 149.8 146.2 177.8 90.8 132.0 106.0 223.2 284.6 177.7 54.0 +9.5 125.6 85.8 75.0 +8.3 126.0 76.3 185.7 87.6 275.8 164.7 162.0 197.8 60 Temperature, °C Formula C12H12 40 52.4 152.6 211.7 115.0 12.0 −34.0 78.0 42.4 34.2 −35.8 64.0 21.0 114.4 32.7 204.0 105.3 101.6 122.7 47 −118.6 −45 −4 46.5 −30.2 −72.6 1.3 −5.9 −95.5 −99.3 −10 295 19 5 35 113 −42.1 −80 −110.8 −92 8.2 97.5 17.9 −31 97 28.3 40.4 59.5 22.5 −42 −90.6 −10 34.6 230 186.6 56.6 18.5 4 49.3 (Continued ) 2-72 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name n-Hexadecylamine (cetylamine) Hexaethylbenzene n-Hexane 1-Hexanol 2-Hexanol 3-Hexanol 1-Hexene n-Hexyl levulinate n-Hexyl phenyl ketone (enanthophenone) Hydrocinnamic acid Hydrogen cyanide (hydrocyanic acid) Hydroquinone 4-Hydroxybenzaldehyde α-Hydroxyisobutyric acid α-Hydroxybutyronitrile 4-Hydroxy-3-methyl-2-butanone 4-Hydroxy-4-methyl-2-pentanone 3-Hydroxypropionitrile Indene Iodobenzene Iodononane 2-Iodotoluene α-Ionone Isoprene Lauraldehyde Lauric acid Levulinaldehyde Levulinic acid d-Limonene Linalyl acetate Maleic anhydride Menthane 1-Menthol Menthyl acetate benzoate formate Mesityl oxide Methacrylic acid Methacrylonitrile Methane Methanethiol Methoxyacetic acid N-Methylacetanilide Methyl acetate acetylene (propyne) acrylate alcohol (methanol) Methylamine N-Methylaniline Methyl anthranilate benzoate 2-Methylbenzothiazole α-Methylbenzyl alcohol Methyl bromide 2-Methyl-1-butene 2-Methyl-2-butene Methyl isobutyl carbinol (2-methyl4-pentanol) n-butyl ketone (2-hexanone) isobutyl ketone (4-methyl-2-pentanone) n-butyrate isobutyrate caprate caproate caprylate chloride chloroacetate cinnamate α-Methylcinnamic acid Methylcyclohexane Methylcyclopentane Methylcyclopropane Methyl n-decyl ketone (n-dodecan-2-one) dichloroacetate N-Methyldiphenylamine 1 5 10 20 123.6 157.8 134.3 −34.5 47.2 34.8 25.7 −38.0 120.0 130.3 133.5 −55.3 153.3 153.2 98.5 65.8 69.3 46.7 87.8 44.3 50.6 96.2 65.9 108.8 −62.3 108.4 150.6 54.9 128.1 40.4 82.5 63.4 35.7 83.2 85.8 154.2 75.8 +14.1 48.5 −23.3 −199.0 −75.3 79.3 103.8 −38.6 −97.5 −23.6 −25.3 −81.3 62.8 109.0 64.4 97.5 75.2 −80.6 −72.8 −57.0 +22.1 176.0 150.3 −25.0 58.2 45.0 36.7 −28.1 134.7 145.5 148.7 −47.7 163.5 169.7 110.5 77.8 81.0 58.8 102.0 58.5 64.0 109.0 79.8 123.0 −53.3 123.7 166.0 68.0 141.8 53.8 96.0 78.7 48.3 96.0 100.0 170.0 90.0 26.0 60.0 −12.5 −195.5 −67.5 92.0 118.6 −29.3 −90.5 −13.5 −16.2 −73.8 76.2 124.2 77.3 111.2 88.0 −72.8 −64.3 −47.9 33.3 195.7 168.0 −14.1 70.3 55.9 49.0 −17.2 150.2 161.0 165.0 −39.7 174.6 186.8 123.8 90.7 94.0 72.0 117.9 73.9 78.3 123.0 95.6 139.0 −43.5 140.2 183.6 82.7 154.1 68.2 111.4 95.0 62.7 110.3 115.4 186.3 105.8 37.9 72.7 −0.6 −191.8 −58.8 106.5 135.1 −19.1 −82.9 −2.7 −6.0 −65.9 90.5 141.5 91.8 125.5 102.1 −64.0 −54.8 −37.9 45.4 C6H12O C6H12O C5H10O2 C5H10O2 C11H22O2 C7H14O2 C9H18O2 CH3Cl C3H5ClO2 C10H10O2 C10H10O2 C7H14 C6H12 C4H8 C12H24O C3H4Cl2O2 C13H13N 60 100 215.7 187.7 −2.3 83.7 67.9 62.2 −5.0 167.8 178.9 183.3 −30.9 192.0 206.0 138.0 104.8 108.2 86.7 134.1 90.7 94.4 138.1 112.4 155.6 −32.6 157.8 201.4 98.3 169.5 84.3 127.7 111.8 78.3 126.1 132.1 204.3 123.0 51.7 86.4 +12.8 −187.7 −49.2 122.0 152.2 −7.9 −74.3 +9.2 +5.0 −56.9 106.0 159.7 107.8 141.2 117.8 −54.2 −44.1 −26.7 58.2 228.8 199.7 +5.4 92.0 76.0 70.7 +2.8 179.0 189.8 194.0 −25.1 203.0 217.5 146.4 113.9 117.4 96.0 144.7 100.8 105.0 147.7 123.8 166.3 −25.4 168.7 212.7 108.4 178.0 94.6 138.1 122.0 88.6 136.1 143.2 215.8 133.8 60.4 95.3 21.5 −185.1 −43.1 131.8 164.2 −0.5 −68.8 17.3 12.1 −51.3 115.8 172.0 117.4 150.4 127.4 −48.0 −37.3 −19.4 67.0 245.8 216.0 15.8 102.8 87.3 81.8 13.0 193.6 204.2 209.0 −17.8 216.5 233.5 157.7 125.0 129.0 108.2 157.7 114.7 118.3 159.8 138.1 181.2 −16.0 184.5 227.5 121.8 190.2 108.3 151.8 135.8 102.1 149.4 156.7 230.4 148.0 72.1 106.6 32.8 −181.4 −34.8 144.5 179.8 +9.4 −61.3 28.0 21.2 −43.7 129.8 187.8 130.8 163.9 140.3 −39.4 −28.0 −9.9 78.0 28.8 +19.7 −5.5 −13.0 93.5 30.0 61.7 −99.5 19.0 108.1 155.0 −14.0 −33.8 −80.6 106.0 26.7 134.0 38.8 30.0 +5.0 −2.9 108.0 42.0 74.9 −92.4 30.0 123.0 169.8 −3.2 −23.7 −72.8 120.4 38.1 149.7 50.0 40.8 16.7 +8.4 123.0 55.4 89.0 −84.8 41.5 140.0 185.2 +8.7 −12.8 −64.0 136.0 50.7 165.8 62.0 52.8 29.6 21.0 139.0 70.0 105.3 −76.0 54.5 157.9 201.8 22.0 −0.6 −54.2 152.4 64.7 184.0 69.8 60.4 37.4 28.9 148.6 79.7 115.3 −70.4 63.0 170.0 212.0 30.5 +7.2 −48.0 163.8 73.6 195.4 79.8 70.4 48.0 39.6 161.5 91.4 128.0 −63.0 73.5 185.8 224.8 42.1 17.9 −39.3 177.5 85.4 210.1 200 400 760 Temperature, °C Formula C16H35N C18H30 C6H14 C6H14O C6H14O C6H14O C6H12 C11H20O3 C13H18O C9H10O2 CHN C6H6O2 C7H6O2 C4H8O3 C5H9NO C5H10O2 C6H12O2 C3H5NO C9H8 C6H5I C9H19I C7H7I C13H20O C5H8 C12H24O C12H24O2 C5H8O2 C5H8O3 C10H16 C12H20O2 C4H2O3 C10H20 C10H20O C12H22O2 C17H24O2 C11H20O2 C6H10O C4H6O2 C4H5N CH4 CH4S C3H6O3 C9H11NO C3H6O2 C3H4 C4H6O2 CH4O CH5N C7H9N C8H9NO2 C8H8O2 C8H7NS C8H10O CH3Br C5H10 C5H10 C6H14O 40 −53.9 24.4 14.6 +2.5 −57.5 90.0 100.0 102.2 −71.0 132.4 121.2 73.5 41.0 44.6 22.0 58.7 16.4 24.1 70.0 37.2 79.5 −79.8 77.7 121.0 28.1 102.0 14.0 55.4 44.0 +9.7 56.0 57.4 123.2 47.3 −8.7 25.5 −44.5 −205.9 −90.7 52.5 −57.2 −111.0 −43.7 −44.0 −95.8 36.0 77.6 39.0 70.0 49.0 −96.3 −89.1 −75.4 −0.3 +7.7 −1.4 −26.8 −34.1 63.7 +5.0 34.2 −2.9 77.4 125.7 −35.9 −53.7 −96.0 77.1 3.2 103.5 272.2 300.4 330.0 241.7 268.5 298.3 31.6 49.6 68.7 119.6 138.0 157.0 103.7 121.8 139.9 98.3 117.0 135.5 29.0 46.8 66.0 215.7 241.0 266.8 225.0 248.3 271.3 230.8 255.0 279.8 −5.3 +10.2 25.9 238.0 262.5 286.2 256.8 282.6 310.0 175.2 193.8 212.0 142.0 159.8 178.8 146.5 165.5 185.0 126.8 147.5 167.9 178.0 200.0 221.0 135.6 157.8 181.6 139.8 163.9 188.6 179.0 199.3 219.5 160.0 185.7 211.0 202.5 225.2 250.0 −1.2 +15.4 32.6 207.8 231.8 257.0 249.8 273.8 299.2 142.0 164.0 187.0 208.3 227.4 245.8 128.5 151.4 175.0 173.3 196.2 220.0 155.9 179.5 202.0 122.7 146.0 169.5 168.3 190.2 212.0 178.8 202.8 227.0 253.2 277.1 301.0 169.8 194.2 219.0 90.0 109.8 130.0 123.9 142.5 161.0 50.0 70.3 90.3 −175.5 −168.8 −161.5 −22.1 −7.9 +6.8 163.5 184.2 204.0 202.3 227.4 253.0 24.0 40.0 57.8 −49.8 −37.2 −23.3 43.9 61.8 80.2 34.8 49.9 64.7 −32.4 −19.7 −6.3 149.3 172.0 195.5 212.4 238.5 266.5 151.4 174.7 199.5 183.2 204.5 225.5 159.0 180.7 204.0 −26.5 −11.9 +3.6 −13.8 +2.5 20.2 +4.9 21.6 38.5 94.9 113.5 131.7 94.3 85.6 64.3 55.7 181.6 109.8 148.1 −51.2 90.5 209.6 245.0 59.6 34.0 −26.0 199.0 103.2 232.8 111.0 102.0 83.1 73.6 202.9 129.8 170.0 −38.0 109.5 235.0 266.8 79.6 52.3 −11.3 222.5 122.6 257.0 127.5 119.0 102.3 92.6 224.0 150 193.0 −24.0 130.3 263.0 288.0 100.9 71.8 +4.5 246.5 143.0 282.0 Melting point, °C 130 −95.3 −51.6 −98.5 48.5 −13.2 170.3 115.5 79 −47 −2 −28.5 −146.7 44.5 48 33.5 −96.9 58 42.5 54.5 −59 15 −182.5 −121 102 −98.7 −102.7 −97.8 −93.5 −57 24 −12.5 15.4 −93 −135 −133 −56.9 −84.7 −84.7 −18 −40 −97.7 −31.9 33.4 −126.4 −142.4 −7.6 VAPOR PRESSURES 2-73 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Methyl n-dodecyl ketone (2-tetradecanone) Methylene bromide (dibromomethane) chloride (dichloromethane) Methyl ethyl ketone (2-butanone) 2-Methyl-3-ethylpentane 3-Methyl-3-ethylpentane Methyl fluoride formate α-Methylglutaric anhydride Methyl glycolate 2-Methylheptadecane 2-Methylheptane 3-Methylheptane 4-Methylheptane 2-Methyl-2-heptene 6-Methyl-3-hepten-2-ol 6-Methyl-5-hepten-2-ol 2-Methylhexane 3-Methylhexane Methyl iodide laurate levulinate methacrylate myristate α-naphthyl ketone (1-acetonaphthone) β-naphthyl ketone (2-acetonaphthone) n-nonyl ketone (undecan-2-one) palmitate n-pentadecyl ketone (2-heptdecanone) 2-Methylpentane 3-Methylpentane 2-Methyl-1-pentanol 2-Methyl-2-pentanol Methyl n-pentyl ketone (2-heptanone) phenyl ether (anisole) 2-Methylpropene Methyl propionate 4-Methylpropiophenone 2-Methylpropionyl bromide Methyl propyl ether n-propyl ketone (2-pentanone) isopropyl ketone (3-Methyl-2-butanone) 2-Methylquinoline Methyl salicylate α-Methyl styrene 4-Methyl styrene Methyl n-tetradecyl ketone (2-hexadecanone) thiocyanate isothiocyanate undecyl ketone (2-tridecanone) isovalerate Monovinylacetylene (butenyne) Myrcene Myristaldehyde Myristic acid (tetradecanoic acid) Naphthalene 1-Naphthoic acid 2-Naphthoic acid 1-Naphthol 2-Naphthol 1-Naphthylamine 2-Naphthylamine Nicotine 2-Nitroaniline 3-Nitroaniline 4-Nitroaniline 2-Nitrobenzaldehyde 3-Nitrobenzaldehyde Nitrobenzene Nitroethane Nitroglycerin Nitromethane 2-Nitrophenol 2-Nitrophenyl acetate 1 5 10 20 99.3 −35.1 −70.0 −48.3 −24.0 −23.9 −147.3 −74.2 93.8 +9.6 119.8 −21.0 −19.8 −20.4 −16.1 41.6 41.9 −40.4 −39.0 130.0 −13.2 −52.1 −28.0 −1.8 −1.4 −137.0 −57.0 125.4 33.7 152.0 +1.3 +2.6 +1.5 +6.7 65.0 66.0 −19.5 −18.1 −55.0 117.9 66.4 −10.0 145.7 146.3 152.3 95.5 166.8 161.6 −41.7 −39.8 38.0 +16.8 43.6 30.0 −96.5 −21.5 89.3 38.4 −54.3 +8.0 −1.0 104.0 81.6 34.0 42.0 145.5 −2.4 −43.3 −17.7 +9.5 +9.9 −131.6 −48.6 141.8 45.3 168.7 12.3 13.3 12.4 17.8 76.7 77.8 −9.1 −7.8 −45.8 133.2 79.7 +1.0 160.8 161.5 168.5 108.9 184.3 178.0 −32.1 −30.1 49.6 27.6 55.5 42.2 −81.9 −11.8 103.8 50.6 −45.4 17.9 +8.3 119.0 95.3 47.1 55.1 161.3 +9.7 −33.4 −6.5 21.7 22.3 −125.9 −39.2 157.7 58.1 186.0 24.4 25.4 24.5 30.4 89.3 90.4 +2.3 +3.6 −35.6 149.0 93.7 11.0 177.8 178.4 185.7 123.1 202.0 196.4 −21.4 −19.4 61.6 38.8 67.7 55.8 −73.4 −1.0 120.2 64.1 −35.4 28.5 18.3 134.0 110.0 61.8 69.2 179.8 23.3 −22.3 +6.0 35.2 36.2 −119.1 −28.7 177.5 72.3 204.8 37.9 38.9 38.0 44.0 102.7 104.0 14.9 16.4 −24.2 166.0 109.5 25.5 195.8 196.8 203.8 139.0 C16H32O C2H3NS C2H3NS C13H26O C6H12O2 C4H4 C10H16 C14H28O C14H28O2 C10H8 C11H8O2 C11H8O2 C10H8O C10H8O C10H9N C10H9N C10H14N2 C6H6N2O2 C6H6N2O2 C6H6N2O2 C7H5NO3 C7H5NO3 C6H5NO2 C2H5NO2 C3H5N3O9 CH3NO2 C6H5NO3 C8H7NO4 151.5 +9.8 −8.3 117.0 +2.9 −77.7 40.0 132.0 174.1 74.2 184.0 189.7 125.5 128.6 137.7 141.6 91.8 135.7 151.5 177.6 117.7 127.4 71.6 +1.5 167 −7.9 76.8 128.0 167.3 21.6 +5.4 131.8 14.0 −70.0 53.2 148.3 190.8 85.8 196.8 202.8 142.0 145.5 153.8 157.6 107.2 150.4 167.8 194.4 133.4 142.8 84.9 12.5 188 +2.8 90.4 142.0 184.6 34.5 20.4 147.8 26.4 −61.3 67.0 166.2 207.6 101.7 211.2 216.9 158.0 161.8 171.6 175.8 123.7 167.7 185.5 213.2 150.0 159.0 99.3 24.8 210 14.1 105.8 155.8 60 100 200 400 760 191.4 31.6 −15.7 14.0 43.9 45.0 −115.0 −21.9 189.9 81.8 216.3 46.6 47.6 46.6 52.8 111.5 112.8 23.0 24.5 −16.9 176.8 119.3 34.5 207.5 208.6 214.7 148.6 206.0 42.3 −6.3 25.0 55.7 57.1 −109.0 −12.9 205.0 93.7 231.5 58.3 59.4 58.3 64.6 122.6 123.8 34.1 35.6 −7.0 190.8 133.0 47.0 222.6 223.8 229.8 161.0 228.2 58.5 +8.0 41.6 73.6 75.3 −99.9 +0.8 229.1 111.8 254.5 76.0 77.1 76.1 82.3 139.5 140.0 50.8 52.4 +8.0 253.3 79.0 24.1 60.0 94.0 96.2 −89.5 16.0 255.5 131.7 279.8 96.2 97.4 96.3 102.2 156.6 156.6 69.8 71.6 25.3 278.0 98.6 40.7 79.6 115.6 118.3 −78.2 32.0 282.5 151.5 306.5 117.6 118.9 117.7 122.5 175.5 174.3 90.0 91.9 42.4 153.4 63.0 245.3 246.7 251.6 181.2 175.8 82.0 269.8 270.5 275.8 202.3 197.7 101.0 295.8 295.5 301.0 224.0 214.3 −9.7 −7.3 74.7 51.3 81.2 70.7 −63.8 +11.0 138.0 79.4 −24.3 39.8 29.6 150.8 126.2 77.8 85.0 226.7 −1.9 +0.1 83.4 58.8 89.8 80.1 −57.7 18.7 149.3 88.8 −17.4 47.3 36.2 161.7 136.7 88.3 95.0 242.0 +8.1 10.5 94.2 69.2 100.0 93.0 −49.3 29.0 164.2 101.6 −8.1 56.8 45.5 176.2 150.0 102.2 108.6 265.8 24.1 26.5 111.3 85.0 116.1 112.3 −36.7 44.2 187.4 120.5 +6.0 71.0 59.0 197.8 172.6 121.8 128.7 291.7 41.6 44.2 129.8 102.6 133.2 133.8 −22.2 61.8 212.7 141.7 22.5 86.8 73.8 211.7 197.5 143.0 151.2 319.5 60.3 63.3 147.9 121.2 150.2 155.5 −6.9 79.8 238.5 163.0 39.1 103.3 88.9 246.5 223.2 165.4 175.0 203.7 49.0 38.2 165.7 39.8 −51.7 82.6 186.0 223.5 119.3 225.0 231.5 177.8 181.7 191.5 195.7 142.1 186.0 204.2 234.2 168.8 177.7 115.4 38.0 235 27.5 122.1 172.8 215.0 58.1 47.5 176.6 48.2 −45.3 92.6 198.3 237.2 130.2 234.5 241.3 190.0 193.7 203.8 208.1 154.7 197.8 216.5 245.9 180.7 189.5 125.8 46.5 251 35.5 132.6 181.7 230.5 70.4 59.3 191.5 59.8 −37.1 106.0 214.5 250.5 145.5 245.8 252.7 206.0 209.8 220.0 224.3 169.5 213.0 232.1 261.8 196.2 204.3 139.9 57.8 254.4 89.8 77.5 214.0 77.3 −24.1 126.0 240.4 272.3 167.7 263.5 270.3 229.6 234.0 244.9 249.7 193.8 236.3 255.3 284.5 220.0 227.4 161.2 74.8 279.8 110.8 97.8 238.3 96.7 −10.1 148.3 267.9 294.6 193.2 281.4 289.5 255.8 260.6 272.2 277.4 219.8 260.0 280.2 310.2 246.8 252.1 185.8 94.0 307.0 132.9 119.0 262.5 116.7 +5.3 171.5 297.8 318.0 217.9 300.0 308.5 282.5 288.0 300.8 306.1 247.3 284.5 305.7 336.0 273.5 278.3 210.6 114.0 46.6 146.4 194.1 63.5 167.6 213.0 82.0 191.0 233.5 101.2 214.5 253.0 Temperature, °C Formula C14H28O CH2Br2 CH2Cl2 C4H8O C8H18 C8H18 CH3F C2H4O2 C6H8O3 C3H6O3 C18H38 C8H18 C8H18 C8H18 C8H16 C8H16O C8H16O C7H16 C7H16 CH3I C13H26O2 C6H10O3 C5H8O2 C15H30O2 C12H10O C12H10O C11H22O C17H34O2 C17H34O C6H14 C6H14 C6H14O C6H14O C7H14O C7H8O C4H8 C4H8O2 C10H12O C4H7BrO C4H10O C5H10O C5H10O C10H9N C8H8O3 C9H10 C9H10 40 87.8 39.8 −30.5 115.0 115.6 120.2 68.2 134.3 129.6 −60.9 −59.0 15.4 −4.5 19.3 +5.4 −105.1 −42.0 59.6 13.5 −72.2 −12.0 −19.9 75.3 54.0 7.4 16.0 109.8 −14.0 −34.7 86.8 −19.2 −93.2 14.5 99.0 142.0 52.6 156.0 160.8 94.0 104.3 108.0 61.8 104.0 119.3 142.4 85.8 96.2 44.4 −21.0 127 −29.0 49.3 100.0 Melting point, °C −52.8 −96.7 −85.9 −114.5 −90 −99.8 −109.5 −120.8 −121.1 −118.2 −64.4 5 18.5 55.5 15 30 −154 −118 −103 −37.3 −140.3 −87.5 −77.8 −92 −1 −8.3 −23.2 −51 35.5 28.5 23.5 57.5 80.2 160.5 184 96 122.5 50 111.5 71.5 114 146.5 40.9 58 +5.7 −90 11 −29 45 (Continued ) 2-74 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name 1-Nitropropane 2-Nitropropane 2-Nitrotoluene 3-Nitrotoluene 4-Nitrotoluene 4-Nitro-1,3-xylene (4-nitro-m-xylene) Nonacosane Nonadecane n-Nonane 1-Nonanol 2-Nonanone Octacosane Octadecane n-Octane n-Octanol (1-octanol) 2-Octanone n-Octyl acrylate iodide (1-Iodooctane) Oleic acid Palmitaldehyde Palmitic acid Palmitonitrile Pelargonic acid Pentachlorobenzene Pentachloroethane Pentachloroethylbenzene Pentachlorophenol Pentacosane Pentadecane 1,3-Pentadiene 1,4-Pentadiene Pentaethylbenzene Pentaethylchlorobenzene n-Pentane iso-Pentane (2-methylbutane) neo-Pentane (2,2-dimethylpropane) 2,3,4-Pentanetriol 1-Pentene α-Phellandrene Phenanthrene Phenethyl alcohol (phenyl cellosolve) 2-Phenetidine Phenol 2-Phenoxyethanol 2-Phenoxyethyl acetate Phenyl acetate Phenylacetic acid Phenylacetonitrile Phenylacetyl chloride Phenyl benzoate 4-Phenyl-3-buten-2-one Phenyl isocyanate isocyanide Phenylcyclohexane Phenyl dichlorophosphate m-Phenylene diamine (1,3-phenylenediamine) Phenylglyoxal Phenylhydrazine N-Phenyliminodiethanol 1-Phenyl-1,3-pentanedione 2-Phenylphenol 4-Phenylphenol 3-Phenyl-1-propanol Phenyl isothiocyanate Phorone iso-Phorone Phosgene (carbonyl chloride) Phthalic anhydride Phthalide Phthaloyl chloride 2-Picoline Pimelic acid α-Pinene β-Pinene 1 5 10 20 −9.6 −18.8 50.0 50.2 53.7 65.6 234.2 133.2 +1.4 59.5 32.1 226.5 119.6 −14.0 54.0 23.6 58.5 45.8 176.5 121.6 153.6 134.3 108.2 98.6 +1.0 96.2 +13.5 +4.1 79.1 81.0 85.0 95.0 269.8 166.3 25.8 86.1 59.0 260.3 152.1 +8.3 76.5 48.4 87.7 74.8 208.5 154.6 188.1 168.3 126.0 129.7 27.2 130.0 25.3 15.8 93.8 96.0 100.5 109.8 286.4 183.5 38.0 99.7 72.3 277.4 169.6 19.2 88.3 60.9 102.0 90.0 223.0 171.8 205.8 185.8 137.4 144.3 39.8 148.0 194.2 91.6 −71.8 −83.5 86.0 90.0 −76.6 −82.9 −102.0 155.0 −80.4 20.0 118.2 58.2 67.0 40.1 78.0 82.6 38.2 97.0 60.0 48.0 106.8 81.7 10.6 12.0 67.5 66.7 230.0 121.0 −53.8 −66.2 120.0 123.8 −62.5 −65.8 −85.4 189.3 −63.3 45.7 154.3 85.9 94.7 62.5 106.6 113.5 64.8 127.0 89.0 75.3 141.5 112.2 36.0 37.0 96.5 95.9 248.2 135.4 −45.0 −57.1 135.8 140.7 −50.1 −57.0 −76.7 204.5 −54.5 58.0 173.0 100.0 108.6 73.8 121.2 128.0 78.0 141.3 103.5 89.0 157.8 127.4 48.5 49.7 111.3 110.0 37.9 28.2 109.6 112.8 117.7 125.8 303.6 200.8 51.2 113.8 87.2 295.4 187.5 31.5 101.0 74.3 117.8 105.9 240.0 190.0 223.8 204.2 149.8 160.0 53.9 166.0 192.2 266.1 150.2 −34.8 −47.7 152.4 158.1 −40.2 −47.3 −67.2 220.5 −46.0 72.1 193.7 114.8 123.7 86.0 136.0 144.5 92.3 156.0 119.4 103.6 177.0 143.8 62.5 63.4 126.4 125.9 51.8 41.8 126.3 130.7 136.0 143.3 323.2 220.0 66.0 129.0 103.4 314.2 207.4 45.1 115.2 89.8 135.6 123.8 257.2 210.0 244.4 223.8 163.7 178.5 69.9 186.2 211.2 285.6 167.7 −23.4 −37.0 171.9 178.2 −29.2 −36.5 −56.1 239.6 −34.1 87.8 215.8 130.5 139.9 100.1 152.2 162.3 108.1 173.6 136.3 119.8 197.6 161.3 77.7 78.3 144.0 143.4 C6H8N2 C8H6O2 C6H8N2 C10H15NO2 C11H12O2 C12H10O C12H10O C9H12O C7H5NS C9H14O C9H14O CCl2O C8H4O3 C8H6O2 C8H4Cl2O2 C6H7N C7H12O4 C10H16 C10H16 99.8 71.8 145.0 98.0 100.0 131.2 75.0 101.6 179.2 128.5 131.6 74.7 47.2 42.0 38.0 −92.9 96.5 95.5 86.3 −11.1 163.4 −1.0 +4.2 102.4 75.6 68.3 66.7 −77.0 121.3 127.7 118.3 +12.6 196.2 +24.6 30.0 147.0 87.8 115.8 195.8 144.0 146.2 176.2 116.0 89.8 81.5 81.2 −69.3 134.0 144.0 134.2 24.4 212.0 37.3 42.3 163.8 100.7 131.5 213.4 159.9 163.3 193.8 131.2 115.5 95.6 96.8 −60.3 151.7 161.3 151.0 37.4 229.3 51.4 58.1 182.5 115.5 148.2 233.0 178.0 180.3 213.0 147.4 122.5 111.3 114.5 −50.3 172.0 181.0 170.0 51.2 247.0 66.8 71.5 60 100 200 400 760 60.5 50.3 137.6 142.5 147.9 153.8 334.8 232.8 75.5 139.0 113.8 326.8 219.7 53.8 123.8 99.0 145.6 135.4 269.8 222.6 256.0 236.6 172.3 190.1 80.0 199.0 223.4 298.4 178.4 −16.5 −30.0 184.2 191.0 −22.2 −29.6 −49.0 249.8 −27.1 97.6 229.9 141.2 149.8 108.4 163.2 174.0 118.1 184.5 147.7 129.8 210.8 172.6 87.7 88.0 154.2 153.6 72.3 62.0 151.5 156.9 163.0 168.5 350.0 248.0 88.1 151.3 127.4 341.8 236.0 65.7 135.2 111.7 159.1 150.0 286.0 239.5 271.5 251.5 184.4 205.5 93.5 216.0 239.6 314.0 194.0 −6.7 −20.6 200.0 208.0 −12.6 −20.2 −39.1 263.5 −17.7 110.6 249.0 154.0 163.5 121.4 176.5 189.2 131.6 198.2 161.8 143.5 227.8 187.8 100.6 101.0 169.3 168.0 90.2 80.0 173.7 180.3 186.7 191.7 373.2 271.8 107.5 170.5 148.2 364.8 260.6 83.6 152.0 130.4 180.2 173.3 309.8 264.1 298.7 277.1 203.1 227.0 114.0 241.8 261.8 339.0 216.1 +8.0 −6.7 224.1 230.3 +1.9 −5.9 −23.7 284.5 −3.4 130.6 277.1 175.0 184.0 139.0 197.6 211.3 151.2 219.5 184.2 163.8 254.0 211.0 120.8 120.8 191.3 189.8 110.6 99.8 197.7 206.8 212.5 217.5 397.2 299.8 128.2 192.1 171.2 388.9 288.0 104.0 173.8 151.0 204.0 199.3 334.7 292.3 326.0 304.5 227.5 251.6 137.2 269.3 285.0 365.4 242.8 24.7 +8.3 250.2 257.2 18.5 +10.5 −7.1 307.0 +12.8 152.0 308.0 197.5 207.0 160.0 221.0 235.0 173.5 243.0 208.5 186.0 283.5 235.4 142.7 142.3 214.6 213.0 131.6 120.3 222.3 231.9 238.3 244.0 421.8 330.0 150.8 213.5 195.0 412.5 317.0 125.6 195.2 172.9 227.0 225.5 360.0 321.0 353.8 332.0 253.5 276.0 160.5 299.0 309.3 390.3 270.5 42.1 26.1 277.0 285.0 36.1 27.8 +9.5 327.2 30.1 175.0 340.2 219.5 228.0 181.9 245.3 259.7 195.9 265.5 233.5 210.0 314.0 261.0 165.6 165.0 240.0 239.5 194.0 124.2 158.7 245.3 189.8 192.2 225.3 156.8 133.3 121.4 125.6 −44.0 185.3 193.5 182.2 59.9 258.2 76.8 81.2 209.9 136.2 173.5 260.6 204.5 205.9 240.9 170.3 147.7 134.0 140.6 −35.6 202.3 210.0 197.8 71.4 272.0 90.1 94.0 233.0 153.8 195.4 284.5 226.7 227.9 263.2 191.2 169.6 153.5 163.3 −22.3 228.0 234.5 222.0 89.0 294.5 110.2 114.1 259.0 173.5 218.2 311.3 251.2 251.8 285.5 212.8 194.0 175.3 188.7 −7.6 256.8 261.8 248.3 108.4 318.5 132.3 136.1 285.5 193.5 243.5 337.8 276.5 275.0 308.0 235.0 218.5 197.2 215.2 +8.3 284.5 290.0 275.8 128.8 342.1 155.0 158.3 Temperature, °C Formula C3H7NO2 C3H7NO2 C7H7NO2 C7H7NO2 C7H7NO2 C8H9NO2 C29H60 C19H40 C9H20 C9H20O C9H18O C28H58 C18H38 C8H18 C8H18O C8H16O C11H20O2 C8H17I C18H34O2 C16H32O C16H32O2 C16H31N C9H18O2 C6HCl5 C2HCl5 C8H5Cl5 C6HCl5O C25H52 C15H32 C5H8 C5H8 C16H26 C16H25Cl C5H12 C5H12 C5H12 C5H12O3 C5H10 C10H16 C14H10 C8H10O2 C8H11NO C6H6O C8H10O2 C10H12O3 C8H8O2 C8H8O2 C8H7N C8H7ClO C13H10O2 C10H10O C7H5NO C7H5N C12H16 C6H5Cl2O2P 40 Melting point, °C −108 −93 −4.1 15.5 51.9 +2 63.8 32 −53.7 −5 −19 61.6 28 −56.8 −15.4 −16 −45.9 14 34 64.0 31 12.5 85.5 −22 188.5 53.3 10 −129.7 −159.7 −16.6 99.5 40.6 11.6 −6.7 76.5 −23.8 70.5 41.5 +7.5 62.8 73 19.5 56.5 164.5 −21.0 28 −104 130.8 73 88.5 −70 103 −55 VAPOR PRESSURES TABLE 2-10 2-75 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Piperidine Piperonal Propane Propenylbenzene Propionamide Propionic acid anhydride Propionitrile Propiophenone n-Propyl acetate iso-Propyl acetate n-Propyl alcohol (1-propanol) iso-Propyl alcohol (2-propanol) n-Propylamine Propylbenzene Propyl benzoate n-Propyl bromide (1-bromopropane) iso-Propyl bromide (2-bromopropane) n-Propyl n-butyrate isobutyrate iso-Propyl isobutyrate Propyl carbamate n-Propyl chloride (1-chloropropane) iso-Propyl chloride (2-chloropropane) iso-Propyl chloroacetate Propyl chloroglyoxylate Propylene Propylene glycol (1,2-Propanediol) Propylene oxide n-Propyl formate iso-Propyl formate 4,4′-iso-Propylidenebisphenol n-Propyl iodide (1-iodopropane) iso-Propyl iodide (2-iodopropane) n-Propyl levulinate iso-Propyl levulinate Propyl mercaptan (1-propanethiol) 2-iso-Propylnaphthalene iso-Propyl β-naphthyl ketone (2-isobutyronaphthone) 2-iso-Propylphenol 3-iso-Propylphenol 4-iso-Propylphenol Propyl propionate 4-iso-Propylstyrene Propyl isovalerate Pulegone Pyridine Pyrocatechol Pyrocaltechol diacetate (1,2-phenylene diacetate) Pyrogallol Pyrotartaric anhydride Pyruvic acid Quinoline iso-Quinoline Resorcinol Safrole Salicylaldehyde Salicylic acid Sebacic acid Selenophene Skatole Stearaldehyde Stearic acid Stearyl alcohol (1-octadecanol) Styrene Styrene dibromide [(1,2-dibromoethyl) benzene] Suberic acid Succinic anhydride Succinimide Succinyl chloride α-Terpineol Terpenoline 1 5 10 20 87.0 −128.9 17.5 65.0 4.6 20.6 −35.0 50.0 −26.7 −38.3 −15.0 −26.1 −64.4 6.3 54.6 −53.0 −61.8 −1.6 −6.2 −16.3 52.4 −68.3 −78.8 +3.8 9.7 −131.9 45.5 −75.0 −43.0 −52.0 193.0 −36.0 −43.3 59.7 48.0 −56.0 76.0 −7.0 117.4 −115.4 43.8 91.0 28.0 45.3 −13.6 77.9 −5.4 −17.4 +5.0 −7.0 −46.3 31.3 83.8 −33.4 −42.5 +22.1 +16.8 +5.8 77.6 −50.0 −61.1 28.1 32.3 −120.7 70.8 −57.8 −22.7 −32.7 224.2 −13.5 −22.1 86.3 74.5 −36.3 107.9 +3.9 132.0 −108.5 57.0 105.0 39.7 57.7 −3.0 92.2 +5.0 −7.2 14.7 +2.4 −37.2 43.4 98.0 −23.3 −32.8 34.0 28.3 17.0 90.0 −41.0 −52.0 40.2 43.5 −112.1 83.2 −49.0 −12.6 −22.7 240.8 −2.4 −11.7 99.9 88.0 −26.3 123.4 15.8 148.0 −100.9 71.5 119.0 52.0 70.4 +8.8 107.6 16.0 +4.2 25.3 12.7 −27.1 56.8 114.3 −12.4 −22.0 47.0 40.6 29.0 103.2 −31.0 −42.0 53.9 55.6 −104.7 96.4 −39.3 −1.7 −12.1 255.5 +10.0 0.0 114.0 102.4 −15.4 140.3 29.2 165.7 −92.4 87.7 134.8 65.8 85.6 22.0 124.3 28.8 17.0 36.4 23.8 −16.0 71.6 131.8 −0.3 −10.1 61.5 54.3 42.4 117.7 −19.5 −31.0 68.7 68.8 −96.5 111.2 −28.4 +10.8 −0.2 273.0 23.6 +13.2 130.1 118.1 −3.2 159.0 60 Melting point, °C 100 200 400 760 37.7 177.0 −87.0 97.8 144.3 74.1 94.5 30.1 135.0 37.0 25.1 43.5 30.5 −9.0 81.1 143.3 +7.5 −2.5 70.3 63.0 51.4 126.5 −12.1 −23.5 78.0 77.2 −91.3 119.9 −21.3 18.8 +7.5 282.9 32.1 21.6 140.6 127.8 +4.6 171.4 49.0 191.7 −79.6 111.7 156.0 85.8 107.2 41.4 149.3 47.8 35.7 52.8 39.5 +0.5 94.0 157.4 18.0 +8.0 82.6 73.9 62.3 138.3 −2.5 −13.7 90.3 88.0 −84.1 132.0 −12.0 29.5 17.8 297.0 43.8 32.8 154.0 141.8 15.3 187.6 66.2 214.3 −68.4 132.0 174.2 102.5 127.8 58.2 170.2 64.0 51.7 66.8 53.0 15.0 113.5 180.1 34.0 23.8 101.0 91.8 80.2 155.8 +12.2 +1.3 108.8 104.7 −73.3 149.7 +2.1 45.3 33.6 317.5 61.8 50.0 175.6 161.6 31.5 211.8 85.7 238.5 −55.6 154.7 194.0 122.0 146.0 77.7 194.2 82.0 69.8 82.0 67.8 31.5 135.7 205.2 52.0 41.5 121.7 112.0 100.0 175.8 29.4 18.1 128.0 123.0 −60.9 168.1 17.8 62.6 50.5 339.0 81.8 69.5 198.0 185.2 49.2 238.5 106.0 263.0 −42.1 179.0 213.0 141.1 167.0 97.1 218.0 101.8 89.0 97.8 82.5 48.5 159.2 231.0 71.0 60.0 142.7 133.9 120.5 195.0 46.4 36.5 148.6 150.0 −47.7 188.2 34.5 81.3 68.3 360.5 102.5 89.5 221.2 208.2 67.4 266.0 Temperature, °C Formula C5H11N C8H6O3 C 3 H8 C9H10 C3H7NO C3H6O2 C6H10O3 C3H5N C9H10O C5H10O2 C5H10O2 C3H8O C3H8O C3H9N C9H12 C10H12O2 C3H7Br C3H7Br C7H14O2 C7H14O2 C7H14O2 C4H9NO2 C3H7Cl C3H7Cl C5H9ClO2 C5H7ClO3 C3H6 C3H8O2 C3H6O C4H8O2 C4H8O2 C15H16O2 C3H7I C3H7I C8H14O3 C8H14O3 C3H8S C13H14 40 C14H14O C9H12O C9H12O C9H12O C6H12O2 C11H14 C8H16O2 C10H16O C5H5N C6H6O2 133.2 56.6 62.0 67.0 −14.2 34.7 +8.0 58.3 −18.9 165.4 83.8 90.3 94.7 +8.0 62.3 32.8 82.5 +2.5 104.0 181.0 97.0 104.1 108.0 19.4 76.0 45.1 94.0 13.2 118.3 197.7 111.7 119.8 123.4 31.6 91.2 58.0 106.8 24.8 134.0 215.6 127.5 136.2 139.8 45.0 108.0 72.8 121.7 38.0 150.6 227.0 137.7 146.6 149.7 53.8 118.4 82.3 130.2 46.8 161.7 242.3 150.3 160.2 163.3 65.2 132.8 95.0 143.1 57.8 176.0 264.0 170.1 182.0 184.0 82.7 153.9 113.9 162.5 75.0 197.7 288.2 192.6 205.0 206.1 102.0 178.0 135.0 189.8 95.6 221.5 313.0 214.5 228.0 228.2 122.4 202.5 155.9 221.0 115.4 245.5 C10H10O4 C6H6O3 C5H6O3 C3H4O3 C9H7N C9H7N C6H6O2 C10H10O2 C7H6O2 C7H6O3 C10H18O4 C4H4Se C9H9N C18H36O C18H36O2 C18H36O C8H8 98.0 69.7 21.4 59.7 63.5 108.4 63.8 33.0 113.7 183.0 −39.0 95.0 140.0 173.7 150.3 −7.0 129.8 151.7 99.7 45.8 89.6 92.7 138.0 93.0 60.1 136.0 215.7 −16.0 124.2 174.6 209.0 185.6 +18.0 145.7 167.7 114.2 57.9 103.8 107.8 152.1 107.6 73.8 146.2 232.0 −4.0 139.6 192.1 225.0 202.0 30.8 161.8 185.3 130.0 70.8 119.8 123.7 168.0 123.0 88.7 156.8 250.0 +9.1 154.3 210.6 243.4 220.0 44.6 179.8 204.2 147.8 85.3 136.7 141.6 185.3 140.1 105.2 172.2 268.2 24.1 171.9 230.8 263.3 240.4 59.8 191.6 216.3 158.6 94.1 148.1 152.0 195.8 150.3 115.7 182.0 279.8 33.8 183.6 244.2 275.5 252.7 69.5 206.5 232.0 173.8 106.5 163.2 167.6 209.8 165.1 129.4 193.4 294.5 47.0 197.4 260.0 291.0 269.4 82.0 228.7 255.3 196.1 124.7 186.2 190.0 230.8 186.2 150.0 210.0 313.2 66.7 218.8 285.0 316.5 293.5 101.3 253.3 281.5 221.0 144.7 212.3 214.5 253.4 210.0 173.7 230.5 332.8 89.8 242.5 313.8 343.0 320.3 122.5 278.0 309.0 247.4 165.0 237.7 240.5 276.5 233.0 196.5 256.0 352.3 114.3 266.2 342.5 370.0 349.5 145.2 C8H8Br2 C8H14O4 C4H4O3 C4H5NO2 C4H4Cl2O2 C10H18O C10H16 86.0 172.8 92.0 115.0 39.0 52.8 32.3 115.6 205.5 115.0 143.2 65.0 80.4 58.0 129.8 219.5 128.2 157.0 78.0 94.3 70.6 145.2 238.2 145.3 174.0 91.8 109.8 84.8 161.8 254.6 163.0 192.0 107.5 126.0 100.0 172.2 265.4 174.0 203.0 117.2 136.3 109.8 186.3 279.8 189.0 217.4 130.0 150.1 122.7 207.8 300.5 212.0 240.0 149.3 171.2 142.0 230.0 322.8 237.0 263.5 170.0 194.3 163.5 254.0 345.5 261.0 287.5 192.5 217.5 185.0 −9 37 −187.1 −30.1 79 −22 −45 −91.9 21 −92.5 −127 −85.8 −83 −99.5 −51.6 −109.9 −89.0 −95.2 −122.8 −117 −185 −112.1 −92.9 −98.8 −90 −112 15.5 26 61 −76 −42 105 133 13.6 −15 24.6 110.7 11.2 −7 159 134.5 95 63.5 69.3 58.5 −30.6 142 119.6 125.5 17 35 (Continued ) 2-76 PHYSICAL AnD CHEMICAL DATA TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Formula 1,1,1,2-Tetrabromoethane 1,1,2,2-Tetrabromoethane Tetraisobutylene Tetracosane 1,2,3,4-Tetrachlorobenzene 1,2,3,5-Tetrachlorobenzene 1,2,4,5-Tetrachlorobenzene 1,1,2,2-Tetrachloro-1,2-difluoroethane 1,1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane 1,2,3,5-Tetrachloro-4-ethylbenzene Tetrachloroethylene 2,3,4,6-Tetrachlorophenol 3,4,5,6-Tetrachloro-1,2-xylene Tetradecane Tetradecylamine Tetradecyltrimethylsilane Tetraethoxysilane 1,2,3,4-Tetraethylbenzene Tetraethylene glycol Tetraethylene glycol chlorohydrin Tetraethyllead Tetraethylsilane Tetralin 1,2,3,4-Tetramethylbenzene 1,2,3,5-Tetramethylbenzene 1,2,4,5-Tetramethylbenzene 2,2,3,3-Tetramethylbutane Tetramethylene dibromide (1,4-dibromobutane) Tetramethyllead Tetramethyltin Tetrapropylene glycol monoisopropyl ether Thioacetic acid (mercaptoacetic acid) Thiodiglycol (2,2′-thiodiethanol) Thiophene Thiophenol (benzenethiol) α-Thujone Thymol Tiglaldehyde Tiglic acid Tiglonitrile Toluene Toluene-2,4-diamine 2-Toluic nitrile (2-tolunitrile) 4-Toluic nitrile (4-tolunitrile) 2-Toluidine 3-Toluidine 4-Toluidine 2-Tolyl isocyanide 4-Tolylhydrazine Tribromoacetaldehyde 1,1,2-Tribromobutane 1,2,2-Tribromobutane 2,2,3-Tribromobutane 1,1,2-Tribromoethane 1,2,3-Tribromopropane Triisobutylamine Triisobutylene 2,4,6-Tritertbutylphenol Trichloroacetic acid Trichloroacetic anhydride Trichloroacetyl bromide 2,4,6-Trichloroaniline 1,2,3-Trichlorobenzene 1,2,4-Trichlorobenzene 1,3,5-Trichlorobenzene 1,2,3-Trichlorobutane 1,1,1-Trichloroethane 1,1,2-Trichloroethane Trichloroethylene Trichlorofluoromethane 2,4,5-Trichlorophenol 2,4,6-Trichlorophenol C2H2Br4 C2H2Br4 C16H32 C24H50 C6H2Cl4 C6H2Cl4 C6H2Cl4 C2Cl4F2 C2H2Cl4 C2H2Cl4 C8H6Cl4 C2Cl4 C6H2Cl4O C8H6Cl4 C14H30 C14H31N C17H38Si C8H20O4Si C14H22 C8H18O5 C8H17ClO4 C8H20Pb C8H20Si C10H12 C10H14 C10H14 C10H14 C8H18 C4H8Br2 C4H12Pb C4H12Sn C15H32O5 C2H4O2S C4H10O2S C4H4S C6H6S C10H16O C10H14O C5H8O C5H8O2 C5H7N C7H8 C7H10N2 C8H7N C8H7N C7H9N C7H9N C7H9N C8H7N C7H10N2 C2HBr3O C4H7Br3 C4H7Br3 C4H7Br3 C2H3Br3 C3H5Br3 C12H27N C12H24 C18H30O C2HCl3O2 C4Cl6O3 C2BrCl3O C6H4Cl3N C6H3Cl3 C6H3Cl3 C6H3Cl3 C4H7Cl3 C2H3Cl3 C2H3Cl3 C2HCl3 CCl3F C6H3Cl3O C6H3Cl3O 1 5 10 20 58.0 65.0 63.8 183.8 68.5 58.2 83.3 95.5 93.7 219.6 99.6 89.0 95.7 110.0 108.5 237.6 114.7 104.1 108.5 126.0 124.5 255.3 131.2 121.6 −37.5 −16.3 −3.8 77.0 −20.6 100.0 94.4 76.4 102.6 120.0 16.0 65.7 153.9 110.1 38.4 −1.0 38.0 42.6 40.6 45.0 −17.4 −16.0 +7.4 +20.7 110.0 +2.4 130.3 125.0 106.0 135.8 150.7 40.3 96.2 183.7 141.8 63.6 +23.9 65.3 68.7 65.8 65.0 +3.2 −5.0 19.3 33.0 126.0 13.8 145.3 140.3 120.7 152.0 166.2 52.6 111.6 197.1 156.1 74.8 36.3 79.0 81.8 77.8 74.6 13.5 32.0 −29.0 −51.3 116.6 60.0 42.0 −40.7 18.6 38.3 64.3 −25.0 52.0 −25.5 −26.7 106.5 36.7 42.5 44.0 41.0 42.0 25.2 82.4 18.5 45.0 41.0 38.2 32.6 47.5 32.3 18.0 95.2 51.0 56.2 −7.4 134.0 40.0 38.4 58.8 −6.8 −31.0 147.8 87.7 96.0 −20.8 43.7 65.7 92.8 −1.6 77.8 −2.4 −4.4 137.2 64.0 71.3 69.3 68.0 68.2 51.0 110.0 45.0 73.5 69.0 66.0 58.0 75.8 57.4 44.0 126.1 76.0 85.3 +16.7 157.8 70.0 67.3 63.8 27.2 −32.0 −2.0 −22.8 −67.6 102.1 105.9 72.4 +4.4 −20.6 163.0 101.5 128.0 −10.9 56.0 79.3 107.4 +10.0 90.2 +9.2 +6.4 151.7 77.9 85.8 81.4 82.0 81.8 64.0 123.8 58.0 87.8 83.2 79.8 70.6 90.0 69.8 56.5 142.0 88.2 99.6 29.3 170.0 85.6 81.7 78.0 40.0 −21.9 +8.3 −12.4 −59.0 117.3 120.2 40 60 100 200 400 760 Temperature, °C +0.5 −52.0 −24.0 −43.8 −84.3 72.0 76.5 Melting point, °C +6.7 32.1 46.2 143.7 26.3 161.0 156.0 135.6 170.0 183.5 65.8 127.7 212.3 172.6 88.0 50.0 93.8 95.8 91.0 88.0 24.6 123.2 144.0 142.2 276.3 149.2 140.0 146.0 19.8 46.7 60.8 162.1 40.1 179.1 174.2 152.7 189.0 201.5 81.1 145.8 228.0 190.0 102.4 65.3 110.4 111.5 105.8 104.2 36.8 132.0 155.1 152.6 288.4 160.0 152.0 157.7 28.1 56.0 70.0 175.0 49.2 190.0 185.8 164.0 200.2 213.3 90.7 156.7 237.8 200.5 111.7 74.8 121.3 121.8 115.4 114.8 44.5 144.0 170.0 167.5 305.2 175.7 168.0 173.5 38.6 68.0 83.2 191.6 61.3 205.2 200.5 178.5 215.7 227.8 103.6 172.4 250.0 214.7 123.8 88.0 135.3 135.7 128.3 128.1 54.8 161.5 192.5 190.0 330.5 198.0 193.7 196.0 55.0 87.2 102.2 215.3 79.8 227.2 223.0 201.8 239.8 250.0 123.5 196.0 268.4 236.5 142.0 108.0 157.2 155.7 149.9 149.5 70.2 181.0 217.5 214.6 358.0 225.5 220.0 220.5 73.1 108.2 124.0 243.0 100.0 250.4 248.3 226.8 264.6 275.0 146.2 221.4 288.0 258.2 161.8 130.2 181.8 180.0 173.7 172.1 87.4 200.0 243.5 240.0 386.4 254.0 246.0 245.0 92.0 130.5 145.9 270.0 120.8 275.0 273.5 252.5 291.2 300.0 168.5 248.0 307.8 281.5 183.0 153.0 207.2 204.4 197.9 195.9 106.3 87.6 16.6 −9.3 179.8 115.8 165.0 0.0 69.7 93.7 122.6 23.2 103.8 22.1 18.4 167.9 93.0 101.7 95.1 96.7 95.8 78.2 138.6 72.1 103.2 98.6 94.6 84.2 105.8 83.0 70.0 158.0 101.8 114.3 42.1 182.6 101.8 97.2 93.7 55.0 −10.8 21.6 −1.0 −49.7 134.0 135.8 104.0 30.3 +3.5 197.7 131.8 210.0 +12.5 84.2 110.0 139.8 37.0 119.0 36.7 31.8 185.7 110.0 109.5 110.0 113.5 111.5 94.0 154.1 87.8 120.2 116.0 111.8 100.0 122.8 97.8 86.7 177.4 116.3 131.2 57.2 195.8 119.8 114.8 110.8 71.5 +1.6 35.2 +11.9 −39.0 151.5 152.2 115.1 39.2 11.7 209.0 142.0 240.5 20.1 93.9 120.2 149.8 45.8 127.8 46.0 40.3 196.2 120.8 130.0 119.8 123.8 121.5 104.0 165.0 97.5 131.6 127.0 122.2 110.0 134.0 107.3 96.7 188.0 125.9 141.8 66.7 204.5 131.5 125.7 121.8 82.0 9.5 44.0 20.0 −32.3 162.5 163.5 128.7 50.8 22.8 223.3 154.0 285 30.5 106.6 134.0 164.1 57.7 140.5 58.2 51.9 211.5 135.0 145.2 133.0 136.7 133.7 117.7 178.0 110.2 146.0 141.8 136.3 123.5 148.0 119.7 110.0 203.0 137.8 155.2 79.5 214.6 146.0 140.0 136.0 96.2 20.0 55.7 31.4 −23.0 178.0 177.8 149.8 68.8 39.8 245.0 173.8 89.0 58.5 268.3 197.5 110.0 78.0 292.7 −20 −27.5 46.5 125.8 154.2 185.5 75.4 158.0 77.8 69.5 232.8 156.0 167.3 153.0 157.6 154.0 137.8 198.0 130.0 167.8 163.5 157.8 143.5 170.0 138.0 130.2 226.2 155.4 176.2 98.4 229.8 168.2 162.0 157.7 118.0 36.2 73.3 48.0 −9.1 201.5 199.0 64.7 146.7 177.8 209.2 95.5 179.2 99.7 89.5 256.0 180.0 193.0 176.2 180.6 176.9 159.9 219.5 151.6 192.0 188.0 182.2 165.4 195.0 157.8 153.0 250.6 175.2 199.8 120.2 246.4 193.5 187.7 183.0 143.0 54.6 93.0 67.0 +6.8 226.5 222.5 84.4 168.0 201.0 231.8 116.4 198.5 122.0 110.6 280.0 205.2 217.6 199.7 203.3 200.4 183.5 242.0 174.0 216.2 213.8 206.5 188.4 220.0 179.0 179.0 276.3 195.6 223.0 143.0 262.0 218.5 213.0 208.4 169.0 74.1 113.9 86.7 23.7 251.8 246.0 −38.3 51.1 46.5 54.5 139 26.5 −68.7 −36 −19.0 69.5 5.5 11.6 −136 −31.0 −6.2 −24.0 79.5 −102.2 −16.5 51.5 64.5 −95.0 99 −13 29.5 −16.3 −31.5 44.5 65.5 −26 16.5 −22 57 78 52.5 17 63.5 −30.6 −36.7 −73 62 68.5 VAPOR PRESSURES 2-77 TABLE 2-10 Vapor Pressures of Organic Compounds, up to 1 atm (Continued ) Pressure, mmHg Compound Name Tri-2-chlorophenylthiophosphate 1,1,1-Trichloropropane 1,2,3-Trichloropropane 1,1,2-Trichloro-1,2,2-trifluoroethane Tricosane Tridecane Tridecanoic acid Triethoxymethylsilane Triethoxyphenylsilane 1,2,4-Triethylbenzene 1,3,4-Triethylbenzene Triethylborine Triethyl camphoronate citrate Triethyleneglycol Triethylheptylsilane Triethyloctylsilane Triethyl orthoformate phosphate Triethylthallium Trifluorophenylsilane Trimethallyl phosphate 2,3,5-Trimethylacetophenone Trimethylamine 2,4,5-Trimethylaniline 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene 2,2,3-Trimethylbutane Trimethyl citrate Trimethyleneglycol (1,3-propanediol) 1,2,4-Trimethyl-5-ethylbenzene 1,3,5-Trimethyl-2-ethylbenzene 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane 2,2,4-Trimethyl-3-pentanone Trimethyl phosphate 2,4,5-Trimethylstyrene 2,4,6-Trimethylstyrene Trimethylsuccinic anhydride Triphenylmethane Triphenylphosphate Tripropyleneglycol Tripropyleneglycol monobutyl ether Tripropyleneglycol monoisopropyl ether Tritolyl phosphate Undecane Undecanoic acid 10-Undecenoic acid Undecan-2-ol n-Valeric acid iso-Valeric acid γ-Valerolactone Valeronitrile Vanillin Vinyl acetate 2-Vinylanisole 3-Vinylanisole 4-Vinylanisole Vinyl chloride (1-chloroethylene) cyanide (acrylonitrile) fluoride (1-fluoroethylene) Vinylidene chloride (1,1-dichloroethene) 4-Vinylphenetole 2-Xenyl dichlorophosphate 2,4-Xyaldehyde 2-Xylene (2-xylene) 3-Xylene (3-xylene) 4-Xylene (4-xylene) 2,4-Xylidine 2,6-Xylidine 1 5 10 20 188.2 217.2 231.2 246.7 261.7 −28.8 +9.0 −68.0 170.0 59.4 137.8 −1.5 71.0 46.0 47.9 −7.0 33.7 −49.4 206.3 98.3 166.3 +22.8 98.8 74.2 76.0 107.0 114.0 70.0 73.7 +5.5 39.6 +9.3 −31.0 93.7 79.0 −97.1 68.4 16.8 13.6 9.6 150.2 138.7 144.0 99.8 104.8 29.2 67.8 37.6 −9.7 131.0 108.0 −81.7 95.9 42.9 38.3 34.7 106.2 59.4 43.7 38.8 −29.0 −36.5 −25.8 −26.3 14.7 26.0 48.1 37.5 53.5 169.7 193.5 96.0 101.5 82.4 154.6 32.7 101.4 114.0 71.1 42.2 34.5 37.5 −6.0 107.0 −48.0 41.9 43.4 45.2 −105.6 −51.0 −149.3 −77.2 64.0 138.2 59.0 −3.8 −6.9 −8.1 52.6 44.0 146.2 87.2 71.2 67.0 −7.1 −15.0 −3.9 −4.1 36.0 53.7 77.0 65.7 82.6 188.4 230.4 125.7 131.6 112.4 184.2 59.7 133.1 142.8 99.0 67.7 59.6 65.8 +18.1 138.4 −28.0 68.0 69.9 72.0 −90.8 −30.7 −138.0 −60.0 91.7 171.1 85.9 +20.2 +16.8 +15.5 79.8 72.6 +4.2 46.0 −40.3 223.0 104.0 181.0 34.6 112.6 88.5 90.2 −148.0 166.0 144.0 158.1 114.6 120.6 40.5 82.1 51.7 +0.8 149.8 122.3 −73.8 109.0 55.9 50.7 47.4 −18.8 160.4 100.6 84.6 80.5 +3.9 −4.3 +6.9 +7.1 46.4 67.8 91.6 79.7 97.4 197.0 249.8 140.5 147.0 127.3 198.0 73.9 149.0 156.3 112.8 79.8 71.3 79.8 30.0 154.0 −18.0 81.0 83.0 85.7 −83.7 −20.3 −132.2 −51.2 105.6 187.0 99.0 32.1 28.3 27.3 93.0 87.0 16.2 59.3 −30.0 242.0 120.2 195.8 47.2 127.2 104.0 105.8 −140.6 183.6 171.1 174.0 130.3 137.7 53.4 97.8 67.7 12.3 169.8 137.5 −65.0 123.7 69.9 64.5 61.0 −7.5 177.2 115.5 99.7 96.0 16.0 +7.5 19.2 19.3 57.6 83.0 107.1 94.8 113.8 206.8 269.7 155.8 161.8 143.7 213.2 85.6 166.0 172.0 127.5 93.1 84.0 95.2 43.3 170.5 −7.0 94.7 97.2 100.0 −75.7 −9.0 −125.4 −41.7 120.3 205.0 114.0 45.1 41.1 40.1 107.6 102.7 29.9 74.0 −18.5 261.3 137.7 212.4 61.7 143.5 121.7 122.6 −131.4 201.8 190.4 191.3 148.0 155.7 67.5 115.7 85.4 25.4 192.0 154.2 −55.2 139.8 85.4 79.8 76.1 +5.2 194.2 131.0 106.0 113.2 29.5 20.7 33.0 32.9 69.8 100.0 124.2 111.8 131.0 215.5 290.3 173.7 179.8 161.4 229.7 104.4 185.6 188.7 143.7 107.8 98.0 101.9 57.8 188.7 +5.3 110.0 112.5 116.0 −66.8 +3.8 −118.0 −31.1 136.3 223.8 129.7 59.5 55.3 54.4 123.8 120.2 60 100 200 400 760 271.5 283.8 302.8 322.0 341.3 38.3 83.6 −11.2 273.8 148.2 222.0 70.4 153.2 132.2 133.4 −125.2 213.5 202.5 201.5 158.2 168.0 76.0 126.3 95.7 33.2 207.0 165.7 −48.8 149.5 95.3 89.5 85.8 13.3 205.5 141.1 126.3 123.8 38.1 29.1 41.8 41.6 77.3 110.0 135.5 122.3 142.2 221.2 305.2 184.6 190.2 173.2 239.8 115.2 197.2 199.5 153.7 116.6 107.3 122.4 66.9 199.8 13.0 119.8 122.3 126.1 −61.1 11.8 −113.0 −24.0 146.4 236.0 139.8 68.8 64.4 63.5 133.7 131.5 50.0 96.1 −1.7 289.8 162.5 236.0 82.7 167.5 146.8 147.7 −116.0 228.6 217.8 214.6 174.0 184.3 88.0 141.6 112.1 44.2 225.7 179.7 −40.3 162.0 108.8 102.8 98.9 24.4 219.6 153.4 140.3 137.9 49.9 40.7 53.8 53.4 87.6 124.0 149.8 136.8 156.5 228.4 322.5 199.0 204.4 187.8 252.2 128.1 212.5 213.5 167.2 128.3 118.9 136.5 78.6 214.5 23.3 132.3 135.3 139.7 −53.2 22.8 −106.2 −15.0 159.8 251.5 152.2 81.3 76.8 75.9 146.8 146.0 67.7 115.6 +13.5 313.5 185.0 255.2 101.0 188.0 168.3 168.3 −101.0 250.8 242.2 235.2 196.0 208.0 106.0 163.7 136.0 60.1 255.0 201.3 −27.0 182.3 129.0 122.7 118.6 41.2 241.3 172.8 160.3 158.4 67.8 58.1 72.0 71.3 102.2 145.0 171.8 157.8 179.8 239.7 349.8 220.2 224.4 209.7 271.8 149.3 237.8 232.8 187.7 146.0 136.2 157.7 97.7 237.3 38.4 151.0 154.0 159.0 −41.3 38.7 −95.4 −1.0 180.0 275.3 172.3 100.2 95.5 94.6 166.4 168.0 87.5 137.0 30.2 339.8 209.4 276.5 121.8 210.5 193.7 193.2 −81.0 276.0 267.5 256.6 221.0 235.0 125.7 187.0 163.5 78.7 288.5 224.3 −12.5 203.7 152.0 145.4 141.0 60.4 264.2 193.8 184.5 183.5 88.2 78.0 92.7 91.8 118.4 167.8 196.1 182.3 205.5 249.8 379.2 244.3 247.0 232.8 292.7 171.9 262.8 254.0 209.8 165.0 155.2 182.3 118.7 260.0 55.5 172.1 175.8 182.0 −28.0 58.3 −84.0 +14.8 202.8 301.5 194.1 121.7 116.7 115.9 188.3 193.7 108.2 158.0 47.6 366.5 234.0 299.0 143.5 233.5 218.0 217.5 −56.2 301.0 294.0 278.3 247.0 262.0 146.0 211.0 192.1 98.3 324.0 247.5 +2.9 234.5 176.1 169.2 164.7 80.9 287.0 214.2 208.1 208.0 109.8 99.2 114.8 113.5 135.0 192.7 221.2 207.0 231.0 259.2 413.5 267.2 269.5 256.6 313.0 195.8 290.0 275.0 232.0 184.4 175.1 207.5 140.8 285.0 72.5 194.0 197.5 204.5 −13.8 78.5 −72.2 31.7 225.0 328.5 215.5 144.4 139.1 138.3 211.5 217.9 Temperature, °C Formula C18H12Cl3O3 PS C3H5Cl3 C3H5Cl3 C2Cl3F3 C23H48 C13H28 C13H26O2 C7H18O3Si C12H20O3Si C12H18 C12H18 C6H15B C15H26O6 C12H20O7 C6H14O4 C13H30Si C14H32Si C7H16O3 C6H15O4P C6H15Tl C6H5F3Si C12H21PO4 C11H14O C3H9N C9H13N C9H12 C9H12 C9H12 C7H16 C9H14O7 C3H8O2 C11H16 C11H16 C8H18 C8H18 C8H18 C8H18 C8H16O C3H9O4P C11H14 C11H14 C7H10O3 C19H16 C18H15O4P C9H20O4 C13H28O4 C12H26O4 C21H21O4P C11H24 C11H22O2 C11H20O2 C11H24O C5H10O2 C5H10O2 C5H8O2 C5H9N C8H8O3 C4H6O2 C9H10O C9H10O C9H10O C2H3Cl C3H3N C2H3F C2H2Cl2 C10H12O C12H9Cl2PO C9H10O C8H10 C8H10 C8H10 C8H11N C8H11N 40 Melting point, °C −77.7 −14.7 −35 47.7 −6.2 41 135 −63.0 −117.1 67 −25.5 −44.1 −44.8 −25.0 78.5 −112.3 −107.3 −101.5 −109.2 93.4 49.4 −25.6 29.5 24.5 −34.5 −37.6 81.5 −153.7 −82 −160.5 −122.5 75 −25.2 −47.9 +13.3 2-78 PHYSICAL AnD CHEMICAL DATA VAPOR PRESSURES OF SOLUTIOnS TABLE 2-11 Partial Pressures of Water over Aqueous Solutions of HCl* log10 pmm = A − B/T, (T in K), which, however, agrees only approximately with the table. The table is more nearly correct. Partial pressure of H2O, mmHg, °C % HCl A B 0° 5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 60° 6 10 14 18 20 8.99156 8.99864 8.97075 8.98014 8.97877 2282 2295 2300 2323 2334 4.18 3.84 3.39 2.87 2.62 6.04 5.52 4.91 4.21 3.83 8.45 7.70 6.95 5.92 5.40 11.7 10.7 9.65 8.26 7.50 15.9 14.6 13.1 11.3 10.3 21.8 20.0 18.0 15.4 14.1 29.1 26.8 24.1 20.6 19.0 39.4 35.5 31.9 27.5 25.1 50.6 47.0 42.1 36.4 33.3 66.2 61.5 55.3 47.9 43.6 86.0 80.0 72.0 62.5 57.0 139 130 116 102 93.5 22 24 26 28 30 9.02708 8.96022 9.01511 8.97611 9.00117 2363 2356 2390 2395 2422 2.33 2.05 1.76 1.50 1.26 3.40 3.04 2.60 2.24 1.90 4.82 4.31 3.71 3.21 2.73 6.75 6.03 5.21 4.54 3.88 9.30 8.30 7.21 6.32 5.41 12.6 11.4 9.95 8.75 7.52 17.1 15.4 13.5 11.8 10.2 22.8 20.4 18.0 15.8 13.7 30.2 27.1 24.0 21.1 18.4 39.8 35.7 31.7 27.9 24.3 52.0 46.7 41.5 36.5 32.0 32 34 36 38 40 42 9.03317 9.07143 9.11815 9.20783 9.33923 9.44953 2453 2487 2526 2579 2647 2709 1.04 0.85 0.68 0.53 0.41 0.31 1.57 1.29 1.03 0.81 0.63 0.48 2.27 1.87 1.50 1.20 0.94 0.72 3.25 2.70 2.19 1.75 1.37 1.06 4.55 3.81 3.10 2.51 2.00 1.56 6.37 5.35 4.41 3.60 2.88 2.30 11.7 9.95 8.33 6.92 5.68 4.60 15.7 13.5 11.4 9.52 7.85 6.45 21.0 18.1 15.4 13.0 10.7 8.90 27.7 24.0 20.4 17.4 14.5 12.1 8.70 7.32 6.08 5.03 4.09 3.28 70° 80° 90° 100° 110° 220 204 185 162 150 333 310 273 248 230 492 463 425 374 345 715 677 625 550 510 960 892 783 729 85.6 77.0 69.0 60.7 53.5 138 124 112 99.0 87.5 211 194 173 154 136 317 290 261 234 207 467 426 387 349 310 670 611 555 499 444 46.5 40.5 34.8 29.6 25.0 21.2 76.5 66.5 57.0 49.1 42.1 35.8 120 104 90.0 77.5 67.3 57.2 184 161 140 120 105 89.2 275 243 212 182 158 135 396 355 311 266 230 195 ∗Uncertainty, ca. 2 percent for solutions of 15 to 30 percent HCl between 0 and 100°; for solutions of > 30 percent HCl the accuracy is ca. 5 percent at the lower temperatures and ca. 15 percent at the higher temperatures. Below 15 percent HCl, the uncertainty is ca. 5 percent at the lower temperatures and higher strengths to ca. 15 to 20 percent at the lower strengths and perhaps 15 to 20 percent at the higher temperatures and lower strengths. International Critical Tables, vol. 3, p. 301. FIG. 2-1 Vapor pressures of H3PO4 aqueous: partial pressure of H2O vapor. (Courtesy of Victor Chemical Works, Stauffer Chemical Company; measurements by W. H. Woodstock.) VAPOR PRESSURES OF SOLUTIOnS 2-79 TABLE 2-12 Water Partial Pressure, Bar, over Aqueous Sulfuric Acid Solutions* Weight percent, H2SO4 °C 0 10 20 30 40 50 60 70 80 90 10.0 20.0 .582E−02 .117E−01 .223E−01 .404E−01 .703E−01 .117 .189 .296 .449 .664 .534E−02 .107E−01 .205E−01 .373E−01 .649E−01 .109 .175 .275 .417 .617 30.0 .448E−02 .909E−02 .174E−01 .319E−01 .558E−01 .939E−01 .152 .239 .365 .542 40.0 .326E−02 .670E−02 .130E−01 .241E−01 .427E−01 .725E−01 .119 .188 .290 .434 50.0 60.0 70.0 75.0 80.0 85.0 .193E−02 .405E−02 .802E−02 .151E−01 .272E−01 .470E−01 .782E−01 .126 .196 .298 .836E−03 .180E−02 .367E−02 .710E−02 .131E−01 .232E−01 .395E−01 .651E−01 .104 .161 .207E−03 .467E−03 .995E−03 .201E−02 .387E−02 .715E−02 .127E−01 .217E−01 .360E−01 .578E−01 .747E−04 .175E−03 .388E−03 .811E−03 .162E−02 .309E−02 .565E−02 .997E−02 .170E−01 .281E−01 .197E−04 .490E−04 .115E−04 .253E−03 .531E−03 .106E−02 .204E−02 .376E−02 .668E−02 .115E−01 .343E−05 .952E−05 .245E−04 .589E−04 .133E−03 .286E−03 .584E−03 .114E−02 .213E−02 .383E−02 .905E−01 .138 .206 .301 .481 .605 .837 1.138 1.525 2.017 .452E−01 .708E−01 .108 .162 .236 .339 .478 .662 .902 1.212 .192E−01 .312E−01 .493E−01 .760E−01 .115 .170 .246 .350 .489 .673 .666E−02 .112E−01 .183E−01 .291E−01 .451E−01 .682E−01 .101 .147 .208 .291 100 110 120 130 140 150 160 170 180 190 .957 1.349 1.863 2.524 3.361 4.404 5.685 7.236 9.093 11.289 .891 1.258 1.740 2.361 3.149 4.132 5.342 6.810 8.571 10.658 .786 1.113 1.544 2.101 2.810 3.697 4.793 6.127 7.731 9.640 .634 .904 1.264 1.732 2.333 3.090 4.031 5.185 6.584 8.259 .441 .638 .903 1.253 1.708 2.289 3.021 3.930 5.045 6.397 .244 .360 .519 .734 1.020 1.392 1.870 2.475 3.233 4.169 200 210 220 230 240 250 260 270 280 290 13.861 16.841 20.264 24.160 28.561 33.494 38.984 45.055 51.726 59.015 13.107 15.951 19.225 22.960 27.188 31.939 37.240 43.116 49.590 56.681 11.887 14.505 17.529 20.992 24.927 29.364 34.334 39.865 45.984 52.715 10.245 12.576 15.287 18.414 21.992 26.056 30.642 35.784 41.514 47.865 8.020 9.948 12.217 14.864 17.929 21.452 25.472 30.030 35.168 40.926 5.312 6.696 8.354 10.322 12.641 15.351 18.496 22.121 26.274 31.003 2.632 3.395 4.331 5.466 6.831 8.458 10.382 12.640 15.269 18.311 1.606 2.101 2.714 3.467 4.381 5.480 6.788 8.333 10.142 12.242 .913 1.220 1.609 2.096 2.699 3.435 4.326 5.395 6.663 8.155 .401 .542 .724 .952 1.237 1.587 2.012 2.525 3.136 3.857 300 310 320 330 340 350 66.934 75.495 84.705 94.567 105.083 116.251 64.407 72.781 81.816 91.518 101.894 112.946 60.081 68.100 76.792 86.172 96.252 107.043 54.868 62.553 70.947 80.077 89.969 100.646 47.346 54.470 62.337 70.988 80.463 90.802 36.360 42.395 49.164 56.721 65.123 74.426 21.808 25.804 30.343 35.473 41.240 47.692 14.665 17.438 20.591 24.153 28.154 32.622 9.897 11.912 14.227 16.867 19.855 23.217 4.701 5.680 6.806 8.093 9.551 11.193 Weight percent, H2SO4 °C 90.0 92.0 94.0 96.0 97.0 99.0 99.5 100.0 0 10 20 30 40 50 60 70 80 90 .518E−06 .159E−05 .448E−05 .117E−04 .285E−04 .652E−04 .141E−03 .290E−03 .569E−03 .107E−02 .242E−06 .762E−06 .220E−05 .587E−05 .146E−04 .341E−04 .754E−04 .158E−03 .316E−03 .606E−03 .107E−06 .344E−06 .101E−05 .275E−05 .696E−05 .166E−04 .372E−04 .795E−04 .162E−03 .315E−03 .401E−07 .130E−06 .390E−06 .108E−05 .278E−05 .672E−05 .154E−04 .334E−04 .691E−04 .137E−03 .218E−07 .713E−07 .215E−06 .598E−06 .155E−05 .379E−05 .875E−05 .192E−04 .400E−04 .801E−04 .980E−08 .323E−07 .978E−07 .275E−06 .720E−06 .177E−05 .413E−05 .912E−05 .192E−04 .388E−04 .569E−08 .188E−07 .572E−07 .161E−06 .424E−06 .105E−05 .245E−05 .544E−05 .115E−04 .234E−04 .268E−08 .888E−08 .271E−07 .766E−07 .202E−06 .503E−06 .118E−05 .263E−05 .559E−05 .114E−04 .775E−09 .258E−08 .789E−08 .224E−07 .595E−07 .149E−06 .350E−06 .784E−06 .168E−05 .343E−05 .196E−09 .655E−09 .201E−08 .575E−08 .153E−07 .384E−07 .910E−07 .205E−06 .439E−06 .903E−06 100 110 120 130 140 150 160 170 180 190 .194E−02 .338E−02 .571E−02 .938E−02 .150E−01 .233E−01 .354E−01 .526E−01 .766E−01 .110 .112E−02 .198E−02 .341E−02 .569E−02 .923E−02 .146E−01 .225E−01 .340E−01 .502E−01 .729E−01 .590E−03 .107E−02 .186E−02 .315E−02 .519E−02 .832E−02 .130E−01 .199E−01 .298E−01 .438E−01 .261E−03 .479E−03 .851E−03 .146E−02 .245E−02 .399E−02 .633E−02 .983E−02 .149E−01 .222E−01 .154E−03 .285E−03 .511E−03 .886E−03 .149E−02 .245E−02 .393E−02 .614E−02 .941E−02 .141E−01 .752E−04 .141E−03 .254E−03 .445E−03 .757E−03 .125E−02 .202E−02 .319E−02 .492E−02 .744E−02 .455E−04 .855E−04 .155E−03 .278E−03 .467E−03 .776E−03 .126E−02 .199E−02 .309E−02 .469E−02 .223E−04 .420E−04 .766E−04 .135E−03 .232E−03 .387E−03 .629E−03 .999E−03 .155E−02 .236E−02 .674E−05 .128E−04 .233E−04 .414E−04 .711E−04 .119E−03 .194E−03 .309E−03 .482E−03 .735E−03 .178E−05 .339E−05 .623E−05 .111E−04 .191E−04 .321E−04 .526E−04 .840E−04 .131E−03 .201E−03 .631E−01 .894E−01 .125 .171 .232 .310 .409 .534 .689 .880 .325E−01 .467E−01 .660E−01 .918E−01 .126 .170 .227 .300 .391 .505 .208E−01 .300E−01 .427E−01 .598E−01 .825E−01 .112 .151 .200 .263 .341 .110E−01 .161E−01 .230E−01 .325E−01 .451E−01 .618E−01 .835E−01 .111 .147 .192 .698E−02 .102E−01 .147E−01 .208E−01 .290E−01 .398E−01 .540E−01 .723E−01 .957E−01 .125 .352E−02 .516E−02 .743E−02 .105E−01 .147E−01 .202E−01 .274E−01 .366E−01 .485E−01 .634E−01 .110E−02 .161E−02 .232E−02 .329E−02 .460E−02 .633E−02 .858E−02 .115E−01 .152E−01 .199E−01 .300E−03 .442E−03 .638E−03 .906E−03 .127E−02 .174E−02 .237E−02 .317E−02 .420E−02 .548E−02 .248 .316 .400 .502 .624 .770 .162 .208 .264 .331 .413 .511 .820E−01 .105 .133 .167 .208 .256 .257E−01 .328E−01 .415E−01 .520E−01 .646E−01 .795E−01 .708E−02 .905E−02 .114E−01 .143E−01 .178E−01 .218E−01 200 210 220 230 240 250 260 270 280 290 .154 .213 .290 .389 .514 .673 .870 1.112 1.407 1.763 .104 .146 .201 .273 .366 .485 .635 .822 1.052 1.335 300 310 320 330 340 350 2.190 2.696 3.292 3.990 4.801 5.738 1.676 2.088 2.578 3.159 3.843 4.641 1.112 1.394 1.732 2.133 2.608 3.164 .646 .817 1.025 1.274 1.571 1.922 .437 .556 .701 .875 1.083 1.331 98.0 98.5 ∗Vermeulen, Dong, Robinson, Nguyen, and Gmitro, AIChE meeting, Anaheim, Calif., 1982; and private communication from Prof. Theodore Vermeulen, Chemical Engineering Dept., University of California, Berkeley. 2-80 PHYSICAL AnD CHEMICAL DATA TABLE 2-13 Partial Vapor Pressure of Sulfur Dioxide over Water, mmHg g SO2 / 100 g H2O Temperature, °C 0 10 0.01 0.05 0.10 0.15 0.20 0.02 0.38 1.15 2.10 3.17 0.04 0.66 1.91 3.44 5.13 0.25 0.30 0.40 0.50 1.00 4.34 5.57 8.17 10.9 25.8 6.93 8.84 12.8 17.0 39.5 2.00 3.00 4.00 5.00 6.00 8.00 10.00 15.00 20.00 20 0.07 1.07 3.03 5.37 7.93 10.6 13.5 19.4 25.6 58.4 30 40 50 60 90 120 0.12 1.68 4.62 8.07 11.8 0.19 2.53 6.80 11.7 17.0 0.29 3.69 9.71 16.5 23.8 0.43 5.24 13.5 22.7 32.6 1.21 12.9 31.7 52.2 73.7 2.82 27.0 63.9 104 145 15.7 19.8 28.3 37.1 83.7 58.6 93.2 129 165 202 88.5 139 192 245 299 129 202 277 353 430 183 285 389 496 602 275 351 542 735 407 517 796 585 741 818 22.5 28.2 40.1 52.3 117 31.4 39.2 55.3 72.0 159 42.8 53.3 74.7 96.8 212 95.8 118 164 211 454 253 393 535 679 824 342 530 720 453 700 955 186 229 316 404 856 Condensed from Rabe, A. E. and Harris, J. F., J. Chem. Eng. Data, 8 (3), 333–336, 1963. Copyright © American Chemical Society and reproduced by permission of the copyright owner. TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3* mmHg Percentages are weight % HNO3 in solution. 20% °C HNO3 25% H2O HNO3 30% H2O HNO3 35% H2O 0 5 10 15 20 4.1 5.7 8.0 10.9 15.2 3.8 5.4 7.6 10.3 14.2 3.6 5.0 7.1 9.7 13.2 25 30 35 40 45 20.6 27.6 36.5 47.5 62 19.2 25.7 33.8 44 57.5 17.8 23.8 31.1 41 53 0.09 0.11 .17 HNO3 40% H2O HNO3 3.3 4.6 6.5 8.9 12.0 0.09 .13 .20 .28 16.2 21.7 28.3 37.7 48 0.12 .17 .25 .36 .52 45% H2O 50% HNO3 H2O HNO3 H2O 3.0 4.2 5.8 8.0 10.8 0.10 .15 2.6 3.6 5.0 6.9 9.4 0.12 .18 .27 2.1 3.0 4.2 5.8 7.9 14.6 19.5 25.5 33.5 43 .23 .33 .48 .68 .96 12.7 16.9 22.3 29.3 38.0 .39 .56 .80 1.13 1.57 10.7 14.4 19.0 25.0 32.5 49.5 62.5 80 100 126 2.18 2.95 4.05 5.46 7.25 42.5 54 70 88 110 50 55 60 65 70 0.09 .13 .19 .27 80 100 128 162 200 .13 .18 .28 .40 .54 75 94 121 151 187 .25 .35 .51 .71 1.00 69 87 113 140 174 .42 .59 .85 1.18 1.63 63 79 102 127 159 .75 1.04 1.48 2.05 2.80 56 71 90 114 143 1.35 1.83 2.54 3.47 4.65 75 80 85 90 95 .38 .53 .74 1.01 1.37 250 307 378 458 555 .77 1.05 1.44 1.95 2.62 234 287 352 426 517 1.38 1.87 2.53 3.38 4.53 217 267 325 393 478 2.26 3.07 4.15 5.50 7.32 198 243 297 359 436 3.80 5.10 6.83 9.0 11.7 178 218 268 325 394 6.20 8.15 10.7 13.7 17.8 158 195 240 292 355 9.6 12.5 16.3 20.9 26.8 138 170 211 258 315 6.05 7.90 580 690 530 631 755 15.5 20.0 25.7 32.5 480 573 688 810 23.0 29.2 37.0 46 430 520 625 740 34.2 43.0 54.5 67 84 383 463 560 665 785 100 1.87 675 3.50 628 105 2.50 800 4.65 745 110 115 120 ∗International Critical Tables, vol. 3, pp. 304–305. 9.7 12.7 16.5 (Continued ) VAPOR PRESSURES OF SOLUTIOnS 2-81 TABLE 2-14 Partial Pressures of HnO3 and H2O over Aqueous Solutions of HnO3 (Continued ) mmHg Percentages are weight % HNO3 in solution. 55% °C 60% 65% 70% 80% HNO3 H2O HNO3 H2O HNO3 H2O HNO3 H2O 0 5 10 15 20 0.14 .21 .31 .45 1.8 2.5 3.5 4.9 6.7 0.19 .28 .41 .59 .84 1.5 2.1 3.0 4.1 5.6 0.41 .60 .86 1.21 1.68 1.3 1.8 2.6 3.5 4.9 0.79 1.12 1.58 2.18 3.00 1.1 1.6 2.2 3.0 4.1 25 30 35 40 45 .66 .93 1.30 1.82 2.50 9.1 12.2 16.1 21.3 28.0 1.21 1.66 2.28 3.10 4.20 7.7 10.3 13.6 18.1 23.7 2.32 3.17 4.26 5.70 7.55 6.6 8.8 11.6 15.5 20.0 4.10 5.50 7.30 9.65 12.6 5.5 7.4 9.8 12.8 16.7 50 55 60 65 70 3.41 4.54 6.15 8.18 10.7 36.3 46 60 76 95 5.68 7.45 9.9 13.0 16.8 31 39 51 64 81 10.0 12.8 16.8 21.7 27.5 26.0 33.0 43.0 54.5 68 16.5 21.0 27.1 34.5 43.3 21.8 27.3 35.3 44.5 56 75 80 85 90 95 13.9 18.0 23.0 29.4 37.3 120 148 182 223 272 21.8 27.5 34.8 43.7 55.0 102 126 156 192 233 35.0 43.5 54.5 67.5 83.5 100 105 110 115 120 125 47 58.5 73 90 110 331 400 485 575 685 69.5 84.5 103 126 156 187 285 345 417 495 590 700 103 124 152 181 218 260 HNO3 90% 100% H 2O HNO3 H 2O 2 3 4 6 8 1.2 1.7 2.4 5.5 8 11 15 20 10.5 14 18.5 24.5 32 3.2 4 5.5 7 9.5 27 36 47 62 80 1 1.3 1.8 2.4 3 57 77 102 133 170 11 15 22 30 42 41 52 67 85 106 12 15 20 25 31 103 127 157 192 232 4 5 6.5 8 10 215 262 320 385 460 540 625 720 820 86 106 131 160 195 54.5 67.5 83 103 125 70 86 107 130 158 130 158 192 230 278 38 48 60 73 89 282 338 405 480 570 13 16 20 24 29 238 288 345 410 490 580 152 183 221 262 312 372 192 231 278 330 393 469 330 392 465 545 640 108 129 155 185 219 675 790 35 42 TABLE 2-15 Total Vapor Pressures of Aqueous Solutions of CH3COOH* Percentages of weight % acetic acid in the solution mmHg °C 25% 50% 75% 20 25 30 35 40 16.3 22.1 29.6 39.4 51.7 15.7 21.4 28.8 38.3 50.2 15.3 20.8 27.8 36.6 48.1 45 50 55 60 65 67.0 87.2 110 141 178 65.0 85.0 107 138 172 62.0 80.1 102 130 162 70 75 80 85 90 223 277 342 419 510 216 269 331 407 497 203 251 310 376 458 95 100 618 743 602 725 550 666 ∗International Critical Tables, vol. 3, p. 306. HNO3 2-82 TABLE 2-16 Partial Pressure of H2O over Aqueous Solutions of nH3 (psia) Liquid mole percent NH3 (liquid weight percent NH3) 0 5 10 15 (0) (4.74) (9.5) (14.29) 32 40 50 60 70 0.089 0.122 0.178 0.256 0.363 0.083 0.115 0.168 0.242 0.343 0.077 0.106 0.156 0.225 0.320 0.071 0.097 0.143 0.207 0.294 80 90 100 110 120 0.507 0.699 0.951 1.277 1.695 0.479 0.661 0.899 1.209 1.607 0.448 0.618 0.843 1.135 1.510 130 140 150 160 170 2.226 2.893 3.723 4.747 6.000 2.112 2.748 3.540 4.519 5.717 180 190 200 210 220 7.520 9.350 11.538 14.136 17.201 230 240 250 20.796 24.986 29.844 t, °F 20 25 30 35 40 45 80 85 90 (23.94) (28.81) (33.71) (38.64) (43.59) (48.57) (53.58) (58.62) (63.69) (68.79) (73.91) (79.07) (84.26) (89.47) (94.72) 0.063 0.087 0.129 0.186 0.266 0.055 0.077 0.113 0.164 0.235 0.047 0.065 0.097 0.142 0.204 0.039 0.054 0.081 0.119 0.172 0.031 0.044 0.066 0.098 0.143 0.025 0.035 0.053 0.079 0.116 0.019 0.027 0.041 0.062 0.093 0.014 0.021 0.032 0.049 0.073 0.011 0.016 0.025 0.038 0.058 0.008 0.012 0.019 0.030 0.045 0.006 0.009 0.014 0.023 0.036 0.004 0.007 0.011 0.018 0.028 0.003 0.005 0.008 0.014 0.022 0.002 0.004 0.006 0.010 0.016 0.002 0.002 0.004 0.007 0.011 0.001 0.001 0.002 0.004 0.006 0.413 0.571 0.780 1.052 1.402 0.374 0.518 0.710 0.960 1.283 0.332 0.462 0.634 0.861 1.154 0.289 0.403 0.556 0.758 1.021 0.245 0.345 0.479 0.656 0.889 0.205 0.290 0.405 0.559 0.763 0.168 0.240 0.338 0.470 0.647 0.136 0.196 0.279 0.392 0.544 0.109 0.159 0.228 0.324 0.455 0.087 0.128 0.186 0.268 0.380 0.069 0.103 0.152 0.220 0.316 0.055 0.083 0.123 0.181 0.263 0.043 0.066 0.100 0.148 0.217 0.034 0.052 0.079 0.119 0.176 0.025 0.040 0.061 0.092 0.137 0.018 0.028 0.043 0.065 0.099 0.010 0.015 0.024 0.036 0.056 1.988 2.591 3.343 4.273 5.416 1.850 2.415 3.122 4.000 5.079 1.696 2.221 2.879 3.698 4.709 1.532 2.012 2.618 3.374 4.312 1.361 1.796 2.347 3.039 3.902 1.192 1.582 2.078 2.706 3.493 1.030 1.376 1.821 2.387 3.101 0.881 1.186 1.582 2.090 2.736 0.747 1.016 1.367 1.821 2.405 0.632 0.867 1.177 1.584 2.110 0.532 0.738 1.013 1.376 1.851 0.448 0.628 0.870 1.194 1.622 0.376 0.532 0.746 1.033 1.418 0.313 0.448 0.634 0.887 1.229 0.257 0.371 0.529 0.748 1.047 0.202 0.295 0.425 0.607 0.858 0.147 0.216 0.314 0.453 0.647 0.083 0.124 0.183 0.267 0.386 7.174 8.931 11.035 13.538 16.496 6.807 8.488 10.504 12.910 15.758 6.397 7.994 9.916 12.213 14.941 5.947 7.452 9.270 11.449 14.047 5.465 6.873 8.580 10.635 13.095 4.968 6.275 7.869 9.796 12.115 4.472 5.680 7.160 8.962 11.141 3.995 5.107 6.479 8.160 10.205 3.551 4.573 5.842 7.410 9.331 3.148 4.086 5.262 6.725 8.534 2.787 3.650 4.740 6.110 7.817 2.468 3.262 4.275 5.559 7.175 2.184 2.914 3.856 5.061 6.592 1.928 2.598 3.470 4.598 6.045 1.688 2.297 3.098 4.146 5.504 1.451 1.994 2.718 3.675 4.932 1.201 1.669 2.300 3.147 4.277 0.917 1.290 1.802 2.502 3.455 0.555 0.793 1.129 1.600 2.262 19.971 24.029 28.744 19.111 23.037 27.607 18.162 21.943 26.358 17.124 20.748 24.996 16.020 19.479 23.549 14.886 18.179 22.070 13.760 16.889 20.608 12.679 15.654 19.212 11.672 14.506 17.917 10.754 13.463 16.748 9.930 12.530 15.708 9.192 11.696 14.783 8.522 10.938 13.946 7.889 10.221 13.153 7.255 9.496 12.346 6.573 8.703 11.452 5.777 7.759 10.369 4.751 6.508 8.891 3.196 4.520 6.413 (19.1) 50 55 60 65 70 75 95 The values in Table 2-16 were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002). The primary source for the properties of aqueous ammonia mixtures is R. Tillner-Roth and D. G. Friend, “A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia},” J. Phys. Chem. Ref. Data 27:63–96 (1998). VAPOR PRESSURES OF SOLUTIOnS TABLE 2-17 Partial Pressures of H2O over Aqueous Solutions of Sodium Carbonate* TABLE 2-18 Partial Pressures of H2O and CH3OH over Aqueous Solutions of Methyl Alcohol* mmHg %Na2CO3 t, °C 0 5 10 0 10 20 30 40 50 60 70 80 90 100 4.5 9.2 17.5 31.8 55.3 92.5 149.5 239.8 355.5 526.0 760.0 4.5 9.0 17.2 31.2 54.2 90.7 146.5 235 348 516 746 8.8 16.8 30.4 53.0 88.7 143.5 230.5 342 506 731 15 20 16.3 29.6 57.6 86.5 139.9 225 334 494 715 25 28.8 50.2 84.1 136.1 219 325 482 697 27.8 48.4 81.2 131.6 211.5 315 467 676 2-83 30 39.9°C Mole fraction CH3OH PH2O, mmHg PCH3OH , mmHg 0 14.99 17.85 21.07 27.31 31.06 40.1 47.0 55.8 68.9 86.0 100.0 54.7 39.2 38.5 37.2 35.8 34.9 32.8 31.5 27.3 20.7 10.1 0 0 66.1 75.5 85.2 100.6 108.8 127.7 141.6 158.4 186.6 225.2 260.7 26.4 46.1 77.5 125.7 202.5 301 447 648 ∗International Critical Tables, vol. 3, p. 372. 59.4°C Mole fraction CH3OH PH2O, mmHg PCH3OH , mmHg 0 22.17 27.40 33.24 39.80 47.08 55.5 69.2 78.5 85.9 100.0 145.4 106.9 102.2 96.6 91.7 84.8 76.9 57.8 43.8 30.1 0 0 210.1 240.2 272.1 301.9 335.6 373.7 439.4 486.6 526.9 609.3 ∗International Critical Tables, vol. 3, p. 290. TABLE 2-19 Partial Pressures of H2O over Aqueous Solutions of Sodium Hydroxide* mmHg Conc. g NaOH/ 100 g H2O Temperature, °C 0 20 40 0 4.6 17.5 55.3 5 4.4 16.9 53.2 10 4.2 16.0 50.6 20 3.6 13.9 44.2 30 2.9 11.3 36.6 40 2.2 8.7 28.7 50 6.3 20.7 60 4.4 15.5 70 3.0 10.9 80 2.0 7.6 90 1.3 5.2 100 0.9 3.6 120 1.7 140 160 180 200 250 300 350 400 500 700 1000 2000 4000 8000 ∗International Critical Tables, vol. 3, p. 370. 60 80 100 120 160 200 250 300 350 149.5 143.5 137.0 120.5 101.0 81.0 62.5 47.0 34.5 24.5 17.5 12.5 6.3 3.0 1.5 355.5 341.5 325.5 288.5 246.0 202.0 160.5 124.0 94.0 70.5 53.0 38.5 20.5 11.0 6.0 3.5 2.0 0.5 0.1 760.0 730.0 697.0 621.0 537.0 450.0 368.0 294.0 231.0 179.0 138.0 105.0 61.0 35.5 20.5 12.0 7.0 2.0 0.5 1,489 1,430 1,365 1,225 1,070 920 770 635 515 415 330 262 164 102 63 40 25 8 2.7 0.9 4,633 4,450 4,260 3,860 3,460 3,090 2,690 2,340 2,030 1,740 1,490 1,300 915 765 470 340 245 110 50 23 11 11,647 11,200 10,750 9,800 8,950 8,150 7,400 6,750 6,100 5,500 5,000 4,500 3,650 2,980 2,430 1,980 1,620 985 610 380 240 100 29,771 28,600 27,500 25,300 23,300 21,500 19,900 18,400 17,100 15,800 14,700 13,650 11,800 10,300 8,960 7,830 6,870 5,000 3,690 2,750 2,080 1,210 440 64,200 61,800 59,300 54,700 50,800 47,200 44,100 41,200 38,700 36,300 34,200 32,200 28,800 25,900 23,300 21,200 19,200 15,400 12,500 10,300 8,600 6,100 3,300 1,470 150 123,600 118,900 114,100 105,400 98,000 91,600 85,800 80,700 76,000 71,900 68,100 64,600 58,600 53,400 49,000 45,100 41,800 35,000 29,800 25,700 22,400 17,500 11,500 6,800 1,760 120 7 2-84 PHYSICAL AnD CHEMICAL DATA WATER VAPOR COnTEnT In GASES The accompanying figure is useful in determining the water vapor content of air at high pressure in contact with liquid water. FIG. 2-2 Water content in air at pressures over atmospheric. (Landsbaum, E.M., W.S. Dodds, and L.F. Stutzman. Reprinted from vol. 47, January 1955 issue of Ind. Eng. Chem. [p. 192]. Copyright 1955 by the American Chemical Society and reproduced by permission of the copyright owner.) For other water-in-air data, see Table 2-111, Fig. 2-3 and Section 12 figures and tables. SOLUBILITIES Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32. To convert cubic centimeters to cubic feet, multiply by 3.532 × 10−5. To convert millimeters of mercury to pounds-force per square inch, multiply by 0.01934. To convert grams per liter to pounds per cubic foot, multiply by 6.243 × 10−2. Introduction The database containing solubilities was originally published in the International Union for Pure and Applied Chemistry (IUPAC)National Institute of Standards and Technology (NIST) Solubility Data Series. It is available at no cost online at http://srdata.nist.gov/solubility. The H in the following tables is the proportionality constant in Henry’s law, p = Hx, where x is the mole fraction of the solute in the aqueous liquid phase; p is the partial pressure in atm of the solute in the gas phase; and H is a proportionality constant, generally referred to as Henry’s constant. Values of H often have considerable uncertainty and are strong functions of temperature. To convert values of H at 25°C from atm to atm/(mol/m3), divide by the molar density of water at 25°C, which is 55,342 mol/m3. Henry’s law is valid only for dilute solutions. Additional values of Henry’s constant can be found in “Environmental Simulation Program,” OLI Systems, Inc., Morris Plains, N.J.; “Estimated Henry’s Law Constant,” EPA Online Tools for Site Assessment Calculation (http://www.epa .gov/athens/learn2model/part-two/onsite/esthenry.htm); Rolf Sander, “Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in Environmental Chemistry,” Air Chemistry Department, Max-Planck Institute of Chemistry, Mainz, Germany; Rolf Sander, “Modeling Atmospheric Chemistry: Interactions between Gas-Phase Species and Liquid Cloud/Aerosol Particles,” Surv. Geophys. 20: 1–31, 1999 (http:// www.henrys-law.org). TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures* This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance Formula Solid phase AlCl3 Al2(SO4)3 (NH4)2Al2(SO4)4 6H2O 18H2O 24H2O 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Aluminum chloride sulfate Ammonium aluminum sulfate bicarbonate bromide chloride chloroplatinate chromate chromium sulfate dichromate dihydrogen phosphite hydrogen phosphate iodide magnesium phosphate manganese phosphate nitrate oxalate perchlorate† persulfate sulfate thiocyanate vanadate (meta) Antimonious fluoride sulfide Arsenic oxide Arsenious sulfide NH4HCO3 NH4Br NH4Cl (NH4)2PtCl6 (NH4)2CrO4 (NH4)2Cr2(SO4)4 (NH4)2Cr2O7 NH4H2PO3 (NH4)2HPO4 NH4I NH4MgPO4 NH4MnPO4 NH4NO3 (NH4)2C2O4 NH4ClO4† (NH4)2S2O8 (NH4)2SO4 NH4CNS NH4VO3 SbF3 Sb2S3 As2O5 As2S3 27 28 29 Barium acetate acetate carbonate Ba(C2H3O2)2 Ba(C2H3O2)2 BaCO3 3H2O 1H2O 30 31 32 33 34 35 36 37 38 chlorate chloride chromate hydroxide iodide iodide nitrate nitrite oxalate Ba(ClO3)2 BaCl2 BaCrO4 Ba(OH)2 BaI2 BaI2 Ba(NO3)2 Ba(NO2)2 BaC2O4 1H2O 2H2O 1 2 3 39 40 41 42 43 44 45 46 47 48 49 50 51 perchlorate sulfate Beryllium sulfate sulfate sulfate Boric acid Boron oxide Bromine Cadmium chloride chloride chloride cyanide hydroxide Ba(ClO4)2 BaSO4 BeSO4 BeSO4 BeSO4 H3BO3 B2O3 Br2 CdCl2 CdCl2 CdCl2 Cd(CN)2 Cd(OH)2 52 53 54 sulfate Calcium acetate acetate CdSO4 Ca(C2H3O2)2 Ca(C2H3O2)2 0°C 10°C 31.2 2.1 33.5 4.99 11.9 60.6 29.4 15.8 68 33.3 0.7 171 1H2O 154.2 0.023 118.3 2.2 11.56 58.2 70.6 119.8 163.2 3.1 73.0 144 384.7 8H2O 6H2O 2H2O 1H2O 3H2O 6H2O 4H2O 2H2O 4H2O 2½H2O 1H2O 2H2O 1H2O 30°C 40°C 50°C 60°C 70°C 80°C 90°C 100°C 40.4 10.94 46.1 14.88 52.2 20.10 59.2 26.70 66.1 73.0 80.8 89.0 109.796° 21 75.5 37.2 27 83.2 41.4 91.1 45.8 99.2 50.4 107.8 55.2 116.8 60.2 126 65.6 135.6 71.3 145.6 77.3 1.25 190.5 0.036 0 297.0 8.0 30.58 199.6 0.030 208.9 0.040 0 421.0 218.7 0.016 0.005 499.0 228.8 0.019 0.007 580.0 10.7825° 24II2O 6H2O 7H2O 20°C 69.8615° 36.4 7.74 59.5 5.17 × 10−5 at 18° 59 62.1 63 0.00168° 20.34 31.6 0.0002 1.67 170.2 5.0 26.95 33.3 0.00028 2.48 185.7 7.0 0.00168° 205.8 1.15 × 10−4 2.66 1.1 4.22 97.59 90.01 76.48 37.4 2.0 × 10−4 19014.5° 13115 172.3 0.052 0 192 4.4 20.85 75.4 170 0.48 444.7 0.00017518° 65.8 71 0.002218° 33.80 35.7 0.00037 3.89 203.1 9.2 67.5 0.002218° 289.1 2.4 × 10−4 3.57 1.5 3.4 125.1 5.04 2.2 3.20 135.1 134.5 1.715° 76.00 36.0 76.60 34.7 40.4 47.17 26031° 181.4 241.8 5.9 78.0 207.7 0.84 563.6 81.0 69.5 71.2 1.32 75 0.0024 at 24.2° 41.70 38.2 0.00046 5.59 219.6 11.6 0.0024 at 24.2° 2.85 × 10−4 52 43.78 6.60 3.13 48.19 95.3 103.3 75.1 76.7 77 74 74 49.61 40.7 43.6 66.81 46.4 49.4 8.22 13.12 20.94 358.7 426.3 46.74 135.3 75 84.84 52.4 261.0 27.0 205.8 495.2 62 14.81 6.2 136.5 104.9 58.8 101.4 247.3 20.3 60.67 11.54 57.01 3.05 73.0 17.1 871.0 88.0 1.78 231.9 14.2 740.0 39.05 79 8.72 4.0 132.1 344.0 10.3 250.3 16.73 271.7 34.2 300 562.3 84.76 23.75 9.5 83 98 30.38 140.4 100 110 40.25 15.7 147.0 −4 2.6 × 10 at 25° 33.8 78.54 33.2 83.68 32.7 33.5 63.13 60.77 31.1 29.7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 2-85 (Continued ) 2-86 TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures* (Continued ) This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance Formula 1 2 3 4 5 6 7 8 9 10 11 Calcium bicarbonate chloride chloride fluoride hydroxide nitrate nitrate nitrate nitrite nitrite oxalate Ca(HCO3)2 CaCl2 CaCl2 CaF2 Ca(OH)2 Ca(NO3)2 Ca(NO3)2 Ca(NO3)2 Ca(NO2)2 Ca(NO2)2 CaC2O4 12 13 14 15 16 17 18 19 20 21 22 23 24 sulfate Carbon dioxide, 760 mm ‡ monoxide, 760 mm ‡ Cesium chloride nitrate sulfate Chlorine, 760 mm ‡ Chromic anhydride Cuprio chloride nitrate nitrate sulfate sulfide CaSO4 CO2 CO CsCl CsNO3 Cs2SO4 Cl2 CrO3 CuCl2 Cu(NO3)2 Cu(NO3)2 CuSO4 CuS 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 Cuprous chloride Ferric chloride Ferrous chloride chloride nitrate sulfate sulfate Hydrobromic acid, 760 mm Hydrochloric acid, 760 mm Iodine Lead acetate bromide carbonate chloride chromate fluoride nitrate sulfate Magnesium bromide chloride hydroxide nitrate sulfate sulfate sulfate Manganous sulfate sulfate sulfate sulfate Mercurous chloride Molybdic oxide Nickel chloride nitrate nitrate sulfate sulfate Nitric oxide, 760 mm Nitrous oxide CuCl FeCl3 FeCl2 FeCl2 Fe(NO3)2 FeSO4 FeSO4 HBr HCl I2 Pb(C2H3O2)2 PbBr2 PbCO3 PbCl2 PbCrO4 PbF2 Pb(NO3)2 PbSO4 MgBr2 MgCl2 Mg(OH)2 Mg(NO3)2 MgSO4 MgSO4 MgSO4 MnSO4 MnSO4 MnSO4 MnSO4 HgCl MoO3 NiCl2 Ni(NO3)2 Ni(NO3)2 NiSO4 NiSO4 NO N2O Solid phase 6H2O 2H2O 4H2O 3H2O 0°C 16.15 59.5 65.0 0.185 102.0 0.176 115.3 4H2O 2H2O 62.07 2H2O 0.1759 0.3346 0.0044 161.4 9.33 167.1 1.46 164.9 70.7 81.8 2H2O 6H2O 3H2O 5H2O 4H2O 6H2O 7H2O 1H2O 3H2O 10°C 6.7 × 10−4 at 13° 0.1928 0.2318 0.0035 174.7 14.9 173.1 0.980 73.76 95.28 17.4 74.4 81.9 64.5 221.2 82.3 20.51 210.3 0.6728 6H2O 6H2O 6H2O 7H2O 6H2O 1H2O 7H2O 5H2O 4H2O 1H2O 2H2O 6H2O 6H2O 3H2O 7H2O 6H2O 66.55 40.8 53.23 0.060 48.3 0.0035 94.5 53.5 30.9 42.2 60.01 59.5 0.00014 53.9 79.58 59.5 27.22 32 0.00984 0.001618° 0.165 129.3 6.8 × 10−4 at 25° 0.1688 0.0028 186.5 23.0 178.7 0.716 77.0 125.1 20.7 3.3 × 10−5 at 18° 1.5225° 91.8 83.8 26.5 198 0.029 0.4554 38.8 0.0028 91.0 52.8 16.60 74.5 30°C 102 0.001726° 0.153 152.6 40°C 50°C 17.05 0.00757 0.1705 0.85 0.00011 0.99 7 × 10−6 0.064 56.5 0.0041 96.5 54.5 0.000918° 9.5 × 10−4 at 50° 0.2090 0.1257 0.0024 197.3 33.9 184.1 0.562 0.141 195.9 237.5 70°C 17.50 0.128 0.116 80.34 25 159.8 28.5 33.3 73.0 77.3 315.1 82.5 32.9 40.2 48.6 90°C 0.106 147.0 0.094 0.2047 0.0576 0.0015 229.7 83.8 199.9 0.324 151.9 0.085 0.077 244.8 0.0010 250.0 134.0 210.3 0.219 91.2 99.2 178.8 40 207.8 55 88.7 525.8 100 165.6 50.9 159 363.6 0.1966 0.0013 239.5 107.0 205.0 0.274 100°C 18.40 152.7 358.7 132.6 0.0761 0.0018 218.5 64.4 194.9 0.386 182.1 87.44 80°C 17.95 141.7 281.5 14 × 10−4 at 95° 0.2097 0.0973 0.0021 208.0 47.2 189.9 0.451 174.0 83.8 43.6 0.0006 260.1 163.0 214.9 0.125 217.5 0.1619 0 0 270.5 197.0 220.3 0 206.8 107.9 75.4 535.7 105.3 37.3 105.8 67.3 0.04 55.0425° 1.15 63.3 0.056 171.5 59.6 0.078 1.53 1.94 2.36 3.34 4.75 1.20 1.45 1.70 1.98 2.62 3.34 0.068 66 0.0049 99.2 35.5 44.5 40.8 45.3 62.9 64.5 67.76 66.44 0.0002 0.138 64.2 96.31 0.264 68.9 75 0.0056 101.6 57.5 84.74 45.6 68.8 0.0007 0.476 73.3 122.2 42.46 0.00618 0.1211 60°C 136.8 76.68 14.3 71.02 15.65 20°C 0.00517 0.00440 56.1 85 95 104.1 107.5 61.0 115 130 38.8 113.7 66.0 120.2 73.0 137.0 50.4 53.5 59.5 64.2 62.9 69.0 74.0 68.3 72.6 58.17 55.0 52.0 48.0 42.5 34.0 0.687 78.3 1.206 82.2 2.055 85.2 163.1 50.15 0.00376 54.80 0.00324 2.106 169.1 59.44 0.00267 87.6 235.1 63.17 0.00199 0.00114 76.7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Potassium acetate acetate alum bicarbonate bisulfate bitartrate carbonate chlorate chloride chromate dichromate ferricyanide hydroxide hydroxide nitrate nitrite perchlorate permanganate persulfate† sulfate thiocyanate Silver cyanide nitrate sulfate Sodium acetate acetate bicarbonate carbonate carbonate chlorate chloride chromate chromate chromate dichromate dichromate dihydrogen phosphate dihydrogen phosphate dihydrogen phosphate hydrogen arsenate hydrogen phosphate hydrogen phosphate hydrogen phosphate hydrogen phosphate hydroxide hydroxide hydroxide hydroxide nitrate nitrite oxalate phosphate, tripyrophosphate sulfate sulfate sulfate sulfide sulfide sulfide sulfite sulfite tetraborate tetraborate vanadate (meta) KC2H3O2 KC2H3O2 K2SO4⋅Al2(SO4)3 KHCO3 KHSO4 KHC4H4O6 K2CO3 KClO3 KCl K2CrO4 K2Cr2O7 K3Fe(CN)6 KOH KOH KNO3 KNO2 KClO4 KMnO4 K2S2O8† K2SO4 KCNS AgCN AgNO3 Ag2SO4 NaC2H3O2 NaC2H3O2 NaHCO3 Na2CO3 Na2CO3 NaClO8 NaCl Na2CrO4 Na2CrO4 Na2CrO4 Na2Cr2O7 Na2Cr2O7 NaH2PO4 NaH2PO4 NaH2PO4 Na2HAsO4 Na2HPO4 Na2HPO4 Na2HPO4 Na2HPO4 NaOH NaOH NaOH NaOH NaNO3 NaNO2 Na2C2O4 Na3PO4 Na4P2O7 Na2SO4 Na2SO4 Na2SO4 Na2S Na2S Na2S Na2SO3 Na2SO3 Na2B4O7 Na2B4O7 NaVO8 1½H2O ½H2O 24H2O 2H2O 2H2O 1H2O † 3H2O 10H2O 1H2O 10H2O 4H2O 216.7 233.9 255.6 3.0 22.4 36.3 0.32 105.5 3.3 27.6 58.2 5 31 97 4.0 27.7 5.9 33.2 51.4 0.53 110.5 7.4 34.0 61.7 12 43 112 13.3 278.8 0.75 2.83 1.62 7.35 177.0 20.9 122 0.573 36.3 119 6.9 7 170 0.695 40.8 121 8.15 12.5 31.6 298.4 1.80 6.4 4.49 11.11 217.5 2.2 × 10−5 222 0.796 46.5 123.5 9.6 21.5 79 35.65 31.70 89 35.72 50.17 101 35.89 88.7 2H2O 163.0 2H2O 1H2O 57.9 12H2O 12H2O 7H2O 2H2O 4H2O 3½H2O 1H2O 12H2O 10H2O 10H2O 7H2O 9H2O 5½H2O 6H2O 7H2O 10H2O 5H2O 2H2O 0.40 108 5 31.0 60.0 7 36 103 7.3 1.67 42 1.05 4.4 2.60 9.22 0.90 113.7 10.5 37.0 63.4 20 50 126 45.8 2.6 9.0 7.19 12.97 11.70 45.4 67.3 1.32 116.9 14 40.0 65.2 26 60 63.9 334.9 4.4 12.56 9.89 14.76 4.1 3.95 9.0 30 15.42 18.8 22.5 20 26.9 36 20 9.95 40.8 3.9 202 16.50 18.17 19.75 21.4 22.8 1.22 669 1.30 114.6 96 91.6 169 54.0 73.9 70 18 158.6 80.2 1.36 146 153 172 37.46 45.8 189 37.93 123.0 316.7 124.8 376.2 179.3 65 190.3 207.3 85 225.3 82.9 88.1 92.4 102.9 244.8 88 84.5 3.7 11 6.23 19.4 44 138 147.5 14.8 104 119 48.3 70.4 52 4.6 139.8 38.5 51.1 72.1 61 396.3 109.0 11.8 95.96 51.8 133.1 380.1 71.0 9 22.2 88.7 47 364.8 40.0 6.5 16.89 46.4 155 37.04 37 20.8 15.325° 110.0 140 36.69 26.5 7.7 2.7 140 85.5 48.5 126 36.37 15.5 3.6 1.6 2.46 126.8 24.5 45.5 68.6 43 66 525 1.15 139 139.5 16.4 138.2 1.5 3.16 5.0 19.5 1.83 121.2 19.3 42.6 66.8 34 455 1.08 83 134 14.45 106.5 109 350 24.75 60.0 376 0.979 65.5 129.5 12.7 85.2 51.5 337.3 17.00 300 0.888 54.5 126 11.1 38.8 50.5 113 36.09 69.9 80 78.0 1.3 8.39 39.1 323.3 177.8 73 72.1 13.9 283.8 129 145 174 104 98.4 114 104.1 124 161 38.47 121.6 6.95 155.7 57 56.7 75.6 80 82.6104 178 246 412.8 21.8 24.1 952 1.41 170 45.5 230 38.99 125.9 426.3 102.2 31 13.50 43 17.45 55 21.83 81 30.04 347 180 163.2 6.33 108 40.26 48.8 28.5 46.7 45.3 43.7 42.5 39.82 36.4 42.69 39.1 28 28.2 10.5 28.8 20.3 30.2 68.4 148 132.6 45.73 43.31 51.40 49.14 313 246.6 59.23 57.28 28.3 24.4 31.5 41 52.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 2-87 ∗By N. A. Lange; abridged from “Table of Solubilities of Inorganic Compounds in Water at Various Temperatures” in Lange’s Handbook of Chemistry, 10th ed., McGraw-Hill, New York, 1961 (except for NaCl, which is from CRC Handbook of Chemistry and Physics, 86th ed., CRC Press, 2005). For tables of the solubility of gases in water at various temperatures, Atack (Handbook of Chemical Data, Reinhold, New York, 1957) gives values at closer temperature intervals, usually 1 or 5°C, than are tabulated here. For materials marked by ‡, additional data are given in tables subsequent to this one. For the solubility of various hydrocarbons in water at high pressures see J. Chem. Eng. Data, 4, 212 (1959). 2-88 TABLE 2-20 Solubilities of Inorganic Compounds in Water at Various Temperatures (Continued ) This table shows the grams of anhydrous substance that are soluble in 100 g of water at the temperature in degrees Celsius as indicated; when the name is followed by †, the value is expressed in grams of substance in 100 cm3 of saturated solution. Solid phase gives the hydrated form in equilibrium with the saturated solution. Substance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sodium vanadate (meta) Stannous chloride sulfate Strontium acetate acetate chloride chloride nitrate nitrate nitrate sulfate Sulfur dioxide, 760 mm† Thallium sulfate Thorium sulfate sulfate sulfate sulfate Zinc chlorate chlorate nitrate nitrate sulfate sulfate sulfate Formula NaVO3 SnCl2 SnSO4 Sr(C2H3O2)2 Sr(C2H3O2)2 SrCl2 SrCl2 Sr(NO3)2 Sr(NO3)2 Sr(NO3)2 SrSO4 SO2 Tl2SO4 Th(SO4)2 Th(SO4)2 Th(SO4)2 Th(SO4)2 ZnClO3 ZnClO3 Zn(NO3)2 Zn(NO3)2 ZnSO4 ZnSO4 ZnSO4 Solid phase 0°C 10°C 20°C 30°C 21.10 ° 269.815° 19 25 83.9 4H2O ½H2O 6H2O 2H2O 1H2O 4H2O 9H2O 8H2O 6H2O 4H2O 6H2O 4H2O 6H2O 3H2O 7H2O 6H2O 1H2O 36.9 43.5 43.61 42.95 47.7 41.6 52.9 52.7 40.1 64.0 70.5 0.0113 22.83 2.70 0.74 1.0 1.50 0.0114 11.29 4.87 1.38 1.62 1.90 145.0 16.21 3.70 0.98 1.25 152.5 94.78 41.9 47 200.3 118.3 54.4 40°C 50°C 26.23 60°C 70°C 80°C 36.9 38.8 ° 36.24 36.10 85.9 90.5 93.8 96 98 10.92 12.74 14.61 16.53 18.45 6.64 1.63 1.09 86.6 83.7 80.8 32.97 90°C 100°C 75 18 39.5 58.7 88.6 0.0114 7.81 6.16 1.995 2.45 209.2 65.3 37.35 72.4 81.8 83.8 97.2 90.1 2.998 5.41 4.5 9.21 5.22 4.04 2.54 223.2 36.4 130.4 100.8 139 100 273.1 206.9 70.1 76.8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 SOLUBILITIES 2-89 TABLE 2-21 Solubility as a Function of Temperature and Henry’s Constant at 25çC for Gases in Water Name Acetylene Carbon dioxide Carbon monoxide Ethane Ethylene Helium Hydrogen Methane Nitrogen Oxygen Formula A −156.51 −159.854 −171.764 −250.812 −153.027 −105.9768 −125.939 −338.217 −181.587 −171.2542 C2H2 CO2 CO C2H6 C2H4 He H2 CH4 N2 O2 C D T range, K H at 25°C, atm 21.403 21.6694 23.3376 34.7413 20.5248 14.0094 16.8893 51.9144 24.7981 23.24323 0 −1.10261E-03 0 0 0 0 0 −0.0425831 0 0 274–343 273–353 273–353 275–323 287–346 273–348 273–345 273–523 273–350 273–333 1,330 1,635 58,000 29,400 11,726 142,900 70,800 39,200 84,600 43,400 B 8,160.2 8,741.68 8,296.9 12,695.6 7,965.2 4,259.62 5,528.45 13,282.1 8,632.13 8,391.24 The constants can be used to calculate solubility by the equation ln x = A + B/T + C ln T + DT, where T is in K and x is the mole fraction of the solute dissolved in water when the solute partial pressure is 1 atm. With the assumption that Henry’s law is valid up to 1 atm, H = 1/x. Values of the constants are from P. G. T. Fogg and W. Gerrard, Solubility of Gases in Liquids, Wiley, 1991, New York, and Solubility Data Series, vol. 1, Helium and Neon, IUPAC, Pergamon Press, Oxford, 1979. For higher-temperature behavior and an up-to-date reference list, see R. Fernandez-Prini, J. L. Alvarez, and A. H. Harvey, J. Phys. Chem. Ref. Data 32(2):903, 2003. To find H at temperatures other than 25°C, first find the solubility and then take the reciprocal. TABLE 2-22 Henry’s Constant H for Various Compounds in Water at 25çC Group Paraffin hydrocarbons Olefins Aromatics Aldehydes Ketones Esters Chlorine containing Alcohols Miscellaneous Compound Methane Ethane Propane Butane Pentane Octane Nonane Ethylene Propylene Benzene Toluene o-Xylene Cumene Phenol Acetaldehyde Propionaldehyde Methylethyl ketone Methyl formate Ethyl formate Methyl acetate Butyl acetate Chloromethane Chloroethane Chlorobenzene Methanol Ethanol 1-Propanol 1-Butanol Acrylonitrile Dimethyl sulfide Dimethyl disulfide Methyl mercaptan Ethyl mercaptan Pyridine Formula CH4 C2H6 C3H8 C4H10 C5H12 C8H18 C9H20 C2H4 C3H6 C6H6 C7H8 C8H10 C9H12 C6H6O C2H4O C3H6O C4H8O C2H4O2 C3H6O2 C3H6O2 C6H12O2 CH3Cl C2H5Cl C6H5Cl CH4O C2H6O C3H8O C4H10O C3H3N C2H6S C2H6S2 CH4S C2H6S C5H5N CAS 74-82-8 74-84-0 74-98-6 106-97-8 109-66-0 111-65-9 111-84-2 74-85-1 115-07-1 71-43-2 108-88-3 95-47-6 98-82-8 108-95-2 75-07-0 123-38-6 78-93-3 107-31-3 109-94-4 79-20-9 123-86-4 74-87-3 75-00-3 108-90-7 67-56-1 64-17-5 71-23-8 71-36-3 107-13-1 75-18-3 624-92-0 74-93-1 75-08-1 110-86-1 H, atm† 36,600 26,700 37,800 51,100 70,000 2,74,000 3,29,000 11,700 11,700 299 354 272 724 0.0394 5.56 4.36 2.59 13.6 13.6 5.04 13.6 556 681 204 0.272 0.272 0.507 0.482 5.54 121 68.1 177 161 0.817 Rating∗ 4 3 3 3 3 3 3 3 4 10 10 10 9 7 3 4 5 3 3 3 3 ? 10 10 4 4 3 3 3 3 3 3 3 3 Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York (2016). ∗The ratings reflect DIPPR ESP’s effort to provide a critical evaluation and quality assessment of each data point with 15 being the highest score possible. The rating is not directly correlated with the estimated experimental uncertainty. † Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if used for calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of singlepoint values over the ambient temperature range (4°C < T < 50°C) are presented in Sec. 22, under “Air Pollution Control” > “Biological APC Technologies” > “Estimating Henry’s law constants”. Estimation procedures for the larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H. Harvey, “Avoid Common Pitfalls When Using Henry’s Law,” Chem. Eng. Prog., 103(9), 2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31, pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the databank of 404 compounds of environmental interest and other useful property data.) 2-90 PHYSICAL AnD CHEMICAL DATA TABLE 2-23 Henry’s Constant H for Various Compounds in Water at 25çC from Infinite Dilution Activity Coefficients Compound CAS no. Formula H = γ ∞Pvp, atm Pentane Hexane Heptane Benzene Toluene o-Xylene Cumene Styrene Formaldehyde Acetaldehyde Propanal Acetone Methyl ethyl ketone Methyl n-propyl ketone Formic acid Methyl acetate Ethyl acetate Butyl acetate Chloroethane 1-Chloropropane Chlorobenzene Methanol Ethanol Pyridine Diethyl ether Thiophene 109660 1100543 142825 71432 108883 95476 98,828 100425 50000 75070 123386 67641 78933 107879 64186 79209 141786 123864 75003 74986 108907 67561 64175 110861 60297 110021 C5H12 C6H14 C7H16 C6H6 C7H8 C8H10 C9H12 C8H8 CH2O C2H4O C3H6O C3H6O C4H8O C5H10O CH2O2 C3H6O2 C4H8O2 C6H12O2 C2H5Cl C3H7Cl C6H5Cl CH4O C2H6O C5H5N C4H10O C4H4S 63700 84600 120000 309 344 267 613 145 14.3 4.54 5.45 2.13 3.11 4.60 0.0404 6.38 8.01 12.3 626 792 219 0.263 0.293 0.544 48.7 160 TABLE 2-24 Air* t, °C 0 5 10 15 20 25 30 35 10−4 × H † 4.32 4.88 5.49 6.07 6.64 7.20 7.71 8.23 t, °C 40 45 50 60 70 80 90 100 10−4 × H † 8.70 9.11 9.46 10.1 10.5 10.7 10.8 10.7 ∗International Critical Tables, vol. 3, p. 257. † H is calculated from the absorption coefficients of O2 and N2, taking into consideration the correction for constant argon content. TABLE 2-25 Ammonia-Water at 10 and 20çC* 10°C Mass fraction NH3 in liquid 0.0 0.00467 0.00495 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Henry’s constant H at 25°C is the vapor pressure at 25°C times the infinite dilution activity coefficient, also at 25°C. Infinite dilution activity coefficients are from Mitchell and Jurs, J. Chem. Inf. Comput. Sci. 38: 200 (1998). Henry’s constant is a strong nonlinear function of temperature. A single value measured at one temperature, if used for calculation at a different temperature, can lead to serious errors. Procedures for extrapolation of single-point values over the ambient temperature range (4°C < T < 50°C) are presented in Sec. 22, pp. 22–49, under “Estimating Henry’s law constants.” Estimation procedures for the larger range (4°C < T < 200°C) are presented in F. L. Smith and A. H. Harvey, “Avoid Common Pitfalls When Using Henry’s Law,” Chem. Eng. Prog., 103(9), 2007. See also Y.-L. Huang, J. D. Olson, and G. E. Keller II, “Steam Stripping for Removal of Organic Pollutants from Water. 2. Vapor-Liquid Equilibrium Data,” Ind. Eng. Chem. Res., 31, pp. 1759–1768, 1992. (Also see the Supplementary Material, which contains the databank of 404 compounds of environmental interest and other useful property data.) P, kPa 1.23 1.37 7.07 20.07 47.37 99.84 184.44 292.15 399.03 486.44 554.33 615.05 20°C Mass fraction NH3 in vapor 0.0 0.1 P, kPa 2.34 0.84164 0.95438 0.98565 0.99544 0.99848 0.99943 0.99975 0.99988 0.99995 1.0 2.60 11.95 32.34 73.85 150.56 269.50 416.63 560.61 678.61 771.87 857.48 Mass fraction NH3 in vapor 0.0 0.1 0.82096 0.94541 0.98199 0.99393 0.99783 0.99913 0.99960 0.99980 0.99991 1.0 ∗Selected values from R. Tillner-Roth and D. G. Friend, J. Phys. Chem. Ref. Data 27:63 (1998). This reference lists solubilities for temperatures from −70 to 340°C. Densities, enthalpies, and entropies are listed for both the two-phase and single-phase regions for pressures up to 40 MPa. TABLE 2-26 Carbon Dioxide (CO2)* Liquid mol fraction CO2 × 103 Total pressure, atm 1 2 10 20 30 36 0°C 10°C 15°C 20°C 25°C 35°C 50°C 75°C 100°C 1.445 2.89 12.71 21.23 25.79 0.985 1.946 8.81 15.38 19.80 21.45 0.802 1.587 7.32 13.13 17.49 19.42 0.692 1.374 6.44 11.84 16.22 18.30 0.608 1.207 5.74 10.75 15.05 17.29 0.473 0.943 4.54 8.64 12.80 14.80 0.342 0.683 3.30 6.34 9.10 10.63 0.248 0.495 2.41 4.65 6.78 7.90 0.187 0.373 1.841 3.62 5.35 6.35 ∗Values selected from G. Houghton, A. M. McLean, and P. D. Ritchie, Chem. Eng. Sci. 6:132–137, 1957. SOLUBILITIES TABLE 2-27 Chlorine (Cl2) Partial pressure of Cl2, mmHg TABLE 2-28 Chlorine Dioxide (ClO2) Solubility, g of Cl2 per liter 10°C 20°C 30°C 40°C 50°C 5 10 30 50 100 0.488 0.679 1.221 1.717 2.79 0.451 0.603 1.024 1.354 2.08 0.438 0.575 0.937 1.210 1.773 0.424 0.553 0.873 1.106 1.573 0.412 0.532 0.821 1.025 1.424 0.398 0.512 0.781 0.962 1.313 150 200 250 300 350 3.81 4.78 5.71 2.73 3.35 3.95 4.54 5.13 2.27 2.74 3.19 3.63 4.06 1.966 2.34 2.69 3.03 3.35 1.754 2.05 2.34 2.61 2.86 1.599 1.856 2.09 2.31 2.53 400 450 500 550 600 5.71 6.26 6.85 7.39 7.97 4.48 4.88 5.29 5.71 6.12 3.69 3.98 4.30 4.60 4.91 3.11 3.36 3.61 3.84 4.08 2.74 2.94 3.14 3.33 3.52 650 700 750 800 900 8.52 9.09 9.65 10.21 6.52 6.90 7.29 7.69 8.46 5.21 5.50 5.80 6.08 6.68 4.32 4.54 4.77 4.99 5.44 3.71 3.89 4.07 4.27 4.62 9.27 10.84 13.23 17.07 21.0 7.27 8.42 10.14 13.02 15.84 5.89 6.81 8.05 10.22 12.32 4.97 5.67 6.70 8.38 10.03 18.73 21.7 24.7 27.7 30.8 14.47 16.62 18.84 20.7 23.3 11.70 13.38 15.04 16.75 18.46 Cl2.8H2O2 separates 3000 3500 4000 4500 5000 Partial pressure of Cl2, mmHg Weight of ClO2, grams per liter of solution Vol % of ClO2 in gas phase 0°C 1000 1200 1500 2000 2500 2-91 1 3 5 7 10 11 12 13 14 15 16 0°C 5°C 10°C 15°C 20°C 30°C 40°C 2.00 6.00 10.0 14.0 20.0 1.50 4.7 7.8 10.9 15.5 17.0 18.6 20.3 1.25 3.85 6.30 8.95 12.8 14.0 15.3 16.6 18.0 19.2 20.3 1.00 3.20 5.25 7.35 10.5 11.7 12.8 13.8 14.9 16.0 17.0 0.90 2.70 4.30 6.15 8.80 9.70 10.55 11.5 12.3 13.2 14.2 0.60 1.95 3.20 4.40 6.30 7.00 7.50 8.20 8.80 9.50 10.1 0.46 1.30 2.25 3.20 4.50 5.00 5.45 5.85 6.35 6.80 7.20 Ishi, Chem. Eng. (Japan), 22:153 (1958). TABLE 2-29 Hydrogen Chloride (HCl) Weights of HCl per 100 weights of H2O 78.6 66.7 56.3 47.0 38.9 31.6 25.0 19.05 13.64 8.70 4.17 2.04 Partial pressure of HCl, mmHg 0°C 10°C 20°C 30°C 510 130 29.0 5.7 1.0 0.175 0.0316 0.0056 0.00099 0.000118 0.000018 840 233 56.4 11.8 2.27 0.43 0.084 0.016 0.00305 0.000583 0.000069 0.0000117 399 105.5 23.5 4.90 1.00 0.205 0.0428 0.0088 0.00178 0.00024 0.000044 627 188 44.5 9.90 2.17 0.48 0.106 0.0234 0.00515 0.00077 0.000151 Weights of HCl per 100 weights of H2O Solubility, g of Cl2 per liter 60°C 70°C 80°C 90°C 100°C 110°C 5 10 30 50 100 0.383 0.492 0.743 0.912 1.228 0.369 0.470 0.704 0.863 1.149 0.351 0.447 0.671 0.815 1.085 0.339 0.431 0.642 0.781 1.034 0.326 0.415 0.627 0.747 0.987 0.316 0.402 0.598 0.722 0.950 150 200 250 300 350 1.482 1.706 1.914 2.10 2.28 1.382 1.580 1.764 1.932 2.10 1.294 1.479 1.642 1.793 1.940 1.227 1.396 1.553 1.700 1.831 1.174 1.333 1.480 1.610 1.736 1.137 1.276 1.413 1.542 1.661 400 450 500 550 600 2.47 2.64 2.80 2.97 3.13 2.25 2.41 2.55 2.69 2.83 2.08 2.22 2.35 2.47 2.59 1.965 2.09 2.21 2.32 2.43 1.854 1.972 2.08 2.19 2.29 1.773 1.880 1.986 2.09 2.19 650 700 750 800 900 3.29 3.44 3.59 3.75 4.04 2.97 3.10 3.23 3.37 3.63 2.72 2.84 2.96 3.08 3.30 2.55 2.66 2.76 2.87 3.08 2.41 2.50 2.60 2.69 2.89 2.28 2.37 2.47 2.56 2.74 1000 1200 1500 2000 2500 4.36 4.92 5.76 7.14 8.48 3.88 4.37 5.09 6.26 7.40 3.53 3.95 4.58 5.63 6.61 3.28 3.67 4.23 5.17 6.05 3.07 3.43 3.95 4.78 5.59 2.91 3.25 3.74 4.49 5.25 3000 3500 4000 4500 5000 9.83 11.22 12.54 13.88 15.26 8.52 9.65 10.76 11.91 13.01 7.54 8.53 9.52 10.46 11.42 6.92 7.79 8.65 9.49 10.35 6.38 7.16 7.94 8.72 9.48 5.97 6.72 7.42 8.13 8.84 78.6 66.7 56.3 47.0 38.9 31.6 25.0 19.05 13.64 8.70 4.17 2.04 50°C Partial pressure of HCl, mm Hg 80°C 535 141 35.7 8.9 2.21 0.55 0.136 0.0344 0.0064 0.00140 623 188 54.5 15.6 4.66 1.34 0.39 0.095 0.0245 110°C 760 253 83 28 9.3 3.10 0.93 0.280 Enthalpy and phase-equilibrium data for the binary system HCl-H2O are given by Van Nuys, Trans. Am. Inst. Chem. Engrs., 39, 663 (1943). TABLE 2-30 Hydrogen Sulfide (H2S) t, °C 0 5 10 15 20 25 30 35 10−2 × H 2.68 3.15 3.67 4.23 4.83 5.45 6.09 6.76 t, °C 40 45 50 60 70 80 90 100 10−2 × H 7.45 8.14 8.84 10.3 11.9 13.5 14.4 14.8 International Critical Tables, vol. 3, p. 259. 2-92 PHYSICAL AnD CHEMICAL DATA DEnSITIES Unit Conversions Unless otherwise noted, densities are given in grams per cubic centimeter. To convert to pounds per cubic foot, multiply by 62.43. Temperature conversion: °F = 9⁄5°C + 32. Additional References and Comments The aqueous solution data tables are from International Critical Tables, vol. 3, pp. 115–129, unless otherwise stated. All compositions are in weight percent in vacuo. All density values are d 4t = g/mL in vacuo. For more detailed data on densities, see also the CRC Handbook of Chemistry and Physics, Chemical Rubber Publishing Co., 97th ed.; or http://hbcponline.com. DEnSITIES OF PURE SUBSTAnCES TABLE 2-31 Density (kg/m3) of Saturated Liquid Water from the Triple Point to the Critical Point T, K ρ, kg/m3 T, K ρ, kg/m3 T, K ρ, kg/m3 T, K ρ, kg/m3 T, K ρ, kg/m3 273.160∗ 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306 308 310 312 314 316 318 320 322 324 326 328 330 332 334 336 338 340 342 344 346 348 350 999.793 999.843 999.914 999.919 999.862 999.746 999.575 999.352 999.079 998.758 998.392 997.983 997.532 997.042 996.513 995.948 995.346 994.711 994.042 993.342 992.610 991.848 991.056 990.235 989.387 988.512 987.610 986.682 985.728 984.750 983.747 982.721 981.671 980.599 979.503 978.386 977.247 976.086 974.904 973.702 352 354 356 358 360 362 364 366 368 370 372 374 376 378 380 382 384 386 388 390 392 394 396 398 400 402 404 406 408 410 412 414 416 418 420 422 424 426 428 430 972.479 971.235 969.972 968.689 967.386 966.064 964.723 963.363 961.984 960.587 959.171 957.737 956.285 954.815 953.327 951.822 950.298 948.758 947.199 945.624 944.030 942.420 940.793 939.148 937.486 935.807 934.111 932.398 930.668 928.921 927.157 925.375 923.577 921.761 919.929 918.079 916.212 914.328 912.426 910.507 432 434 436 438 440 442 444 446 448 450 452 454 456 458 460 462 464 466 468 470 472 474 476 478 480 482 484 486 488 490 492 494 496 498 500 502 504 506 508 510 908.571 906.617 904.645 902.656 900.649 898.624 896.580 894.519 892.439 890.341 888.225 886.089 883.935 881.761 879.569 877.357 875.125 872.873 870.601 868.310 865.997 863.664 861.310 858.934 856.537 854.118 851.678 849.214 846.728 844.219 841.686 839.130 836.549 833.944 831.313 828.658 825.976 823.269 820.534 817.772 512 514 516 518 520 522 524 526 528 530 532 534 536 538 540 542 544 546 548 550 552 554 556 558 560 562 564 566 568 570 572 574 576 578 580 582 584 586 588 590 814.982 812.164 809.318 806.441 803.535 800.597 797.629 794.628 791.594 788.527 785.425 782.288 779.115 775.905 772.657 769.369 766.042 762.674 759.263 755.808 752.308 748.762 745.169 741.525 737.831 734.084 730.283 726.425 722.508 718.530 714.489 710.382 706.206 701.959 697.638 693.238 688.757 684.190 679.533 674.781 592 594 596 598 600 602 604 606 608 610 612 614 616 618 620 622 624 626 628 630 632 634 636 638 640 641 642 643 644 645 646 647 647.096† 669.930 664.974 659.907 654.722 649.411 643.97 638.38 632.64 626.74 620.65 614.37 607.88 601.15 594.16 586.88 579.26 571.25 562.81 553.84 544.25 533.92 522.71 510.42 496.82 481.53 473.01 463.67 453.14 440.73 425.05 402.96 357.34 322 ∗Triple point † Critical point From Wagner, W., and Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002. TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) Eqn 2-93 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2 CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 70.906 C1 1.711365 1.016 1.4486 0.79388 1.2332 1.0693 2.4507 1.3261 1.2414 1.0379 2.8963 3.5383 0.77488 3.8469 0.7371 1.0259 0.83573 0.71587 0.72184 0.43743 0.59867 0.60917 0.70797 0.52257 2.1872 0.8226 1.3285 1.796 1.187 1.2346 1.0677 0.81696 0.81856 0.98279 0.97552 1.0877 1.1591 1.1448 0.67794 0.50812 0.89458 0.89137 1.3409 1.033873 0.88443 0.79716 2.768 1.7968 2.897 0.99835 1.955 2.23 C2 0.26355 0.21845 0.25892 0.24119 0.25886 0.20656 0.27448 0.26124 0.25822 0.22465 0.26733 0.25443 0.26114 0.2881 0.25487 0.26666 0.26326 0.24812 0.24606 0.24833 0.22849 0.26925 0.25982 0.25833 0.29527 0.26632 0.2708 0.27065 0.26114 0.27216 0.27188 0.24755 0.24967 0.2683 0.26339 0.26454 0.27085 0.27154 0.2637 0.25238 0.27463 0.27365 0.27892 0.266739 0.25828 0.23168 0.26212 0.28749 0.27532 0.274 0.27884 0.27645 C3 466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15 C4 0.28571 0.26116 0.2529 0.29817 0.2913 0.24699 0.28752 0.2489 0.30701 0.28921 0.27341 0.2888 0.28234 0.29783 0.28571 0.28394 0.30798 0.2857 0.28789 0.27555 0.23567 0.2632 0.32144 0.27026 0.3295 0.2821 0.3012 0.28947 0.3065 0.28707 0.28688 0.24535 0.22023 0.25488 0.26864 0.2843 0.28116 0.28419 0.29318 0.29373 0.28512 0.2953 0.29661 0.28571 0.248 0.28071 0.2908 0.3226 0.2813 0.287 0.28571 0.2926 C5 C6 C7 Tmin, K 149.78 353.33 289.81 200.15 178.45 229.32 192.40 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403.00 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.20 265.85 242.43 154.25 173.00 136.95 164.25 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 199.65 185.30 157.46 133.02 147.43 176.80 267.95 161.30 216.58 161.11 68.15 250.33 89.56 172.12 Density at Tmin 21.423 16.936 17.492 11.626 15.683 20.544 23.692 16.822 14.693 17.254 33.279 43.141 9.6675 35.491 8.9381 11.422 10.074 8.8935 10.008 5.9496 9.9051 7.0651 8.8623 6.4251 20.109 9.9087 15.809 20.787 15.123 14.058 12.62 11.734 11.872 12.035 12.473 14.264 13.894 13.08 8.3365 7.0264 10.585 10.761 14.901 12.602 11.087 13.087 26.828 19.064 30.18 10.843 21.211 24.242 Tmax, K 466.00 761.00 591.95 606.00 508.20 545.50 308.30 506.00 615.00 540.00 132.45 405.65 645.60 150.86 824.00 562.05 689.00 751.00 702.30 830.00 720.15 662.00 718.00 773.00 584.15 670.15 503.80 464.00 452.00 425.00 425.12 680.00 676.00 563.10 535.90 419.50 435.50 428.60 575.40 660.50 570.10 554.00 440.00 537.20 615.70 585.40 304.21 552.00 132.92 556.35 227.51 417.15 Density at Tmax 6.4935 4.6509 5.5948 3.2915 4.7640 5.1767 8.9285 5.0762 4.8075 4.6201 10.8340 13.9070 2.9673 13.3530 2.8921 3.8472 3.1745 2.8852 2.9336 1.7615 2.6201 2.2625 2.7248 2.0229 7.4075 3.0888 4.9058 6.6359 4.5455 4.5363 3.9271 3.3002 3.2786 3.6630 3.7037 4.1117 4.2795 4.2160 2.5709 2.0133 3.2574 3.2573 4.8075 3.8760 3.4243 3.4408 10.5600 6.2500 10.5220 3.6436 7.0112 8.0666 (Continued ) 2-94 TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn Cmpd. no. 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 Name Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–sopropyl amine Di–sopropyl ether Di–sopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Formula C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 CAS 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 Mol. wt. 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 C1 0.8711 1.39625 1.0841 1.8651 1.12465 1.1202 0.9061 0.95937 1.1503 0.58711 1.7805 1.3931 0.88998 0.8243 0.86464 0.92997 1.0897 1.1035 1.7411 0.78578 0.478542 0.41084 0.39348 0.38208 0.43981 0.44289 0.46877 5.2115 0.95523 1.0132 1.1136 0.55941 0.74495 0.74404 0.74858 1.1055 1.2591 1.3897 0.9551 0.89833 0.68184 0.85379 0.9554 0.82227 1.4345 1.173 1.9973 0.6181 0.69213 0.64619 0.89368 0.76327 C2 0.26805 0.26867 0.2581 0.2627 0.2728 0.27669 0.28268 0.2882 0.31861 0.25583 0.26846 0.29255 0.27376 0.26545 0.26888 0.27056 0.28356 0.27035 0.28205 0.27882 0.275162 0.25175 0.2492 0.24645 0.25661 0.27636 0.25875 0.315 0.26364 0.26634 0.24834 0.27243 0.26147 0.26112 0.26276 0.26533 0.27698 0.25678 0.27794 0.26142 0.23796 0.25675 0.26847 0.26314 0.25774 0.22856 0.24653 0.25786 0.26974 0.26881 0.26599 0.26742 C3 632.35 460.35 536.4 416.25 503.15 489 705.85 697.55 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.26 523.1 500.05 576 507.8 543 C4 0.2799 0.28571 0.2741 0.28571 0.28571 0.27646 0.2707 0.2857 0.30104 0.28498 0.26079 0.24913 0.28571 0.28495 0.29943 0.28943 0.25142 0.28699 0.29598 0.31067 0.28571 0.28571 0.28571 0.26125 0.29148 0.27668 0.29479 0.28571 0.29825 0.28571 0.27583 0.29932 0.31526 0.30815 0.30788 0.287 0.30492 0.2902 0.24132 0.2868 0.2062 0.27027 0.2814 0.27369 0.28178 0.28571 0.28153 0.271 0.28571 0.28036 0.28571 0.28571 C5 C6 C7 Tmin, K 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.60 242.00 169.67 179.28 138.13 145.59 189.64 285.00 243.51 304.55 280.05 206.89 247.56 229.15 18.73 210.15 282.85 220.60 175.30 248.39 256.15 326.14 176.19 237.49 178.01 192.50 172.71 301.15 223.35 156.85 169.20 154.56 179.60 136.95 176.85 187.65 204.81 159.95 226.10 Density at Tmin 10.385 17.055 13.702 22.272 13.333 12.855 9.6115 9.5725 9.4494 7.9387 18.517 14.074 9.3804 9.4693 10.09 11.16 11.906 13.47 18.658 8.9048 5.2396 5.3927 5.1809 5.2609 5.7328 5.0048 5.8954 42.945 11.799 11.704 15.358 6.6071 9.1207 9.1658 8.5175 13.549 13.462 17.974 10.925 11.526 10.39 10.575 11.487 10.47 18.006 18.336 27.399 8.0541 8.0673 7.6796 11.029 8.8431 Tmax, K 632.35 460.35 536.40 416.25 503.15 489.00 705.85 697.55 704.65 631.00 400.15 459.93 553.80 650.10 653.00 560.40 511.70 507.00 398.00 664.00 674.00 617.70 722.10 688.00 616.60 696.00 619.85 38.35 628.00 650.15 611.00 584.10 683.95 705.00 684.75 523.00 561.60 510.00 560.00 572.00 736.60 496.60 466.70 557.15 386.44 445.00 351.26 523.10 500.05 576.00 507.80 543.00 Density at Tmax 3.2498 5.1969 4.2003 7.0997 4.1226 4.0486 3.2054 3.3288 3.6104 2.2949 6.6323 4.7619 3.2509 3.1053 3.2157 3.4372 3.8429 4.0817 6.1730 2.8182 1.7391 1.6319 1.5790 1.5503 1.7139 1.6026 1.8117 16.5440 3.6232 3.8042 4.4842 2.0534 2.8491 2.8494 2.8489 4.1665 4.5458 5.4120 3.4364 3.4363 2.8654 3.3254 3.5587 3.1248 5.5657 5.1321 8.1017 2.3970 2.5659 2.4039 3.3598 2.8542 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 1.1717 1.5436 0.7565 0.55873 0.52953 0.54405 1.1058 1.5693 0.89615 0.72352 0.47977 1.0214 1.4029 1.1096 0.48611 1.1819 0.52133 0.659 0.33267 0.18166 1.9122 1.6288 0.8996 1.0936 0.70041 0.48864 0.66085 0.63566 0.61587 0.71751 2.0961 0.7842 1.315 1.3462 1.836 1.1343 0.47428 0.55729 0.8185 0.68162 1.3047 0.7405 0.7908 0.61243 4.2895 1.0146 1.693858 2.2261 3.897011 1.2486 1.938 1.1339 7.2475 0.21897 0.577362 0.25895 0.27784 0.27305 0.25143 0.24358 0.25026 0.27866 0.2679 0.23478 0.28629 0.25428 0.26351 0.27991 0.25189 0.25715 0.2813 0.26218 0.26428 0.24664 0.23351 0.27937 0.27469 0.25856 0.22636 0.26162 0.23894 0.25707 0.25613 0.26477 0.26903 0.27657 0.20702 0.25125 0.23289 0.26024 0.26168 0.25028 0.2714 0.26929 0.25152 0.2694 0.25563 0.266 0.24681 0.28587 0.27277 0.269323 0.25072 0.331636 0.20352 0.24225 0.24741 0.41865 0.23642 0.250575 473.2 437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587 766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620 0.27289 0.2572 0.27408 0.27758 0.26809 0.2658 0.31082 0.2882 0.28091 0.27121 0.30722 0.28421 0.2741 0.3311 0.28571 0.3047 0.31033 0.2766 0.28571 0.28571 0.29187 0.23178 0.278 0.25522 0.28454 0.28421 0.31103 0.27829 0.28054 0.27733 0.29147 0.20254 0.21868 0.23357 0.2696 0.2791 0.25442 0.29538 0.30621 0.3182 0.27866 0.2795 0.292 0.30858 0.28776 0.28291 0.28571 0.27343 0.28571 0.25178 0.24435 0.2612 0.24096 0.28571 0.28571 240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 212.72 141.23 274.18 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 159.05 189.60 192.15 178.20 238.45 258.15 175.15 161.84 134.71 104.00 284.29 260.15 195.20 160.65 193.55 155.15 180.00 140.00 204.15 125.26 199.25 145.65 167.55 53.48 230.94 129.95 131.35 155.15 275.60 281.45 187.55 2.20 295.13 229.80 13.767 16.964 9.031 7.3417 7.5783 7.6258 12.413 18.95 13.954 7.9932 6.2334 12.898 15.556 14.111 5.6397 11.838 6.2648 7.9929 4.5205 2.7293 21.64 19.41 11.478 17.588 9.0407 7.2908 8.2198 8.4912 7.8679 9.0179 23.326 15.055 18.31 21.45 23.477 14.006 6.926 6.612 9.9236 8.9749 16.242 9.6317 9.8474 8.6934 44.888 11.374 20.099 29.345 30.92 25.488 26.806 15.702 37.115 3.2189 7.7462 473.20 437.20 500.00 591.15 606.15 596.15 615.00 400.10 649.60 537.30 766.00 402.00 503.04 729.00 777.40 587.00 766.80 550.00 658.00 768.00 305.32 514.00 523.30 456.15 617.15 698.00 655.00 571.00 609.15 569.50 282.34 593.00 720.00 537.00 469.15 508.40 674.60 583.00 489.00 567.00 499.15 546.00 500.23 559.95 144.12 560.09 375.31 317.42 420.00 771.00 588.00 490.15 5.20 736.00 620.00 4.5248 5.5557 2.7706 2.2222 2.1739 2.1739 3.9683 5.8578 3.8170 2.5272 1.8868 3.8761 5.0120 4.4051 1.8904 4.2016 1.9884 2.4936 1.3488 0.7780 6.8447 5.9296 3.4793 4.8312 2.6772 2.0450 2.5707 2.4818 2.3261 2.6670 7.5789 3.7880 5.2338 5.7804 7.0550 4.3347 1.8950 2.0534 3.0395 2.7100 4.8430 2.8968 2.9729 2.4814 15.0050 3.7196 6.2893 8.8788 11.7510 6.1350 8.0000 4.5831 17.3120 0.9262 2.3041 2-95 (Continued ) 2-96 TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn Cmpd. no. 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 Name Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Formula C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CAS 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 Mol. wt. 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 C1 0.61259 0.53066 0.55687 0.59339 0.59268 0.58247 0.66016 0.58622 0.67304 0.23289 0.668504 0.70824 0.62833 0.70093 0.67393 0.67816 0.67666 0.76925 0.78045 0.66372 0.84427 0.76277 1.0516 5.414 2.832 3.342 1.3413 2.8061 2.7672 0.88575 1.2801 0.87969 0.87025 2.9214 2.3267 0.88268 1.13 1.6085 0.97286 1.39 0.53382 0.84623 0.91991 0.72762 0.8189 0.91619 0.93391 1.1157 0.8363 0.75509 0.94575 0.76983 C2 0.26211 0.24729 0.24725 0.2602 0.25663 0.25279 0.26657 0.2726 0.26045 0.23659 0.252695 0.26411 0.25598 0.26776 0.25948 0.25634 0.25578 0.26809 0.26065 0.27345 0.27185 0.25248 0.16613 0.34893 0.2832 0.2729 0.18589 0.19362 0.27369 0.25736 0.2828 0.24543 0.24383 0.28976 0.27073 0.23568 0.2593 0.26436 0.26267 0.21405 0.23274 0.24625 0.27815 0.25244 0.26974 0.26752 0.27275 0.27671 0.27514 0.27183 0.26008 0.26173 C3 540.2 677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.56 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5 C4 0.28141 0.28289 0.31471 0.26968 0.27766 0.29818 0.28571 0.29644 0.28388 0.28571 0.28571 0.27537 0.25304 0.24919 0.26552 0.28365 0.27746 0.28571 0.28571 0.29185 0.2771 0.31611 0.1898 0.2706 0.28571 0.3217 0.28206 0.29847 0.29015 0.26265 0.2972 0.28571 0.28571 0.28881 0.24713 0.27379 0.2764 0.27987 0.2508 0.2275 0.28147 0.29041 0.28667 0.28571 0.23573 0.28164 0.2578 0.30821 0.27553 0.29127 0.30807 0.26879 C5 C6 C7 Tmin, K 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 158.97 259.83 189.79 187.68 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 193.00 155.95 135.58 139.39 160.15 157.48 175.30 183.45 187.35 Density at Tmin 7.6998 7.2212 7.5022 7.5173 7.5751 7.5514 8.2257 6.7277 8.4922 3.415 8.8708 8.747 8.0964 8.456 8.5181 8.7319 8.7631 9.5815 10.021 7.7733 10.23 10.133 31.934 38.487 27.985 34.854 27.202 58.861 29.13 11.42 13.561 11.417 11.834 28.18 27.915 13.012 14.475 19.031 12.203 25.378 8.2202 11.994 10.764 9.9915 10.248 11.332 11.216 12.581 9.7581 9.0056 11.519 9.7638 Tmax, K 540.20 677.30 632.30 608.30 606.60 611.40 537.40 645.00 547.00 723.00 594.00 507.60 660.20 611.30 585.30 587.61 582.82 504.00 544.00 623.00 516.20 549.00 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605.00 471.85 834.00 662.00 190.56 512.50 718.00 506.55 402.40 536.00 430.05 693.00 490.00 460.40 643.00 577.20 465.00 470.00 492.00 512.74 593.00 463.20 554.50 Density at Tmax 2.3371 2.1459 2.2523 2.2805 2.3095 2.3042 2.4765 2.1505 2.5841 0.9844 2.6455 2.6816 2.4546 2.6178 2.5972 2.6455 2.6455 2.8694 2.9942 2.4272 3.1056 3.0211 6.3300 15.5160 10.0000 12.2460 7.2156 14.4930 10.1110 3.4417 4.5265 3.5843 3.5691 10.0820 8.5942 3.7452 4.3579 6.0845 3.7037 6.4938 2.2936 3.4365 3.3072 2.8823 3.0359 3.4248 3.4241 4.0320 3.0395 2.7778 3.6364 2.9413 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 1.0674 0.73109 0.7013 0.70973 0.72836 0.84758 0.88824 0.9109 0.97608 1.2635 0.93767 1.067 1.525 0.84005 0.71687 1.0228 0.97887 0.86567 0.78912 1.9323 0.7761 0.4416 0.72701 0.71004 1.0631 0.92128 1.1446 0.9147 0.96145 0.87496 1.3052 0.64856 0.817948 1.2587 0.6348 7.3718 1.0024 3.2091 2.3736 1.3728 2.781 5.246 0.19199 0.473233 0.46321 0.41582 0.43682 0.419258 0.48661 0.47377 0.52152 0.20448 0.525901 0.5266 0.48251 0.26257 0.26971 0.266 0.26544 0.27241 0.27037 0.26914 0.276 0.28209 0.27878 0.25035 0.27102 0.2634 0.27638 0.26453 0.20692 0.27017 0.26836 0.25915 0.28018 0.25068 0.2521 0.26754 0.26981 0.27506 0.25442 0.2724 0.2594 0.26536 0.26862 0.26757 0.25877 0.269105 0.26433 0.25838 0.3067 0.23655 0.2861 0.2817 0.23793 0.27244 0.3044 0.23337 0.256918 0.25444 0.24284 0.25161 0.241912 0.25722 0.27052 0.25918 0.23474 0.25664 0.25693 0.25196 442 572.1 686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5 654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26 0.26569 0.29185 0.28571 0.26016 0.2478 0.28258 0.27874 0.26756 0.22529 0.2744 0.29964 0.29364 0.2806 0.27645 0.28918 0.28571 0.28998 0.28364 0.26512 0.28523 0.29773 0.28532 0.28268 0.29974 0.2758 0.27586 0.28172 0.2774 0.30088 0.30259 0.28799 0.31444 0.28571 0.25819 0.27727 0.2786 0.278 0.2966 0.29529 0.29601 0.2882 0.242 0.28571 0.28571 0.28571 0.30036 0.2498 0.28571 0.28571 0.30284 0.29177 0.28571 0.28571 0.28571 0.26842 139.05 146.58 285.15 280.15 269.15 130.73 146.62 168.54 182.55 160.00 186.48 167.23 174.15 188.00 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 113.54 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 151.15 333.15 24.56 183.63 63.15 66.46 244.60 182.30 109.50 305.04 267.30 219.66 285.55 268.15 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65 13.626 9.0173 8.2091 8.2931 8.2628 10.491 10.98 10.538 10.789 13.995 12.663 12.671 18.811 9.3871 8.8617 17.666 11.933 10.46 10.352 21.564 10.176 5.938 9.2041 8.445 12.574 10.556 13.507 11.678 12.043 10.689 15.791 8.0099 9.7955 15.691 7.7545 61.796 15.556 31.063 26.555 19.632 27.928 44.487 2.8889 5.9415 6.0427 5.7592 5.8496 6.0223 6.3717 5.4532 6.5369 3.0418 6.6608 6.7049 6.3107 442.00 572.10 686.00 614.00 617.00 532.70 542.00 526.00 483.00 437.80 535.50 533.00 487.20 497.00 574.60 488.00 464.48 553.40 553.10 469.95 566.00 694.00 497.70 546.49 407.80 506.20 417.90 530.60 476.25 565.00 352.50 654.00 497.10 437.00 748.40 44.40 593.00 126.20 234.00 588.15 309.57 180.15 758.00 658.50 594.60 710.70 670.90 649.50 593.10 681.00 598.05 747.00 638.90 568.70 694.26 4.0652 2.7107 2.6365 2.6738 2.6738 3.1349 3.3003 3.3004 3.4602 4.5322 3.7454 3.9370 5.7897 3.0395 2.7100 4.9430 3.6232 3.2258 3.0450 6.8966 3.0960 1.7517 2.7174 2.6316 3.8650 3.6211 4.2019 3.5262 3.6232 3.2572 4.8780 2.5063 3.0395 4.7619 2.4568 24.0360 4.2376 11.2170 8.4260 5.7698 10.2080 17.2340 0.8227 1.8420 1.8205 1.7123 1.7361 1.7331 1.8918 1.7513 2.0122 0.8711 2.0492 2.0496 1.9150 2-97 (Continued ) 2-98 TABLE 2-32 Densities of Inorganic and Organic Liquids (mol/dm3) (Continued ) Eqn Cmpd. no. 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 Name 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Formula C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 CAS 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 Mol. wt. 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 C1 0.48979 0.52497 0.50006 0.5108 0.55449 0.52577 0.58945 1.1911 3.9143 3.3592 0.25142 0.85658 0.84947 0.73455 0.81754 0.81577 0.90411 0.71811 0.89816 0.65858 0.75345 0.8491 0.92099 0.45554 1.3798 0.63163 0.5393 1.6087 1.3757 1.2457 1.1799 0.61255 1.2861 1.0969 0.91281 0.73041 0.9195 0.57233 1.4403 0.915 1.093 1.0714 1.0923 0.83228 1.1945 0.7397 C2 0.24931 0.26186 0.24851 0.25386 0.25952 0.27234 0.26052 0.27038 0.28772 0.29884 0.23837 0.26811 0.26726 0.25636 0.26732 0.26594 0.27207 0.24129 0.26608 0.25367 0.27047 0.2352 0.25419 0.2523 0.31598 0.23373 0.22704 0.26543 0.27453 0.27281 0.2644 0.26769 0.26236 0.25568 0.22125 0.25456 0.23878 0.25171 0.26852 0.26134 0.27762 0.27214 0.26106 0.25385 0.24128 0.2603 C3 652.3 629.8 632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85 538 517 536.6 626 683 259 636 C4 0.27824 0.25257 0.29942 0.26735 0.28571 0.30063 0.28532 0.28571 0.2924 0.28523 0.28571 0.27354 0.27789 0.25522 0.25348 0.25551 0.30669 0.27996 0.28571 0.28571 0.30583 0.353 0.31077 0.24841 0.32768 0.28571 0.248 0.29895 0.29359 0.23994 0.24653 0.28571 0.3004 0.26857 0.26811 0.27666 0.2461 0.29616 0.28775 0.28 0.29781 0.29481 0.20459 0.23658 0.16693 0.3009 C5 C6 C7 Tmin, K 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.35 80.15 283.07 191.59 143.42 239.15 195.56 200.00 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 146.95 185.26 199.00 165.00 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15 388.85 186.35 242.54 Density at Tmin 6.5738 6.5625 6.6477 6.6283 7.2155 6.0987 7.4832 12.405 40.77 33.361 3.6423 10.353 10.474 9.5869 10.061 10.017 10.398 10.102 11.521 9.073 8.8575 12.532 12.24 5.9853 11.244 9.6466 8.2218 19.479 16.583 15.206 14.663 7.4763 16.075 13.935 16.067 9.7941 13.764 7.9821 18.07 11.59 12.61 12.716 14.363 10.082 15.635 9.1088 Tmax, K 652.30 629.80 632.70 627.70 566.90 667.30 574.00 828.00 154.58 261.00 708.00 566.10 469.70 639.16 588.10 561.00 561.08 560.95 464.80 584.30 598.00 481.20 519.00 869.00 694.25 653.00 791.00 394.00 369.83 536.80 508.30 636.00 503.60 600.81 561.30 549.73 496.95 638.35 364.85 538.00 517.00 536.60 626.00 683.00 259.00 636.00 Density at Tmax 1.9646 2.0048 2.0122 2.0121 2.1366 1.9306 2.2626 4.4053 13.6050 11.2410 1.0547 3.1949 3.1784 2.8653 3.0583 3.0675 3.3231 2.9761 3.3755 2.5962 2.7857 3.6101 3.6232 1.8055 4.3667 2.7024 2.3754 6.0607 5.0111 4.5662 4.4626 2.2883 4.9020 4.2901 4.1257 2.8693 3.8508 2.2738 5.3638 3.5012 3.9370 3.9369 4.1841 3.2786 4.9507 2.8417 105 105 105 105 105 105 100 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 105 100 119 105 105 105 313 314 315 316 317 318 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 342 343 344 345 Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water Water m-Xylene o-Xylene p-Xylene C4H6O4 O2S F6S O3S C8H6O4 C18H14 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O H2O C8H10 C8H10 C8H10 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 7732-18-5 108-38-3 95-47-6 106-42-3 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 18.01528 106.165 106.165 106.165 0.65882 2.106 1.3587 1.4969 0.41922 0.3448 5.7136 0.27248 1.2543 0.67717 1.1628 0.58988 1.2874 0.8792 0.9062 0.29934 0.7035 1.0116 0.6531 0.60394 0.59059 0.6028 0.48195 0.37378 0.36703 0.33113 0.9591 1.2703 1.5115 0.59595 –13.851 17.874 0.68902 0.69962 0.67752 0.21741 0.25842 0.2701 0.19013 0.17775 0.25116 –0.003474 0.24007 0.28084 0.27772 0.28954 0.27201 0.28194 0.27136 0.25475 0.2433 0.27386 0.25683 0.27002 0.25956 0.27424 0.27446 0.23093 0.21379 0.24876 0.23676 0.2593 0.26041 0.2707 0.24314 0.64038 35.618 0.26086 0.26143 0.25887 838 430.75 318.69 490.85 883.6 857 0.28571 0.2895 0.2921 0.4359 0.28571 0.29268 693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 –0.0019124 19.655 617 630.3 616.2 0.28571 0.2912 0.2878 0.28674 0.27341 0.30781 0.29241 0.31 0.28571 0.2872 0.2696 0.26268 0.27713 0.2847 0.2741 0.28571 0.29905 0.28571 0.2762 0.27448 0.297 0.2716 0.24856 1.8211E-06 –9.1306 0.27479 0.27365 0.27596 –31.367 –813.56 – 17421000 460.85 197.67 223.15 289.95 700.15 329.35 288.15 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.50 267.76 158.45 156.08 243.15 229.33 165.78 172.22 398.40 354.00 247.57 288.45 180.35 173.15 119.36 178.35 273.16 273.16 225.30 247.98 286.41 10.21 25.298 12.631 24.241 7.102 4.5526 4.7126 3.889 13.998 7.638 12.408 5.7242 13.43 10.487 11.478 4.1817 8.2843 13.144 7.7278 7.689 6.9146 7.0934 7.0825 6.4521 4.9453 4.8594 12.287 15.664 18.481 8.8236 55.497 55.487 8.648 8.6229 8.1614 838.00 430.75 318.69 490.85 883.60 857.00 313.19 693.00 540.15 720.00 631.95 568.00 579.35 591.75 602.00 675.00 535.15 433.25 664.50 649.10 543.80 573.50 846.00 828.00 639.00 703.90 519.13 454.00 432.00 543.15 353.15 647.096 617.00 630.30 616.20 3.0303 8.1495 5.0304 7.8730 2.3585 1.3728 4.6256 1.1350 4.4662 2.4383 4.0160 2.1686 4.5662 3.2400 3.5572 1.2303 2.5688 3.9388 2.4187 2.3268 2.1536 2.1963 2.0870 1.7484 1.4754 1.3986 3.6988 4.8781 5.5837 2.4511 54.0010 17.8740 2.6413 2.6761 2.6172 Except for o-terphenyl and water, liquid density ρ is calculated by Eqn 105: ρ = C1/(C2[1 + (1 – T/C3)^C4]) where ρ is in mol/dm3 and T is in K. The pressure is equal to the vapor pressure for pressures greater than 1 atm and equal to 1 atm when the vapor pressure is less than 1 atm. Equation (2-100), used for the limited temperature ranges as noted for o-terphenyl and water, is ρ = C1 + C2T + C3T 2 + C4T 3. Equation (2-119), used for water, is ρ = C1 + C2τ1/3 + C3τ2/3 + C4τ5/3 + C5τ16/3 + C6τ43/3 + C7τ110/3 where τ = 1 − T/TC, and TC = critical temperature (647.096 K). Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016). 2-99 2-100 PHYSICAL AnD CHEMICAL DATA DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM TABLE 2-33 Ammonia (nH3)* % −15°C −10°C 1 2 4 8 12 16 20 24 28 30 −5°C 0°C 5°C 10°C 20°C 25°C TABLE 2-38 Ferric nitrate [Fe(nO3)3]* d 415 % 0.9943 0.9954 0.9959 0.9958 0.9955 0.9939 0.993 32 0.889 .9906 .9915 .9919 .9917 .9913 .9895 .988 36 .877 .9834 .9840 .9842 .9837 .9832 .9811 .980 40 .865 0.970 .9701 .9701 .9695 .9686 .9677 .9651 .964 45 .849 .958 .9576 .9571 .9561 .9548 .9534 .9501 .948 50 .832 .947 .9461 .9450 .9435 .9420 .9402 .9362 .934 60 .796 .9353 .9335 .9316 .9296 .9275 .9229 70 .755 .9249 .9226 .9202 .9179 .9155 .9101 80 .711 .9150 .9122 .9094 .9067 .9040 .8980 90 .665 .9101 .9070 .9040 .9012 .8983 .8920 100 .618 0°C 10°C 20°C 30°C 50°C 80°C 100°C 1 2 4 8 12 16 20 24 1.0033 1.0067 1.0135 1.0266 1.0391 1.0510 1.0625 1.0736 1.0029 1.0062 1.0126 1.0251 1.0370 1.0485 1.0596 1.0705 1.0013 1.0045 1.0107 1.0227 1.0344 1.0457 1.0567 1.0674 0.9987 1.0018 1.0077 1.0195 1.0310 1.0422 1.0532 1.0641 0.9910 .9940 .9999 1.0116 1.0231 1.0343 1.0454 1.0564 0.9749 .9780 .9842 .9963 1.0081 1.0198 1.0312 1.0426 0.9617 .9651 .9718 .9849 .9975 1.0096 1.0213 1.0327 ∗International Critical Tables, vol. 3, p. 60. TABLE 2-35 Calcium Chloride (CaCl2)* 2 4 8 12 16 20 25 30 35 40 1.0708 1.1083 1.1471 1.1874 1 2 4 8 12 16 20 25 1.0065 1.0144 1.0304 1.0636 1.0989 1.1359 1.1748 1.2281 Ammonium Chloride (nH4Cl)* % % −5°C d4 ∗International Critical Tables, vol. 3, p. 68. ∗International Critical Tables, vol. 3, p. 59. TABLE 2-34 18 % 0°C 20°C 30°C 40°C 60°C 80°C 100°C 120°C† 140°C 1.0171 1.0346 1.0703 1.1072 1.1454 1.1853 1.2376 1.2922 1.0148 1.0316 1.0659 1.1015 1.1386 1.1775 1.2284 1.2816 1.3373 1.3957 1.0120 1.0286 1.0626 1.0978 1.1345 1.1730 1.2236 1.2764 1.3316 1.3895 1.0084 1.0249 1.0586 1.0937 1.1301 1.1684 1.2186 1.2709 1.3255 1.3826 0.9994 1.0158 1.0492 1.0840 1.1202 1.1581 1.2079 1.2597 1.3137 1.3700 0.9881 1.0046 1.0382 1.0730 1.1092 1.1471 1.1965 1.2478 1.3013 1.3571 0.9748 0.9915 1.0257 1.0610 1.0973 1.1352 1.1846 1.2359 1.2893 1.3450 0.9596 0.9765 1.0111 1.0466 1.0835 1.1219 0.9428 0.9601 0.9954 1.0317 1.0691 1.1080 ∗International Critical Tables, vol. 3, pp. 72–73. † Corrected to atmospheric pressure. TABLE 2-36 Ferric Chloride (FeCl3)* % 0°C 10°C 20°C 30°C 1 2 4 8 12 16 20 25 30 35 40 45 50 1.0086 1.0174 1.0347 1.0703 1.1088 1.1475 1.1870 1.2400 1.2970 1.3605 1.4280 1.0084 1.0168 1.0341 1.0692 1.1071 1.1449 1.1847 1.2380 1.2950 1.3580 1.4235 1.4920 1.5610 1.0068 1.0152 1.0324 1.0669 1.1040 1.1418 1.1820 1.2340 1.2910 1.3530 1.4175 1.4850 1.5510 1.0040 1.0122 1.0292 1.0636 1.1006 1.1386 1.1786 1.2290 1.2850 1.3475 1.4115 TABLE 2-37 Ferric Sulfate [Fe2(SO4)3]* 1 2 4 8 12 16 20 30 40 50 60 % 15°C 18°C TABLE 2-40 Hydrogen Cyanide (HCn)* 20°C 0.2 1.00068 1.0002 0.4 1.00275 1.0022 0.8 1.00645 1.0062 1.0 1.0090 1.0085 1.0082 4.0 1.0380 1.0375 8.0 1.0790 1.0785 12.0 1.1235 1.1220 16.0 1.1690 1.1675 20.0 1.2150 1.2135 ∗International Critical Tables, vol. 3, p. 68. 17.5 d4 1.0072 1.0157 1.0327 1.0670 1.1028 1.1409 1.1811 1.3073 1.4487 1.6127 1.7983 ∗International Critical Tables, vol. 3, p. 68. 15 % d4 1 2 4 8 12 16 82 90 100 0.998 0.996 0.993 0.984 0.971 0.956 0.752 0.724 0.691 ∗International Critical Tables, vol. 3, p. 61. TABLE 2-41 Hydrogen Chloride (HCl) % −5°C 0°C 10°C 20°C 40°C 60°C 80°C 100°C 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 1.0048 1.0104 1.0213 1.0321 1.0428 1.0536 1.0645 1.0754 1.0864 1.0975 1.1087 1.1200 1.1314 1.1426 1.1537 1.1648 1.0052 1.0106 1.0213 1.0319 1.0423 1.0528 1.0634 1.0741 1.0849 1.0958 1.1067 1.1177 1.1287 1.1396 1.1505 1.1613 1.0048 1.0100 1.0202 1.0303 1.0403 1.0504 1.0607 1.0711 1.0815 1.0920 1.1025 1.1131 1.1238 1.1344 1.1449 1.1553 1.0032 1.0082 1.0181 1.0279 1.0376 1.0474 1.0574 1.0675 1.0776 1.0878 1.0980 1.1083 1.1187 1.1290 1.1392 1.1493 1.1593 1.1691 1.1789 1.1885 1.1980 0.9970 1.0019 1.0116 1.0211 1.0305 1.0400 1.0497 1.0594 1.0692 1.0790 1.0888 1.0986 1.1085 1.1183 1.1280 1.1376 0.9881 0.9930 1.0026 1.0121 1.0215 1.0310 1.0406 1.0502 1.0598 1.0694 1.0790 1.0886 1.0982 1.1076 1.1169 1.1260 0.9768 0.9819 0.9919 1.0016 1.0111 1.0206 1.0302 1.0398 1.0494 1.0590 1.0685 1.0780 1.0874 1.0967 1.1058 1.1149 0.9636 0.9688 0.9791 0.9892 0.9992 1.0090 1.0188 1.0286 1.0383 1.0479 1.0574 1.0668 1.0761 1.0853 1.0942 1.1030 ∗International Critical Tables, vol. 3, p. 54. TABLE 2-42 Hydrogen Peroxide (H2O2)* ∗International Critical Tables, vol. 3, p. 68. % TABLE 2-39 Ferrous Sulfate (FeSO4)* 18 18 % d4 % d4 1 2 4 6 8 10 12 14 16 18 20 22 24 1.0022 1.0058 1.0131 1.0204 1.0277 1.0351 1.0425 1.0499 1.0574 1.0649 1.0725 1.0802 1.0880 26 28 30 35 40 45 50 55 60 70 80 90 100 1.0959 1.1040 1.1122 1.1327 1.1536 1.1749 1.1966 1.2188 1.2416 1.2897 1.3406 1.3931 1.4465 ∗International Critical Tables, vol. 3, p. 54. DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM 2-101 TABLE 2-43 nitric Acid (HnO3)* % 0°C 5°C 10°C 15°C 20°C 25°C 30°C 40°C 50°C 60°C 80°C 100°C 1 2 3 4 1.0058 1.0117 1.0176 1.0236 1.00572 1.01149 1.01730 1.02315 1.00534 1.01099 1.01668 1.02240 1.00464 1.01018 1.01576 1.02137 1.00364 1.00909 1.01457 1.02008 1.00241 1.00778 1.01318 1.01861 1.0009 1.0061 1.0114 1.0168 0.9973 1.0025 1.0077 1.0129 0.9931 0.9982 1.0033 1.0084 0.9882 0.9932 0.9982 1.0033 0.9767 0.9816 0.9865 0.9915 0.9632 0.9681 0.9730 0.9779 5 6 7 8 9 1.0296 1.0357 1.0418 1.0480 1.0543 1.02904 1.03497 1.0410 1.0471 1.0532 1.02816 1.03397 1.0399 1.0458 1.0518 1.02702 1.03272 1.0385 1.0443 1.0502 1.02563 1.03122 1.0369 1.0427 1.0485 1.02408 1.02958 1.0352 1.0409 1.0466 1.0222 1.0277 1.0333 1.0389 1.0446 1.0182 1.0235 1.0289 1.0344 1.0399 1.0136 1.0188 1.0241 1.0295 1.0349 1.0084 1.0136 1.0188 1.0241 1.0294 0.9965 1.0015 1.0066 1.0117 1.0169 0.9829 0.9879 0.9929 0.9980 1.0032 10 11 12 13 14 1.0606 1.0669 1.0733 1.0797 1.0862 1.0594 1.0656 1.0718 1.0781 1.0845 1.0578 1.0639 1.0700 1.0762 1.0824 1.0561 1.0621 1.0681 1.0742 1.0803 1.0543 1.0602 1.0661 1.0721 1.0781 1.0523 1.0581 1.0640 1.0699 1.0758 1.0503 1.0560 1.0618 1.0676 1.0735 1.0455 1.0511 1.0567 1.0624 1.0681 1.0403 1.0458 1.0513 1.0568 1.0624 1.0347 1.0401 1.0455 1.0509 1.0564 1.0221 1.0273 1.0326 1.0379 1.0432 1.0083 1.0134 1.0186 1.0238 1.0289 15 16 17 18 19 1.0927 1.0992 1.1057 1.1123 1.1189 1.0909 1.0973 1.1038 1.1103 1.1168 1.0887 1.0950 1.1014 1.1078 1.1142 1.0865 1.0927 1.0989 1.1052 1.1115 1.0842 1.0903 1.0964 1.1026 1.1088 1.0818 1.0879 1.0940 1.1001 1.1062 1.0794 1.0854 1.0914 1.0974 1.1034 1.0739 1.0797 1.0855 1.0913 1.0972 1.0680 1.0737 1.0794 1.0851 1.0908 1.0619 1.0675 1.0731 1.0787 1.0843 1.0485 1.0538 1.0592 1.0646 1.0700 1.0341 1.0393 1.0444 1.0496 1.0547 20 21 22 23 24 1.1255 1.1322 1.1389 1.1457 1.1525 1.1234 1.1300 1.1366 1.1433 1.1501 1.1206 1.1271 1.1336 1.1402 1.1469 1.1178 1.1242 1.1306 1.1371 1.1437 1.1150 1.1213 1.1276 1.1340 1.1404 1.1123 1.1185 1.1247 1.1310 1.1374 1.1094 1.1155 1.1217 1.1280 1.1343 1.1031 1.1090 1.1150 1.1210 1.1271 1.0966 1.1024 1.1083 1.1142 1.1201 1.0899 1.0956 1.1013 1.1070 1.1127 1.0754 1.0808 1.0862 1.0917 1.0972 1.0598 1.0650 1.0701 1.0753 1.0805 25 26 27 28 29 1.1594 1.1663 1.1733 1.1803 1.1874 1.1569 1.1638 1.1707 1.1777 1.1847 1.1536 1.1603 1.1670 1.1738 1.1807 1.1503 1.1569 1.1635 1.1702 1.1770 1.1469 1.1534 1.1600 1.1666 1.1733 1.1438 1.1502 1.1566 1.1631 1.1697 1.1406 1.1469 1.1533 1.1597 1.1662 1.1332 1.1394 1.1456 1.1519 1.1582 1.1260 1.1320 1.1381 1.1442 1.1503 1.1185 1.1244 1.1303 1.1362 1.1422 1.1027 1.1083 1.1139 1.1195 1.1251 1.0857 1.0910 1.0963 1.1016 1.1069 30 31 32 33 34 1.1945 1.2016 1.2088 1.2160 1.2233 1.1917 1.1988 1.2059 1.2131 1.2203 1.1876 1.1945 1.2014 1.2084 1.2155 1.1838 1.1906 1.1974 1.2043 1.2113 1.1800 1.1867 1.1934 1.2002 1.2071 1.1763 1.1829 1.1896 1.1963 1.2030 1.1727 1.1792 1.1857 1.1922 1.1988 1.1645 1.1708 1.1772 1.1836 1.1901 1.1564 1.1625 1.1687 1.1749 1.1812 1.1482 1.1542 1.1602 1.1662 1.1723 1.1307 1.1363 1.1419 1.1476 1.1533 1.1122 1.1175 1.1228 1.1281 1.1335 35 36 37 38 39 1.2306 1.2375 1.2444 1.2513 1.2581 1.2275 1.2344 1.2412 1.2479 1.2546 1.2227 1.2294 1.2361 1.2428 1.2494 1.2183 1.2249 1.2315 1.2381 1.2446 1.2140 1.2205 1.2270 1.2335 1.2399 1.2098 1.2163 1.2227 1.2291 1.2354 1.2055 1.2119 1.2182 1.2245 1.2308 1.1966 1.2028 1.2089 1.2150 1.2210 1.1876 1.1936 1.1995 1.2054 1.2112 1.1784 1.1842 1.1899 1.1956 1.2013 1.1591 1.1645 1.1699 1.1752 1.1805 1.1390 1.1440 1.1490 1.1540 1.1589 40 41 42 43 44 1.2649 1.2717 1.2786 1.2854 1.2922 1.2613 1.2680 1.2747 1.2814 1.2880 1.2560 1.2626 1.2692 1.2758 1.2824 1.2511 1.2576 1.2641 1.2706 1.2771 1.2463 1.2527 1.2591 1.2655 1.2719 1.2417 1.2480 1.2543 1.2606 1.2669 1.2370 1.2432 1.2494 1.2556 1.2618 1.2270 1.2330 1.2390 1.2450 1.2510 1.2170 1.2229 1.2287 1.2345 1.2403 1.2069 1.2126 1.2182 1.2238 1.2294 1.1858 1.1911 1.1963 1.2015 1.2067 1.1638 1.1687 1.1735 1.1783 1.1831 45 46 47 48 49 1.2990 1.3058 1.3126 1.3194 1.3263 1.2947 1.3014 1.3080 1.3147 1.3214 1.2890 1.2955 1.3021 1.3087 1.3153 1.2836 1.2901 1.2966 1.3031 1.3096 1.2783 1.2847 1.2911 1.2975 1.3040 1.2732 1.2795 1.2858 1.2921 1.2984 1.2680 1.2742 1.2804 1.2867 1.2929 1.2570 1.2630 1.2690 1.2750 1.2811 1.2461 1.2519 1.2577 1.2635 1.2693 1.2350 1.2406 1.2462 1.2518 1.2575 1.2119 1.2171 1.2223 1.2275 1.2328 1.1879 1.1927 1.1976 1.2024 1.2073 50 51 52 53 54 1.3327 1.3391 1.3454 1.3517 1.3579 1.3277 1.3339 1.3401 1.3462 1.3523 1.3215 1.3277 1.3338 1.3399 1.3459 1.3157 1.3218 1.3278 1.3338 1.3397 1.3100 1.3160 1.3219 1.3278 1.3336 1.3043 1.3102 1.3160 1.3218 1.3275 1.2987 1.3045 1.3102 1.3159 1.3215 1.2867 1.2923 1.2978 1.3033 1.3087 1.2748 1.2802 1.2856 1.2909 1.2961 1.2628 1.2680 1.2731 1.2782 1.2833 1.2377 1.2425 1.2473 1.2521 1.2568 1.2118 1.2163 1.2208 1.2252 1.2296 55 56 57 58 59 1.3640 1.3700 1.3759 1.3818 1.3875 1.3583 1.3642 1.3700 1.3757 1.3813 1.3518 1.3576 1.3634 1.3691 1.3747 1.3455 1.3512 1.3569 1.3625 1.3680 1.3393 1.3449 1.3505 1.3560 1.3614 1.3331 1.3386 1.3441 1.3495 1.3548 1.3270 1.3324 1.3377 1.3430 1.3482 1.3141 1.3194 1.3246 1.3298 1.3348 1.3013 1.3064 1.3114 1.3164 1.3213 1.2883 1.2932 1.2981 1.3029 1.3077 1.2615 1.2661 1.2706 1.2751 1.2795 1.2339 1.2382 1.2424 1.2466 1.2507 60 61 62 63 64 1.3931 1.3986 1.4039 1.4091 1.3868 1.3922 1.3975 1.4027 1.4078 1.3801 1.3855 1.3907 1.3958 1.4007 1.3734 1.3787 1.3838 1.3888 1.3936 1.3667 1.3719 1.3769 1.3818 1.3866 1.3600 1.3651 1.3700 1.3748 1.3795 1.3533 1.3583 1.3632 1.3679 1.3725 1.3398 1.3447 1.3494 1.3540 1.3261 1.3308 1.3354 1.3398 1.3124 1.3169 1.3213 1.3255 1.2839 1.2881 1.2922 1.2962 1.2547 1.2587 1.2625 1.2661 (Continued ) 2-102 PHYSICAL AnD CHEMICAL DATA TABLE 2-43 nitric Acid (HnO3) (Continued ) % 5°C 10°C 15°C 20°C 25°C 30°C 65 66 67 68 69 0°C 1.4128 1.4177 1.4224 1.4271 1.4317 1.4055 1.4103 1.4150 1.4196 1.4241 1.3984 1.4031 1.4077 1.4122 1.4166 1.3913 1.3959 1.4004 1.4048 1.4091 1.3841 1.3887 1.3932 1.3976 1.4019 1.3770 1.3814 1.3857 1.3900 1.3942 70 71 72 73 74 1.4362 1.4406 1.4449 1.4491 1.4532 1.4285 1.4328 1.4371 1.4413 1.4454 1.4210 1.4252 1.4294 1.4335 1.4376 1.4134 1.4176 1.4218 1.4258 1.4298 1.4061 1.4102 1.4142 1.4182 1.4221 1.3983 1.4023 1.4063 1.4103 1.4142 75 76 77 78 79 1.4573 1.4613 1.4652 1.4690 1.4727 1.4494 1.4533 1.4572 1.4610 1.4647 1.4415 1.4454 1.4492 1.4529 1.4565 1.4337 1.4375 1.4413 1.4450 1.4486 1.4259 1.4296 1.4333 1.4369 1.4404 1.4180 1.4217 1.4253 1.4288 1.4323 80 81 82 83 84 1.4764 1.4800 1.4835 1.4869 1.4903 1.4683 1.4718 1.4753 1.4787 1.4820 1.4601 1.4636 1.4670 1.4704 1.4737 1.4521 1.4555 1.4589 1.4622 1.4655 1.4439 1.4473 1.4507 1.4540 1.4572 1.4357 1.4391 1.4424 1.4456 1.4487 85 86 87 88 89 1.4936 1.4968 1.4999 1.5029 1.5058 1.4852 1.4883 1.4913 1.4942 1.4970 1.4769 1.4799 1.4829 1.4858 1.4885 1.4686 1.4716 1.4745 1.4773 1.4800 1.4603 1.4633 1.4662 1.4690 1.4716 1.4518 1.4548 1.4577 1.4605 1.4631 90 91 92 93 94 1.5085 1.5111 1.5136 1.5156 1.5177 1.4997 1.5023 1.5048 1.5068 1.5088 1.4911 1.4936 1.4960 1.4979 1.4999 1.4826 1.4850 1.4873 1.4892 1.4912 1.4741 1.4766 1.4789 1.4807 1.4826 1.4656 1.4681 1.4704 1.4722 1.4741 95 96 97 98 99 100 1.5198 1.5220 1.5244 1.5278 1.5327 1.5402 1.5109 1.5130 1.5152 1.5187 1.5235 1.5310 1.5019 1.5040 1.5062 1.5096 1.5144 1.5217 1.4932 1.4952 1.4974 1.5008 1.5056 1.5129 1.4846 1.4867 1.4889 1.4922 1.4969 1.5040 1.4761 1.4781 1.4802 1.4835 1.4881 1.4952 40°C 50°C 60°C 80°C 100°C ∗International Critical Tables, vol. 3, pp. 58–59. TABLE 2-44 Perchloric Acid (HClO4)* 15 % d4 1 2 4 6 8 10 12 14 16 18 20 22 24 26 1.0050 1.0109 1.0228 1.0348 1.0471 1.0597 1.0726 1.0589 1.0995 1.1135 1.1279 1.1428 1.1581 1.1738 20 d4 25 50 TABLE 2-46 Potassium Bicarbonate (KHCO3)* 15 20 50 d4 d4 % d4 d4 d4 1.0020 1.0070 1.0169 1.0270 1.0372 1.0475 0.9933 0.9986 0.9906 1.0205 1.0320 1.0440 1.0560 1.0680 1.0810 1.0940 1.1070 1.1205 1.1345 1.1490 28 30 32 34 36 38 40 45 50 55 60 65 70 1.1900 1.2067 1.2239 1.2418 1.2603 1.2794 1.2991 1.3521 1.4103 1.4733 1.5389 1.6059 1.6736 1.1851 1.2013 1.2183 1.2359 1.2542 1.2732 1.2927 1.3450 1.4018 1.4636 1.5298 1.5986 1.6680 1.1645 1.1800 1.1960 1.2130 1.2310 1.2490 1.2680 1.3180 1.3730 1.4320 1.4950 1.5620 1.6290 1.1697 ∗International Critical Tables, vol. 3, p. 54. 2% 6% 14% 20% 26% 0 1.0113 1.0339 1.0811 1.1192 10 1.0109 1.0330 1.0792 1.1167 1.1567 20 1.0092 1.0309 1.0764 1.1134 1.1529 30 1.0065 1.0279 1.0728 1.1094 1.1484 40 1.0029 1.0241 1.0685 1.1048 ∗International Critical Tables, vol. 3, p. 61. 1% 2% 4% 0 1.0066 1.0134 1.0270 10 1.0064 1.0132 1.0268 15 1.0058 1.0125 1.0260 20 1.0049 1.0117 1.0252 30 1.0024 1.0092 1.0228 40 0.9990 1.0058 1.0195 50 0.9949 1.0017 1.0154 60 0.9901 0.9969 1.0106 80 0.9786 0.9855 0.9993 100 0.9653 0.9722 0.9860 ∗International Critical Tables, vol. 3, p. 90. 6% 8% 10% 1.0396 1.0534 1.0674 TABLE 2-47 Potassium Carbonate (K2CO3)* TABLE 2-45 Phosphoric Acid (H3PO4)* °C °C 35% 50% 75% 100% 1.221 1.216 1.211 1.341 1.335 1.329 1.579 1.572 1.870 1.862 % 0°C 10°C 20°C 40°C 60°C 80°C 100°C 1 2 4 8 12 16 20 24 28 30 35 40 45 50 1.0094 1.0189 1.0381 1.0768 1.1160 1.1562 1.1977 1.2405 1.2846 1.3071 1.3646 1.4244 1.4867 1.5517 1.0089 1.0182 1.0369 1.0746 1.1131 1.1530 1.1941 1.2366 1.2804 1.3028 1.3600 1.4195 1.4815 1.5462 1.0072 1.0163 1.0345 1.0715 1.1096 1.1490 1.1898 1.2320 1.2756 1.2979 1.3548 1.4141 1.4759 1.5404 1.0010 1.0098 1.0276 1.0640 1.1013 1.1399 1.1801 1.2219 1.2652 1.2873 1.3440 1.4029 1.4644 1.5285 0.9919 1.0005 1.0180 1.0538 1.0906 1.1290 1.1690 1.2106 1.2538 1.2759 1.3324 1.3913 1.4528 1.5169 0.9803 0.9889 1.0063 1.0418 1.0786 1.1170 1.1570 1.1986 1.2418 1.2640 1.3206 1.3795 1.4408 1.5048 0.9670 0.9756 0.9951 1.0291 1.0663 1.1049 1.1451 1.1869 1.2301 1.2522 1.3089 1.3678 1.4290 1.4928 ∗International Critical Tables, vol. 3, p. 90. DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM TABLE 2-48 Potassium Chloride (KCl)* 2-103 TABLE 2-52 Sodium Carbonate (na2CO3)* % 0°C 20°C 25°C 40°C 60°C 80°C 100°C % 0°C 10°C 20°C 30°C 40°C 60°C 80°C 100°C 1.0 2.0 4.0 8.0 12.0 16.0 20.0 24.0 28.0 1.00661 1.01335 1.02690 1.05431 1.08222 1.11068 1.13973 1.00462 1.01103 1.02391 1.05003 1.07679 1.10434 1.13280 1.16226 1.00342 1.00977 1.02255 1.04847 1.07506 1.10245 1.13072 1.15995 0.99847 1.00471 1.01727 1.04278 1.06897 1.09600 1.12399 1.15299 1.18304 0.9894 0.9956 1.0080 1.0333 1.0592 1.0861 1.1138 1.1425 1.1723 0.9780 0.9842 0.9966 1.0219 1.0478 1.0746 1.1024 1.1311 1.1609 0.9646 0.9708 0.9634 1.0888 1.0350 1.0619 1.0897 1.1185 1.1483 1 2 4 8 12 14 16 18 20 24 28 30 1.0109 1.0219 1.0439 1.0878 1.1319 1.1543 1.0103 1.0210 1.0423 1.0850 1.1284 1.1506 1.0086 1.0190 1.0398 1.0816 1.1244 1.1463 1.0058 1.0159 1.0363 1.0775 1.1200 1.1417 1.1636 1.1859 1.2086 1.2552 1.3031 1.3274 1.0022 1.0122 1.0323 1.0732 1.1150 1.1365 0.9929 1.0027 1.0223 1.0625 1.1039 1.1251 0.9814 0.9910 1.0105 1.0503 1.0914 1.1125 0.9683 0.9782 0.9980 1.0380 1.0787 1.0996 % 110°C 120°C 130°C 3.79 7.45 13.62 0.9733 0.9978 1.0388 0.9663 0.9899 1.0313 0.9583 0.9827 1.0238 140°C 0.9502 0.9745 1.0159 ∗International Critical Tables, vol. 3, pp. 82–83. ∗International Critical Tables, vol. 3, p. 87. TABLE 2-53 Sodium Chloride (naCl)* TABLE 2-49 Potassium Hydroxide (KOH)* % d 15 4 1.0 1.0083 2.0 1.0175 4.0 1.0359 6.0 1.0544 8.0 1.0730 10.0 1.0918 15.0 1.1396 20.0 1.1884 25.0 1.2387 30.0 1.2905 35.0 1.3440 40.0 1.3991 45.0 1.4558 50.0 1.5143 51.7 1.5355 (sat’d. soln.) ∗International Critical Tables, vol. 3, p. 86. 0°C 10°C 20°C 1 2 4 8 12 16 20 24 1.00654 1.01326 1.02677 1.05419 1.08221 1.00615 1.01262 1.02566 1.05226 1.07963 1.00447 1.01075 1.02344 1.04940 1.07620 1.10392 1.13261 1.16233 10°C 25°C 40°C 60°C 80°C 100°C 1.00747 1.01509 1.03038 1.06121 1.09244 1.12419 1.15663 1.18999 1.20709 1.00707 1.01442 1.02920 1.05907 1.08946 1.12056 1.15254 1.18557 1.20254 1.00409 1.01112 1.02530 1.05412 1.08365 1.11401 1.14533 1.17776 1.19443 0.99908 1.00593 1.01977 1.04798 1.07699 1.10688 1.13774 1.16971 1.18614 0.9900 0.9967 1.0103 1.0381 1.0667 1.0962 1.1268 1.1584 1.1747 0.9785 0.9852 0.9988 1.0264 1.0549 1.0842 1.1146 1.1463 1.1626 0.9651 0.9719 0.9855 1.0134 1.0420 1.0713 1.1017 1.1331 1.1492 TABLE 2-54 Sodium Hydroxide (naOH)* 40°C 60°C 80°C 100°C 0.99825 1.00430 1.01652 1.04152 1.06740 1.09432 1.12240 1.15175 0.9890 0.9949 1.0068 1.0313 1.0567 1.0831 1.1106 1.1391 0.9776 0.9834 0.9951 1.0192 1.0442 1.0703 1.0974 1.1256 0.9641 0.9699 0.9816 1.0056 1.0304 1.0562 1.0831 1.1110 ∗International Critical Tables, vol. 3, p. 89. 0°C 1 2 4 8 12 16 20 24 26 ∗International Critical Tables, vol. 3, p. 79. TABLE 2-50 Potassium nitrate (KnO3)* % % % 0°C 15°C 20°C 40°C 60°C 80°C 100°C 1 2 4 8 12 16 20 24 28 32 36 40 44 48 50 1.0124 1.0244 1.0482 1.0943 1.1399 1.1849 1.2296 1.2741 1.3182 1.3614 1.4030 1.4435 1.4825 1.5210 1.5400 1.01065 1.02198 1.04441 1.08887 1.13327 1.17761 1.22183 1.26582 1.3094 1.3520 1.3933 1.4334 1.4720 1.5102 1.5290 1.0095 1.0207 1.0428 1.0869 1.1309 1.1751 1.2191 1.2629 1.3064 1.3490 1.3900 1.4300 1.4685 1.5065 1.5253 1.0033 1.0139 1.0352 1.0780 1.1210 1.1645 1.2079 1.2512 1.2942 1.3362 1.3768 1.4164 1.4545 1.4922 1.5109 0.9941 1.0045 1.0254 1.0676 1.1101 1.1531 1.1960 1.2388 1.2814 1.3232 1.3634 1.4027 1.4405 1.4781 1.4967 0.9824 0.9929 1.0139 1.0560 1.0983 1.1408 1.1833 1.2259 1.2682 1.3097 1.3498 1.3889 1.4266 1.4641 1.4827 0.9693 0.9797 1.0009 1.0432 1.0855 1.1277 1.1700 1.2124 1.2546 1.2960 1.3360 1.3750 1.4127 1.4503 1.4690 ∗International Critical Tables, vol. 3, p. 79. TABLE 2-51 Sodium Acetate (naC2H3O2)* 20 % d4 1 2 4 8 12 18 20 26 28 1.0033 1.0084 1.0186 1.0392 1.0598 1.0807 1.1021 1.1351 1.1462 ∗International Critical Tables, vol. 3, p. 83. 2-104 PHYSICAL AnD CHEMICAL DATA TABLE 2-55 Sulfuric Acid (H2SO4)* % 0°C 10°C 15°C 20°C 25°C 30°C 40°C 50°C 60°C 80°C 100°C 1 2 3 4 1.0074 1.0147 1.0219 1.0291 1.0068 1.0138 1.0206 1.0275 1.0060 1.0129 1.0197 1.0264 1.0051 1.0118 1.0184 1.0250 1.0038 1.0104 1.0169 1.0234 1.0022 1.0087 1.0152 1.0216 0.9986 1.0050 1.0113 1.0176 0.9944 1.0006 1.0067 1.0129 0.9895 0.9956 1.0017 1.0078 0.9779 0.9839 0.9900 0.9961 0.9645 0.9705 0.9766 0.9827 5 6 7 8 9 1.0364 1.0437 1.0511 1.0585 1.0660 1.0344 1.0414 1.0485 1.0556 1.0628 1.0332 1.0400 1.0469 1.0539 1.0610 1.0317 1.0385 1.0453 1.0522 1.0591 1.0300 1.0367 1.0434 1.0502 1.0571 1.0281 1.0347 1.0414 1.0481 1.0549 1.0240 1.0305 1.0371 1.0437 1.0503 1.0192 1.0256 1.0321 1.0386 1.0451 1.0140 1.0203 1.0266 1.0330 1.0395 1.0022 1.0084 1.0146 1.0209 1.0273 0.9888 0.9950 1.0013 1.0076 1.0140 10 11 12 13 14 1.0735 1.0810 1.0886 1.0962 1.1039 1.0700 1.0773 1.0846 1.0920 1.0994 1.0681 1.0753 1.0825 1.0898 1.0971 1.0661 1.0731 1.0802 1.0874 1.0947 1.0640 1.0710 1.0780 1.0851 1.0922 1.0617 1.0686 1.0756 1.0826 1.0897 1.0570 1.0637 1.0705 1.0774 1.0844 1.0517 1.0584 1.0651 1.0719 1.0788 1.0460 1.0526 1.0593 1.0661 1.0729 1.0338 1.0403 1.0469 1.0536 1.0603 1.0204 1.0269 1.0335 1.0402 1.0469 15 16 17 18 19 1.1116 1.1194 1.1272 1.1351 1.1430 1.1069 1.1145 1.1221 1.1298 1.1375 1.1045 1.1120 1.1195 1.1271 1.1347 1.1020 1.1094 1.1168 1.1243 1.1318 1.0994 1.1067 1.1141 1.1215 1.1290 1.0968 1.1040 1.1113 1.1187 1.1261 1.0914 1.0985 1.1057 1.1129 1.1202 1.0857 1.0927 1.0998 1.1070 1.1142 1.0798 1.0868 1.0938 1.1009 1.1081 1.0671 1.0740 1.0809 1.0879 1.0950 1.0537 1.0605 1.0674 1.0744 1.0814 20 21 22 23 24 1.1510 1.1590 1.1670 1.1751 1.1832 1.1453 1.1531 1.1609 1.1688 1.1768 1.1424 1.1501 1.1579 1.1657 1.1736 1.1394 1.1471 1.1548 1.1626 1.1704 1.1365 1.1441 1.1517 1.1594 1.1672 1.1335 1.1410 1.1486 1.1563 1.1640 1.1275 1.1349 1.1424 1.1500 1.1576 1.1215 1.1288 1.1362 1.1437 1.1512 1.1153 1.1226 1.1299 1.1373 1.1448 1.1021 1.1093 1.1166 1.1239 1.1313 1.0885 1.0957 1.1029 1.1102 1.1176 25 26 27 28 29 1.1914 1.1996 1.2078 1.2160 1.2243 1.1848 1.1929 1.2010 1.2091 1.2173 1.1816 1.1896 1.1976 1.2057 1.2138 1.1783 1.1862 1.1942 1.2023 1.2104 1.1750 1.1829 1.1909 1.1989 1.2069 1.1718 1.1796 1.1875 1.1955 1.2035 1.1653 1.1730 1.1808 1.1887 1.1966 1.1588 1.1665 1.1742 1.1820 1.1898 1.1523 1.1599 1.1676 1.1753 1.1831 1.1388 1.1463 1.1539 1.1616 1.1693 1.1250 1.1325 1.1400 1.1476 1.1553 30 31 32 33 34 1.2326 1.2409 1.2493 1.2577 1.2661 1.2255 1.2338 1.2421 1.2504 1.2588 1.2220 1.2302 1.2385 1.2468 1.2552 1.2185 1.2267 1.2349 1.2432 1.2515 1.2150 1.2232 1.2314 1.2396 1.2479 1.2115 1.2196 1.2278 1.2360 1.2443 1.2046 1.2126 1.2207 1.2289 1.2371 1.1977 1.2057 1.2137 1.2218 1.2300 1.1909 1.1988 1.2068 1.2148 1.2229 1.1771 1.1849 1.1928 1.2008 1.2088 1.1630 1.1708 1.1787 1.1866 1.1946 35 36 37 38 39 1.2746 1.2831 1.2917 1.3004 1.3091 1.2672 1.2757 1.2843 1.2929 1.3016 1.2636 1.2720 1.2805 1.2891 1.2978 1.2599 1.2684 1.2769 1.2855 1.2941 1.2563 1.2647 1.2732 1.2818 1.2904 1.2526 1.2610 1.2695 1.2780 1.2866 1.2454 1.2538 1.2622 1.2707 1.2793 1.2383 1.2466 1.2550 1.2635 1.2720 1.2311 1.2394 1.2477 1.2561 1.2646 1.2169 1.2251 1.2334 1.2418 1.2503 1.2027 1.2109 1.2192 1.2276 1.2361 40 41 42 43 44 1.3179 1.3268 1.3357 1.3447 1.3538 1.3103 1.3191 1.3280 1.3370 1.3461 1.3065 1.3153 1.3242 1.3332 1.3423 1.3028 1.3116 1.3205 1.3294 1.3384 1.2991 1.3079 1.3167 1.3256 1.3346 1.2953 1.3041 1.3129 1.3218 1.3308 1.2880 1.2967 1.3055 1.3144 1.3234 1.2806 1.2893 1.2981 1.3070 1.3160 1.2732 1.2819 1.2907 1.2996 1.3086 1.2589 1.2675 1.2762 1.2850 1.2939 1.2446 1.2532 1.2619 1.2707 1.2796 45 46 47 48 49 1.3630 1.3724 1.3819 1.3915 1.4012 1.3553 1.3646 1.3740 1.3835 1.3931 1.3515 1.3608 1.3702 1.3797 1.3893 1.3476 1.3569 1.3663 1.3758 1.3854 1.3437 1.3530 1.3624 1.3719 1.3814 1.3399 1.3492 1.3586 1.3680 1.3775 1.3325 1.3417 1.3510 1.3604 1.3699 1.3251 1.3343 1.3435 1.3528 1.3623 1.3177 1.3269 1.3362 1.3455 1.3549 1.3029 1.3120 1.3212 1.3305 1.3399 1.2886 1.2976 1.3067 1.3159 1.3253 50 51 52 53 54 1.4110 1.4209 1.4310 1.4412 1.4515 1.4029 1.4128 1.4228 1.4329 1.4431 1.3990 1.4088 1.4188 1.4289 1.4391 1.3951 1.4049 1.4148 1.4248 1.4350 1.3911 1.4009 1.4109 1.4209 1.4310 1.3872 1.3970 1.4069 1.4169 1.4270 1.3795 1.3893 1.3991 1.4091 1.4191 1.3719 1.3816 1.3914 1.4013 1.4113 1.3644 1.3740 1.3837 1.3936 1.4036 1.3494 1.3590 1.3687 1.3785 1.3884 1.3348 1.3444 1.3540 1.3637 1.3735 55 56 57 58 59 1.4619 1.4724 1.4830 1.4937 1.5045 1.4535 1.4640 1.4746 1.4852 1.4959 1.4494 1.4598 1.4703 1.4809 1.4916 1.4453 1.4557 1.4662 1.4768 1.4875 1.4412 1.4516 1.4621 1.4726 1.4832 1.4372 1.4475 1.4580 1.4685 1.4791 1.4293 1.4396 1.4500 1.4604 1.4709 1.4214 1.4317 1.4420 1.4524 1.4629 1.4137 1.4239 1.4342 1.4446 1.4551 1.3984 1.4085 1.4187 1.4290 1.4393 1.3834 1.3934 1.4035 1.4137 1.4240 60 61 62 63 64 1.5154 1.5264 1.5375 1.5487 1.5600 1.5067 1.5177 1.5287 1.5398 1.5510 1.5024 1.5133 1.5243 1.5354 1.5465 1.4983 1.5091 1.5200 1.5310 1.5421 1.4940 1.5048 1.5157 1.5267 1.5378 1.4898 1.5006 1.5115 1.5225 1.5335 1.4816 1.4923 1.5031 1.5140 1.5250 1.4735 1.4842 1.4950 1.5058 1.5167 1.4656 1.4762 1.4869 1.4977 1.5086 1.4497 1.4602 1.4708 1.4815 1.4923 1.4344 1.4449 1.4554 1.4660 1.4766 DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM 2-105 TABLE 2-55 Sulfuric Acid (H2SO4) (Continued ) % 0°C 10°C 15°C 20°C 25°C 30°C 40°C 50°C 60°C 80°C 100°C 65 66 67 68 69 1.5714 1.5828 1.5943 1.6059 1.6176 1.5623 1.5736 1.5850 1.5965 1.6081 1.5578 1.5691 1.5805 1.5920 1.6035 1.5533 1.5646 1.5760 1.5874 1.5989 1.5490 1.5602 1.5715 1.5829 1.5944 1.5446 1.5558 1.5671 1.5785 1.5899 1.5361 1.5472 1.5584 1.5697 1.5811 1.5277 1.5388 1.5499 1.5611 1.5724 1.5195 1.5305 1.5416 1.5528 1.5640 1.5031 1.5140 1.5249 1.5359 1.5470 1.4873 1.4981 1.5089 1.5198 1.5307 70 71 72 73 74 1.6293 1.6411 1.6529 1.6648 1.6768 1.6198 1.6315 1.6433 1.6551 1.6670 1.6151 1.6268 1.6385 1.6503 1.6622 1.6105 1.6221 1.6338 1.6456 1.6574 1.6059 1.6175 1.6292 1.6409 1.6526 1.6014 1.6130 1.6246 1.6363 1.6480 1.5925 1.6040 1.6155 1.6271 1.6387 1.5838 1.5952 1.6067 1.6182 1.6297 1.5753 1.5867 1.5981 1.6095 1.6209 1.5582 1.5694 1.5806 1.5919 1.6031 1.5417 1.5527 1.5637 1.5747 1.5857 75 76 77 78 79 1.6888 1.7008 1.7128 1.7247 1.7365 1.6789 1.6908 1.7026 1.7144 1.7261 1.6740 1.6858 1.6976 1.7093 1.7209 1.6692 1.6810 1.6927 1.7043 1.7158 1.6644 1.6761 1.6878 1.6994 1.7108 1.6597 1.6713 1.6829 1.6944 1.7058 1.6503 1.6619 1.6734 1.6847 1.6959 1.6412 1.6526 1.6640 1.6751 1.6862 1.6322 1.6435 1.6547 1.6657 1.6766 1.6142 1.6252 1.6361 1.6469 1.6575 1.5966 1.6074 1.6181 1.6286 1.6390 80 81 82 83 84 1.7482 1.7597 1.7709 1.7815 1.7916 1.7376 1.7489 1.7599 1.7704 1.7804 1.7323 1.7435 1.7544 1.7649 1.7748 1.7272 1.7383 1.7491 1.7594 1.7693 1.7221 1.7331 1.7437 1.7540 1.7639 1.7170 1.7279 1.7385 1.7487 1.7585 1.7069 1.7177 1.7281 1.7382 1.7479 1.6971 1.7077 1.7180 1.7279 1.7375 1.6873 1.6978 1.7080 1.7179 1.7274 1.6680 1.6782 1.6882 1.6979 1.7072 1.6493 1.6594 1.6692 1.6787 1.6878 85 86 87 88 89 1.8009 1.8095 1.8173 1.8243 1.8306 1.7897 1.7983 1.8061 1.8132 1.8195 1.7841 1.7927 1.8006 1.8077 1.8141 1.7786 1.7872 1.7951 1.8022 1.8087 1.7732 1.7818 1.7897 1.7968 1.8033 1.7678 1.7763 1.7842 1.7914 1.7979 1.7571 1.7657 1.7736 1.7809 1.7874 1.7466 1.7552 1.7632 1.7705 1.7770 1.7364 1.7449 1.7529 1.7602 1.7669 1.7161 1.7245 1.7324 1.7397 1.7464 1.6966 1.7050 1.7129 1.7202 1.7269 90 91 92 93 94 1.8361 1.8410 1.8453 1.8490 1.8520 1.8252 1.8302 1.8346 1.8384 1.8415 1.8198 1.8248 1.8293 1.8331 1.8363 1.8144 1.8195 1.8240 1.8279 1.8312 1.8091 1.8142 1.8188 1.8227 1.8260 1.8038 1.8090 1.8136 1.8176 1.8210 1.7933 1.7986 1.8033 1.8074 1.8109 1.7829 1.7883 1.7932 1.7974 1.8011 1.7729 1.7783 1.7832 1.7876 1.7914 1.7525 1.7581 1.7633 1.7681 1.7331 1.7388 1.7439 1.7485 95 96 97 98 99 100 1.8544 1.8560 1.8569 1.8567 1.8551 1.8517 1.8439 1.8457 1.8466 1.8463 1.8445 1.8409 1.8388 1.8406 1.8414 1.8411 1.8393 1.8357 1.8337 1.8355 1.8364 1.8361 1.8342 1.8305 1.8286 1.8305 1.8314 1.8310 1.8292 1.8255 1.8236 1.8255 1.8264 1.8261 1.8242 1.8205 1.8137 1.8157 1.8166 1.8163 1.8145 1.8107 1.8040 1.8060 1.8071 1.8068 1.8050 1.8013 1.7944 1.7965 1.7977 1.7976 1.7958 1.7922 % d 45.96 % d 413.00 d 418.00 0.005 .01 .02 .03 .04 1.000 0140 1.000 0576 1.000 1434 1.000 2276 1.000 3104 0.05 0.1 0.2 0.3 0.4 0.999 810 1.000 185 1.000 912 1.001 623 1.002 326 0.999 028 0.999 400 1.000 119 1.000 820 1.001 512 .05 .06 .07 .08 .09 1.000 3920 1.000 4726 1.000 5523 1.000 6313 1.000 7098 0.5 0.6 0.8 1.0 1.2 1.003 023 1.003 716 1.005 090 1.006 452 1.007 807 1.002 197 1.002 877 1.004 227 1.005 570 1.006 909 .10 .15 .20 .25 .30 1.000 7880 1.001 1732 1.001 5514 1.001 9254 1.002 2961 1.4 1.6 1.8 2.0 2.2 1.009 159 1.010 510 1.011 860 1.013 209 1.014 557 1.008 247 1.009 583 1.010 918 1.012 252 1.013 586 .35 .40 .45 .50 1.002 6639 1.003 0292 1.003 3923 1.003 7534 2.4 1.015 904 1.014 919 ∗International Critical Tables, vol. 3, pp. 56–57. 2-106 PHYSICAL AnD CHEMICAL DATA DEnSITIES OF AQUEOUS ORGAnIC SOLUTIOnS TABLE 2-56 Acetic Acid (CH3COOH) % 0°C 10°C 15°C 20°C 25°C 30°C 40°C % 0°C 10°C 15°C 20°C 25°C 30°C 40°C 0 1 2 3 4 0.9999 1.0016 1.0033 1.0051 1.0070 0.9997 1.0013 1.0029 1.0044 1.0060 0.9991 1.0006 1.0021 1.0036 1.0051 0.9982 0.9996 1.0012 1.0025 1.0040 0.9971 0.9987 1.0000 1.0013 1.0027 0.9957 0.9971 0.9984 0.9997 1.0011 0.9922 0.9934 0.9946 0.9958 0.9970 50 51 52 53 54 1.0729 1.0738 1.0748 1.0757 1.0765 1.0654 1.0663 1.0671 1.0679 1.0687 1.0613 1.0622 1.0629 1.0637 1.0644 1.0575 1.0582 1.0590 1.0597 1.0604 1.0534 1.0542 1.0549 1.0555 1.0562 1.0492 1.0499 1.0506 1.0512 1.0518 1.0408 1.0414 1.0421 1.0427 1.0432 5 6 7 8 9 1.0088 1.0106 1.0124 1.0142 1.0159 1.0076 1.0092 1.0108 1.0124 1.0140 1.0066 1.0081 1.0096 1.0111 1.0126 1.0055 1.0069 1.0083 1.0097 1.0111 1.0041 1.0055 1.0068 1.0081 1.0094 1.0024 1.0037 1.0050 1.0063 1.0076 0.9982 0.9994 1.0006 1.0018 1.0030 55 56 57 58 59 1.0774 1.0782 1.0790 1.0798 1.0805 1.0694 1.0701 1.0708 1.0715 1.0722 1.0651 1.0658 1.0665 1.0672 1.0678 1.0611 1.0618 1.0624 1.0631 1.0637 1.0568 1.0574 1.0580 1.0586 1.0592 1.0525 1.0531 1.0536 1.0542 1.0547 1.0438 1.0443 1.0448 1.0453 1.0458 10 11 12 13 14 1.0177 1.0194 1.0211 1.0228 1.0245 1.0156 1.0171 1.0187 1.0202 1.0217 1.0141 1.0155 1.0170 1.0184 1.0199 1.0125 1.0139 1.0154 1.0168 1.0182 1.0107 1.0120 1.0133 1.0146 1.0159 1.0089 1.0102 1.0115 1.0127 1.0139 1.0042 1.0054 1.0065 1.0077 1.0088 60 61 62 63 64 1.0813 1.0820 1.0826 1.0833 1.0838 1.0728 1.0734 1.0740 1.0746 1.0752 1.0684 1.0690 1.0696 1.0701 1.0706 1.0642 1.0648 1.0653 1.0658 1.0662 1.0597 1.0602 1.0607 1.0612 1.0616 1.0552 1.0557 1.0562 1.0566 1.0571 1.0462 1.0466 1.0470 1.0473 1.0477 15 16 17 18 19 1.0262 1.0278 1.0295 1.0311 1.0327 1.0232 1.0247 1.0262 1.0276 1.0291 1.0213 1.0227 1.0241 1.0255 1.0269 1.0195 1.0209 1.0223 1.0236 1.0250 1.0172 1.0185 1.0198 1.0210 1.0223 1.0151 1.0163 1.0175 1.0187 1.0198 1.0099 1.0110 1.0121 1.0132 1.0142 65 66 67 68 69 1.0844 1.0850 1.0856 1.0860 1.0865 1.0757 1.0762 1.0767 1.0771 1.0775 1.0711 1.0716 1.0720 1.0725 1.0729 1.0666 1.0671 1.0675 1.0678 1.0682 1.0621 1.0624 1.0628 1.0631 1.0634 1.0575 1.0578 1.0582 1.0585 1.0588 1.0480 1.0483 1.0486 1.0489 1.0491 20 21 22 23 24 1.0343 1.0358 1.0374 1.0389 1.0404 1.0305 1.0319 1.0333 1.0347 1.0361 1.0283 1.0297 1.0310 1.0323 1.0336 1.0263 1.0276 1.0288 1.0301 1.0313 1.0235 1.0248 1.0260 1.0272 1.0283 1.0210 1.0222 1.0233 1.0244 1.0256 1.0153 1.0164 1.0174 1.0185 1.0195 70 71 72 73 74 1.0869 1.0874 1.0877 1.0881 1.0884 1.0779 1.0783 1.0786 1.0789 1.0792 1.0732 1.0736 1.0738 1.0741 1.0743 1.0685 1.0687 1.0690 1.0693 1.0694 1.0637 1.0640 1.0642 1.0644 1.0645 1.0590 1.0592 1.0594 1.0595 1.0596 1.0493 1.0495 1.0496 1.0497 1.0498 25 26 27 28 29 1.0419 1.0434 1.0449 1.0463 1.0477 1.0375 1.0388 1.0401 1.0414 1.0427 1.0349 1.0362 1.0374 1.0386 1.0399 1.0326 1.0338 1.0349 1.0361 1.0372 1.0295 1.0307 1.0318 1.0329 1.0340 1.0267 1.0278 1.0289 1.0299 1.0310 1.0205 1.0215 1.0225 1.0234 1.0244 75 76 77 78 79 1.0887 1.0889 1.0891 1.0893 1.0894 1.0794 1.0796 1.0797 1.0798 1.0798 1.0745 1.0746 1.0747 1.0747 1.0747 1.0696 1.0698 1.0699 1.0700 1.0700 1.0647 1.0648 1.0648 1.0648 1.0648 1.0597 1.0598 1.0598 1.0598 1.0597 1.0499 1.0499 1.0499 1.0498 1.0497 30 31 32 33 34 1.0491 1.0505 1.0519 1.0532 1.0545 1.0440 1.0453 1.0465 1.0477 1.0489 1.0411 1.0423 1.0435 1.0446 1.0458 1.0384 1.0395 1.0406 1.0417 1.0428 1.0350 1.0361 1.0372 1.0382 1.0392 1.0320 1.0330 1.0341 1.0351 1.0361 1.0253 1.0262 1.0272 1.0281 1.0289 80 81 82 83 84 1.0895 1.0895 1.0895 1.0895 1.0893 1.0798 1.0797 1.0796 1.0795 1.0793 1.0747 1.0745 1.0743 1.0741 1.0738 1.0700 1.0699 1.0698 1.0696 1.0693 1.0647 1.0646 1.0644 1.0642 1.0638 1.0596 1.0594 1.0592 1.0589 1.0585 1.0495 1.0493 1.0490 1.0487 1.0483 35 36 37 38 39 1.0558 1.0571 1.0584 1.0596 1.0608 1.0501 1.0513 1.0524 1.0535 1.0546 1.0469 1.0480 1.0491 1.0501 1.0512 1.0438 1.0449 1.0459 1.0469 1.0479 1.0402 1.0412 1.0422 1.0432 1.0441 1.0371 1.0380 1.0390 1.0399 1.0408 1.0298 1.0306 1.0314 1.0322 1.0330 85 86 87 88 89 1.0891 1.0887 1.0883 1.0877 1.0872 1.0790 1.0787 1.0783 1.0778 1.0773 1.0735 1.0731 1.0726 1.0721 1.0715 1.0689 1.0685 1.0680 1.0675 1.0668 1.0635 1.0630 1.0626 1.0620 1.0613 1.0582 1.0576 1.0571 1.0564 1.0557 1.0479 1.0473 1.0467 1.0460 1.0453 40 41 42 43 44 1.0621 1.0633 1.0644 1.0656 1.0667 1.0557 1.0568 1.0578 1.0588 1.0598 1.0522 1.0532 1.0542 1.0551 1.0561 1.0488 1.0498 1.0507 1.0516 1.0525 1.0450 1.0460 1.0469 1.0477 1.0486 1.0416 1.0425 1.0433 1.0441 1.0449 1.0338 1.0346 1.0353 1.0361 1.0368 90 91 92 93 94 1.0865 1.0857 1.0848 1.0838 1.0826 1.0766 1.0758 1.0749 1.0739 1.0727 1.0708 1.0700 1.0690 1.0680 1.0667 1.0661 1.0652 1.0643 1.0632 1.0619 1.0605 1.0597 1.0587 1.0577 1.0564 1.0549 1.0541 1.0530 1.0518 1.0506 1.0445 1.0436 1.0426 1.0414 1.0401 45 46 47 48 49 1.0679 1.0689 1.0699 1.0709 1.0720 1.0608 1.0618 1.0627 1.0636 1.0645 1.0570 1.0579 1.0588 1.0597 1.0605 1.0534 1.0542 1.0551 1.0559 1.0567 1.0495 1.0503 1.0511 1.0518 1.0526 1.0456 1.0464 1.0471 1.0479 1.0486 1.0375 1.0382 1.0389 1.0395 1.0402 95 96 97 98 99 1.0813 1.0798 1.0780 1.0759 1.0730 1.0714 1.0652 1.0632 1.0611 1.0590 1.0567 1.0605 1.0588 1.0570 1.0549 1.0524 1.0551 1.0535 1.0516 1.0495 1.0468 1.0491 1.0473 1.0454 1.0431 1.0407 1.0386 1.0368 1.0348 1.0325 1.0299 100 1.0697 1.0545 1.0498 1.0440 1.0380 1.0271 DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM 2-107 TABLE 2-57 Methyl Alcohol (CH3OH)* % 0°C 10°C 20°C 15°C % 0°C 10°C 20°C 15°C % 0°C 10°C 20°C 15°C 0 1 2 3 4 0.9999 0.9981 0.9963 0.9946 0.9930 0.9997 0.9980 0.9962 0.9945 0.9929 15.56°C 0.9990 0.9973 0.9955 0.9938 0.9921 0.9982 0.9965 0.9948 0.9931 0.9914 0.99913 0.99727 0.99543 0.99370 0.99198 35 36 37 38 39 0.9534 0.9520 0.9505 0.9490 0.9475 0.9484 0.9469 0.9453 0.9437 0.9420 15.56°C 0.9456 0.9440 0.9422 0.9405 0.9387 0.9433 0.9416 0.9398 0.9381 0.9363 0.94570 0.94404 0.94237 0.94067 0.93894 70 71 72 73 74 0.8869 0.8847 0.8824 0.8801 0.8778 0.8794 0.8770 0.8747 0.8724 0.8699 15.56°C 0.8748 0.8726 0.8702 0.8678 0.8653 0.8715 0.8690 0.8665 0.8641 0.8616 0.87507 0.87271 0.87033 0.86792 0.86546 5 6 7 8 9 0.9914 0.9899 0.9884 0.9870 0.9856 0.9912 0.9896 0.9881 0.9865 0.9849 0.9904 0.9889 0.9872 0.9857 0.9841 0.9896 0.9880 0.9863 0.9847 0.9831 0.99029 0.98864 0.98701 0.98547 0.98394 40 41 42 43 44 0.9459 0.9443 0.9427 0.9411 0.9395 0.9403 0.9387 0.9370 0.9352 0.9334 0.9369 0.9351 0.9333 0.9315 0.9297 0.9345 0.9327 0.9309 0.9290 0.9272 0.93720 0.93543 0.93365 0.93185 0.93001 75 76 77 78 79 0.8754 0.8729 0.8705 0.8680 0.8657 0.8676 0.8651 0.8626 0.8602 0.8577 0.8629 0.8604 0.8579 0.8554 0.8529 0.8592 0.8567 0.8542 0.8518 0.8494 0.86300 0.86051 0.85801 0.85551 0.85300 10 11 12 13 14 0.9842 0.9829 0.9816 0.9804 0.9792 0.9834 0.9820 0.9805 0.9791 0.9778 0.9826 0.9811 0.9796 0.9781 0.9766 0.9815 0.9799 0.9784 0.9768 0.9754 0.98241 0.98093 0.97945 0.97802 0.97660 45 46 47 48 49 0.9377 0.9360 0.9342 0.9324 0.9306 0.9316 0.9298 0.9279 0.9260 0.9240 0.9279 0.9261 0.9242 0.9223 0.9204 0.9252 0.9234 0.9214 0.9196 0.9176 0.92815 0.92627 0.92436 0.92242 0.92048 80 81 82 83 84 0.8634 0.8610 0.8585 0.8560 0.8535 0.8551 0.8527 0.8501 0.8475 0.8449 0.8503 0.8478 0.8452 0.8426 0.8400 0.8469 0.8446 0.8420 0.8394 0.8366 0.85048 0.84794 0.84536 0.84274 0.84009 15 16 17 18 19 0.9780 0.9769 0.9758 0.9747 0.9736 0.9764 0.9751 0.9739 0.9726 0.9713 0.9752 0.9738 0.9723 0.9709 0.9695 0.9740 0.9725 0.9710 0.9696 0.9681 0.97518 0.97377 0.97237 0.97096 0.96955 50 51 52 53 54 0.9287 0.9269 0.9250 0.9230 0.9211 0.9221 0.9202 0.9182 0.9162 0.9142 0.9185 0.9166 0.9146 0.9126 0.9106 0.9156 0.9135 0.9114 0.9094 0.9073 0.91852 0.91653 0.91451 0.91248 0.91044 85 86 87 88 89 0.8510 0.8483 0.8456 0.8428 0.8400 0.8422 0.8394 0.8367 0.8340 0.8314 0.8374 0.8347 0.8320 0.8294 0.8267 0.8340 0.8314 0.8286 0.8258 0.8230 0.83742 0.83475 0.83207 0.82937 0.82667 20 21 22 23 24 0.9725 0.9714 0.9702 0.9690 0.9678 0.9700 0.9687 0.9673 0.9660 0.9646 0.9680 0.9666 0.9652 0.9638 0.9624 0.9666 0.9651 0.9636 0.9622 0.9607 0.96814 0.96673 0.96533 0.96392 0.96251 55 56 57 58 59 0.9191 0.9172 0.9151 0.9131 0.9111 0.9122 0.9101 0.9080 0.9060 0.9039 0.9086 0.9065 0.9045 0.9024 0.9002 0.9052 0.9032 0.9010 0.8988 0.8968 0.90839 0.90631 0.90421 0.90210 0.89996 90 91 92 93 94 0.8374 0.8347 0.8320 0.8293 0.8266 0.8287 0.8261 0.8234 0.8208 0.8180 0.8239 0.8212 0.8185 0.8157 0.8129 0.8202 0.8174 0.8146 0.8118 0.8090 0.82396 0.82124 0.81849 0.81568 0.81285 25 26 27 28 29 0.9666 0.9654 0.9642 0.9629 0.9616 0.9632 0.9618 0.9604 0.9590 0.9575 0.9609 0.9595 0.9580 0.9565 0.9550 0.9592 0.9576 0.9562 0.9546 0.9531 0.96108 0.95963 0.95817 0.95668 0.95518 60 61 62 63 64 0.9090 0.9068 0.9046 0.9024 0.9002 0.9018 0.8998 0.8977 0.8955 0.8933 0.8980 0.8958 0.8936 0.8913 0.8890 0.8946 0.8924 0.8902 0.8879 0.8856 0.89781 0.89563 0.89341 0.89117 0.88890 95 96 97 98 99 0.8240 0.8212 0.8186 0.8158 0.8130 0.8152 0.8124 0.8096 0.8068 0.8040 0.8101 0.8073 0.8045 0.8016 0.7987 0.8062 0.8034 0.8005 0.7976 0.7948 0.80999 0.80713 0.80428 0.80143 0.79859 30 31 32 33 34 0.9604 0.9590 0.9576 0.9563 0.9549 0.9560 0.9546 0.9531 0.9516 0.9500 0.9535 0.9521 0.9505 0.9489 0.9473 0.9515 0.9499 0.9483 0.9466 0.9450 0.95366 0.95213 0.95056 0.94896 0.94734 65 66 67 68 69 0.8980 0.8958 0.8935 0.8913 0.8891 0.8911 0.8888 0.8865 0.8842 0.8818 0.8867 0.8844 0.8820 0.8797 0.8771 0.8834 0.8811 0.8787 0.8763 0.8738 0.88662 0.88433 0.88203 0.87971 0.87739 100 0.8102 0.8009 0.7959 0.7917 0.79577 ∗It should be noted that the values for 100 percent do not agree with some data available elsewhere, e.g., American Institute of Physics Handbook, McGraw-Hill, New York, 1957. Also, see Atack, Handbook of Chemical Data, Reinhold, New York, 1957. Also, see Tables 2-120 and 2-135 for pure methanol and water densities. 2-108 PHYSICAL AnD CHEMICAL DATA TABLE 2-58 Ethyl Alcohol (C2H5OH)* % 10°C 15°C 20°C 25°C 30°C 35°C 40°C % 10°C 15°C 20°C 25°C 30°C 35°C 40°C 0 1 2 3 4 0.99973 785 602 426 258 0.99913 725 542 365 195 0.99823 636 453 275 103 0.99708 520 336 157 0.98984 0.99568 379 194 014 0.98839 0.99406 217 031 0.98849 672 0.99225 034 0.98846 663 485 50 51 52 53 54 0.92126 0.91943 723 502 279 0.91776 555 333 110 0.90885 0.91384 160 0.90936 711 485 0.90985 760 534 307 079 0.90580 353 125 0.89896 667 0.90168 0.89940 710 479 248 0.89750 519 288 056 0.88823 5 6 7 8 9 098 0.98946 801 660 524 032 0.98877 729 584 442 0.98938 780 627 478 331 817 656 500 346 193 670 507 347 189 031 501 335 172 009 0.97846 311 142 0.97975 808 641 55 56 57 58 59 055 0.90831 607 381 154 659 433 207 0.89980 752 258 031 0.89803 574 344 0.89850 621 392 162 0.88931 437 206 0.88975 744 512 016 0.88784 552 319 085 589 356 122 0.87888 653 10 11 12 13 14 393 267 145 026 0.97911 304 171 041 0.97914 790 187 047 0.97910 775 643 043 0.97897 753 611 472 0.97875 723 573 424 278 685 527 371 216 063 475 312 150 0.96989 829 60 61 62 63 64 0.89927 698 468 237 006 523 293 062 0.88830 597 113 0.88882 650 417 183 699 466 233 0.87998 763 278 044 0.87809 574 337 0.87851 615 379 142 0.86905 417 180 0.86943 705 466 15 16 17 18 19 800 692 583 473 363 669 552 433 313 191 514 387 259 129 0.96997 334 199 062 0.96923 782 133 0.96990 844 697 547 0.96911 760 607 452 294 670 512 352 189 023 65 66 67 68 69 0.88774 541 308 074 0.87839 364 130 0.87895 660 424 0.87948 713 477 241 004 527 291 054 0.86817 579 100 0.86863 625 387 148 667 429 190 0.85950 710 227 0.85987 747 507 266 20 21 22 23 24 252 139 024 0.96907 787 068 0.96944 818 689 558 864 729 592 453 312 639 495 348 199 048 395 242 087 0.95929 769 134 0.95973 809 643 476 0.95856 687 516 343 168 70 71 72 73 74 602 365 127 0.86888 648 187 0.86949 710 470 229 0.86766 527 287 047 0.85806 340 100 0.85859 618 376 0.85908 667 426 184 0.84941 470 228 0.84986 743 500 025 0.84783 540 297 053 25 26 27 28 29 665 539 406 268 125 424 287 144 0.95996 844 168 020 0.95867 710 548 0.95895 738 576 410 241 607 442 272 098 0.94922 306 133 0.94955 774 590 0.94991 810 625 438 248 75 76 77 78 79 408 168 0.85927 685 442 0.85988 747 505 262 018 564 322 079 0.84835 590 134 0.84891 647 403 158 698 455 211 0.83966 720 257 013 0.83768 523 277 0.83809 564 319 074 0.82827 30 31 32 33 34 0.95977 823 665 502 334 686 524 357 186 011 382 212 038 0.94860 679 067 0.94890 709 525 337 741 557 370 180 0.93986 403 214 021 0.93825 626 055 0.93860 662 461 257 80 81 82 83 84 197 0.84950 702 453 203 0.84772 525 277 028 0.83777 344 096 0.83848 599 348 0.83911 664 415 164 0.82913 473 224 0.82974 724 473 029 0.82780 530 279 027 578 329 079 0.81828 576 35 36 37 38 39 162 0.94986 805 620 431 0.94832 650 464 273 079 494 306 114 0.93919 720 146 0.93952 756 556 353 790 591 390 186 0.92979 425 221 016 0.92808 597 051 0.92843 634 422 208 85 86 87 88 89 0.83951 697 441 181 0.82919 525 271 014 0.82754 492 095 0.82840 583 323 062 660 405 148 0.81888 626 220 0.81965 708 448 186 0.81774 519 262 003 0.80742 322 067 0.80811 552 291 40 41 42 43 44 238 042 0.93842 639 433 0.93882 682 478 271 062 518 314 107 0.92897 685 148 0.92940 729 516 301 770 558 344 128 0.91910 385 170 0.91952 733 513 0.91992 774 554 332 108 90 91 92 93 94 654 386 114 0.81839 561 227 0.81959 688 413 134 0.81797 529 257 0.80983 705 362 094 0.80823 549 272 0.80922 655 384 111 0.79835 478 211 0.79941 669 393 028 0.79761 491 220 0.78947 45 46 47 48 49 226 017 0.92806 593 379 0.92852 640 426 211 0.91995 472 257 041 0.91823 604 085 0.91868 649 429 208 692 472 250 028 0.90805 291 069 0.90845 621 396 0.90884 660 434 207 0.89979 95 96 97 98 99 278 0.80991 698 399 094 0.80852 566 274 0.79975 670 424 138 0.79846 547 243 0.79991 706 415 117 0.78814 555 271 0.78981 684 382 114 0.78831 542 247 0.77946 670 388 100 0.77806 507 100 0.79784 360 0.78934 506 075 641 203 ∗For data from −78° to 78°C, see p. 2-142, Table 2N-5, American Institute of Physics Handbook, McGraw-Hill, New York, 1957. See Tables 2-115 and 2-135 for pure ethanol and pure water densities. DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM 2-109 TABLE 2-59 n-Propyl Alcohol (C3H7OH) % 0°C 15°C 30°C % 0°C 15°C 30°C % 0°C 15°C 30°C % 0°C 15°C 30°C % 0°C 15°C 30°C 0 1 2 3 4 0.9999 0.9982 0.9967 0.9952 0.9939 0.9991 0.9974 0.9960 0.9944 0.9929 0.9957 0.9940 0.9924 0.9908 0.9893 20 21 22 23 24 0.9789 0.9776 0.9763 0.9748 0.9733 0.9723 0.9705 0.9688 0.9670 0.9651 0.9643 0.9622 0.9602 0.9583 0.9563 40 41 42 43 44 0.9430 0.9411 0.9391 0.9371 0.9352 0.9331 0.9310 0.9290 0.9269 0.9248 0.9226 0.9205 0.9184 0.9164 0.9143 60 61 62 63 64 0.9033 0.9013 0.8994 0.8974 0.8954 0.8922 0.8902 0.8882 0.8861 0.8841 0.8807 0.8786 0.8766 0.8745 0.8724 80 81 82 83 84 0.8634 0.8614 0.8594 0.8574 0.8554 0.8516 0.8496 0.8475 0.8454 0.8434 0.8394 0.8373 0.8352 0.8332 0.8311 5 6 7 8 9 0.9926 0.9914 0.9904 0.9894 0.9883 0.9915 0.9902 0.9890 0.9877 0.9864 0.9877 0.9862 0.9848 0.9834 0.9819 25 26 27 28 29 0.9717 0.9700 0.9682 0.9664 0.9646 0.9633 0.9614 0.9594 0.9576 0.9556 0.9543 0.9522 0.9501 0.9481 0.9460 45 46 47 48 49 0.9332 0.9311 0.9291 0.9272 0.9252 0.9228 0.9207 0.9186 0.9165 0.9145 0.9122 0.9100 0.9079 0.9057 0.9036 65 66 67 68 69 0.8934 0.8913 0.8894 0.8874 0.8854 0.8820 0.8800 0.8779 0.8759 0.8739 0.8703 0.8682 0.8662 0.8641 0.8620 85 86 87 88 89 0.8534 0.8513 0.8492 0.8471 0.8450 0.8413 0.8393 0.8372 0.8351 0.8330 0.8290 0.8269 0.8248 0.8227 0.8206 10 11 12 13 14 0.9874 0.9865 0.9857 0.9849 0.9841 0.9852 0.9840 0.9828 0.9817 0.9806 0.9804 0.9790 0.9775 0.9760 0.9746 30 31 32 33 34 0.9627 0.9608 0.9589 0.9570 0.9550 0.9535 0.9516 0.9495 0.9474 0.9454 0.9439 0.9418 0.9396 0.9375 0.9354 50 51 52 53 54 0.9232 0.9213 0.9192 0.9173 0.9153 0.9124 0.9104 0.9084 0.9064 0.9044 0.9015 0.8994 0.8973 0.8952 0.8931 70 71 72 73 74 0.8835 0.8815 0.8795 0.8776 0.8756 0.8719 0.8700 0.8680 0.8659 0.8639 0.8600 0.8580 0.8559 0.8539 0.8518 90 91 92 93 94 0.8429 0.8408 0.8387 0.8364 0.8342 0.8308 0.8287 0.8266 0.8244 0.8221 0.8185 0.8164 0.8142 0.8120 0.8098 15 16 17 18 19 0.9833 0.9825 0.9817 0.9808 0.9800 0.9793 0.9780 0.9768 0.9752 0.9739 0.9730 0.9714 0.9698 0.9680 0.9661 35 36 37 38 39 0.9530 0.9511 0.9491 0.9471 0.9450 0.9434 0.9413 0.9392 0.9372 0.9351 0.9333 0.9312 0.9289 0.9269 0.9247 55 56 57 58 59 0.9132 0.9112 0.9093 0.9073 0.9053 0.9023 0.9003 0.8983 0.8963 0.8942 0.8911 0.8890 0.8869 0.8849 0.8828 75 76 77 78 79 0.8736 0.8716 0.8695 0.8675 0.8655 0.8618 0.8598 0.8577 0.8556 0.8536 0.8497 0.8477 0.8456 0.8435 0.8414 95 96 97 98 99 0.8320 0.8296 0.8272 0.8248 0.8222 0.8199 0.8176 0.8153 0.8128 0.8104 0.8077 0.8054 0.8031 0.8008 0.7984 100 0.8194 0.8077 0.7958 TABLE 2-60 Isopropyl Alcohol (C3H7OH) % 0°C 15°C∗ 15°C∗ 20°C 30°C % 0°C 15°C∗ 20°C 30°C % 0°C 15°C∗ 15°C∗ 20°C 30°C 0 1 2 3 4 0.9999 0.9980 0.9962 0.9946 0.9930 0.9991 0.9973 0.9956 0.9938 0.9922 0.99913 0.9972 0.9954 0.9936 0.9920 0.9982 0.9962 0.9944 0.9926 0.9909 0.9957 0.9939 0.9921 0.9904 0.9887 35 36 37 38 39 0.9557 0.9536 0.9514 0.9493 0.9472 15°C∗ 0.9446 0.9424 0.9401 0.9379 0.9356 0.9419 0.9399 0.9377 0.9355 0.9333 0.9338 0.9315 0.9292 0.9269 0.9246 70 71 72 73 74 0.8761 0.8738 0.8714 0.8691 0.8668 0.8639 0.8615 0.8592 0.8568 0.8545 0.86346 0.8611 0.8588 0.8564 0.8541 0.8584 0.8560 0.8537 0.8513 0.8489 0.8511 0.8487 0.8464 0.8440 0.8416 5 6 7 8 9 0.9916 0.9902 0.9890 0.9878 0.9866 0.9906 0.9892 0.9878 0.9864 0.9851 0.9904 0.9890 0.9875 0.9862 0.9849 0.9893 0.9877 0.9862 0.9847 0.9833 0.9871 0.9855 0.9839 0.9824 0.9809 40 41 42 43 44 0.9450 0.9428 0.9406 0.9384 0.9361 0.93333 0.9311 0.9288 0.9266 0.9243 0.9310 0.9287 0.9264 0.9239 0.9215 0.9224 0.9201 0.9177 0.9154 0.9130 75 76 77 78 79 0.8644 0.8621 0.8598 0.8575 0.8551 0.8521 0.8497 0.8474 0.8450 0.8426 0.8517 0.8493 0.8470 0.8446 0.8422 0.8464 0.8439 0.8415 0.8391 0.8366 0.8392 0.8368 0.8344 0.8321 0.8297 10 11 12 13 14 0.9856 0.9846 0.9838 0.9829 0.9821 0.9838 0.9826 0.9813 0.9802 0.9790 0.98362 0.9824 0.9812 0.9800 0.9788 0.9820 0.9808 0.9797 0.9876 0.9776 0.9794 0.9778 0.9764 0.9750 0.9735 45 46 47 48 49 0.9338 0.9315 0.9292 0.9270 0.9247 0.9220 0.9197 0.9174 0.9150 0.9127 0.9191 0.9165 0.9141 0.9117 0.9093 0.9106 0.9082 0.9059 0.9036 0.9013 80 81 82 83 84 0.8528 0.8503 0.8479 0.8456 0.8432 0.8403 0.8379 0.8355 0.8331 0.8307 0.83979 0.8374 0.8350 0.8326 0.8302 0.8342 0.8317 0.8292 0.8268 0.8243 0.8273 0.8248 0.8224 0.8200 0.8175 15 16 17 18 19 0.9814 0.9806 0.9799 0.9792 0.9784 0.9779 0.9768 0.9756 0.9745 0.9730 0.9777 0.9765 0.9753 0.9741 0.9728 0.9765 0.9754 0.9743 0.9731 0.9717 0.9720 0.9705 0.9690 0.9675 0.9658 50 51 52 53 54 0.9224 0.9201 0.9178 0.9155 0.9132 0.91043 0.9081 0.9058 0.9035 0.9011 0.9069 0.9044 0.9020 0.8996 0.8971 0.8990 0.8966 0.8943 0.8919 0.8895 85 86 87 88 89 0.8408 0.8384 0.8360 0.8336 0.8311 0.8282 0.8259 0.8234 0.8209 0.8184 0.8278 0.8254 0.8229 0.8205 0.8180 0.8219 0.8194 0.8169 0.8145 0.8120 0.8151 0.8127 0.8201 0.8078 0.8053 20 21 22 23 24 0.9777 0.9768 0.9759 0.9749 0.9739 0.9719 0.9704 0.9690 0.9675 0.9660 0.97158 0.9703 0.9689 0.9674 0.9659 0.9703 0.9688 0.9669 0.9651 0.9634 0.9642 0.9624 0.9606 0.9587 0.9569 55 56 57 58 59 0.9109 0.9086 0.9063 0.9040 0.9017 0.8988 0.8964 0.8940 0.8917 0.8893 0.8946 0.8921 0.8896 0.8874 0.8850 0.8871 0.8847 0.8823 0.8800 0.8777 90 91 92 93 94 0.8287 0.8262 0.8237 0.8212 0.8186 0.8161 0.8136 0.8110 0.8085 0.8060 0.81553 0.8130 0.8104 0.8079 0.8052 0.8096 0.8072 0.8047 0.8023 0.7998 0.8029 0.8004 0.7979 0.7954 0.7929 25 26 27 28 29 0.9727 0.9714 0.9699 0.9684 0.9669 0.9643 0.9626 0.9608 0.9590 0.9570 0.9642 0.9624 0.9605 0.9586 0.9568 0.9615 0.9597 0.9577 0.9558 0.9540 0.9549 0.9529 0.9509 0.9488 0.9467 60 61 62 63 64 0.8994 0.8970 0.8947 0.8924 0.8901 0.8829 0.8805 0.8781 0.88690 0.8845 0.8821 0.8798 0.8775 0.8825 0.8800 0.8776 0.8751 0.8727 0.8752 0.8728 0.8704 0.8680 0.8656 95 96 97 98 99 0.8160 0.8133 0.8106 0.8078 0.8048 0.8034 0.8008 0.7981 0.7954 0.7926 0.8026 0.7999 0.7972 0.7945 0.7918 0.7973 0.7949 0.7925 0.7901 0.7877 0.7904 0.7878 0.7852 0.7826 0.7799 30 31 32 33 34 0.9652 0.9634 0.9615 0.9596 0.9577 0.9551 0.95493 0.9530 0.9510 0.9489 0.9468 0.9520 0.9500 0.9481 0.9460 0.9440 0.9446 0.9426 0.9405 0.9383 0.9361 65 66 67 68 69 0.8878 0.8854 0.8831 0.8807 0.8784 0.8757 0.8733 0.8710 0.8686 0.8662 0.8752 0.8728 0.8705 0.8682 0.8658 0.8702 0.8679 0.8656 0.8632 0.8609 0.8631 0.8607 0.8583 0.8559 0.8535 100 0.8016 0.7896 0.78913 0.7854 0.7770 ∗Two different observers; see International Critical Tables, vol. 3, p. 120. 2-110 PHYSICAL AnD CHEMICAL DATA TABLE 2-61 Glycerol* Density Density Density Glycerol, % 15°C 15.5°C 20°C 25°C 30°C Glycerol, % 15°C 15.5°C 20°C 25°C 30°C Glycerol, % 15°C 15.5°C 20°C 25°C 30°C 100 99 98 97 96 1.26415 1.26160 1.25900 1.25645 1.25385 1.26381 1.26125 1.25865 1.25610 1.25350 1.26108 1.25850 1.25590 1.25335 1.25080 1.15802 1.25545 1.25290 1.25030 1.24770 1.25495 1.25235 1.24975 1.24710 1.24450 65 64 63 62 61 1.17030 1.16755 1.16480 1.16200 1.15925 1.17000 1.16725 1.16445 1.16170 1.15895 1.16750 1.16475 1.16205 1.15930 1.15655 1.16475 1.16200 1.15925 1.15655 1.15380 1.16195 1.15925 1.15650 1.15375 1.15100 30 29 28 27 26 1.07455 1.07195 1.06935 1.06670 1.06410 1.07435 1.07175 1.06915 1.06655 1.06390 1.07270 1.07010 1.06755 1.06495 1.06240 1.07070 1.06815 1.06560 1.06305 1.06055 1.06855 1.06605 1.06355 1.06105 1.05855 95 94 93 92 91 1.25130 1.24865 1.24600 1.24340 1.24075 1.25095 1.24830 1.24565 1.24305 1.24040 1.24825 1.24560 1.24300 1.24035 1.23770 1.24515 1.24250 1.23985 1.23725 1.23460 1.24190 1.23930 1.23670 1.23410 1.23150 60 59 58 57 56 1.15650 1.15370 1.15095 1.14815 1.14535 1.15615 1.15340 1.15065 1.14785 1.14510 1.15380 1.15105 1.14830 1.14555 1.14280 1.15105 1.14835 1.14560 1.14285 1.14015 1.14830 1.14555 1.14285 1.14010 1.13740 25 24 23 22 21 1.06150 1.05885 1.05625 1.05365 1.05100 1.06130 1.05870 1.05610 1.05350 1.05090 1.05980 1.05720 1.05465 1.05205 1.04950 1.05800 1.05545 1.05290 1.05035 1.04780 1.05605 1.05350 1.05100 1.04850 1.04600 90 89 88 87 86 1.23810 1.23545 1.23280 1.23015 1.22750 1.23775 1.23510 1.23245 1.22980 1.22710 1.23510 1.23245 1.22975 1.22710 1.22445 1.23200 1.22935 1.22665 1.22400 1.22135 1.22890 1.22625 1.22360 1.22095 1.21830 55 54 53 52 51 1.14260 1.13980 1.13705 1.13425 1.13150 1.14230 1.13955 1.13680 1.13400 1.13125 1.14005 1.13730 1.13455 1.13180 1.12905 1.13740 1.13465 1.13195 1.12920 1.12650 1.13470 1.13195 1.12925 1.12650 1.12380 20 19 18 17 16 1.04840 1.04590 1.04335 1.04085 1.03835 1.04825 1.04575 1.04325 1.04075 1.03825 1.04690 1.04440 1.04195 1.03945 1.03695 1.04525 1.04280 1.04035 1.03790 1.03545 1.04350 1.04105 1.03860 1.03615 1.03370 85 84 83 82 81 1.22485 1.22220 1.21955 1.21690 1.21425 1.22445 1.22180 1.21915 1.21650 1.21385 1.22180 1.21915 1.21650 1.21380 1.21115 1.21870 1.21605 1.21340 1.21075 1.20810 1.21565 1.21300 1.21035 1.20770 1.20505 50 49 48 47 46 1.12870 1.12600 1.12325 1.12055 1.11780 1.12845 1.12575 1.12305 1.12030 1.11760 1.12630 1.12360 1.12090 1.11820 1.11550 1.12375 1.12110 1.11840 1.11575 1.11310 1.12110 1.11845 1.11580 1.11320 1.11055 15 14 13 12 11 1.03580 1.03330 1.03080 1.02830 1.02575 1.03570 1.03320 1.03070 1.02820 1.02565 1.03450 1.03200 1.02955 1.02705 1.02455 1.03300 1.03055 1.02805 1.02560 1.02315 1.03130 1.02885 1.02640 1.02395 1.02150 80 79 78 77 76 1.21160 1.20885 1.20610 1.20335 1.20060 1.21120 1.20845 1.20570 1.20300 1.20025 1.20850 1.20575 1.20305 1.20030 1.19760 1.20545 1.20275 1.20005 1.19735 1.19465 1.20240 1.19970 1.19705 1.19435 1.19170 45 44 43 42 41 1.11510 1.11235 1.10960 1.10690 1.10415 1.11490 1.11215 1.10945 1.10670 1.10400 1.11280 1.11010 1.10740 1.10470 1.10200 1.11040 1.10775 1.10510 1.10240 1.09975 1.10795 1.10530 1.10265 1.10005 1.09740 10 9 8 7 6 1.02325 1.02085 1.01840 1.01600 1.01360 1.02315 1.02075 1.01835 1.01590 1.01350 1.02210 1.01970 1.01730 1.01495 1.01255 1.02070 1.01835 1.01600 1.01360 1.01125 1.01905 1.01670 1.01440 1.01205 1.00970 75 74 73 72 71 1.19785 1.19510 1.19235 1.18965 1.18690 1.19750 1.19480 1.19205 1.18930 1.18655 1.19485 1.19215 1.18940 1.18670 1.18395 1.19195 1.18925 1.18650 1.18380 1.18110 1.18900 1.18635 1.18365 1.18100 1.17830 40 39 38 37 36 1.10145 1.09875 1.09605 1.09340 1.09070 1.10130 1.09860 1.09590 1.09320 1.09050 1.09930 1.09665 1.09400 1.09135 1.08865 1.09710 1.09445 1.09180 1.08915 1.08655 1.09475 1.09215 1.08955 1.08690 1.08430 5 4 3 2 1 1.01120 1.00875 1.00635 1.00395 1.00155 1.01110 1.00870 1.00630 1.00385 1.00145 1.01015 1.00780 1.00540 1.00300 1.00060 1.00890 1.00655 1.00415 1.00180 0.99945 1.00735 1.00505 1.00270 1.00035 0.99800 70 69 68 67 66 1.18415 1.18135 1.17860 1.17585 1.17305 1.18385 1.18105 1.17830 1.17555 1.17275 1.18125 1.17850 1.17575 1.17300 1.17025 1.17840 1.17565 1.17295 1.17020 1.16745 1.17565 1.17290 1.17020 1.16745 1.16470 35 34 33 32 31 1.08800 1.08530 1.08265 1.07995 1.07725 1.08780 1.08515 1.08245 1.07975 1.07705 1.08600 1.08335 1.08070 1.07800 1.07535 1.08390 1.08125 1.07860 1.07600 1.07335 1.08165 1.07905 1.07645 1.07380 1.07120 0 0.99913 0.99905 0.99823 0.99708 0.99568 ∗Bosart and Snoddy, Ind. Eng. Chem., 20, (1928): 1378. TABLE 2-62 Hydrazine (n2H4)* % d 415 % d 415 1 2 4 8 12 16 20 24 28 1.0002 1.0013 1.0034 1.0077 1.0121 1.0164 1.0207 1.0248 1.0286 30 40 50 60 70 80 90 100 1.0305 1.038 1.044 1.047 1.046 1.040 1.030 1.011 ∗International Critical Tables, vol. 3, p. 55. DEnSITIES OF AQUEOUS InORGAnIC SOLUTIOnS AT 1 ATM 2-111 TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds* d, dw, and ds are the density of the solution, pure water, and pure liquid solute, respectively, all in g/mL. ps is the wt % solute. 0.03255 means 2.55 × 10−4. Section A Name Acetaldehyde Acetamide Formula C2H4O C2H5NO Acetone C3H6O Acetonitrile Allyl alcohol Benzenepentacarboxylic acid Butyl alcohol (n-) C2H3N C3H6O C11H6O10 C4H10O Butyric acid (n-) C4H8O2 Chloral hydrate C2H3Cl3O2 Chloroacetic acid C2H3ClO2 Citric acid (hydrate) C6H3O7 + H2O Dichloroacetic acid C2H2Cl2O2 Diethylamine hydrochloride Ethylamine hydrochloride C4H12ClN C2H8ClN Ethylene glycol C2H6O2 Ethyl ether C4H10O tartrate Formaldehyde Formamide C8H14O6 CH2O CH3NO Furfural C5H4O2 Isoamyl alcohol C5H12O Isobutyl alcohol C4H10O Isobutyric acid C4H8O2 Isovaleric acid Lactic acid Maleic acid C5H10O2 C3H6O C4H4O4 Malic acid C4H6O5 Malonic acid Methyl acetate C3H4O4 C3H6O2 glucoside (α-) Nicotine Nitrophenol (p-) Oxalic acid C7H14O6 C10H14N2 C6H5NO3 C2H2O4 Phenol C6H6O Phenylglycolic acid Picoline (α-) (β-) C8H8O3 C6H7N C6H7N Propionic acid C3H6O2 Pyridine Resorcinol Succinic acid C5H5N C6H6O2 C4H6O4 Tartaric acid (d, l, or dl) C4H6O6 ∗From International Critical Tables, vol. 3, pp. 111–114. d = d w + Aps + Bp s2 + Cps3 t, °C Range, ps A B 18 15 0 4 15 20 25 15 0 25 20  18   25  0  15  30  20   25 18  20   25 21 21  0  15  20   25 15 15 25  20   25 20  15   20  15  18  25 25 25 25  20   25 20 20  0   30 20 15 0 15 17.5 20 25  15   80 25 25 25  18   25 25 18 25 15 17.5 20 30 40 50 60 0–30 0–6 0–100 0–100 0–100 0–100 0–100 0–16 0–89 0–0.6 0–7.9 0–10 0–62 0–70 0–78 0–90 0–32 0–86 0–50 0–30 0–97 0–36 0–65 0–100 0–6 0–5 0–4.5 0–95 0–40 22–96 0–8 0–8 0–2.5 0–8 0–8 0–9 0–9 0–12 0–5 0–9 0–40 0–40 0–40 0–40 0–20 26–51 26–51 0–60 0–1.5 0–4 0–4 0–9 0–4 0–4 0–5 0–65 0–11 0–70 0–60 0–10 0–40 0–60 0–52 0–5.5 0–15 0–50 0–50 0–50 0–50 0–50 0–50 +0.03255 +0.03639 −0.03856 −0.027648 −0.021009 −0.021233 −0.021171 −0.021175 −0.033729 +0.025615 −0.021651 +0.03414 +0.035135 +0.024489 +0.024455 +0.024401 +0.023648 +0.023602 +0.023824 +0.024427 +0.024427 +0.0334 +0.021193 +0.021483 +0.02133 −0.02221 −0.02221 +0.022367 +0.022518 +0.021217 +0.021827 +0.021664 +0.02155 −0.02146 −0.02169 +0.0352 +0.0345 +0.0337 +0.03253 +0.02231 +0.0234 +0.023933 +0.023736 +0.02389 +0.0340 +0.023336 +0.023151 +0.03642 +0.023216 +0.025898 +0.02494 +0.02494 +0.025264 +0.025108 +0.02111 +0.03462 +0.02207 −0.04386 −0.04683 +0.0395 +0.039245 +0.03229 +0.02201 +0.02304 +0.024482 +0.024455 +0.024432 +0.024335 +0.024265 +0.024205 +0.024155 −0.0516 +0.04171 −0.05449 −0.041193 −0.059682 −0.053529 −0.05904 −0.042024 −0.041232 −0.02117 +0.04285 +0.04131 −0.04166 +0.042802 +0.042198 +0.041887 +0.05302 +0.05552 +0.041141 +0.05537 +0.05537 +0.0676 −0.05307 +0.052992 −0.05108 +0.0448 +0.0435 +0.05358 −0.05658 +0.053199 +0.05366 +0.0421 +0.043 +0.056 +0.0438          −0.04282 +0.05186 +0.0575 +0.05957 +0.04175 +0.041066 −0.0574 +0.05996 +0.05975 +0.05454 −0.0455 −0.033185 −0.058 −0.058 −0.031996 −0.031607 −0.04283 −0.0686 +0.0423 −0.051405 −0.0513 −0.04172 −0.0599 −0.05204 +0.05519 C −0.07588 +0.08272 −0.08624 −0.075327 −0.0856 +0.072984 +0.0611 −0.071291 +0.074366 +0.076549 +0.0722 +0.0717 +0.077534 +0.077534 −0.0747 −0.075248 −0.076005 +0.06542 −0.072529 +0.01544 +0.08978 −0.07687 +0.0441 +0.04254 +0.04208 −0.074167 +0.07361 −0.0828 −0.0819 +0.04185 +0.04185 +0.041837 +0.04185 +0.04185 +0.04185 +0.04185 (Continued ) 2-112 PHYSICAL AnD CHEMICAL DATA TABLE 2-63 Densities of Aqueous Solutions of Miscellaneous Organic Compounds (Continued ) d = d w + Aps + Bp s2 + Cps3 (Cont.) Section A Name t, °C Formula Tetraethyl ammonium chloride Thiourea C8H20ClN CH4N2S Trichloroacetic acid C2HCl3O2 Triethylamine hydrochloride C6H16ClN Trimethyl carbinol C4H10O Urea CH4N2O Urethane Valeric acid (n-) C3H7NO2 C5H10O2 Section B Name Formula Butyl alcohol (n-) Butyric acid (n-) Ethyl ether C4H10O C4H8O2 C4H10O Isobutyl alcohol C4H10O Isobutyric acid Nicotine Picoline (α-) (β-) Pyridine Trimethyl carbinol C4H8O2 C10H14N2 C6H7N C6H7N C5H5N C4H10O ds 0.8097 0.9534 0.7077  0.8170   0.8055 0.9425 1.0093 0.9404 0.9515 0.9776 0.7856 Section C Name Formula Allyl alcohol Butyl alcohol (n-) C3H6O C4H10O Chloral hydrate C2H3Cl3O2 Ethyl tartrate C7H14O6 Furfural C5H4O2 Pyridine C5H5N Range, ps 21 15  12.5  20  25 21  20   25 14.8  18  20  25 20 25 ps 76.60 80.95  2.00  10.00  5.00 10.00 25.00  4.62  5.69  6.56 9.34 21.20 29.50 40.40 0–63 0–7 0–61 10–30 0–94 0–54 0–100 0–100 0–12 0–51 0–35 0–10 0–56 0–3 A B C +0.031884 +0.022995 +0.02499 +0.025053 +0.025051 +0.046 −0.02117 −0.021286 +0.023213 +0.022718 +0.022702 +0.022728 +0.021278 +0.0334 +0.056 +0.05374 +0.04153 +0.041387 +0.056119 +0.05558 −0.041908 −0.04176 −0.044802 +0.051552 +0.053712 −0.041817 −0.05245 −0.0427 +0.07122 +0.061038 −0.0869 +0.07957 +0.07887 +0.051216 +0.072573 −0.072285 +0.051379 −0.073437 d = ds + Apw + Bp w2 + Cp w3 t, °C Range, pw A B 20 25 25 0 15 26 20 25 25 25 20 0–20 0–38 0–1.1 0–14 0–16 0–80 0–40 0–30 0–40 0–40 0–20 +0.022103 +0.021854 +0.0234 +0.022437 +0.02224 +0.021808 +0.02199 +0.022715 +0.021925 +0.021157 +0.022287 −0.04113 −0.042314 +0.0336 −0.04285 −0.04129 −0.042358 −0.04331 −0.04393 −0.04352 −0.05536 +0.05275 C +0.061253 +0.07315 +0.0625 −0.062 dt = do + At + Bt2 do Range, °C A B 0.9122 0.8614 1.0094 1.0476 1.0150 1.0270 1.0665 1.0125 1.0140 1.0155 1.0055 1.0115 1.0145 1.0182 0–45 0–43 7–80 7–80 15–80 15–80 15–80 22–74 22–74 22–74 11–73 14–73 12–72 9–74 −0.038 −0.037292 −0.042597 −0.047955 −0.032103 −0.032116 −0.03401 −0.03232 −0.03221 −0.03211 −0.03171 −0.03378 −0.03463 −0.03605 −0.0527 −0.0675 −0.054313 −0.054253 −0.052544 −0.062929 −0.0523 −0.05254 −0.05268 −0.05290 −0.053615 −0.05248 −0.05235 −0.05167 DEnSITIES OF MISCELLAnEOUS MATERIALS 2-113 DEnSITIES OF MISCELLAnEOUS MATERIALS TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids* Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material. Substance Metals, Alloys, Ores Aluminum, cast-hammered bronze Brass, cast-rolled Bronze, 7.9 to 14% Sn phosphor Sp. gr. Aver. density lb/ft 3 Substance Sp. gr. Aver. density lb/ft 3 Timber, Air-dry Apple Ash, black white Birch, sweet, yellow Cedar, white, red 0.66–0.74 0.55 0.64–0.71 0.71–0.72 0.35 44 34 42 44 22 2.55–2.80 7.7 8.4–8.7 7.4–8.9 8.88 165 481 534 509 554 Copper, cast-rolled ore, pyrites German silver Gold, cast-hammered coin (U.S.) 8.8–8.95 4.1–4.3 8.58 19.25–19.35 17.18–17.2 556 262 536 1205 1073 Cherry, wild red Chestnut Cypress Elm, white Fir, Douglas 0.43 0.48 0.45–0.48 0.56 0.48–0.55 27 30 29 35 32 Iridium Iron, gray cast cast, pig wrought spiegeleisen 21.78–22.42 7.03–7.13 7.2 7.6–7.9 7.5 1383 442 450 485 468 balsam Hemlock Hickory Locust Mahogany 0.40 0.45–0.50 0.74–0.80 0.67–0.77 0.56–0.85 25 29 48 45 44 ferro-silicon ore, hematite ore, limonite ore, magnetite slag 6.7–7.3 5.2 3.6–4.0 4.9–5.2 2.5–3.0 437 325 237 315 172 Maple, sugar white Oak, chestnut live red, black 0.68 0.53 0.74 0.87 0.64–0.71 43 33 46 54 42 Lead ore, galena Manganese ore, pyrolusite Mercury 11.34 7.3–7.6 7.42 3.7–4.6 13.6 710 465 475 259 849 8.97 8.9 21.5 10.4–10.6 7.83 7.80 7.70–7.73 7.2–7.5 6.4–7.0 19.22 555 537 1330 656 489 487 481 459 418 1200 white Pine, Norway Oregon red Southern white 0.77 0.55 0.51 0.48 0.61–0.67 0.43 48 34 32 30 38–42 27 Poplar Redwood, California Spruce, white, red Teak, African Indian Walnut, black Willow 0.43 0.42 0.45 0.99 0.66–0.88 0.59 0.42–0.50 27 26 28 62 48 37 28 6.9–7.2 3.9–4.2 440 253 Various Solids Cereals, oats, bulk barley, bulk corn, rye, bulk wheat, bulk Cork 0.51 0.62 0.73 0.77 0.22–0.26 26 39 45 48 15 Various Liquids Alcohol, ethyl (100%) methyl (100%) Acid, muriatic, 40% nitric, 91% sulfuric, 87% 0.789 0.796 1.20 1.50 1.80 49 50 75 94 112 Cotton, flax, hemp Fats Flour, loose pressed Glass, common 1.47–1.50 0.90–0.97 0.40–0.50 0.70–0.80 2.40–2.80 93 58 28 47 162 Chloroform Ether Lye, soda, 66% Oils, vegetable mineral, lubricants 1.500 0.736 1.70 0.91–0.94 0.88–0.94 95 46 106 58 57 plate or crown crystal dint Hay and straw, bales Leather 2.45–2.72 2.90–3.00 3.2–4.7 0.32 0.86–1.02 161 184 247 20 59 0.861–0.867 1.0 0.9584 0.88–0.92 0.125 54 62.428 59.830 56 8 1.02–1.03 64 Paper Potatoes, piled Rubber, caoutchouc goods Salt, granulated, piled 0.70–1.15 0.67 0.92–0.96 1.0–2.0 0.77 58 44 59 94 48 Ashlar Masonry Bluestone Granite, syenite, gneiss Limestone Marble Sandstone 2.3–2.6 2.4–2.7 2.1–2.8 2.4–2.8 2.0–2.6 153 159 153 162 143 Saltpeter Starch Sulfur Wool 1.07 1.53 1.93–2.07 1.32 67 96 125 82 Rubble Masonry Bluestone Granite, syenite, gneiss Limestone Marble Sandstone 2.2–2.5 2.3–2.6 2.0–2.7 2.3–2.7 1.9–2.5 147 153 147 156 137 Monel metal, rolled Nickel Platinum, cast-hammered Silver, cast-hammered Steel, cold-drawn machine tool Tin, cast-hammered cassiterite Tungsten Zinc, cast-rolled blende Turpentine Water, 4°C max. density 100°C ice snow, fresh fallen sea water ∗From Marks’ Standard Handbook for Mechanical Engineers, 10th ed., McGraw-Hill, 1996. Sp. gr. Aver. density lb/ft 3 Dry Rubble Masonry Granite, syenite, gneiss Limestone, marble Sandstone, bluestone 1.9–2.3 1.9–2.1 1.8–1.9 130 125 110 Brick Masonry Hard brick Medium brick Soft brick Sand-lime brick 1.8–2.3 1.6–2.0 1.4–1.9 1.4–2.2 128 112 103 112 Concrete Masonry Cement, stone, sand slag, etc. cinder, etc. 2.2–2.4 1.9–2.3 1.5–1.7 144 130 100 0.64–0.72 1.5 0.85–1.00 1.4–1.9 2.08–2.25 40–45 94 53–64 103 94–135 Portland cement Slags, bank slag bank screenings machine slag slag sand 3.1–3.2 1.1–1.2 1.5–1.9 1.5 0.8–0.9 196 67–72 98–117 96 49–55 Earth, etc., Excavated Clay, dry damp plastic and gravel, dry Earth, dry, loose dry, packed moist, loose moist, packed mud, flowing mud, packed Riprap, limestone 1.0 1.76 1.6 1.2 1.5 1.3 1.6 1.7 1.8 1.3–1.4 63 110 100 76 95 78 96 108 115 80–85 1.4 1.7 1.4–1.7 1.6–1.9 1.89–2.16 90 105 90–105 100–120 126 1.28 1.44 0.96 1.00 1.12 1.00 80 90 60 65 70 65 Minerals Asbestos Barytes Basait Bauxite Bluestone 2.1–2.8 4.50 2.7–3.2 2.55 2.5–2.6 153 281 184 159 159 Borax Chalk Clay, marl Dolomite Feldspar, orthoclase 1.7–1.8 1.8–2.8 1.8–2.6 2.9 2.5–2.7 109 143 137 181 162 Gneiss Granite Greenstone, trap Gypsum, alabaster Hornblende Limestone Marble Magnesite Phosphate rock, apatite Porphyry 2.7–2.9 2.6–2.7 2.8–3.2 2.3–2.8 3.0 2.1–2.86 2.6–2.86 3.0 3.2 2.6–2.9 175 165 187 159 187 155 170 187 200 172 Substance Various Building Materials Ashes, cinders Cement, Portland, loose Lime, gypsum, loose Mortar, lime, set Portland cement Riprap, sandstone Riprap, shale Sand, gravel, dry, loose gravel, dry, packed gravel, wet Excavations in Water Clay River mud Sand or gravel and clay Soil Stone riprap (Continued ) 2-114 PHYSICAL AnD CHEMICAL DATA TABLE 2-64 Approximate Specific Gravities and Densities of Miscellaneous Solids and Liquids (Continued ) Water at 4°C and normal atmospheric pressure taken as unity. For more detailed data on any material, see the section dealing with the properties of that material. Substance Aver. density lb/ft3 Substance 0.37–0.90 2.5–2.8 2.0–2.6 2.7–2.8 2.6–2.9 40 165 143 171 172 Bituminous Substances Asphaltum Coal, anthracite bituminous lignite peat, turf, dry 1.1–1.5 1.4–1.8 1.2–1.5 1.1–1.4 0.65–0.85 81 97 84 78 47 2.6–2.8 2.6–2.7 169 165 1.5 1.7 1.5 1.3 1.5 96 107 95 82 92 charcoal, pine charcoal, oak coke Graphite Paraffin 0.28–0.44 0.47–0.57 1.0–1.4 1.64–2.7 0.87–0.91 23 33 75 135 56 Sp. gr. Minerals (Cont.) Pumice, natural Quartz, flint Sandstone Serpentine Shale, slate Soapstone, talc Syenite Stone, Quarried, Piled Basalt, granite, gneiss Greenstone, hornblende Limestone, marble, quartz Sandstone Shale Aver. density lb/ft 3 Sp. gr. Substance Sp. gr. Aver. density lb/ft3 Bituminous Substances (Cont.) Petroleum refined (kerosene) benzine gasoline Pitch Tar, bituminous 0.87 0.78–0.82 0.73–0.75 0.70–0.75 1.07–1.15 1.20 54 50 46 45 69 75 Coal and Coke, Piled Coal, anthracite bituminous, lignite peat, turf charcoal coke 0.75–0.93 0.64–0.87 0.32–0.42 0.16–0.23 0.37–0.51 47–58 40–54 20–26 10–14 23–32 note: To convert pounds per cubic foot to kilograms per cubic meter, multiply by 16.02. °F = 9⁄5°C + 32. TABLE 2-65 Density (kg/m3) of Selected Elements as a Function of Temperature Element symbol Temperature, K∗ Al Be† Cr Cu Au Ir Fe Pb Mo Ni Pt Ag Zn† 50 100 150 200 250 2736 2732 2726 2719 2710 3650 3640 3630 3620 3610 7160 7155 7150 7145 7140 9019 9009 8992 8973 8951 19,490 19,460 19,420 19,380 19,340 22,600 22,580 22,560 22,540 22,520 7910 7900 7890 7880 7870 11,570 11,520 11,470 11,430 11,380 10,260 10,260 10,250 10,250 10,250 8960 8950 8940 8930 8910 21,570 21,550 21,530 21,500 21,470 10,620 10,600 10,575 10,550 10,520 7280 7260 7230 7200 7170 300 400 500 600 800 2701 2681 2661 2639 2591 3600 3580 3555 3530 7135 7120 7110 7080 7040 8930 8885 8837 8787 8686 19,300 19,210 19,130 19,040 18,860 22,500 22,450 22,410 22,360 22,250 7860 7830 7800 7760 7690 11,330 11,230 11,130 11,010 10,430 10,240 10,220 10,210 10,190 10,160 8900 8860 8820 8780 8690 21,450 21,380 21,330 21,270 21,140 10,490 10,430 10,360 10,300 10,160 7135 7070 7000 6935 6430 1000 1200 1400 1600 1800 2365 2305 2255 7000 6945 6890 6760 6700 8568 8458 7920 7750 7600 18,660 18,440 17,230 16,950 22,140 22,030 21,920 21,790 21,660 7650 7620 7520 7420 7320 10,190 9,940 10,120 10,080 10,040 10,000 9,950 8610 8510 8410 8320 7690 21,010 20,870 20,720 20,570 20,400 10,010 9,850 9,170 8,980 6260 21,510 7030 9,900 7450 20,220 2000 7460 note: Above the horizontal line the condensed phase is solid; below the line, it is liquid. ∗°R = 9⁄ 5 K. † Polycrystalline form tabulated. Similar tables for an additional 45 elements appear in the Handbook of Heat Transfer, 2d ed., McGraw-Hill, New York, 1984. LATEnT HEATS Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄ 5°C + 32. To convert calories per gram to British thermal units per pound, multiply by 1.799. To convert millimeters of mercury to pounds-force per square inch, multiply by 1.934 × 10−2. LATEnT HEATS 2-115 TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds* Unless stated otherwise, the values have been taken from the compilations by K. K. Kelley on “Heats of Fusion of Inorganic Compounds,” U.S. Bur. Mines Bull. 393 (1936), and “The Free Energies of Vaporization and Vapor Pressures of Inorganic Substances,” U.S. Bur. Mines Bull. 383 (1935). Substance mp, °C Heat of fusion,a,b cal/mol bp at 1 atm, °C Aluminum Al 660.0 2,550 Al2Br6 97.5 5,420 Al2Cl6 192.5 16,960 1000 16,380 AlF3⋅3NaF Al2I6 191.0 7,960 Al2O3 2045 (26,000) Antimony Sb 630.5 4,770 97 3,510 SbBr3 SbCl3 73.4 3,030 SbCl5 4 2,400 655 (27,000) Sb4O6 Sb4S6 546 11,200 Argon A −189.3 290 Arsenic As 814 (6,620) AsBr3 31 2,810 AsCl3 −16 2,420 AsF5 −80.7 2,800 As4O6 313 8,000 Barium Ba 704 (1,400)e 847 6,000 BaBr2 BaCl2 960 5,370 BaF2 1287 3,000 Ba(NO3)2 595 (5,980) Ba3(PO4)2 1730 18,600 BaSO4 1350 9,700 Beryllium Be 1280 2,500e Bismuth Bi 271.3 2,505 BiBr3 BiCl3 224 2,600 Bi2O3 817 6,800 Bi2S5 747 8,900 Boron BBr3 BCl3 BF3 −128 480 B2H6 −165.5 B3H10 −119.8 B5H9 −46.9 B5H11 B10H14 99.7 7,800 B2H5Br −104 B3N3H6 −58 Bromine Br2 −7.2 2,580 BrF5 −61.3 1,355 Cadmium Cd 320.9 1,460 CdBr2 568 (5,000) CdCl2 568 5,300 CdF2 1110 (5,400) CdI2 387 3,660 CdO CdSO4 1000 4,790 Calcium Ca 851 2,230 CaBr2 730 4,180 CaCO3 1282 (12,700) CaCl2 782 6,100 CaF2 1392 4,100 Ca(NO3)2 561 5,120 CaO 2707 (12,240) CaO⋅Al2O3⋅2SiO2 1550 29,400 CaO⋅MgO⋅2SiO2 1392 (18,200) CaO⋅SiO2 1512 13,400 CaSO4 1297 6,700 Carbon C (graphite) 3600 11,000e CBr4 90 1,050 CCl4 −24.0 644 CF4 CH4 −182.5 224 C2N2 −27.8 1,938u CNBr 52 CNCl −5 2,240 ∗See also subsection “Thermodynamic Properties.” Heat of vaporization,a,b cal/mol 2057 256.4 180.2c 61,020 10,920 26,750c 385.5 3000 15,360 1440 46,670 219 172d 1425 10,360 11,570 17,820 −185.8 1,590 610c 31,000c 122 −52.8 457.2 7,570 4,980 14,300 1638 35,670 1420 461 441 18,020 17,350 91.3 12.5 −100.9 −92.4 16 58 67 f 16 50.4 7,300 5,680 4,620 3,685 6,470 7,700 8,500 11,600 6,230 7,670 58.0 40.4 7,420 7,470 765 23,870 967 29,860 796 1559c 25,400 53,820c 1487 36,580 77 −127.9 −161.4 −21.1 13 7,280 3,110 2,040 5,576u 11,010c 6,300 Substance Carbon (Cont.) CNF CNI CO CO2 COS COCl2 CS2 Cerium Ce Cesium Cs CsBr CsCl CsF CsI CsNO3 Chlorine Cl2 ClF ClF3 Cl2O ClO2 Cl2O7 Chromium Cr Cr O2Cl2 Cobalt Co CoCl2 Copper Cu Cu2Br2 Cu2Cl2 CuI Cu2(CN)2 Cu2O CuO Cu2S Fluorine F2 F2O Gallium Ga Germanium Ge GeH4 Ge2H6 Ge3H8 GeHCl3 GeBr4 GeCl4 Ge(CH3)4 Gold Au Helium He Hydrogen H2 HBr HCl HCN HF (HF)6 HI H2O H22O (= D2O) H2O2 HNO3 H3PO2 H3PO3 H3PO4 H4P2O6 H2S H2S2 H2SO4 H2Se H2SeO4 H2Te Indium In mp, °C Heat of fusion,a,b cal/mol −205.0 −57.5 −138.8 200 1,900 1,129 k −112.0 1,049 l 775 2,120 28.4 500 642 715 3,600 (2,450) 407 3,250 −101.0 1,531m 1550 3,930 1490 727 3,660 7,390 1083.0 3,110 430 4,890 473 1230 1447 1127 (5,400) (13,400) 2,820 5,500 −223 29.8 bp at 1 atm, °C −72.8 141 −191.5 −78.4c −50.2 8.0 5,780c 13,980c 1,444 6,030 c, r 4,423 k 5,990 690 1300 1300 1251 1280 16,320 35,990 35,690 34,330 35,930 −34.1 −101 11.3 2.0 10.9 79 959 −165 −109 −105.6 −71 26.1 −49.5 −88 (8,300) 1063.0 3,030 −271.4 −259.2 −86.9 −114.2 −13.2 −83.0 28 575 476 2,009i 1,094 −50.8 0.0 3.8 −2 −47 17.4 74 42.4 55 −85.5 −87.6 10.5 686 1,436 1,501s 2,520c 600 2,310 3,070 2,520 8,300 568t 1,805 2,360 58 −48.9 3,450 1,670 156.4 781 4,878 m 5,890 6,280 7,100 8,480 2475 117 8,250 1050 27,170 2595 1355 1490 1336 72,810 16,310 11,920 15,940 −188.2 −144.8 1,336 Heat of vaporization,a,b cal/mol 1,640 2,650 2071 −89.1 31.4 110.6 75g 189 84 44 2966 3,580 5,900 7,550 8,000 8,560 7,030 6,460 81,800 −268.4 22 −252.7 −66.7 −85.0 25.7 33.3 51.2 216 4,210 3,860 6,027i 7,460 5,020 100.0 101.4 158 9,729 h,q 9,945 r,q 10,270 −60.3 4,463 t −41.3 4,880 −2.2 5,650 (Continued ) 2-116 PHYSICAL AnD CHEMICAL DATA TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued ) Substance Iodine I2 ICl(α) ICl(β) IF7 Iron Fe FeCl2 Fe2Cl6 Fe(CO)5 FeO FeS Krypton Kr Lead Pb PbBr2 PbCl2 PbF2 PbI2 PbMoO4 PbO PbS PbSO4 PbWO4 Lithium Li LiBO2 LiBr LiCl LiF LiI LiOH Li2MoO4 LiNO3 Li2SiO3 Li4SiO4 Li2SO4 Li2WO4 Magnesium Mg MgBr2 MgCl2 MgF2 MgO Mg3(PO4)2 MgSiO3 MgSO4 MgZn2 Manganese Mn MnCl2 MnSiO3 MnTiO3 Mercury Hg HgBr2 HgCl2 HgI2 HgSO4 Molybdenum Mo MoF6 MoO3 Neon Ne Nickel Ni NiCl2 Ni(CO)4 Ni2S Ni3S2 Nitrogen N2 NF3 NH3 NH4CNS NH4NO3 N2O NO N2O4 N2O5 NOCl Osmium OsF8 OsO4 (yellow) OsO4 (white) Oxygen O2 O3 mp, °C 113.0 17.2 13.9 1530 677 304 −21 1380 1195 −157 Heat of fusion,a,b cal/mol bp at 1 atm, °C Heat of vaporization,a,b cal/mol 3,650 2,660 2,270 183 4c 7,460c 3,560 7,800 20,590 3,250 (7,700) 5,000 2735 1026 319 105 84,600 30,210 12,040 9,000 360 e 152.9 10,390 2,310 e 327.4 488 498 824 412 1065 890 1114 1087 1123 1,224 4,290 5,650 1,860 5,970 (25,800) 2,820 4,150 9,600 (15,200) 179 845 552 614 847 440 462 705 1,100 (5,570) 2,900 3,200 (2,360) (1,420) 2,480 4,200 1177 1249 857 742 7,210 7,430 3,040 (6,700) 650 711 712 1221 2642 1184 1524 1127 589 2,160 8,300 8,100 5,900 18,500 (11,300) 14,700 3,500 (8,270) 1107 32,520 1418 32,690 1220 650 1274 1404 3,450 7,340 (8,200) (7,960) 2152 1190 55,150 29,630 557 3,960 4,150 4,500 (1,440) 361 319 304 354 13,980 14,080 14,080 14,260 (6,660) 2,500 (2,500) (4800) 36 1151 (128,000) 6,000 −38.9 241 277 250 850 2622 17 745 −248.5 1744 914 954 1293 872 42,060 27,700 29,600 38,300 24,850 1472 1281 51,310 (50,000) 1372 32,250 1310 1382 1681 1171 35,420 35,960 50,970 40,770 77 −246.0 440e 1455 4,200 645 790 (2,980) 5,800 2730 987c 42.5 87,300 48,360c 7,000 −195.8 −129.0 −33.4 1,336 3,000 5,581n −88.5 −151.7 30 32.4 −6.4 3,950 3,307 7,040 13,800c 6,140 47.4 130 6,840 9,450 −183.0 −111 1,629 2,880 −210.0 −77.7 146 169.6 −90.8 −163.6 −13 56 42 −218.9 172 1,352 (4,700) 1,460 1,563 550 5,540 n 4,060 2,340 106 Substance Palladium Pd Phosphorus P4 (yellow) P4 (violet) P4 (black) PCl3 PH3 P4O6 P4O10(α) P4O10(β) POCl3 P 2S 3 Platinum Pt Potassium K KBO2 KBr KCl KCN KCNS K2CO3 K2Cr O4 K2Cr2O7 KF KI K2MoO4 KNO3 KOH KPO3 K3PO4 K4P2O7 K2SO4 K2TiO3 K2WO4 Praseodymium Pr Radon Rn Rhenium Re Re2O7 Re2O8 Rubidium Rb RbBr RbCl RbF RbI RbNO3 Selenium Se2 Se6 SeF6 SeO2 SeOCl2 Silicon Si SiCl4 Si2Cl6 Si3Cl8 (SiCl3)2O SiF4 Si2F6 SiF3Cl SiF2Cl2 SiH4 Si2H6 Si3H8 Si4H10 SiH3Br SiH2Br2 SiHCl3 (SiH3)3N (SiH3)2O SiO2 (quartz) SiO2 (cristobalite) Silver Ag AgBr AgCl AgCN AgI AgNO3 Ag2S Ag2SO4 Sodium Na NaBO2 mp, °C 1554 Heat of fusion,a,b cal/mol bp at 1 atm, °C Heat of vaporization,a,b cal/mol 4,120 44.2 615 −133.8 23.8 569 270o 3,360 17,080 1.1 3,110 1773.5 4,700 (4400) (107,000) 63.5 947 742 770 623 179 897 984 398 857 682 922 338 360 817 1340 1092 1074 810 927 574 (5,700) 5,000 6,410 (3,500) 2,250 7,800 6,920 8,770 6,500 4,100 (4,000) 2,840 (2,000) 2,110 8,900 14,000 8,100 (10,600) (4,400) 776 18,920 1383 1407 37,060 38,840 1324 34,690 1327 30,850 932 2,700 −71 (3000) 296 147 15,340 3,800 39.1 677 717 833 638 305 525 3,700 4,400 4,130 2,990 1,340 217 1,220 10 1,010 1427 −67.6 −1 9,470 1,845 −33 −18.5 −138 −144 −185 −132.5 −117 −93.5 −93.8 −70.0 −126.5 −105.6 −144 1470 1700 3,400 2,100 960.5 430 455 350 557 209 842 657 2,700 2,180 3,155 2,750 2,250 2,755 3,360 (4,300) 97.7 966 630 8,660 3,900 280 417c 453c 74.2 −87.7 174 591 358c 105.1 508 12,520 25,600c 33,100 7,280 3,489 o 10,380 20,670 8,380 −61.8 4,010 362.4 18,060 679 1352 1381 1408 1304 753 736 −45.8c 317c 168 2290 56.8 139 211.4 135.6 −94.8c −18.9c −70.1 −31.5 −111.6 −14.3 53.1 100 2.4 70.5 31.8 48.7 −15.4 2230 2212 18,110 37,120 36,920 39,510 35,960 25,490 20,600 6,350c 20,900 6,860 12,340 8,820 6,130c 10,400c 4,460 5,080 2,960 5,110 6,780 8,890 5,650 6,840 6,360 6,850 5,350 60,720 1564 42,520 1506 34,450 914 23,120 (Continued ) LATEnT HEATS 2-117 TABLE 2-66 Heats of Fusion and Vaporization of the Elements and Inorganic Compounds (Continued ) Substance Sodium (Cont.) NaBr NaCl NaClO3 NaCN NaCNS Na2CO3 NaF NaI Na2MoO4 NaNO3 NaOH ½Na2O⋅½Al2O3⋅3SiO2 NaPO3 Na4P2O7 Na2S Na2SiO3 Na2Si2O5 Na2SO4 Na2WO4 Strontium Sr SrBr2 SrCl2 SrF2 Sr3(PO4)2 Sulfur S (rhombic) S (monoclinic) S2Cl2 SF6 SO2 SO3(α) SO3(β) SO3(γ) SOBr2 SOCl2 SO2Cl2 Tellurium Te TeCl4 TeF6 mp, °C Heat of fusion,a,b cal/mol 747 800 255 562 323 854 992 662 687 310 322 1107 988 970 920 1087 884 884 702 6,140 7,220 5,290 (4,400) 4,450 7,000 7,000 5,240 3,600 3,760 2,000 13,150 (5,000) (13,700) (1,200) 10,300 8,460 5,830 5,800 757 643 872 1400 1770 2,190 4,780 4,100 4,260 18,500 112.8 119.2 −75.5 17 32.4 62.2 453 1,769p 2,060 2,890 6,310 3,230 bp at 1 atm, °C Heat of vaporization,a,b cal/mol 1392 1465 37,950 40,810 1500 37,280 1704 53,260 1378 1384 33,610 444.6 2,200 138 −63.5c −5.0 44.8 8,720 5,600c 5,960p 10,190 139.5 75.4 69.2 9,920 7,600 7,760 1090 392 −38.6c 16,830 6,700c Values in parentheses are uncertain. For the freezing point or the normal boiling point unless otherwise stated. c Sublimation. d Decomposes at about 75°C; value obtained by extrapolation. e Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York (1936). f Decomposes before the normal boiling point is reached. g Decomposes at about 40°C; value obtained by extrapolation. h See also pp. 2-304 through 2-307 on steam table. i Giauque and Ruehrwein, J. Am. Chem. Soc., 61 (1939): 2626. j Giauque and Egan, J. Chem. Phys., 5 (1937): 45. Substance Thallium Tl TlBr TlCl Tl2CO3 TlI TlNO3 Tl2S Tl2SO4 Tin Sn4 SnBr2 SnBr4 SnCl2 SnCl4 Sn(CH3)4 SnH4 SnI4 Titanium TiBr4 TiCl4 TiO2 Tungsten W WF6 Uranium UF6 Xenon Xe Zinc Zn ZnCl2 Zn(C2H5)2 ZnO ZnS Zirconium ZrBr4 Zr Cl4 ZrI4 Zr O2 mp, °C Heat of fusion,a,b cal/mol 302.5 460 427 273 440 207 449 632 1,030 5,990 4,260 4,400 3,125 2,290 3,000 5,500 1457 819 807 38,810 23,800 24,420 823 25,030 231.8 232 30 247 −33.2 1,720 (1,700) 3,000 3,050 2,190 2270 68,000 −149.8 143.5 (4,300) 38.2 −23 1825 (2,060) 2,240 (11,400) 136 3390 −0.4 (8,400) 1,800 (5900) 17.3 (176,000) 6,350 55.1c 9,990c −108.0 3,110 907 732 118 27,430 28,710 8,960 357c 311c 431c 25,800c 25,290c 29,030c −111.5 419.5 283 1975 1645 2715 k b l m TABLE 2-67 Heats of Fusion of Miscellaneous Materials Material 1,595 (5,500) 4,470 (9,000) 20,800 623 113 78.3 −52.3 Heat of vaporization,a,b cal/mol 20,740 8,330 7,320 4,420 8,350 Kemp and Giauque, J. Am. Chem. Soc., 59 (1937): 79. Brown and Manov, J. Am. Chem. Soc., 59 (1937): 500. Giauque and Powell, J. Am. Chem. Soc., 61 (1939): 1970. n Overstreet and Giauque, J. Am. Chem. Soc., 59 (1937): 254. o Stephenson and Giauque, J. Chem. Phys., 5 (1937): 149. p Giauque and Stephenson, J. Am. Chem. Soc., 60 (1938): 1389. q Osborne, Stimson, and Ginnings, Bur. Standards J. Research, 23, 197 (1939): 261. r Miles and Menzies, J. Am. Chem. Soc., 58 (1936): 1067. s Long and Kemp, J. Am. Chem. Soc., 58 (1936): 1829. t Giauque and Blue, J. Am. Chem. Soc., 58 (1936): 831. u Ruehrwein and Giauque, J. Am. Chem. Soc., 61 (1939): 2940. a Alloys 30.5 Pb + 69.5 Sn 36.9 Pb + 63.1 Sn 63.7 Pb + 36.3 Sn 77.8 Pb + 22.2 Sn 1 Pb + 9 Sn 24 Pb + 27.3 Sn + 48.7 Bi 25.8 Pb + 14.7 Sn + 52.4 Bi + 7 Cd Silicates Anorthite (CaAl2Si2O8) Orthoclase (KAlSi2O8) Microcline (KAlSi3O8) Wollastonite (CaSiO8) Malacolite (Ca8MgSi4O12) Diopside (CaMgSi2O4) Olivine (Mg2SiO4) Fayalite (Fe2SiO4) Spermaceti Wax (bees’) 740 bp at 1 atm, °C mp, °C Heat of fusion, cal/g 183 179 177.5 176.5 236 98.8 75.5 17 15.5 11.6 9.54 28 6.85 8.4 43.9 61.8 100 100 83 100 94 100 130 85 37.0 42.3 2-118 PHYSICAL AnD CHEMICAL DATA TABLE 2-68 Heats of Fusion of Organic Compounds The values for the hydrocarbons are from the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards, with some from Parks and Huffman, Ind. Eng. Chem., 23, 1138 (1931). The values for the nonhydrocarbon compounds were recalculated from data in International Critical Tables, vol. 5. Hydrocarbon compounds Formula mp, °C Heat of fusion, cal/g Paraffins Methane Ethane Propane n-Butane 2-Methylpropane n-Pentane 2-Methylbutane 2,2-Dimethylpropane n-Hexane 2-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane n-Heptane 2-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbutane n-Octane 2-Methylheptane 3-Methylpentane 4-Methylheptane 2,2-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 2-Methyl-3-ethylpentane 3-Methyl-3-ethylpentane 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane 2,2,3,3-Tetramethylbutane n-Nonane n-Decane n-Undecane n-Dodecane Eicosane Pentacosane Tritriacontane Aromatics Benzene Methylbenzene (Toluene) Ethylbenzene o-Xylene m-Xylene p-Xylene n-Propylbenzene Isopropylbenzene 1-Methyl-2-ethylbenzene CH4 C 2H 6 C 3H 8 C4H10 C4H10 C5H12 C5H12 C5H12 C6H14 C6H14 C6H14 C6H14 C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C8H18 C9H20 C10H22 C11H24 C12H26 C20H42 C25H52 C33H68 −182.48 −183.23 −187.65 −138.33 −159.60 −129.723 −159.890 −16.6 −95.320 −153.680 −99.73 −128.41 −90.595 −118.270 −118.593 −123.790 −119.230 −134.46 −24.96 −56.798 −109.04 −120.50 −120.955 −121.18 −91.200 −126.10 −114.960 −90.870 −112.27 −107.365 −100.70 −109.210 +100.69 −53.9 −30.0 −25.9 −9.6 +36.4 +53.3 +71.1 14.03 22.712 19.100 19.167 18.668 27.874 17.076 10.786 36.138 17.407 1.607 2.251 33.513 21.158 22.555 13.982 15.968 16.856 5.250 43.169 21.458 23.795 22.692 24.226 26.903 14.9 23.690 22.657 18.061 19.278 3.204 19.392 14.900 41.2 48.3 34.1 51.3 52.0 53.6 54.0 C 6H 6 C 7H 8 C8H10 C8H10 C8H10 C8H10 C9H12 C9H12 C9H12 +5.533 −94.991 −94.950 −25.187 −47.872 +13.263 −99.500 −96.028 −80.833 30.100 17.171 20.629 30.614 26.045 38.526 16.97 19.22 21.13 Nonhydrocarbon compounds Formula mp, °C Acetic acid Acetone Acrylic acid Allo-cinnamic acid Aminobenzoic acid (o-) (m-) (p-) Amyl alcohol Anethole Aniline Anthraquinone Apiol Azobenzene Azoxybenzene C2H4O2 C3H6O C3H4O2 C9H8O2 C7H7NO2 C7H7NO2 C7H7NO2 C5H12O C10H12O C6H5NH2 C14H8O2 C12H14O4 C12H10N2 C12H10N2O 16.7 −95.5 12.3 68 145 179.5 188.5 −78.9 22.5 −6.3 284.8 29.5 67.1 36 46.68 23.42 37.03 27.35 35.48 38.03 36.46 26.65 25.80 27.09 37.48 25.80 28.91 21.62 Benzil Benzoic acid Benzophenone Benzylaniline Bromocamphor Bromochlorbenzene (o-) (m-) (p-) Bromoiodobenzene (o-) (m-) (p-) Bromol hydrate Bromophenol (p-) Bromotoluene (p-) C14H10O2 C7H8O2 C13H10O C13H13N C10H15BrO C6H4BrCl C6H4BrCl C6H4BrCl C6H4BrI C6H4BrI C6H4BrI C2H3Br3O2 C6H5BrO C7H7Br 95.2 122.45 47.85 32.37 78 −12.6 −21.2 64.6 21 9.3 90.1 46 63.5 28 22.15 33.90 23.53 21.86 41.57 15.41 15.29 23.41 12.18 10.27 16.60 16.90 20.50 20.86 Heat of fusion, cal/g Hydrocarbon compounds Aromatics—(Cont.) 1-Methyl-3-ethylbenzene 1-Methyl-4-ethylbenzene 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 1,3,5-Trimethylbenzene Naphthalene Camphene Durene Isodurene Prehnitene p-Cymene n-Butyl benzene tert-Butyl benzene β-Methyl naphthalene Diphenyl Hexamethyl benzene Diphenyl methane Anthracene Phenanthrene Tolane Stilbene Dibenzil Triphenyl methane Alkyl cyclohexanes Cyclohexane Methylcyclohexane Alkyl cyclopentanes Cyclopentane Methylcyclopentane Ethylcyclopentane 1,1-Dimethylcyclopentane cis-1,2-Dimethylcyclopentane trans-1,2-Dimethylcyclopentane trans-1,3-Dimethylcyclopentane Monoolefins Ethene (Ethylene) Propene (Propylene) 1-Butene cis-2-Butene trans-2-Butene 2-Methylpropene (isobutene) 1-Pentene cis-2-pentene trans-2-pentene 2-Methyl-1-butene 3-Methyl-1-butene 2-Methyl-2-butene Acetylenes Acetylene 2-Butyne (dimethylacetylene) mp, °C Heat of fusion, cal/g C9H12 C9H12 C9H12 C9H12 C9H12 C10H8 C10H12 C10H14 C10H14 C10H14 C10H14 C10H14 C10H14 C11H10 C12H10 C12H18 C13H12 C14H10 C14H10 C14H10 C14H12 C14H14 C19H16 −95.55 −62.350 −25.375 −43.80 −44.720 +80.0 +51 +79.3 −24.0 −7.7 −68.9 −88.5 −58.1 +34.1 +68.6 +165.5 +25.2 +216.5 +96.3 +60 +124 +51.4 +92.1 15.14 25.29 16.64 24.54 18.97 36.0 57 37.4 23.0 20.0 17.1 19.5 14.9 20.1 28.8 30.4 26.4 38.7 25.0 28.7 40.0 30.7 21.1 C6H12 C7H14 +6.67 −126.58 7.569 16.429 C5H10 C6H12 C7H14 C7H14 C7H14 C7H14 C7H14 −93.80 −142.445 −138.435 −69.73 −53.85 −117.57 −133.680 2.068 19.68 11.10 3.36 3.87 15.68 17.93 C2H4 C3H6 C4H8 C4H8 C4H8 C4H8 C5H10 C5H10 C5H10 C5H10 C5H10 C5H10 −169.15 −185.25 −185.35 −138.91 −105.55 −140.35 −165.27 −151.363 −140.235 −137.560 −168.500 −133.780 28.547 17.054 16.393 31.135 41.564 25.265 16.82 24.239 26.536 26.879 18.009 25.738 C2H2 C4H6 −81.5 −132.23 23.04 40.808 Formula Formula mp, °C Heat of fusion, cal/g Butyl alcohol (n-) (t-) Butyric acid (n-) C4H10O C4H10O C4H8O2 −89.2 25.4 −5.7 29.93 21.88 30.04 Capric acid (n-) Caprylic acid (n-) Carbazole Carbon tetrachloride Carvoxime (d-) (l-) (dl-) Cetyl alcohol Chloracetic acid (α-) (β-) Chloral alcoholate hydrate Chloroaniline (p-) Chlorobenzoic acid (o-) (m-) ( p-) Chloronitrobenzene (m-) (p-) Cinnamic acid anhydride Cresol (p-) Crotonic acid (α-) (cis-) Cyanamide Cyclohexanol C10H20O2 C8H16O2 C12H9N CCl4 C10H15NO C10H15NO C10H15NO C16H34O C2H3ClO2 C2H3ClO2 C4H7Cl3O2 C2H3Cl3O2 C6H6ClN C7H5ClO2 C7H5ClO2 C7H5ClO2 C6H4ClNO2 C6H4ClNO2 C9H8O2 C18H14O3 C7H8O C4H6O2 C4H6O2 CH2N2 C6H12O 31.99 16.3 243 −22.8 71.5 71 91 49.27 61.2 56 9 47.4 71 140.2 154.25 239.7 44.4 83.5 133 48 34.6 72 71.2 44 25.46 38.87 35.40 42.05 41.57 23.29 23.41 24.61 33.80 31.06 35.12 24.03 33.18 37.15 39.30 36.41 49.21 29.38 31.51 36.50 28.14 26.28 25.32 34.90 49.81 4.19 Nonhydrocarbon compounds (Continued ) LATEnT HEATS 2-119 TABLE 2-68 Heats of Fusion of Organic Compounds (Continued ) Heat of fusion, cal/g Nonhydrocarbon compounds Formula mp, °C Dibromobenzene (o-) (m-) (p-) Dibromophenol (2, 4-) Dichloroacetic acid Dichlorobenzene (o-) (m-) (p-) Dihydroxybenzene (o-) (m-) (p-) Di-iodobenzene (o-) (m-) (p-) Dimethyl tartrate (dl-) (d-) pyrone Dinitrobenzene (o-) (m-) (p-) Dinitrotoluene (2, 4-) Dioxane Diphenyl amine C6H4Br2 C6H4Br2 C6H4Br2 C6H4Br2O C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C6H6O2 C6H6O2 C6H6O2 C6H4I2 C6H4I2 C6H4I2 C6H10O6 C6H10O6 C7H8O2 C6H4N2O4 C6H4N2O4 C6H4N2O4 C7H6N2O4 C4H8O2 C12H11N 1.8 −6.9 86 12 −4(?) −16.7 −24.8 53.13 104.3 109.65 172.3 23.4 34.2 129 87 49 132 116.93 89.7 173.5 70.14 11.0 52.98 12.78 13.38 20.55 13.97 14.21 21.02 20.55 29.67 49.40 46.20 58.77 10.15 11.54 16.20 35.12 21.50 56.14 32.25 24.70 39.99 26.40 34.85 25.23 Elaidic acid Ethyl acetate alcohol Ethylene dibromide Ethyl ether C18H34O2 C4H8O2 C2H6O C2H4Br2 C4H10O 44.4 83.8 −114.4 10.012 −116.3 52.08 28.43 25.76 13.52 23.54 Formic acid CH2O2 8.40 58.89 Glutaric acid Glycerol Glycol, ethylene C6H8O4 C3H8O3 C2H6O2 97.5 18.07 −11.5 37.39 47.49 43.26 Hydrazo benzene Hydrocinnamic acid Hydroxyacetanilide C12H12N2 C9H10O2 C8H9NO2 134 48 91.3 22.89 28.14 33.59 Iodotoluene (p-) Isopropyl alcohol ether C7H7I C3H8O C6H14O 34 −88.5 −86.8 18.75 21.08 25.79 Lauric acid (n-) Levulinic acid C12H24O2 C5H8O3 43.22 33 43.72 18.97 Menthol (l-) (α) Methyl alcohol Myristic acid Methyl cinnamate fumarate oxalate phenylpropiolate succinate C10H20O CH4O C14H28O2 C10H10O2 C6H8O4 C4H6O4 C10H8O2 C6H10O4 43.5 −97.8 53.86 36 102 54.35 18 19.5 18.63 23.7 47.49 26.53 57.93 42.64 22.86 35.72 Formula mp, °C Heat of fusion, cal/g Naphthol (α-) (β-) Naphthylamine (α-) Nitroaniline (o-) (m-) (p-) Nitrobenzene Nitrobenzoic acid (o-) (m-) (p-) Nitronaphthalene Nitrophenol (o-) C10H8O C10H8O C10H9N C6H6N2O2 C6H6N2O2 C6H6N2O2 C6H5NO2 C7H5NO4 C7H5NO4 C7H5NO4 C10H7NO2 C6H5NO3 95.0 120.6 50 71.2 114.0 147.3 5.85 145.8 141.1 239.2 56.7 45.13 38.94 31.30 22.34 27.88 40.97 36.46 22.52 40.06 27.59 52.80 25.44 26.76 Palmitic acid Paraldehyde Pelargic acid (n-) (β-) Pelargonic acid (n-) (α-) Phenol Phenylacetic acid Phenylhydrazine Propyl ether (n) C16H32O2 C6H12O3 C9H18O2 C9H18O2 C6H6O C8H8O2 C6H8N2 C6H14O 61.82 10.5 12.35 40.92 76.7 19.6 −126.1 39.18 25.02 39.04 30.63 29.03 25.44 36.31 20.66 Nonhydrocarbon compounds Quinone C6H4O2 115.7 40.85 Stearic acid Succinic anhydride Succinonitrile C18H30O2 C4H4O3 C4H4N2 68.82 119 54.5 47.54 48.74 11.71 Tetrachloroxylene (o-) (p-) Thiophene Thiosinamine Thymol Toluic acid (o-) (m-) (p-) Toluidine (p-) Tribromophenol (2, 4, 6-) Trichloroacetic acid Trinitroglycerol Trinitrotoluene (2, 4, 6-) Tristearin C8H6Cl4 C8H6Cl4 C4H4S C4H8N2S C10H14O C8H8O2 C8H8O2 C8H8O2 C7H9N C6H3Br3O C2HCl3O2 C3H5N3O9 C7H5N3O6 C57H110O6 86 95 −39.4 77 51.5 103.7 108.75 179.6 43.3 93 57.5 12.3 80.83 70.8, 54.5 21.02 22.10 14.11 33.45 27.47 35.40 27.59 39.90 39.90 13.38 8.60 23.02 22.34 45.63 Undecylic acid (α-) (n-) (β-) (n-) Urethane C11H22O2 C11H22O2 C3H7NO2 28.25 48.7 32.20 42.91 40.85 Veratrol C8H10O2 22.5 27.45 Xylene dibromide (o-) (m-) dichloride (o-) (m-) (p-) C8H8Br2 C8H8Br2 C8H8Cl2 C8H8Cl2 C8H8Cl2 95 77 55 34 100 24.25 21.45 29.03 26.64 32.73 2-120 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) Cmpd. no.* 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 Mol. wt. C1 × 1E-07 C2 C3 C4 Tmin , K ΔHv at Tmin × 1E-07 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 3.4088 9.9475 6.127546 5.8564 4.9258 3.8345 1.7059 6.6599 4.3756 4.3052 0.74587 3.1523 7.6926 0.84215 8.7809 5.0007 6.081621 11.374 6.4966 10.523 8.4762 8.2051 11.544 7.6737 5.5242 5.0392 3.9247 3.1988 3.039582 3.8018 3.6238 9.4943 11.344 7.1274 7.5007 3.3774 4.3478 3.8671 8.8262 8.0911 5.0883 4.7563 4.3143 4.17 6.1947 5.1323 0.043317 0.94835 3.683421 0.33055 1.0809 0.033941 -0.52025 2.2443 2.2571 0.095188 0.47571 0.3914 1.4255 0.28333 0.1933 0.65393 0.2724357 1.4864 0.54598 0.87091 0.35251 1.4438 2.2311 0.28923 1.5015 -0.2027 0.28886 0.2896 0.2698591 0.90446 0.8337 0.64824 1.4414 0.0483 0.09616 0.5107 1.3196 1.0672 1.7772 1.2599 0.47166 0.49657 1.0149 0.23488 1.6524 0.32362 0.21502 -0.51011 -6.193052 -0.057073 -1.3684 0.34283 1.0982 -2.9192 -4.5116 0.47381 -0.71131 -0.2289 -1.6901 0.033281 0.30877 -0.27698 0.4430641 -2.3097 -0.42255 -0.45568 0.43853 -1.8053 -2.5186 0.34048 -1.7185 1.2207 0.38616 0.0344 -0.3789853 -0.74555 -0.82274 -0.24961 -1.9412 0.8966 1.1444 -0.17304 -1.5096 -1.2574 -1.926 -1.2911 -0.0078998 -0.13123 -0.99196 0.020947 -2.8505 0.16979 0.23791 0.015094 2.977694 0.083671 0.69723 -0.13415 -0.29832 1.1113 2.5738 -0.26294 0.60517 0.2309 0.72371 0.030551 -0.14162 0.029569 -0.3449689 1.4025 0.2597 149.780 353.150 289.810 200.150 178.450 229.315 192.400 185.450 286.150 189.630 59.150 195.410 235.650 83.780 403.000 278.680 258.270 395.450 260.280 321.350 257.850 275.650 243.950 342.200 265.850 242.430 154.250 179.440 136.950 164.250 134.860 220.000 196.150 183.850 158.450 87.800 134.260 167.620 199.650 185.300 157.460 133.020 147.430 176.800 250.000 161.300 3.23240 6.36890 2.44660 5.14960 3.66050 3.52490 1.62620 3.63950 2.79650 3.89890 0.63247 2.52980 5.10000 0.65440 7.12860 3.49320 5.06340 6.94850 5.33600 7.48950 6.88000 5.24700 6.26740 6.11280 3.28440 4.71870 3.42380 2.75620 2.82540 2.76410 2.86840 7.58750 8.14880 6.36430 6.59780 3.01970 3.10310 2.77200 5.32550 5.94710 4.37960 4.18430 3.20490 3.77230 4.16190 4.57590 -0.3026 0.79682 0.83063 -0.26011 0.6614 -0.70705 -0.35786 0.0114 0.5165115 0.24234 0.39613 0.058188 1.035 -0.5116 -0.78448 0.05181 0.63987 0.62539 0.63659 0.47381 -0.071247 0.027307 0.40891 0.086255 1.6285 -0.18921 Tmax , K 466.000 761.000 591.950 606.000 508.200 545.500 308.300 506.000 615.000 540.000 132.450 405.650 645.600 150.860 824.000 562.050 689.000 751.000 702.300 830.000 720.150 662.000 718.000 773.000 584.150 670.150 503.800 464.000 452.000 425.000 425.120 680.000 676.000 563.100 535.900 419.500 435.500 428.600 575.400 660.500 570.100 554.000 440.000 537.200 615.700 585.400 ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide CO2 CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 44.0095 76.1407 28.0101 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 2.173 4.0359 0.8585 4.6113 1.9311 3.068 4.6746 3.253 5.3032 2.442 3.93706 3.9033 6.87 13.355 8.0979 7.5255 2.3558 3.6762 5.193 5.5761 6.6898 4.698 3.4216 3.6524 2.7681 6.7798 9.0851 8.7515 12.531 7.9041 6.6985 8.4103 10.603 0.11867 4.7061 6.057225 6.1207 6.4978 5.3065 6.4394 7.0416 4.7631 5.6489 4.8739 5.6495 4.2593 12.931 2.595917 5.947 4.7806 0.382 1.0897 0.4921 0.55241 0.94983 0.8458 0.013055 0.321 1.0366 -0.298 0.14297 0.3867 -0.39158 2.3486 -0.33815 1.3714 -0.29499 0.76666 1.0019 -1.7498 1.0012 0.44894 -0.21723 0.17652 0.44645 1.1402 1.3026 1.3204 0.76281 -1.36 0.76944 0.40556 1.7758 -0.31087 0.098096 1.372193 1.2282 0.77464 0.20288 0.67955 0.96641 1.0048 1.0038 0.9583 1.0359 -0.0038971 1.2215 -1.334101 1.6416 0.39507 -0.4339 -1.6483 -0.326 -0.18725 -1.0615 -0.9001 0.51777 -0.252 -0.79572 0.87 0.55088 0.008595 1.7208 -2.5463 2.3495 -1.5024 0.34496 -0.74793 -1.0159 4.5168 -0.96028 0.070295 1.0245 0.2777 -0.28756 -1.1701 -1.6803 -1.2441 -0.32459 4.0854 -0.79975 0.34553 -1.6849 0.28353 0.20134 -2.053024 -1.1989 -0.67379 0.039962 -0.58058 -0.86362 -1.2457 -0.7936 -0.79374 -0.98747 0.58142 -1.3197 2.366723 -1.7394 -0.028657 0.42213 0.9779 0.2231 0.022973 0.51894 0.453 -0.18852 0.295 0.16746 -0.271 -0.3511 -0.016793 -0.97478 0.74218 -1.7015 0.59731 0.24271 0.35979 0.46332 -2.4034 0.37622 -0.14736 -0.49752 -0.10817 0.21791 0.45855 0.86441 0.38061 0.054808 -2.3871 0.42379 -0.4009 0.38281 0.34543 0.22064 1.161394 0.40137 0.31825 0.12466 0.36746 0.32976 0.67919 0.17013 0.28069 0.39006 -0.23734 0.50585 -0.7871881 0.5831 0.014929 216.580 161.110 68.130 250.330 89.560 172.120 227.950 136.750 209.630 175.430 150.350 155.970 285.390 304.190 307.930 177.140 245.250 182.480 279.690 296.600 242.000 169.670 179.280 138.130 145.590 189.640 285.000 243.510 304.550 280.050 206.890 247.560 229.150 18.730 210.150 282.850 220.600 175.300 248.390 256.150 326.140 176.190 237.490 178.010 192.500 172.710 301.150 223.350 156.850 169.200 1.52020 3.17860 0.65166 3.47600 1.42150 2.28780 4.32240 2.95540 3.65460 2.41470 3.56930 3.36320 6.37340 6.06020 6.57120 5.41880 2.33890 2.81720 3.38860 6.25790 4.84470 3.98460 3.30460 3.37950 2.33840 5.10540 6.02700 5.60450 8.84640 8.29590 5.35240 6.81720 6.07920 0.12605 4.35520 4.06410 4.18700 5.24340 4.77510 5.09850 4.68520 3.62860 3.84750 3.58500 4.13210 4.03570 8.64260 3.35400 3.75450 4.15460 304.210 552.000 132.920 556.350 227.510 417.150 632.350 460.350 536.400 416.250 503.150 489.000 705.850 697.550 704.650 631.000 400.150 459.930 553.800 650.100 653.000 560.400 511.700 507.000 398.000 664.000 674.000 617.700 722.100 688.000 616.600 696.000 619.850 38.350 628.000 650.150 611.000 584.100 683.950 705.000 684.750 523.000 561.600 510.000 560.000 572.000 736.600 496.600 466.700 557.150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued ) 2-121 2-122 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 Name 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Formula C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 CAS Mol. wt. C1 × 1E-07 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 3.663 4.2313 3.3907 2.8258 4.630224 5.2429 4.3872 4.7999 3.6881 3.4422 4.8054 5.5503 5.4479 5.8702 5.8328 2.6377 5.9186 5.3387 10.263 2.919 4.5493 7.0161 7.66109 5.0368 6.9745 7.993218 10.962 12.86 2.1091 6.5831 4.8272 4.275 7.4288 6.8245 8.7212 5.7624 6.0933 5.7997 2.0639 5.6091 8.9207 4.7462 4.4514 4.4151 11.08845 C2 0.93553 0.90591 1.1148 -1.5731 1.265631 0.80535 0.56226 0.30724 0.37958 -0.49774 1.0013 0.7692 0.56826 1.0022 0.99061 -0.072806 0.37731 0.9509 1.504 0.47315 0.81834 0.9938 0.36322 0.37438 0.43414 1.697066 1.5544 0.50351 0.60646 1.1905 0.2372 0.5857 1.6218 1.071 0.79255 0.46881 0.96339 1.0161 0.80153 0.077011 0.83021 0.37327 1.1569 0.51536 0.7029 C3 C4 Tmin , K ΔHv at Tmin × 1E-07 -0.9806 -0.59583 -1.2957 2.9709 -2.325122 -1.4147 -0.60662 -0.024545 -0.22063 1.8024 -1.0356 -0.56915 -0.29095 -1.0188 -0.9035 0.54324 0.0051489 -0.97007 -2.441 -0.19035 -0.47199 -1.4767 -0.28551 -0.0004344 -0.26069 -1.895364 -1.5358 0.32986 -0.55492 -1.7666 0.32434 -0.332 -2.0278 -1.943 -0.64882 -0.14511 -0.94933 -0.92313 -0.8128 0.66595 -0.88126 0.047488 -1.2336 -0.39281 -0.10529 0.46753 0.074323 0.58214 -1.1073 1.525306 1.0288 0.4202 0.091361 0.21968 -0.97741 0.4668 0.2328 0.15397 0.46949 0.34792 -0.13977 -0.0027682 0.44354 1.388 0.078322 0.047802 0.97462 0.23966 0.0050378 0.15024 0.6664379 0.46286 -0.42184 0.32799 1.0012 -0.19429 0.169 0.906 1.2788 0.28369 0.061942 0.44931 0.33212 0.4179 -0.43437 0.53255 0.045906 0.50875 0.28461 -0.17295 154.560 215.000 136.950 176.850 187.650 204.810 159.950 226.100 240.910 180.960 145.190 239.660 223.160 184.990 188.440 131.650 212.720 160.000 274.180 122.930 174.880 291.670 413.786 284.950 300.030 210.150 263.570 309.580 90.350 159.050 189.600 192.150 178.200 238.450 258.150 175.150 161.840 134.710 104.000 284.290 260.150 195.200 160.650 193.550 155.150 2.67130 2.78200 2.40150 3.76470 3.47860 4.33570 3.75280 4.05570 2.92830 3.29670 3.72820 4.11250 4.36640 4.47370 4.43890 2.54380 5.09300 4.16640 7.17430 2.50210 3.43160 5.27280 6.19680 3.92500 5.84730 4.77500 6.52590 9.59330 1.78790 5.00600 4.16260 3.29550 5.08620 5.40830 6.51870 4.92230 4.84420 4.65290 1.59660 4.62220 6.87400 3.96760 3.19090 3.63270 9.30840 Tmax , K 386.440 445.000 351.255 523.100 500.050 576.000 507.800 543.000 473.200 437.200 500.000 591.150 606.150 596.150 615.000 400.100 649.600 537.300 766.000 402.000 503.040 729.000 777.400 587.000 766.800 550.000 658.000 768.000 305.320 514.000 523.300 456.150 617.150 698.000 655.000 571.000 609.150 569.500 282.340 593.000 720.000 537.000 469.150 508.400 674.600 ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 6.6828 4.2527 5.6735 4.292 5.033 5.438 5.0124 0.89107 3.7517 2.4749 1.9302 2.9575 5.8307 2.3195 4.4388 0.012504 15.97 4.7135 5.2516 12.916 7.0236 11.119 6.067 6.2857 4.9437 6.7011 4.8235 14.979 5.3802 4.3848 9.0746 7.035 9.591 5.5382 5.8213 4.249938 4.282053 5.9346 6.8856 6.0629 5.9794 0.10127 1.5513 3.4872 3.3907 13.451 2.6092 4.0385 5.6917 7.7143 0.6664 0.42014 0.85864 0.93726 -0.023028 0.60624 0.48381 0.48888 -0.33542 0.18492 -0.2029 0.098296 -0.62844 1.9091 0.82914 1.3038 1.977 -0.27964 0.51283 1.4923 -1.3652 1.3264 0.18619 0.3899 0.35428 0.38694 0.35765 1.89 0.52771 0.34057 0.8926 -0.9575 1.236 0.19854 0.44196 0.52336 0.5862582 0.41114 1.9737 1.1597 0.9424 0.698 -0.80615 2.1553 0.43574 13.36 0.47883 0.82698 1.2441 -1.0139 -0.4545 -0.17341 -1.1249 -1.0593 0.84791 0.20227 0.14204 0.69714 0.54636 -0.44199 -0.1946 -0.44035 1.0497 -0.21197 0.65339 0.28373 1.6751 -5.0003 -0.72757 -2.6954 -2.2318 0.89761 -0.10982 -1.3795 3.987 -1.1057 0.47762 0.17742 0.22149 0.24973 -0.060379 -2.0762 -0.4757 0.063282 -0.75172 3.1431 -1.359 0.47139 0.090968 -0.57323 -0.9710554 0.043753 -2.4886 -0.99686 -1.398 -1.817 1.1788 -2.9128 -0.56984 –23.383 -0.2233 -2.033 -1.0742 2.2898 0.12282 0.31792 -0.40021 0.36038 -0.16704 -0.77554 3.2641 0.33552 1.7098 0.78544 -0.33523 -0.01018 0.39603 -2.2545 0.36023 -0.26967 -0.19455 -0.2353 -0.26228 0.045749 0.71724 0.3242 -0.017037 0.34378 -1.8066 0.717 -0.31556 -0.15346 0.45101 0.8523437 -0.081964 0.99472 0.32547 0.8862 1.447 -0.070978 1.2442 0.36017 10.785 0.12903 1.4769 0.32331 -0.91517 180.000 140.000 204.150 125.260 199.250 145.650 167.550 53.480 230.940 129.950 131.350 155.150 275.700 250.000 196.290 2.200 295.130 229.800 182.570 265.830 239.150 220.000 234.150 238.150 154.120 229.920 192.220 291.310 214.930 177.830 269.250 228.550 223.000 217.350 217.500 133.390 170.050 192.620 141.250 183.650 274.690 13.950 185.150 158.970 259.830 277.560 187.680 227.150 177.950 409.150 5.46390 3.73840 4.45040 3.50010 4.53900 4.41400 4.29170 0.75083 3.69360 2.31740 1.89050 2.69310 6.17220 1.88650 3.27960 0.00966 8.59730 4.69820 4.31810 7.80040 7.64980 7.18220 5.16400 5.08510 4.32080 5.51330 4.15950 8.19340 4.49940 3.75320 6.47830 7.15090 6.46500 4.75590 4.70770 3.75440 3.73310 5.08670 4.44750 4.26690 4.52380 0.09131 1.81940 1.74720 2.79840 0.71043 1.97460 3.55340 3.74360 8.31300 583.000 489.000 567.000 499.150 546.000 500.230 559.950 144.120 560.090 375.310 317.420 420.000 771.000 588.000 490.150 5.200 736.000 620.000 540.200 677.300 632.300 608.300 606.600 611.400 537.400 645.000 547.000 723.000 594.000 507.600 660.200 611.300 585.300 587.610 582.820 504.000 544.000 623.000 516.200 549.000 653.150 33.190 363.150 324.650 456.650 461.150 373.530 605.000 471.850 834.000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued ) 2-123 2-124 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 Name Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane Formula C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 CAS Mol. wt. 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 C1 × 1E-07 176.7855 1.0194 3.2615 6.8795 4.329 3.0066 6.2689 4.2834 5.8474 4.2709 4.233 8.223 10.165 4.5217 4.897 4.5822 4.4918 6.8872 3.1821 5.1299 4.4696 5.3789 7.7573 9.4404 9.4625 5.1137 4.2603 4.2081 4.8242 3.7592 5.2256 4.9455 4.7691 4.266 8.1495 3.2575 3.8148 2.7567 4.0063 3.0851 5.6613 10.53 5.0351 5.0003 3.9654 C2 16.29674 0.26087 -1.0407 0.012343 0.18771 0.25873 1.6462 0.90615 -0.6042 0.70788 0.95448 0.80923 1.4422 1.0678 1.1838 1.3506 0.32576 1.2703 -0.89979 0.10033 1.1838 0.71218 0.56959 0.8722 0.88768 0.98237 0.34248 0.43515 1.3456 0.64544 0.9427 0.78235 0.98928 0.37791 1.8479 -0.58542 0.38959 -1.6298 -0.17489 -0.29985 0.3132 0.7454 1.1424 0.42203 1.274 C3 C4 Tmin , K ΔHv at Tmin × 1E-07 –28.8053 -0.14694 1.8695 0.77544 0.33528 0.033435 -2.2795 -0.93138 2.1528 -0.67299 -0.98289 -0.70838 -1.6123 -1.1735 -1.2079 -1.6049 0.1124 -1.2699 2.8579 0.64085 -0.87047 -0.28902 0.7221 -0.33173 -0.39167 -0.90553 -0.088074 -0.24963 -1.5783 -0.46384 -1.0868 -0.56637 -0.98574 0.0037827 -2.1328 1.4307 -0.15805 3.0001 0.94886 1.4733 0.57076 -0.39297 -1.3269 -0.14687 -1.4255 14.522 0.22154 -0.60801 -0.4379 -0.17125 0.087053 1.0975 0.4776 -1.2871 0.43009 0.45719 0.32497 0.75941 0.55525 0.43353 0.71575 -0.067377 0.44562 -1.7826 -0.38359 0.056694 -0.014989 -0.86278 -0.10938 -0.057899 0.34878 0.13072 0.20811 0.61746 0.21809 0.55491 0.22052 0.42695 -0.001928 0.76628 -0.54833 0.15228 -1.1865 -0.44746 -0.89559 -0.46309 0.047214 0.62481 0.11507 0.60708 288.150 90.690 175.470 301.150 175.150 170.450 196.320 179.690 260.750 159.530 113.250 193.000 155.950 135.580 139.390 160.150 157.480 175.300 183.450 187.350 139.050 146.580 299.150 280.150 269.150 130.730 146.620 168.540 182.550 160.000 186.480 167.230 174.150 188.000 189.150 256.150 127.930 180.150 171.640 150.180 224.950 240.000 119.550 176.000 113.540 4.28480 0.87235 3.97480 5.97080 3.83890 2.56480 4.04870 3.09550 5.78260 3.46030 3.43450 6.57690 7.27510 3.46420 3.61390 3.20970 3.94480 4.96500 3.25930 4.58370 3.16280 4.45440 5.13430 6.16980 6.31440 4.10400 3.84130 3.63850 3.24190 2.98760 3.98780 3.90650 3.51240 3.56270 4.98940 3.22260 3.39970 3.74640 3.89410 2.99210 4.46890 8.11060 3.97590 4.30250 2.93300 Tmax , K 662.000 190.564 512.500 718.000 506.550 402.400 536.000 430.050 693.000 490.000 460.400 643.000 577.200 465.000 470.000 492.000 512.740 593.000 463.200 554.500 442.000 572.100 686.000 614.000 617.000 532.700 542.000 526.000 483.000 437.800 535.500 533.000 487.200 497.000 574.600 488.000 464.480 553.400 553.100 469.950 566.000 694.000 497.700 546.490 407.800 ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 2.2708 4.3172 4.9563 4.2364 5.7015 2.0613 5.3293 4.0052 3.2566 5.093 0.19063 3.8821 0.74905 1.8859 4.7494 2.2724 0.94287 17.161 4.5173 7.888 12.126 7.5429 14.251 5.9054 6.6716 8.7405 17.264 5.7746 6.7138 12.626 7.2468 12.581 11.048 6.6142 5.4859 7.3618 5.367 7.7236 0.9008 1.7289 10.052 5.2373 4.5087 7.3197 7.39 8.8703 5.3818 4.451 3.5027 5.0573 -3.8183 1.5334 0.22568 0.25325 1.0015 0.33885 0.15144 0.19309 0.10042 -0.44584 -0.048268 -1.2495 0.40406 1.0917 0.1535 0.22278 -2.0627 1.7444 -1.1627 1.3126 0.82704 -1.5966 1.418 0.61039 -0.70869 1.5599 2.167 0.16524 1.0769 1.1753 -1.2464 1.3269 2.5722 0.58562 0.26207 0.63204 0.31607 -0.55914 0.4542 0.12106 0.37778 1.0132 0.95886 1.2093 -0.1464 0.90566 0.35111 -0.5483 0.3481 0.45827 6.7137 -1.9 0.45949 0.58114 -0.95589 -0.63279 0.15411 0.20658 0.26926 1.0348 0.11183 3.2285 -0.317 -1.4143 0.49623 0.29352 3.2659 -1.6657 2.3227 -1.3571 -0.42449 4.6489 -0.53849 -0.54533 2.636 -1.7205 -2.6262 0.095968 -1.0124 -0.835 3.6797 -0.69134 -3.7155 -0.40512 0.50642 -0.29459 0.073613 1.8363 -0.4096 0.088716 0.50709 -1.6348 -0.92384 -1.9114 1.4751 -0.67627 0.40264 2.1051 -0.19672 -0.22568 -2.7247 0.83816 -0.31541 -0.4757 0.38421 0.6454 0.066538 -0.010244 -0.0003252 -0.19528 0.25512 -1.8283 0.27343 0.76165 -0.38464 -0.13493 -1.0186 0.43242 -0.89716 0.5034 0.08636 -2.7229 -0.33162 0.30683 -1.6685 0.64325 1.0161 0.10146 0.37075 0.1489 -2.0665 -0.08027 1.7307 0.22144 -0.43873 0.063444 -0.040895 -0.85806 0.3183 0.10749 -0.46599 1.0473 0.39393 1.1591 -0.9208 0.3485 -0.42577 -1.3486 0.22394 0.16393 298.970 132.810 185.650 133.970 160.170 116.340 249.950 164.550 151.150 353.430 24.560 183.630 63.150 66.460 244.600 182.300 109.500 305.040 267.300 219.660 285.550 268.150 238.150 191.910 253.050 223.150 301.310 251.650 216.380 289.650 257.650 241.550 252.850 255.550 171.450 223.950 193.550 462.650 54.360 80.150 283.070 191.590 143.420 239.150 195.560 200.000 196.290 234.180 108.016 160.750 4.65420 2.92920 4.26690 3.73780 4.42340 1.90240 4.79340 3.60720 2.99980 5.09530 0.17706 4.54440 0.60243 1.46720 4.05640 1.66660 1.44210 9.52160 5.47060 5.25710 8.59240 8.24110 8.32860 4.92180 6.54750 5.46000 8.94580 5.17550 4.69860 7.96680 7.67930 7.57060 5.50930 5.20760 4.79270 5.90250 4.67380 6.56310 0.77419 1.63130 7.76350 4.12150 3.47660 5.38130 6.70050 6.48970 4.45330 4.22720 3.22320 4.43430 506.200 417.900 530.600 476.250 565.000 352.500 654.000 497.100 437.000 748.400 44.400 593.000 126.200 234.000 588.150 309.570 180.150 758.000 658.500 594.600 710.700 670.900 649.500 593.100 681.000 598.050 747.000 638.900 568.700 694.260 652.300 629.800 632.700 627.700 566.900 667.300 574.000 828.000 154.580 261.000 708.000 566.100 469.700 639.160 588.100 561.000 561.080 560.950 464.800 584.300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Continued ) 2-125 2-126 TABLE 2-69 Heats of Vaporization of Inorganic and Organic Liquids (J/kmol) (Continued ) Cmpd. no.* 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 Name Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Formula C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 CAS 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 Mol. wt. C1 × 1E-07 C2 C3 C4 Tmin , K ΔHv at Tmin × 1E-07 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 5.4925 5.1346 5.4839 10.336 6.283 7.3079 18.461 2.8092 2.9209 6.8988 8.502 5.9068 3.3611 4 4.6242 6.4745 3.4054 7.2986 2.5216 5.7631 4.2077 4.4542 7.097812 6.2374 2.3637 8.6409 11.447 2.846 1.3661 0.8509 11.928 13.0705 12.007 4.0907 10.07 0.38608 1.3829 0.98943 1.0678 -0.64878 1.3522 3.6123 0.30398 0.78237 0.6458 1.474 0.44605 -0.27575 1.3936 0.12029 0.93113 -0.29885 1.2428 0.33721 0.70122 0.33823 0.31385 -0.5348227 0.73316 0.32997 1.8893 -0.04418 -0.24905 -1.1465 -7.1061 -0.063031 1.329955 1.445 0.12318 1.994 0.12415 -1.6264 -0.46159 -1.0693 2.4219 -1.6409 -5.1111 0.017572 -0.77319 -0.5384 -1.878 -0.18075 0.66467 -2.9465 0.62187 -0.65971 0.72173 -1.361 -0.18399 -0.15754 0.2503 0.30517 1.770112 -1.3874 0.055931 -2.1943 1.1282 0.62158 1.5442 11.558 0.89651 -1.300762 -1.3846 0.46123 -2.5052 -0.13245 0.67069 -0.064298 0.39121 -1.4972 0.66839 1.9668 0.10232 0.39246 0.3317 0.933 0.13426 197.450 167.450 163.830 372.380 314.060 243.150 404.150 136.870 85.470 146.950 185.258 199.000 165.000 252.450 180.370 178.150 188.360 173.550 87.890 180.250 142.610 159.950 213.150 388.850 186.350 242.540 460.850 197.670 223.150 289.950 700.150 329.350 279.010 164.650 237.380 4.65540 3.49690 3.99170 7.05940 5.77350 4.95580 6.24970 2.44810 2.47870 5.83560 5.61950 5.07850 3.43940 3.09220 4.16430 4.85340 3.46570 5.46050 2.31770 4.44670 3.70860 3.88960 7.23780 4.92650 1.48720 4.92460 8.50610 2.79080 1.62200 4.41460 7.16890 8.42870 7.33360 3.74660 6.02700 1.794 -0.48327 0.17587 -0.080173 0.56435 0.22377 -0.11477 -0.21085 -0.24568 -0.9904166 1.0391 -0.011041 0.81388 -0.67562 -0.020421 -0.15766 -4.483 -0.5152 0.5044183 0.42836 -0.23807 1.0593 Tmax , K 598.000 481.200 519.000 869.000 694.250 653.000 791.000 394.000 369.830 536.800 508.300 636.000 503.600 600.810 561.300 549.730 496.950 638.350 364.850 538.000 517.000 536.600 626.000 683.000 259.000 636.000 838.000 430.750 318.690 490.850 883.600 857.000 693.000 540.150 720.000 ΔHv at Tmax 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 5.2918 3.8116 5.2472 5.4643 4.1283 11.72 4.6139 5.1056 7.0138 7.8955 5.935 6.0778 10.688 1.9497 10.136 8.7274 4.6643 3.649 4.2629 4.3817 5.66 6.493 6.5393 6.6475 0.57615 -0.60048 0.78829 0.76764 -0.34796 1.6004 0.41881 1.6568 1.0377 1.513 1.1967 1.207 0.38045 -8.4859 1.5084 -1.5834 0.50913 0.4 1.0111 0.26434 0.612041 1.0653 0.98813 1.1739 -0.32236 1.6501 -0.47503 -0.62056 1.0118 -1.6689 -0.23744 -1.6244 -1.1841 -1.9061 -1.2686 -1.3449 -0.00074017 17.865 -1.473 5.0913 -0.55117 0.043 -0.48757 0.034522 -0.625697 -1.1205 -0.91617 -1.2812 0.15218 -0.73052 0.098333 0.25935 -0.32712 0.56396 0.20257 0.41985 0.56211 0.85016 0.51652 0.58 0.0003222 –10.196 0.44521 -3.2171 0.45397 -0.045787 0.071549 0.398804 0.48226 0.35023 0.54229 176.990 373.960 234.940 178.180 236.500 267.760 158.450 156.080 247.790 229.330 165.780 172.220 398.400 354.000 247.570 288.450 180.350 173.150 119.360 178.350 273.160 225.300 247.980 286.410 4.49330 3.17800 3.81710 4.40060 4.13030 6.97470 4.05710 3.08740 5.12030 5.22830 4.34440 4.47800 8.39050 8.84860 6.19520 8.90070 3.97880 2.98760 3.21450 3.91430 4.49810 4.68030 4.65030 4.30350 631.950 568.000 579.350 591.750 602.000 675.000 535.150 433.250 664.500 649.100 543.800 573.500 846.000 828.000 639.000 703.900 519.130 454.000 432.000 543.150 647.096 617.000 630.300 616.200 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The heat of vaporization ΔHv is calculated by 2 ΔHv = C1(1 - Tr)(C2+C3Tr+C4Tr ) where Tr = T/TC, TC is the critical temperature from Table 2-106, ΔHv is in J/kmol, and T is in K. All substances are listed by chemical family in Table 2-6 and by formula. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York NY (2016). 2-127 2-128 PHYSICAL AnD CHEMICAL DATA SPECIFIC HEATS SPECIFIC HEATS OF PURE COMPOUnDS Unit Conversions For this subsection, the following unit conversions are applicable: °F = 9⁄5°C + 32 and °R = 1.8 K. To convert calories per gram-kelvin to British thermal units (Btu) per pound-degree Rankine, multiply by 1.0. To convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Rankine, multiply by 0.2388. Additional References Additional data are contained in the subsection “Thermodynamic Properties.” Data on water are also contained in that subsection. TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds* Substance Aluminum1 Al AlBr3 AlCl3 AlCl3⋅6H2O AlF3 AlF3⋅3½H2O AlF3⋅3NaF AlI3 Al2O3 Al2O3⋅SiO2 3Al2O3⋅2SiO2 4Al2O3⋅3SiO2 Al2(SO4)3 Al2(SO4)3⋅18H2O Antimony Sb SbBr3 SbCl3 Sb2O3 Sb2O4 Sb2S3 Argon2 A Arsenic As AsCl3 As2O3 As2S3 Barium BaCl2 BaCl2⋅H2O BaCl2⋅2H2O Ba(ClO3)2⋅H2O BaCO3 State † Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % 273–931 931–1273 273–370 370–407 273–465 465–504 288–327 288–326 288–326 273–1273 1273–1373 273–464 464–480 273–1973 273–1573 273–1673 273–1573 273–576 273–575 273–373 288–325 1 5 3 5 3 3 ? ? ? 2 ? 3 5 3 3 2 3 5 3 ? ? c l c l c l c c c c l c l c c, sillimanite c, disthene c, andalusite c, mullite c c c 4.80 + 0.00322T 7.00 18.74 + 0.01866T 29.5 13.25 + 0.02800T 31.2 76 19.3 50.5 38.63 + 0.04760T - 449200/T 2 142 16.88 + 0.02266T 28.8 22.08 + 0.008971T - 522500/T 2 40.79 + 0.004763T - 992800/T 2 41.81 + 0.005283T - 1211000/T 2 43.96 + 0.001923T - 1086000/T 2 59.65 + 0.0670T 113.2 + 0.0652T 63.5 235 c l c c c c c 5.51 + 0.00178T 7.15 17.2 + 0.0293T 10.3 + 0.0511T 19.1 + 0.0171T 22.6 + 0.0162T 24.2 + 0.0132T 273–903 903–1273 273–370 273–346 273–929 273–1198 273–821 2 5 ? ? ? ? ? g 4.97 All 0 c l c c 5.17 + 0.00234T 31.9 8.37 + 0.0486T 25.8 273–1168 286–371 273–548 293–373 5 ? ? ? c c c c c, α c, β c c c 17.0 + 0.00334T 28.2 37.3 51 17.26 + 0.0131T 30.0 34 39.8 21.35 + 0.0141T 273–1198 273–307 273–307 289–320 273–1083 1083–1255 273–297 285–371 273–1323 ? ? ? ? 5 15 ? ? 5 BaMoO4 Ba(NO3)2 BaSO4 Beryllium3,4 Be c 4.698 + 0.001555T - 121000/T 2 273–1173 1 BeO c 8.69 + 0.00365T - 313000/T 2 273–1175 5 BeO ⋅ Al2O3 c 25.4 273–373 ? BeSO4 c 20.8 273–373 ? *From Kelley, U.S. Bur. Mines Bull. 371, 1934. For a revision see Kelley, U.S. Bur. Mines Bull. 477, 1948. Data for many elements and compounds are given by Johnson (ed.), WADD-TR-60-56, 1960, for cryogenic temperatures. Tabulated data for gases can be obtained from many of the references cited in the “Thermodynamic Properties” subsection and other tables in this section. Thinh, Duran, et al., Hydrocarbon Process., 50, 98 (January 1971), review previous equation fits and give newer fits for 408 hydrocarbons and related compounds. Later publications include Duran, Thinh, et al., Hydrocarbon Process., 55, 153 (August 1976); Thompson, J. Chem. Eng. Data, 22(4), 431 (1977); and Passut and Danner, Ind. Eng. Chem. Process Des. Dev., 11, 543 (1972); 13, 193 (1974). † The symbols in this column have the following meaning; c, crystal; l, liquid; g, gas; gls, glass. SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Bismuth4 Bi Bi2O3 Bi2S3 Boron B B2O3 BN Bromine Br2 Cadmium Cd CdO CdS CdSO4⋅8/3H2O Calcium Ca CaCl2 CaCO3 CaF2 CaMg(CO3)2 CaMoO4 CaO Ca(OH)2 CaO⋅Al2O3⋅2SiO2 CaO⋅MgO⋅2SiO2 CaO⋅SiO2 CaP2O6 CaSO4 CaSO4⋅2H2O CaWO4 Carbon5 C CH4 CO6 CO2 CS2 Cerium Ce CeO2 Ce2(MoO4)3 Ce2(SO4)3 Ce2(SO4)3⋅5H2O Cesium Cs CsBr CsCl CsF CsI Chlorine Cl2 Chromium4 Cr CrCl3 Cr2O3 CrSb CrSb2 Cr2(SO4)3 Cobalt4 Co CoAs2⋅CoS2 CoSb Co2Sn CoS CoSO4⋅7H2O Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % c l c c 5.38 + 0.00260T 7.60 23.27 + 0.01105T 30.4 273–544 544–1273 273–777 284–372 3 3 2 ? c gls gls c 1.54 + 0.00440T 5.14 + 0.0320T 30.4 1.61 + 0.00400T 273–1174 273–513 513–623 273–1173 5 3 3 5 g 9.00 300–2000 5 c l c c c 5.46 + 0.002466T 7.13 9.65 + 0.00208T 12.9 + 0.00090T 51.3 273–594 594–973 273–2086 273–1273 293 1 5 ? ? ? c c c c c c c c c c, anorthite gls c, diopside gls c, wollastonite c, pseudowollastonite gls c c c c 5.31 + 0.00333T 6.29 + 0.00140T 16.9 + 0.00386T 19.68 + 0.01189T - 307600/T 2 14.7 + 0.00380T 40.1 33 10.00 + 0.00484T - 108000/T 2 21.4 63.13 + 0.01500T - 1537000/T 2 67.41 + 0.01048T - 1874000/T 2 54.46 + 0.005746T - 1500000/T 2 51.68 + 0.009724T - 1308000/T 2 27.95 + 0.002056T - 745600/T 2 25.48 + 0.004132T - 488100/T 2 23.16 + 0.009672T - 487100/T 2 39.5 18.52 + 0.02197T - 156800/T 2 46.8 27.9 273–673 673–873 273–1055 273–1033 273–1651 299–372 273–297 273–1173 276–373 273–1673 273–973 273–1573 273–973 273–1573 273–1673 273–973 287–371 273–1373 282–373 292–322 2 2 ? 3 ? ? ? 2 ? 1 1 1 1 1 1 1 ? 5 ? ? c, graphite c, diamond g g g l 2.673 + 0.002617T - 116900/T 2 2.162 + 0.003059T - 130300/T 2 5.34 + 0.0115T 6.60 + 0.00120T 10.34 + 0.00274T - 195500/T 2 18.4 273–1373 273–1313 273–1200 273–2500 273–1200 293 2 3 2 1½ 1½ ? c c c c c 5.88 + 0.00123T 15.1 96 66.4 131.6 273–908 273–373 273–297 273–373 273–319 ? ? ? ? ? c l g c c c c 1.96 + 0.0182T 8.00 4.97 12.6 + 0.00259T 11.7 + 0.00309T 11.3 + 0.00285T 11.6 + 0.00268T 273–301 302 All 273–909 273–752 273–957 273–894 3 3 0 ? ? ? ? 1½ g 8.28 + 0.00056T 273–2000 c l c c c c c 4.84 + 0.00295T 9.70 23 26.0 + 0.00400T 12.3 + 0.00120T 19.2 + 0.00184T 67.4 273–1823 1823–1923 286–319 273–2263 273–1383 273–949 273–373 5 10 ? ? ? ? ? c l c c c c c 5.12 + 0.00333T 8.40 32.9 11.7 + 0.00156T 15.83 + 0.00950T 10.6 + 0.00251T 96 273–1763 1763–1873 283–373 273–1464 273–903 273–1373 286–303 5 5 ? ? 2 ? ? (Continued ) 2-129 2-130 PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Copper7 Cu CuAl CuAl2 Cu3Al CuI CuI2 CuO CuO⋅SiO2⋅H2O CuS Cu2S CuS⋅FeS Cu2Sb Cu2Sb Cu2Se Cu3Si CuSO4 CuSO4⋅H2O CuSO4⋅3H2O CuSO4⋅5H2O Fluorine8 F2 Gallium Ga2O3 Ga2(SO4)3 Germanium4 Ge Gold Au AuSb2 Helium9 He Hydrogen10 H H2 HBr HCl HI H2O H2S H2S2O7 Indium In Iodine I2 Iridium Ir Iron4 Fe FeAs2 Fe3C FeCO3 FeO Fe2O3 Fe3O4 Fe2O3⋅3H2O FeS FeS2 FeSi Fe2SiO4 FeSO4 Fe2(SO4)3 FeSO4⋅4H2O FeSO4⋅7H2O Krypton Kr Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % 273–1357 1357–1573 273–733 273–773 273–775 273–675 274–328 273–810 293–323 273–1273 273–376 376–1173 292–321 273–573 273–693 273–383 383–488 273–1135 282 282 282 282 1 3 2 2 2 ? ? 2 ? ? 3 2 ? 2 2 5 5 ? ? ? ? ? c l c c c c c c c c c, α c, β c c c c, α c, β c c c c c 5.44 + 0.001462T 7.50 9.88 + 0.00500T 16.78 + 0.00366T 19.61 + 0.01054T 12.1 + 0.00286T 20.1 10.87 + 0.003576T - 150600/T 2 29 10.6 + 0.00264T 9.38 + 0.0312T 20.9 24 13.73 + 0.01350T 21.79 + 0.00900T 20.85 20.35 20.3 + 0.00587T 24.1 31.3 49.0 67.2 g 6.50 + 0.00100T 300–3000 5 c c 18.2 + 0.0252T 62.4 273–923 273–373 ? ? 273–1336 1336–1573 273–628 628–713 2 5 1 ? c c l c, α c, βγ 5.61 + 0.00144T 7.00 17.12 + 0.00465T 11.47 + 0.01756T g 4.97 All 0 g g g g g l g g c l 4.97 6.62 + 0.00081T 6.80 + 0.00084T 6.70 + 0.00084T 6.93 + 0.00083T See Tables 2-72 and 2-136 8.22 + 0.00015T + 0.00000134T 2 7.20 + 0.00360T 27 58 All 273–2500 273–2000 273–2000 273–2000 0 2 2 1½ 2 300–2500 300–600 281 308 ? 8 ? ? g 9.00 300–2000 5 c 5.50 + 0.00148T 273–1873 1 c, α c, β c, γ c, δ l c c c c c c c c, α c, β c c c c c c c 4.13 + 0.00638T 6.12 + 0.00336T 8.40 10.0 8.15 17.8 25.17 + 0.00223T 22.7 12.62 + 0.001492T - 76200/T 2 24.72 + 0.01604T - 423400/T 2 41.17 + 0.01882T - 979500/T 2 47.8 2.03 + 0.0390T 12.05 + 0.00273T 10.7 + 0.01336T 10.54 + 0.00458T 33.57 + 0.01907T - 879700/T 2 22 66.2 63.6 96 273–1041 1041–1179 1179–1674 1674–1803 1803–1873 283–373 273–1173 293–368 273–1173 273–1097 273–1065 286–373 273–411 411–1468 273–773 273–903 273–1161 293–373 273–373 282 291–319 3 3 5 5 5 ? 10 ? 2 2 2 ? 5 3 ? 2 2 ? ? ? ? g 4.97 c All 0 SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Lanthanum La La2O3 La2(MoO4)3 La2(SO4)3 La2(SO4)3⋅9H2O Lead4 Pb Pb3(AsO4)2 PbB2O4 PbB4O7 PbBr2 PbCl2 2PbCl2⋅NH4Cl PbCO3 PbCrO4 PbF2 PbI2 PbMoO4 Pb(NO3)2 PbO PbO2 Pb2P2O7 PbS PbSO4 PbS2O3 PbWO4 Lithium Li LiBr LiBr⋅H2O LiCl LiCl⋅H2O LiF LiI LiI⋅H2O LiI⋅2H2O LiI⋅3H2O LiNO3 Magnesium4 Mg MgAg Mg4Al3 MgAu Mg2Au Mg3Au MgCl2 MgCl2⋅6H2O MgCO3 MgCu2 Mg2Cu MgNi2 MgO MgO⋅Al2O3 MgO⋅SiO2 6MgO⋅MgCl2⋅8B2O3 Mg(OH)2 Mg3Sb2 Mg2Si MgSO4 MgSO4⋅H2O MgSO4⋅6H2O MgSO4⋅7H2O Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % c c c c c 5.91 + 0.00100T 22.6 + 0.00544T 86 66.9 152 273–1009 273–2273 273–307 273–373 273–319 ? ? ? ? ? c l c c c c l c l c c c c c l c c c c c c c c c 5.77 + 0.00202T 6.8 65.5 26.5 41.4 18.13 + 0.00310T 27.4 15.88 + 0.00835T 27.2 53.1 21.1 29.1 16.5 + 0.00412T 18.66 + 0.00293T 32.3 30.4 36.4 10.33 + 0.00318T 12.7 + 0.00780T 48.3 10.63 + 0.00401T 26.4 29 35 273–600 600–1273 286–370 288–371 289–371 273–761 761–860 273–771 771–851 293 286–320 292–323 273–1091 273–648 648–776 292–322 286–320 273–544 273–? 284–371 273–873 293–372 293–373 273–297 2 5 ? ? ? 2 10 2 10 ? ? ? ? 2 20 ? ? 2 ? ? 3 ? ? ? c g c c c c c c c c c c l 0.68 + 0.0180T 4.97 11.5 + 0.00302T 22.6 11.0 + 0.00339T 23.6 8.20 + 0.00520T 12.5 + 0.00208T 23.6 32.9 43.2 9.17 + 0.0360T 26.8 273–459 All 273–825 278–318 273–887 279–360 273–1117 273–723 277–359 277–345 277–347 273–523 523–575 10 0 ? ? ? ? ? ? ? ? ? 5 5 c l c c c c c c c c c c c c c c, amphibole c, pyroxene gls c, α c, β c c c c c c c 6.20 + 0.00133T - 67800/T 2 7.4 10.58 + 0.00412T 34.4 + 0.0198T 11.3 + 0.00189T 16.2 + 0.00451T 21.2 + 0.00614T 17.3 + 0.00377T 77.1 16.9 14.96 + 0.00776T 15.5 + 0.00652T 15.87 + 0.00692T 10.86 + 0.001197T - 208700/T 2 28 25.60 + 0.004380T - 674200/T 2 23.35 + 0.008062T - 558800/T 2 23.30 + 0.007734T - 542000/T 2 58.7 + 0.408T 107.2 + 0.2876T 18.2 28.2 + 0.00560T 15.4 + 0.00415T 26.7 33 80 89 273–923 923–1048 273–905 273–736 273–1433 273–1073 273–1103 273–991 292–342 290 273–903 273–843 273–903 273–2073 288–319 273–1373 273–773 273–973 273–538 538–623 292–323 273–1234 273–1343 296–372 282 282 291–319 1 10 2 ? ? ? ? ? ? ? 3 ? 2 2 ? 1 1 1 5 5 ? ? ? ? ? ? ? (Continued ) 2-131 2-132 PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % c, α c, β c, γ l c c c c c c c c c c 3.76 + 0.00747T 5.06 + 0.00395T 4.80 + 0.00422T 11.0 16.2 + 0.00520T 7.79 + 0.0421T + 0.0000090T 2 7.43 + 0.01038T - 0.00000362T 2 10.33 + 0.0530T - 0.0000257T 2 19.25 + 0.0538T - 0.0000209T 2 1.92 + 0.0471T - 0.0000297T 2 31 10.21 + 0.00656T - 0.00000242T 2 27.5 78 273–1108 1108–1317 1317–1493 1493–1673 273–923 273–773 273–1923 273–1173 273–1773 273–773 291–322 273–1883 293–373 290–319 5 5 5 10 ? ? ? ? ? ? ? ? ? ? l g g c c c c c, α c, β c c c 6.61 4.97 9.00 11.05 + 0.00370T 15.3 + 0.0103T 25 11.4 + 0.00461T 17.4 + 0.004001T 20.2 11.5 10.9 + 0.00365T 31.0 273–630 All 300–2000 273–798 273–553 285–319 273–563 273–403 403–523 278–371 273–853 273–307 1 0 5 ? ? ? ? 3 3 ? ? ? c c c 5.69 + 0.00188T - 50300/T 2 15.1 + 0.0121T 19.7 + 0.00315T 273–1773 273–1068 273–729 5 ? ? g 4.97 All 0 c, α c, β l c c c c c c c c 4.26 + 0.00640T 6.99 + 0.000905T 8.55 11.3 + 0.00215T 9.25 + 0.00640T 15.8 + 0.00329T 10.0 + 0.00312T 20.78 + 0.0102T 33.4 82 11.00 + 0.00433T g g c c, α c, β c c c g 6.50 + 0.00100T 6.70 + 0.00630T 22.8 9.80 + 0.0368T 5.0 + 0.0340T 17.8 31.8 51.6 8.05 + 0.000233T - 156300/T 2 300–3000 300–800 274–328 273–457 457–523 273–328 273–293 275–328 300–5000 3 1½ ? 5 5 ? ? ? 2 c 5.686 + 0.000875T 273–1877 1 300–5000 1 State† Substance Manganese Mn MnCl2 MnCO3 MnO Mn2O3 Mn3O4 MnO2 Mn2O3⋅H2O MnS MnSO4 MnSO4⋅5H2O Mercury11 Hg Hg2 HgCl HgCl2 Hg(CN)2 HgI HgI2 HgO HgS Hg2SO4 Molybdenum Mo MoO3 MoS2 Neon12 Ne Nickel4 Ni NiO NiS Ni2Si NiSi Ni3Sn NiSO4 NiSO4⋅6H2O NiTe Nitrogen13 N2 NH3 NH4Br NH4Cl NH4I NH4NO3 (NH4)2SO4 NO Osmium Os Oxygen14 O2 Palladium Pd Phosphorus P PCl3 P4O10 Platinum4 Pt Potassium K 273–626 626–1725 1725–1903 273–1273 273–597 273–1582 273–1273 273–904 293–373 291–325 273–700 2 2 5 10 ? 3 ? ? 2 ? ? 2 g 8.27 + 0.000258T - 187700/T c 5.41 + 0.00184T 273–1822 2 c, yellow c, red l l c g 5.50 0.21 + 0.0180T 6.6 28.7 15.72 + 0.1092T 73.6 273–317 273–472 317–373 284–371 273–631 631–1371 5 10 10 ? 2 3 c 5.92 + 0.00116T 273–1873 1 c l 5.24 + 0.00555T 7.7 273–336 336–373 5 5 SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Potassium—(Cont.) K K2 KAsO3 KBO2 K2B4O7 KBr KCl KClO3 KClO4 2KCl⋅CuCl2⋅2H2O 2KCl⋅PtCl4 2KCl⋅SnCl4 2KCl⋅ZnCl2 2KCN⋅Zn(CN)2 K2CO3 K2CrO4 K2Cr2O7 KF K4Fe(CN)6 K4Fe(CN)6⋅3H2O KH2AsO4 KH2PO4 KHSO4 KMnO4 KNO3 K2O⋅Al2O3⋅3SiO2 K4P2O7 K2SO4 K2S2O3 K2SO4⋅Al2(SO4)3⋅24H2O K2SO4⋅Cr2(SO4)3⋅24H2O K2SO4⋅MgSO4⋅6H2O K2SO4⋅NiSO4⋅6H2O K2SO4⋅ZnSO4⋅6H2O Prometheum Pr Radon Rn Rhenium Re Rhodium Rh Rubidium Rb RbBr RbCl Rb2CO3 RbF RbI Scandium Sc2O3 Sc2(SO4)3 Selenium Se Silicon Si SiC SiCl4 SiO2 Silver4 Ag g g c c c c c c c c c c c c c c c l c c c c c c c c c l c, orthoclase gls, orthoclase c, microcline gls, microcline c c c c c c c c Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) 4.97 9.00 25.3 12.6 + 0.0126T 51.3 11.49 + 0.00360T 10.93 + 0.00376T 25.7 26.3 63 55 54.5 43.4 57.4 29.9 35.9 42.80 + 0.0410T 96.9 10.8 + 0.00284T 80.1 114.5 32 28.3 30 28 6.42 + 0.0530T 28.8 29.5 69.26 + 0.00821T - 2331000/T 2 69.81 + 0.01053 - 2403000/T 2 65.65 + 0.01102T - 1748000/T 2 64.83 + 0.01438T - 1641000/T 2 63.1 33.1 37 352 324 106 107 120 Range of temperature, K Uncertainty, % All 300–2000 290–372 273–1220 290–372 273–543 273–1043 289–371 287–318 292–323 286–319 292–323 279–319 277–319 296–372 289–371 273–671 671–757 273–1129 273–319 273–310 289–319 290–320 292–324 287–318 273–401 401–611 611–683 273–1373 273–1373 273–1373 273–1373 290–371 287–371 293–373 292–322 292–324 292–323 289–319 293–317 0 5 ? ? ? 2 2 ? ? ? ? ? ? ? ? ? 5 5 ? ? ? ? ? ? ? 10 5 10 1½ 1½ 1½ 1½ ? ? ? ? ? ? ? ? c g 4.97 All 0 c 6.30 + 0.00053T 273–2273 ? c 5.40 + 0.00219T 273–1877 2 c l c c c c c 3.27 + 0.0131T 7.85 11.6 + 0.00255T 11.5 + 0.00249T 28.4 11.3 + 0.00256T 11.6 + 0.00263T 273–312 312–373 273–954 273–987 291–320 273–1048 273–913 2 5 ? ? ? ? ? c c 21.1 62.0 273–373 273–373 ? ? c l 4.53 + 0.00550T 8.35 273–490 490–570 2 3 c c l c, quartz, α c, quartz, β c, cristobalite, α c, cristobalite, β gls 5.74 + 0.000617T - 101000/T 2 8.89 + 0.00291T - 284000/T 2 32.4 10.87 + 0.008712T - 241200/T 2 10.95 + 0.00550T 3.65 + 0.0240T 17.09 + 0.000454T - 897200/T 2 12.80 + 0.00447T - 302000/T 2 273–1174 273–1629 293–373 273–848 848–1873 273–523 523–1973 273–1973 2 2 ? 1 3½ 2½ 2 3½ c l 5.60 + 0.00150T 8.2 273–1234 1234–1573 1 3 (Continued ) 2-133 2-134 PHYSICAL AnD CHEMICAL DATA TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Silver—(Cont.) Ag3Al Ag2Al AgAl12 AgBr AgCl AgCNO AgI AgNO3 Ag3PO4 Ag2S Ag3Sb Ag2Se Sodium15 Na NaBO2 Na2B4O7 Na2B4O7⋅10H2O NaBr NaCl NaClO3 NaCNO Na2CO3 NaF Na2HPO4⋅7H2O Na2HPO4⋅12H2O NaI NaNO3 Na2O⋅Al2O3⋅3SiO2 NaPO3 Na4P2O7 Na2SO4 Na2S2O3 Na2S2O3⋅5H2O Sodium-potassium alloys15 Strontium SrBr2 SrBr2⋅H2O SrBr2⋅6H2O SrCl2 SrCl2⋅H2O SrCl2⋅2H2O SrCO3 SrI2 SrI2⋅H2O SrI2⋅2H2O SrI2⋅6H2O SrMoO4 Sr(NO3)2 SrSO4 Sulfur16 S S2 S2Cl2 SO2 Tantalum Ta Tellurium Te Thallium Tl Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % 273–902 273–903 273–768 273–703 703–836 273–728 728–806 273–353 273–423 273–433 433–482 482–541 293–325 273–448 448–597 273–694 273–406 406–460 2 2 5 6 5 2 5 ? 6 2 5 5 ? 5 5 5 5 5 273–371 371–451 All 273–1239 289–371 292–323 273–543 273–1074 1073–1205 273–528 528–572 273–353 288–371 273–1261 275–307 275–307 273–936 273–583 583–703 273–1373 273–1173 290–319 290–371 289–371 273–307 273–307 1½ 2 0 ? ? ? 2 2 3 3 5 ? ? ? ? ? ? 5 10 1 1 ? ? ? ? ? c c c c l c l c c, α c, α c, β l c c, α c, β c c, α c, β 22.56 + 0.00570T 16.85 + 0.00450T 58.62 + 0.0575T 8.58 + 0.0141T 14.9 9.60 + 0.00929T 14.05 18.7 8.58 + 0.0141T 18.83 + 0.0160T 25.7 30.2 37.5 18.8 21.8 19.53 + 0.0160T 20.2 20.4 c l g c c c c c l c l c c c c c c c l c, albite gls c c c c c l 5.01 + 0.00536T 7.50 4.97 10.4 + 0.0199T 47.9 147 11.74 + 0.00233T 10.79 + 0.00420T 15.9 9.48 + 0.0468T 31.8 13.1 28.9 10.4 + 0.00289T 86.6 133.4 12.5 + 0.00162T 4.56 + 0.0580T 37.2 63.78 + 0.01171T - 1678000/T 2 61.25 + 0.01768T - 1545000/T 2 22.1 60.7 32.8 34.9 86.2 c c c c c c c c c c c c c c 18.1 + 0.00311T 28.9 82.1 18.2 + 0.00244T 28.7 38.3 21.8 18.6 + 0.00304T 28.5 39.1 84.9 37 38.3 26.2 273–923 277–370 276–327 273–1143 276–365 277–366 281–371 273–783 276–363 275–336 275–333 273–297 290–320 293–369 ? ? ? ? ? ? ? ? ? ? ? ? ? ? c, rhombic c, monoclinic g l g 3.63 + 0.00640T 4.38 + 0.00440T 8.58 + 0.00030T 27.5 7.70 + 0.00530T - 0.00000083T 2 273–368 368–392 300–2500 273–332 300–2500 3 3 5 ? 2½ c 5.91 + 0.00099T 273–1173 2 c 5.19 + 0.00250T 273–600 3 c, α c, β 5.32 + 0.00385T 8.12 273–500 500–576 1 1 SPECIFIC HEATS TABLE 2-70 Heat Capacities of the Elements and Inorganic Compounds (Continued ) State† Substance Thallium—(Cont.) Tl TlBr TlCl Thorium Th ThO2 Th(SO4)2 Tin4 Sn SnAu SnCl2 SnCl4 SnO SnO2 SnPt SnS SnS2 Titanium Ti TiCl4 TiO2 Tungsten W WO3 Uranium U U3O8 Vanadium V Xenon Xe Zinc4 Zn ZnCl2 ZnO ZnS ZnSb ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O Zirconium ZrO2 ZrO2⋅SiO2 1 Heat capacity at constant pressure (T = K; 0°C = 273.1 K), cal/(mol⋅K) Range of temperature, K Uncertainty, % l c l c l 7.12 12.53 + 0.00100T 16.0 12.56 + 0.00088T 14.2 576–773 273–733 733–800 273–700 700–803 3 10 10 5 10 c c c 6.40 14.6 + 0.00507T 41.2 273–373 273–1273 273–373 ? ? ? c l c c l c c c c c 5.05 + 0.00480T 6.6 11.79 + 0.00233T 16.2 + 0.00926T 38.4 9.40 + 0.00362T 13.94 + 0.00565T - 252000/T 2 11.49 + 0.00190T 12.1 + 0.00165T 20.5 + 0.00400T 273–504 504–1273 273–581 273–520 286–371 273–1273 273–1373 273–1318 273–1153 273–873 2 10 1 ? ? ? ? 1 ? ? c l c 8.91 + 0.00114T - 433000/T 2 35.7 11.81 + 0.00754T - 41900/T 2 273–713 285–372 273–713 3 ? 3 c c 5.65 + 0.00866 16.0 + 0.00774T 273–2073 273–1550 1 ? c c 6.64 59.8 273–372 276–314 ? ? c 5.57 + 0.00097T 273–1993 ? g 4.97 All 0 c l c c c c c c c c 5.25 + 0.00270T 7.59 + 0.00055T 15.9 + 0.00800T 11.40 + 0.00145T - 182400/T 2 12.81 + 0.00095T - 194600/T 2 11.5 + 0.00313T 28 34.7 80.8 100.2 273–692 692–1122 273–638 273–1573 273–1173 273–810 293–373 282 282 273–307 1 3 ? 1 5 ? ? ? ? ? c c 11.62 + 0.01046T - 177700/T 2 26.7 273–1673 297–372 5 ? See also Table 2-71. Data to 298 K are also given by Scott, Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959. For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. Stalder, NACA Tech. Note 4141, 1957 (Fig. 5), gives data from 400 to 2600°R. 4 See also Table 2-71. 5 For data from 400 to 5500°R see Stalder, NACA Tech. Note 4141, 1975 (Fig. 4). 6 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 7 For data from 400 to 2350°R see Stalder, NACA Tech. Note 4141, 1957. 8 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 9 For liquid and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 10 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-60-56, 1960. 11 See also Table 2-71. Douglas, Ball, et al., Bur. Stand. J. Res., 46 (1951): 334; Busey and Giaque, J. Am. Chem. Soc., 75 (1953): 806; Sheldon, ASME Pap. 49-A-30, 1949. 12 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. 13 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. 14 For solid, liquid, and gas data, see Johnson (ed.), WADD-TR-56-60, 1960. Ozone: For liquid see Brabets and Waterman, J. Chem. Phys., 28 (1958): 1212. 15 For data on liquid Na-K alloys to 1500°F and for liquid Na to 1460°F, see Lubarsky and Kaufman, NACA Rep. 1270, 1956. 16 See also Evans and Wagman, Bur. Stand. J. Res. 49 (1952): 141; Gratch, OTS PB 124957, 1950; Guthrie, Scott et al., J. Am. Chem. Soc., 76 (1954): 1488. 2 3 2-135 2-136 PHYSICAL AnD CHEMICAL DATA TABLE 2-71 Specific Heat [kJ/(kg·K)] of Selected Elements Temperature, K Symbol 4 6 8 10 20 40 60 80 100 200 250 300 400 600 800 Al Be Bi Cr Co 0.00026 0.00008 0.00054 0.00016 0.00036 0.00050 0.00088 0.214 0.357 0.00541 0.00050 0.00085 0.0089 0.0014 0.0340 0.0021 0.0048 0.0775 0.00220 0.00029 0.00059 0.00140 0.00028 0.01040 0.00081 0.00121 0.0729 0.0107 0.0404 0.092 0.059 0.110 0.102 0.127 0.184 0.481 0.195 0.109 0.190 0.234 0.797 1.109 0.120 0.382 0.376 0.859 1.537 0.121 0.424 0.406 0.902 1.840 0.122 0.450 0.426 0.949 2.191 0.123 0.501 0.451 1.042 2.605 0.142 0.565 0.509 1.134 2.823 0.136 0.611 0.543 Cu Ge Au Ir Fe 0.00011 0.00024 0.00018 0.00047 0.00048 0.00037 0.00126 0.137 0.108 0.084 0.203 0.153 0.100 0.00061 0.00090 0.0076 0.0129 0.0163 0.0021 0.0039 0.059 0.0619 0.0569 0.00038 0.00086 0.00081 0.00255 0.00032 0.00127 0.0276 0.086 0.154 0.254 0.192 0.109 0.090 0.216 0.357 0.286 0.124 0.122 0.384 0.377 0.305 0.127 0.128 0.422 0.386 0.323 0.129 0.131 0.450 0.396 0.343 0.131 0.133 0.491 0.431 0.364 0.136 0.140 0.555 0.448 0.377 0.141 0.146 0.692 Pb Mg Hg Mo Ni 0.00075 0.00034 0.00417 0.00011 0.00054 0.00242 0.00080 0.01420 0.00019 0.00086 0.00747 0.00155 0.01820 0.00032 0.00121 0.01350 0.00172 0.02250 0.00050 0.00178 0.0531 0.0148 0.0515 0.0029 0.0058 0.0944 0.138 0.0895 0.0236 0.0380 0.108 0.336 0.107 0.061 0.103 0.114 0.513 0.116 0.105 0.173 0.118 0.648 0.121 0.140 0.232 0.125 0.929 0.136 0.223 0.383 0.127 0.985 0.141 0.241 0.416 1.129 1.005 0.139 0.248 0.444 0.132 1.082 0.136 0.261 0.490 0.142 1.177 0.135 0.280 0.590 1.263 0.104 0.292 0.530 Pt Ag Sn Zn 0.00019 0.00016 0.00024 0.00011 0.00028 0.00035 0.00127 0.00029 0.00067 0.00093 0.00423 0.00096 0.00112 0.00186 0.00776 0.00250 0.0077 0.0159 0.0400 0.0269 0.0382 0.0778 0.108 0.123 0.069 0.133 0.149 0.205 0.088 0.166 0.173 0.258 0.101 0.187 0.189 0.295 0.127 0.225 0.214 0.366 0.132 0.232 0.220 0.380 0.134 0.236 0.222 0.389 0.136 0.240 0.245 0.404 0.140 0.251 0.257 0.435 0.146 0.264 0.257 0.479 TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] 2-137 Eqn Cmpd. no. 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 C1 C2 C3 152.99 10,2300 13,9640 26,0050 13,5600 73,381 –122,020 103,090 55,300 109,750 –214,460 61.289 150,940 134,390 161,440 129,440 162,940 119,780 -5,480 66,950 156,130 –334,997 87,500 100,320 121,770 179,400 121,600 95,588 102,760 135,150 128,860 191,030 55.136 42.152 191,200 533,390 182,050 126,680 112,760 111,850 182,470 232,190 197,890 136,340 194,170 237,700 154,800 -8,304,300 85,600 65.429 598.64 128.7 -320.8 -565.43 -177 60.042 3082.7 -247.8 300 -108.61 9185.1 80925 93.455 -1989.4 260.66 -169.5 -344.94 180.34 647.12 333.33 454.49 3644.21 480 346.89 429.3 -667.11 -9.45 -110.94 -230.08 -311.14 -323.1 -1675 314200 324580 -730.4 -4986.2 -1611 -65.47 -104.7 384.52 -13.912 -804.35 -491.54 -300.4 -532.38 -746.4 -239.75 104370 -122 28723 -0.89481 0.8985 1.1035 0.2837 -15.895 1.0343 0.35246 -106.12 799.4 0.23602 11.043 C4 C5 0.000689 0.027732 0.41616 -2651 0.64781 0.85562 -7.77514 1.0701 0.358 0.41864 0.51796 0.97007 1.015 12.5 280.19 517.35 2.2998 18.908 11.963 -0.64 0.5214 0.72897 2.7063 1.7219 1.0216 1.4286 1.829 0.68616 -433.33 0.5605 -847.39 0.00591102 -0.0001523 0.000032 -0.03874 1413.9 1449.5 0.000046121 -0.02 -0.037454 0.002912 0.000045027 -0.0023017 -0.0012499 0.60052 -0.001452 1959.6 0.000002008 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 149.78 354.15 289.81 200.15 178.45 229.32 192.40 253.00 286.15 189.63 75.00 203.15 298.15 83.78 403.00 278.68 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.20 265.90 293.15 154.25 179.44 136.95 165.00 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 298.15 185.30 157.46 133.02 147.43 176.80 267.95 161.30 220.00 161.11 68.15 0.69743 1.47880 1.22130 1.91090 1.16960 0.87150 0.80208 1.06600 1.41150 1.01830 0.53065 0.75753 1.99780 0.45230 2.66490 1.32510 1.33260 1.66360 2.50420 1.53710 3.02180 1.89060 2.19810 1.84940 2.68680 0.77675 1.49600 0.88436 0.78152 1.10340 1.03330 1.12720 1.55900 0.62506 1.34650 1.38480 1.10150 1.13400 1.09860 2.26490 2.04920 1.63650 1.60030 1.14260 1.44700 1.69020 1.33980 0.78265 0.75774 0.59115 294.15 571.00 391.05 412.70 329.44 354.81 250.00 379.50 375.00 400.00 115.00 401.15 484.20 135.00 563.15 353.24 500.00 442.29 450.00 464.15 640.00 478.60 458.15 472.03 533.37 331.90 495.08 311.49 280.15 290.00 350.00 400.00 670.00 670.00 391.00 372.90 380.00 350.00 274.03 399.26 400.00 390.00 370.00 298.15 347.94 436.42 390.74 290.00 552.00 132.00 0.98820 1.75790 1.51590 2.14650 1.32710 0.94685 0.88530 1.58010 1.67800 1.22700 0.71317 4.18470 2.51530 0.67080 3.08230 1.50400 2.04380 1.99540 2.85720 2.21670 4.47000 2.76170 3.07410 2.64060 3.50750 0.75866 2.04670 1.01650 0.78955 1.22790 1.41480 2.22370 5.20450 5.24370 2.57210 2.66210 1.81030 1.50220 1.23220 2.65370 2.93540 1.93590 1.88440 1.37590 1.81880 2.60310 1.65880 1.66030 1.31250 6.47990 (Continued ) 2-138 TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 Cmpd. no. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 Name Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Formula CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 CAS 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 Mol. wt. 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 C1 -752,700 104,600 63,936 -1,307,500 118,380 124,850 107,900 134,733 69,362 -246,700 -185,150 259,980 61,723 77,461 101,920 -220,600 -40,000 6,110.4 105,850 122,530 125,380 89,952 177,560 218,480 278,620 219,840 4,988,500 417,440 314,570 276,900 149,400 200,560 202,580 270,720 114,880 93,093 133,950 126,340 179,170 98,968 144,560 111,560 184,200 101,330 44,400 238,520 67.155 82,577 263,980 C2 C3 8966.1 -500.6 46.35 15338 -248.915 -166.34 -330.13 -176.332 215.01 3256.8 3148 -1112.3 494.81 111.51 -215.81 3118.3 853 600.94 -60 -403.8 -349.7 -196.63 -179.12 374.14 -197.91 140.41 -52898 -1616.5 -160.93 -371.23 -30.394 2.2851 -0.1623 -53.974 0.68074 0.43209 0.808 0.55966 0.034455 -7.4202 -8.0367 4.9427 0.0060467 0.007254 -0.0054367 0.8103 -9.4216 0.010687 -231.8 -491.44 -726.3 -259.83 187.25 183.97 -24.84 -94.63 -444.74 -62.941 -53.605 149.44 286 243.18 1301 -1038.4 105580 109.85 -1791.1 0.5946 0.9187 1.3377 0.95427 0.68 1.7344 1.143 0.65237 0.76723 0.11851 1.0737 0.9968 216.35 5.3948 0.95561 1.5774 C4 0.063483 -0.0010975 -0.37538 -0.004348 0.2314 0.48191 0.32 0.93009 0.23265 0.30617 -5.5 4.0587 310.21 4.3666 C5 0.008763 -0.0044691 -490.54 0.00023674 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 250.33 89.56 172.12 227.95 136.75 233.15 175.43 150.35 200.00 285.39 304.20 307.93 177.14 245.25 190.00 279.69 296.60 290.00 169.67 179.28 138.13 150.00 189.64 285.00 243.51 304.75 280.00 206.89 247.56 229.15 1.27630 0.78095 0.67106 1.36170 0.97071 1.09560 0.74852 1.20870 1.12360 2.18950 2.32970 2.27400 1.49370 1.04810 0.90168 1.48360 2.13000 1.80380 1.15250 0.99559 0.98884 0.75136 1.71180 3.34740 2.94090 3.55210 3.53690 2.75410 3.33300 2.74660 388.71 145.10 239.12 360.00 298.15 366.48 303.15 319.67 308.85 400.00 400.00 400.00 425.56 253.82 298.15 400.00 434.00 489.75 356.12 322.40 317.38 298.15 431.95 481.65 460.00 543.15 503.15 494.00 512.35 447.15 1.63740 0.80073 0.65739 1.81010 1.04680 1.21920 0.82076 1.35560 1.35770 2.55780 2.52430 2.57940 2.72290 1.05760 1.09610 2.03230 3.30200 3.00420 1.70720 1.35840 1.29530 0.89318 2.43340 4.26180 4.14780 5.90170 5.01740 4.11250 4.82970 4.26290 210.15 282.85 240.00 175.30 248.39 273.15 326.14 176.19 237.49 180.00 192.50 275.00 301.15 223.35 156.92 181.95 154.56 179.60 200.00 1.26950 1.35060 1.05320 2.54500 1.61390 1.60610 1.77110 1.19600 1.26010 0.95176 1.45590 1.52660 2.70330 1.55640 1.46980 1.57030 0.99146 1.02310 0.80424 381.15 410.00 370.10 450.00 400.00 528.75 513.56 330.45 356.59 320.00 361.25 369.52 541.54 328.60 460.00 322.08 359.98 283.65 250.00 1.47430 1.53500 1.17010 3.47040 1.89780 2.55060 2.48290 1.30010 1.38850 1.02650 1.65150 1.66780 3.39080 1.81240 3.32020 1.75790 1.68740 1.13740 0.89118 2-139 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 149 150 151 152 Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorine Fluorobenzene Fluoroethane Fluoromethane C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 F2 C6H5F C2H5F CH3F 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 7782-41-4 462-06-6 353-36-6 593-53-3 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 37.9968064 96.1023032 48.0595 34.03292 98,434 163,000 179,270 187,790 199,930 88,153 -214,870 129,450 134,500 150,130 155,560 171,580 110,100 147,900 146,420 206,560 131,810 146,950 240,300 195,251 956,860 134,160 49,120 508,210 352,720 44.009 102,640 226,230 121,700 154,040 124,500 56,359 82,434 132,360 178,520 247,390 184,440 35,540 46,848 144,710 80,000 207,670 146,040 106,250 229,250 134,670 76,330 103,680 173,110 -94,585 1,724,400 148,640 65,106 141,790 429.04 -4.5 28.37 -313.41 -191.5 124.16 3787.2 18.5 8.765 -62.38 -145.26 -256.67 -157.47 -106 59.2 325.75 -380.06 -595 419.918 -5559.9 447.67 562.24 -1368.7 807.32 89718 -139.63 -624.8 38.993 -142.29 370.6 603.02 422.45 72.74 -518.35 -4428 -150.2 436.78 205.35 -758.87 223.6 -17.907 458.22 292.15 -404.54 -234.39 400.1 726.3 -697.18 7529.9 -59924 -202.58 103.44 -814.32 0.62 0.5375 1.1023 0.87664 -13.781 0.608 0.81151 0.8851 1.0932 0.5727 0.51853 0.384 0.604 0.016924 1.2035 1.013 -0.00084787 9.6124 3.1015 0.2122 918.77 -0.030341 1.472 –1886 0.0020386 0.80539 0.20992 0.64738 2.3255 40.936 0.37044 -0.18486 -0.0016818 -0.1697 2.8261 -0.003064 0.00026816 1.0493 1.1382 0.59656 -2.6047 3.7615 -139.6 537.85 0.66374 0.67161 2.2673 0.0040957 -0.005289 1.1301 -0.0074083 0 1.6179E-06 -0.0033241 0.000019119 275.00 187.65 204.81 159.95 226.10 240.91 180.96 145.19 239.66 223.16 184.99 188.44 131.65 273.82 90.00 274.16 298.15 174.88 291.67 413.79 284.95 300.03 277.90 263.57 309.58 92.00 159.05 189.60 192.15 178.20 238.45 258.15 285.50 161.84 134.71 104.00 284.29 260.15 250.00 160.65 254.20 155.15 298.15 298.15 204.15 125.26 298.15 145.65 167.55 58.00 53.48 230.94 129.95 131.35 2.16420 1.83990 2.07630 1.65860 2.01450 1.18060 1.19470 1.44950 1.83210 1.80290 1.66100 1.43550 0.98356 1.47670 1.56640 2.95870 1.31810 1.12760 1.52930 3.69010 1.53060 2.68470 2.05370 3.62920 6.22990 0.68554 0.87867 1.60680 1.29190 1.54260 2.12870 2.12030 2.20150 1.61090 1.46780 0.70123 1.71680 1.36660 0.98186 0.83031 1.36840 2.30150 2.82660 1.93350 1.94100 1.14670 1.95620 1.66860 1.38290 0.55414 0.57975 1.37260 0.79084 0.73946 357.05 341.45 410.00 337.45 366.15 300.13 298.15 331.13 392.70 402.94 396.58 360.00 250.00 466.44 380.00 360.00 298.15 310.48 422.15 559.20 374.47 570.00 407.90 433.15 616.93 290.00 390.00 350.21 289.73 409.35 486.55 466.95 428.25 404.95 301.82 252.70 390.41 493.15 329.00 283.85 374.20 510.10 417.15 326.15 386.55 315.25 410.00 320.00 371.05 98.00 56.00 504.08 337.78 285.70 2.51620 2.33750 2.81260 2.07550 2.47340 1.25420 1.37790 2.02240 2.63090 2.68700 2.69890 1.53400 1.03140 1.82000 2.56130 3.23830 1.31810 1.19590 1.69650 4.30070 2.22770 3.89330 2.78460 4.97260 9.31540 1.24440 1.64500 1.87960 1.33000 2.30750 3.04820 3.37940 3.01850 2.67980 1.87670 0.97582 1.82260 2.05980 1.14410 0.86932 1.63670 4.71570 3.37190 2.01530 2.42950 1.20070 2.40370 2.03580 1.92770 0.59663 0.55354 2.15180 1.40050 0.94206 (Continued ) 2-140 TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn Cmpd. no. 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 114 100 100 100 100 114 100 100 100 100 100 100 100 100 153 154 155 156 157 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 Name Formaldehyde Formamide Formic acid Furan Helium-4 Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene Formula CH2O CH3NO CH2O2 C4H4O He He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 CAS 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 Mol. wt. 30.02598 45.04062 46.0257 68.07396 4.0026 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 C1 70,077 63,400 78,060 114,370 387,220 410,430 376,970 176,120 61.26 194,570 2,416,800 1,070,000 270,730 265,040 267,950 236,870 46,798 370,350 157,820 172,120 161,980 1,638,600 1,409,400 208,250 235,960 164,640 82,795 303,320 93,000 94,860 79,815 66.653 57,720 47,300 95,398 62,520 64.666 127,540 -32,469 138,790 146,290 65.708 256,040 62,600 61,260 79,791 275,500 92,520 125,630 135,370 C2 -661.79 150.6 71.54 -215.69 -465570 -464890 347.82 242.92 314410 -23.206 -26105 -9470 -399.89 -375.68 -1315.9 -158.01 761.13 231.47 157.44 -183.78 44.116 -17261 -12553 -107.47 -345.94 -200.37 283.4 -1009 326 254.15 50.929 6765.9 9.9 90 -197.52 -223.02 49354 -65.35 1977.1 121.24 -58.59 38883 -2741.4 243.4 270.9 89.49 -1147 37.45 279.75 -133.34 C3 C4 C5 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 5.9749 -0.01813 0.00001983 155.15 292.00 281.45 187.55 2.20 1.80 295.13 229.80 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 200.00 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 300.00 192.62 200.00 300.00 274.69 13.95 185.15 165.00 259.83 189.79 187.68 270.00 177.95 409.15 288.15 90.69 175.47 359.00 253.40 200.00 196.32 179.69 260.75 159.53 0.55005 1.07380 0.98195 0.99486 0.10866 0.11352 5.30050 2.31940 1.99890 2.50870 2.35900 2.28350 2.35220 2.32420 1.81500 2.42290 1.73870 4.96020 1.91660 1.67500 2.25260 1.98210 2.04940 2.01850 2.05320 1.53540 1.67820 2.14950 1.58200 1.71110 0.97078 0.12622 0.59553 0.62150 0.70291 0.42875 0.67327 1.70310 1.46210 1.88400 1.59150 0.53605 0.71489 1.49980 1.29910 0.97689 1.49300 0.99249 1.98570 1.30350 253.85 493.00 380.00 304.50 4.60 2.10 575.30 426.15 520.00 496.15 448.60 432.90 480.00 490.00 430.00 460.00 372.93 560.01 401.15 460.00 478.85 460.00 412.40 460.00 460.00 404.00 354.35 430.00 344.48 357.67 653.15 32.00 206.45 185.00 298.85 292.67 370.00 427.65 320.00 580.00 434.15 190.00 503.15 538.50 373.40 249.94 353.35 266.82 472.65 314.56 0.72876 1.37650 1.05250 1.16090 0.29652 0.29952 7.68690 2.79640 4.06570 4.00650 3.87660 4.45840 3.23030 3.21630 2.75540 3.31310 2.43190 7.15210 2.20980 2.75340 3.45680 3.51970 3.98500 2.70870 2.76320 2.27060 1.83220 2.76390 2.05300 1.85760 1.31580 1.31220 0.59764 0.63950 0.71049 0.51186 4.91830 2.51140 1.66710 2.09110 1.88370 14.97800 2.46460 1.93670 1.62410 1.02160 1.90840 1.02510 2.57850 1.56620 0.72691 211800 135100 0.57895 1824.6 0.88395 110.03 33.004 1.0601 1.0024 6.5242 0.78982 -0.62882 0.68632 0.88734 0.709 71.721 40.991 0.2062 0.94278 0.8784 3.3885 0.043379 -123.63 0.3883 0.6297 22.493 0.82867 -7.0145 0.3582 -257.95 14.777 2.568 0.63868 -42494 3212.9 -2547.9 -0.19172 -0.0334 0.00011968 0 -0.011994 9.3808E-06 -0.12026 -0.04 0.00070293 0.000071087 -0.002762 478.27 -1623 0.0086913 614.07 -0.035078 0.000032719 2-141 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 108,300 74,200 206,600 149,510 151,600 81,919 177,850 198,390 105,200 102,930 47,726 131,340 50,578 118,600 118,170 155,920 53,271 46,457 27,030 85,383 132,300 161,240 130,200 92,919 183,650 149,770 143,440 191,170 211,170 115,300 255,100 226,650 142,220 251,890 172,370 -925,460 87,680 71,140 144,110 179,850 113,470 76,822 134,580 73,600 29,800 1,034,100 187,740 281,970 101,400 116,270 67,556 –2,979,600 342,570 195,220 146 417.4 -761.14 -247.63 -266.72 181.01 -171.57 -220.35 191.1 129.1 338.4 -63.1 508.59 447.07 447.99 -490 327.92 346.93 413 199.08 200.87 -288.61 -396 324.43 -79.862 -529.82 -154.07 -331.04 -661.97 -263.23 -938.4 15.421 -47.83 -468.32 -1783.9 7894.9 217.1 335.5 -102.09 -264.1 421.6 90.833 184.7 527.5 -138770 -497.6 -12281 -682.11 -135.3 54.373 76602 762.08 378.71 -0.292 0.00151 2.5899 0.91849 0.90847 0.74379 0.76096 0.62516 0.8125 2.1383 -0.061547 -0.9597 0.78179 1.21 0.60769 1.3499 0.7255 0.98445 2.4216 0.60412 2.413 1.0578 0.739 1.2209 14.759 -17.661 -0.9153 -0.0015585 0.0019533 -0.0021383 -0.047909 0.013617 0.002266 0.00005805 0.58113 0.79202 0.011456 7154 1.0691 248 3.8912 0.345 -652.59 0.20481 0.029716 0.00095984 -162.55 -2.2182 1.8879 1.3841 0.0074902 113.25 321.50 155.95 135.58 139.39 298.15 157.48 175.30 200.00 277.25 250.00 146.58 300.00 300.00 300.00 130.73 200.00 200.00 250.00 160.00 186.48 167.23 174.15 298.15 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 113.54 298.96 132.81 300.00 133.97 160.17 298.15 249.95 164.55 151.15 353.43 24.56 183.63 63.15 117.00 244.60 182.30 109.50 305.04 267.30 1.23280 2.08390 1.50890 1.32820 1.32070 1.35890 1.69280 1.83150 1.43420 1.86780 1.32330 1.39550 2.03160 2.52720 2.52570 1.24920 1.18860 1.15840 1.30280 1.15660 1.49050 1.34840 0.97934 1.89650 1.90290 1.02630 1.35600 1.63480 1.58080 0.89393 1.66110 2.91280 1.47060 2.07280 0.99613 2.20160 1.05680 1.71790 1.40860 1.57870 1.13470 1.82200 1.54110 1.01520 2.16230 0.36664 1.32420 0.55925 0.74860 1.03820 0.77468 0.62287 5.94090 2.98570 310.00 481.50 404.15 304.31 311.71 305.40 343.31 510.00 299.49 415.87 325.00 320.00 441.15 438.15 440.15 366.48 348.64 338.05 350.00 280.50 373.15 339.80 304.90 350.00 389.15 366.00 310.00 440.00 357.91 298.15 373.45 518.15 333.41 372.00 380.00 460.00 343.15 390.00 312.20 368.69 298.15 438.65 328.20 278.65 491.14 40.00 387.22 112.00 175.50 473.15 200.00 150.00 603.05 465.52 1.70480 2.75180 3.22010 1.59210 1.56730 1.37200 2.06610 2.83940 1.62430 2.64740 1.57710 1.94350 2.74940 3.14480 3.15350 1.86820 1.67600 1.63740 1.71580 1.36380 1.75110 1.53440 1.21950 2.06470 2.44600 1.36680 1.65400 2.36100 1.86410 0.90520 2.41180 5.18640 2.08420 2.46630 2.07250 2.94550 1.45960 2.01990 1.68880 1.90140 1.13470 2.61760 1.99560 1.25070 2.88880 0.69796 1.55360 0.79596 1.01540 1.29490 0.78431 1.99090 8.76630 3.77960 (Continued ) 2-142 TABLE 2-72 Heat Capacities of Inorganic and Organic Liquids [J/(kmol∙K)] (Continued ) Eqn Cmpd. no. 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 114 100 100 100 100 100 100 100 100 100 100 100 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 Name Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate Formula C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 CAS 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 Mol. wt. 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 C1 383,080 224,336 10,483,000 1,510,000 254,490 265,350 253,580 399,430 171,960 224,830 205,260 571,370 1,115,100 300,400 289,980 509,420 240,040 42,642 63,131 175,430 60,046 346,910 102,000 159,080 145,050 201,200 883,630 194,590 193,020 156,100 188,200 213,760 86,200 68,671 103,370 101,720 60,834 145,400 66,230 62.983 158,760 471,710 201,400 55,679 213,660 121,750 83,400 139,530 174,380 114,140 75,700 C2 -1139.8 49.726 -115220 -12600 -298.06 -46.22 -366.3 374.64 383.28 -186.63 44.392 -4849 -9773.8 -426.2 -417.27 -4279.1 -33.198 886.67 199.92 -6152.3 281.16 219.54 389.95 -270.5 28.344 -651.3 -8220.5 -263.86 -176.43 -456.94 -140.84 -324.4 256.6 246.66 527.03 317.61 215.89 252.4 98.275 113630 -635 -4172.1 -450.6 406.13 -702.7 -149.56 384.1 78 -101.8 -343.72 326.1 C3 2.7101 0.9813 476.87 40.7 1.1707 0.79154 1.4881 0.58156 -0.059074 0.95891 0.8956 19.725 34.252 1.1172 1.2218 21.477 0.67889 -0.69315 113.92 0.65632 -0.32545 0.99537 0.6372 2.275 29.125 0.76808 0.5669 2.255 0.63581 0.9472 C4 -0.85381 -0.0386 0.79 1.0905 0.00056246 -0.021532 -0.03454 -0.044462 0.000035028 -0.92382 0.0027963 -0.02989 -0.003163 0.29552 633.21 1.969 14.745 1.7053 -0.50303 1.6605 0.47759 C5 -873.46 -0.014402 0.00000238 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 219.66 285.55 310.00 238.15 191.91 253.05 223.15 301.31 251.65 216.38 289.65 250.00 241.55 252.86 255.55 171.45 240.00 200.00 462.65 54.36 90.00 283.07 191.59 143.42 239.15 200.14 200.00 196.29 234.18 108.02 160.75 197.45 200.00 200.00 372.39 314.06 243.15 404.15 200.00 85.47 146.95 185.26 199.00 165.00 252.45 180.37 274.70 188.36 173.55 87.89 298.15 2.63480 3.18550 3.50590 2.96270 2.40410 3.04340 2.45940 5.65110 2.64670 2.29340 2.93260 2.55500 2.65930 2.64060 2.63140 2.13270 2.71180 1.92250 1.55620 0.53646 0.85350 4.61650 1.64760 1.40760 1.88270 1.61980 1.65410 1.72390 1.82790 1.29390 1.81990 1.86640 1.37520 1.18000 2.99630 2.01470 1.30800 2.47410 0.85885 0.84879 1.07970 1.13280 1.79260 1.09000 1.42090 1.10310 1.88910 1.54220 1.80510 0.92354 1.72930 325.00 528.75 460.00 471.70 475.00 492.95 423.85 589.86 445.15 460.00 512.85 467.10 452.90 500.00 440.65 454.00 472.19 399.35 516.00 142.00 150.00 543.84 375.15 390.00 458.95 389.15 392.20 375.46 375.14 372.00 385.15 399.79 313.33 329.27 500.00 425.00 489.75 557.65 238.65 360.00 400.00 463.00 431.65 322.15 414.32 370.25 404.70 340.00 432.39 298.15 398.15 2.98900 5.24980 4.64940 5.71150 3.77050 4.34910 3.65660 8.22760 3.30870 3.41890 4.63580 4.15660 5.05560 3.66600 3.43350 3.20980 3.75730 2.86190 1.66290 0.90662 1.02220 6.60420 2.02490 2.04980 2.92280 2.92270 3.36360 2.03800 2.06610 1.80920 2.28270 2.35460 1.66600 1.49890 3.66890 2.36700 2.37450 2.86150 0.89683 2.60790 2.19800 2.71460 3.24630 1.34310 2.07560 1.31850 2.38850 1.66050 2.78060 1.08600 2.05540 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 138,390 167,330 58,080 45,810 829,380 113,340 186,250 85,743 119,500 258,090 131,270 182,900 353,140 171,730 81,760 123,300 43,326 84,864 140,140 103,350 350,180 111,480 136,050 119,450 178,800 95,275 388,620 40,364 133,530 293,980 -1,360,200 136,300 68,720 -10,320 49,516 276,370 133,860 36,500 -35,500 -117.11 -319.1 445.2 368.33 -7331.5 290.2 247.8 5.7443 345.64 635.09 29.13 -800.47 455.38 -130.1 630.73 91.725 -152.3 159.3 -104.7 368.13 -288 324.54 -128.47 696.7 -1439.5 664.46 514.64 -114.98 10964 -106.17 135 322.8 420.35 -2090.1 7.8754 1017.5 1287.2 0.47059 0.8127 19.203 -0.6051 0.86116 2.8934 0.0013567 -0.0025015 0.6229 0.13243 0.695 1.0022 0.9913 0.83741 -1.3765 3.2187 0.0021734 0.96936 -20.86 0.75175 0.013055 8.125 0.52265 -2.63 -2.599 -0.014116 0.00302 0.002426 9.3701E-06 142.61 159.95 213.15 388.85 186.35 242.54 460.85 197.67 230.15 303.15 700.15 329.35 279.01 164.65 237.38 176.98 375.41 234.94 178.18 236.50 267.76 200.00 156.08 247.79 229.33 165.78 280.00 398.40 354.00 247.57 289.05 259.56 200.00 200.00 178.35 273.16 217.00 247.98 286.41 1.31260 1.37080 1.52970 1.89040 1.30000 1.67490 3.00450 0.86878 1.19500 2.58090 3.73270 3.92070 4.28310 1.07210 1.89860 1.19790 2.80110 1.13720 1.35070 1.41020 3.94000 1.85110 1.15250 1.99870 1.93380 1.82850 2.37910 3.05080 3.15710 3.24930 3.81370 1.59390 0.95720 0.54240 1.24490 0.76150 1.60180 1.73140 1.76970 350.00 340.87 460.75 683.00 253.15 418.31 591.00 350.00 230.15 303.15 795.28 609.15 526.73 339.12 480.77 394.27 426.00 357.31 500.00 300.00 508.62 361.92 276.02 449.27 350.00 520.00 320.00 475.47 475.00 433.42 523.15 389.35 278.25 400.00 363.85 533.15 540.15 417.58 600.00 1.55050 1.52990 2.63210 2.97380 2.04030 2.28160 3.32700 0.87754 1.19500 2.58090 4.06150 5.69770 6.07410 1.35460 3.00690 1.68830 3.12020 1.34550 2.37740 1.51140 5.56190 2.44710 1.32080 2.65260 2.36420 3.90950 2.57570 3.56290 3.77980 4.26240 5.35730 2.08920 1.06280 1.18800 2.02460 0.89394 2.90600 2.22690 3.25200 For the 11 substances: ammonia; 1,2-butanediol; 1,3-butanediol; carbon monoxide; 1,1-difluoroethane; ethane; heptane; hydrogen; hydrogen sulfide; methane; and propane; the liquid heat capacity CpL is calculated with Eq. (2-114): CpL = C12/τ + C2 - 2C1C3τ - C1C4τ2 - C32τ3/3 - C3C4τ4/2 - C42τ5/5, where τ = 1 - Tr , Tr = T/TC, TC is the critical temperature from Table 2-106, CpL is in J/(kmol∙K) and T is in K. For all other compounds, Eqn 100 is used. Eqn 100: CpL = C1 + C2T + C3T 2 + C4T 3 + C5T 4. For benzene, fluorine, and helium, two sets of constants are given for Eqn 100 that cover different temperature ranges, as shown in the table. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016). 2-143 2-144 PHYSICAL AnD CHEMICAL DATA TABLE 2-73 Specific Heats of Organic Solids Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound Formula Acetic acid Acetone Aminobenzoic acid (o-) (m-) (p-) Aniline Anthracene C2H4O2 C3H6O C7H7NO2 C7H7NO2 C7H7NO2 C6H7N C14H10 Anthraquinone Apiol Azobenzene C14H8O2 C12H14O4 C12H10N2 Benzene C6H6 Benzoic acid Benzophenone C7H6O2 C13H10O Betol C17H12O3 Bromoiodobenzene (o-) (m-) (p-) Bromonaphthalene (β-) Bromophenol C6H4BrI C6H4BrI C6H4BrI C10H7Br C6H5BrO Camphene Capric acid Caprylic acid Carbon tetrachloride C10H16 C10H20O2 C8H16O2 CCl4 Cerotic acid Chloral alcoholate hydrate Chloroacetic acid Chlorobenzoic acid (o-) (m-) (p-) Chlorobromobenzene (o-) (m-) (p-) Crotonic acid Cyamelide Cyanamide Cyanuric acid C27H54O2 C4H7Cl3O2 C2H3Cl3O2 C2H3ClO2 C7H5ClO2 C7H5ClO2 C7H5ClO2 C6H4BrCl C6H4BrCl C6H4BrCl C4H6O2 C3H3N3O3 CH2N2 C3H3N3O3 Dextrin Dextrose (C6H10O5)x C6H12O6 Dibenzyl Dibromobenzene (o-) (m-) (p-) Dichloroacetic acid Dichlorobenzene (o-) (m-) (p-) Dicyandiamide C14H14 C6H4Br2 C6H4Br2 C6H4Br2 C2H2Cl2O2 C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4N4 Temperature, °C -200 to +25 -210 to -80 85 to mp 120 to mp 128 to mp sp ht, cal/(g⋅°C) 50 100 150 0 to 270 10 28 0.330 + 0.00080t 0.540 + 0.0156t 0.254 + 0.00136t 0.253 + 0.00122t 0.287 + 0.00088t 0.741 0.308 0.350 0.382 0.258 + 0.00069t 0.299 0.330 -250 -225 -200 -150 -100 -50 0 20 to mp -150 -100 -50 0 +20 -150 -100 0 +50 -50 to 0 -75 to -15 -40 to 50 41 32 0.0399 0.0908 0.124 0.170 0.227 0.299 0.375 0.287 + 0.00050t 0.115 0.172 0.220 0.275 0.303 0.129 0.167 0.248 0.308 0.143 + 0.00025t 0.143 0.116 + 0.00032t 0.260 0.263 35 8 -2 -240 -200 -160 -120 -80 -40 15 78 32 60 80 to mp 94 to mp 180 to mp -34 -52 -40 38 to 70 40 20 40 0.380 0.695 0.628 0.013 0.081 0.131 0.162 0.182 0.201 0.387 0.509 0.213 0.363 0.228 + 0.00084t 0.232 + 0.00073t 0.242 + 0.00055t 0.192 0.150 0.150 0.520 + 0.00020t 0.263 0.547 0.318 0 to 90 -250 -200 -100 0 20 28 -36 -25 -50 to +50 0.291 + 0.00096t 0.016 0.077 0.160 0.277 0.300 0.363 0.248 0.134 0.139 + 0.00038t 0.406 0.185 0.186 0.219 + 0.0021t 0.456 -48.5 -52 -50 to +53 0 to 204 SPECIFIC HEATS TABLE 2-73 Specific Heats of Organic Solids (Continued ) Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound Formula Dihydroxybenzene (o-) (m-) (p-) C6H6O2 C6H6O2 C6H6O2 Di-iodobenzene (o-) (m-) (p-) Dimethyl oxalate Dimethylpyrene Dinitrobenzene (o-) (m-) (p-) Diphenyl Diphenylamine Dulcitol C6H4I2 C6H4I2 C6H4I2 C4H6O4 C7H8O2 C6H4N2O4 C6H4N2O4 C6H4N2O4 C12H10 C12H11N C6H14O6 Erythritol Ethyl alcohol C4H10O4 C2H6O (crystalline) (vitreous) Temperature, °C sp. ht., cal/(g⋅°C) -163 to mp -160 to mp -250 -240 -220 -200 -150 to mp -50 to +15 -52 to -42 -50 to +80 10 to 50 50 -160 to mp -160 to mp 119 to mp 40 26 20 0.278 + 0.00098t 0.269 + 0.00118t 0.025 0.038 0.061 0.081 0.268 + 0.00093t 0.109 + 0.00026t 0.100 + 0.00026t 0.101 + 0.00026t 0.212 + 0.0044t 0.368 0.252 + 0.00083t 0.248 + 0.00077t 0.259 + 0.00057t 0.385 0.337 0.282 60 -190 -180 -160 -140 -130 -190 -180 -175 -170 -190 to -40 0.351 0.232 0.248 0.282 0.318 0.376 0.260 0.296 0.380 0.399 0.366 + 0.00110t Ethylene glycol C2H6O2 Formic acid CH2O2 -22 0 0.387 0.430 Glutaric acid Glycerol C5H8O4 C3H8O3 20 -265 -260 -250 -220 -200 -100 0 0.299 0.009 0.022 0.047 0.085 0.115 0.217 0.330 Hexachloroethane Hexadecane Hydroxyacetanilide C2Cl6 C16H34 C8H9NO2 Iodobenzene Isopropyl alcohol C6H5I C3H8O Lactose Lauric acid Levoglucosane Levulose C12H22O11 C12H22O11⋅H2O C12H24O2 C6H10O5 C6H12O6 Malonic acid Maltose Mannitol Melamine Myristic acid Naphthalene Naphthol (α-) (β-) Naphthylamine (α-) Nitroaniline (o-) (m-) (p-) Nitrobenzoic acid (o-) (m-) (p-) Nitronaphthalene 41 to mp 25 0.174 0.495 0.249 + 0.00154t 40 -200 to -160 0.191 0.051 + 0.00165t 20 20 -30 to +40 40 20 0.287 0.299 0.430 + 0.000027t 0.607 0.275 C3H4O4 C12H22O11 C6H14O6 C3H6N6 C14H28O2 20 20 0 to 100 40 0 to 35 0.275 0.320 0.313 + 0.00025t 0.351 0.381 + 0.00545t C10H8 C10H8O C10H8O C10H9N C6H6N2O2 C6H6N2O2 C6H6N2O2 C7H5NO4 C7H5NO4 C7H5NO4 C10H7NO2 -130 to mp 50 to mp 61 to mp 0 to 50 -160 to mp -160 to mp -160 to mp -163 to mp 66 to mp -160 to mp 0 to 55 0.281 + 0.00111t 0.240 + 0.00147t 0.252 + 0.00128t 0.270 + 0.0031t 0.269 + 0.000920t 0.275 + 0.000946t 0.276 + 0.001000t 0.256 + 0.00085t 0.258 + 0.00091t 0.247 + 0.00077t 0.236 + 0.00215t (Continued) 2-145 2-146 PHYSICAL AnD CHEMICAL DATA TABLE 2-73 Specific Heats of Organic Solids (Continued ) Recalculated from International Critical Tables, vol. 5, pp. 101–105 Compound Formula Temperature, °C sp ht, cal/(g⋅°C) Oxalic acid C2H2O4 C2H2O4⋅2H2O -200 to +50 -200 -100 0 +50 100 0.259 + 0.00076t 0.117 0.239 0.338 0.385 0.416 Palmitic acid C16H32O2 Phenol Phthalic acid Picric acid C6H6O C8H6O4 C6H3N3O7 Propionic acid Propyl alcohol (n-) C3H6O2 C3H8O Pyrotartaric acid C6H8O4 -180 -140 -100 -50 0 +20 14 to 26 20 -100 0 +50 100 120 -33 -200 -175 -150 -130 20 0.167 0.208 0.251 0.306 0.382 0.430 0.561 0.232 0.165 0.240 0.263 0.297 0.332 0.726 0.170 0.363 0.471 0.497 0.301 Quinhydrone C12H10O4 Quinone C6H4O2 -250 -225 -200 -100 0 -250 -225 -200 -150 to mp 0.017 0.061 0.098 0.191 0.256 0.031 0.082 0.113 0.282 + 0.00083t Salol Stearic acid Succinic acid Sucrose Sugar (cane) C13H10O3 C18H36O2 C4H6O4 C12H22O11 C12H22O11 32 15 0 to 160 20 22 to 51 0.289 0.399 0.248 + 0.00153t 0.299 0.301 Tartaric acid Tartaric acid C4H6O6 C4H6O6⋅H2O Tetrachloroethylene Tetryl C2Cl4 C7H5N5O8 1 Tetryl + 1 picric acid 1 Tetryl + 2 TNT C13H8N8O15 C21H15N11O20 Thymol Toluic acid (o-) (m-) (p-) Toluidine (p-) C10H14O C8H8O2 C8H8O2 C8H8O2 C7H9N Trichloroacetic acid Trimethyl carbinol Trinitrotoluene C2HCl3O2 C4H10O C7H5N3O6 Trinitroxylene C8H7N3O6 Triphenylmethane C19H16 36 -150 -100 -50 0 +50 -40 to 0 -100 -50 0 +100 -100 to +100 -100 0 +50 0 to 49 54 to mp 54 to mp 130 to mp 0 20 40 solid -4 -100 -50 0 +100 -185 to +23 20 to 50 0 to 91 0.287 0.112 0.170 0.231 0.308 0.366 0.198 + 0.00018t 0.182 0.199 0.212 0.236 0.253 + 0.00072t 0.172 0.280 0.325 0.315 + 0.0031t 0.277 + 0.00120t 0.239 + 0.00195t 0.271 + 0.00106t 0.337 0.387 0.440 0.459 0.559 0.170 0.253 0.311 0.385 0.241 0.423 0.189 + 0.0027t Urea CH4N2O 20 0.320 TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)] Cmpd. no. 1 7 8 14 16 27 29 31 34 37 38 43 59 60 61 64 67 81 88 95 97 98 99 112 120 125 126 134 145 151 156 157 182 183 190 194 197 217 221 231 236 237 238 243 246 247 248 251 Name Acetaldehyde Acetylene Acrolein Argon Benzene Bromoethane 1,2-Butadiene Butane 1-Butanol cis-2-Butene trans-2-Butene 1-Butyne m-Cresol o-Cresol p-Cresol Cyclobutane Cyclohexanone 1,1-Dibromoethane 1,1-Dichloroethane Diethyl ether 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Dimethyl ether 1,4-Dioxane Ethane Ethanol Ethylcyclopentane Ethyl mercaptan Fluoroethane Furan Helium-4 Hydrazine Hydrogen Isopropyl amine Methanol Methyl acetylene Methylcyclopentane Methylethyl ether Methyl mercaptan 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene alpha-Methyl styrene Naphthalene Neon Nitroethane Nitromethane Formula C2H4O C2H2 C3H4O Ar C6H6 C2H5Br C4H6 C4H10 C4H10O C4H8 C4H8 C4H6 C7H8O C7H8O C7H8O C4H8 C6H10O C2H4Br2 C2H4Cl2 C4H10O C2H4F2 C2H4F2 CH2F2 C2H6O C4H8O2 C2H6 C2H6O C7H14 C2H6S C2H5F C4H4O He H4N2 H2 C3H9N CH4O C3H4 C6H12 C3H8O CH4S C4H10 C4H10O C4H8 C9H10 C10H8 Ne C2H5NO2 CH3NO2 CAS 75-07-0 74-86-2 107-02-8 7440-37-1 71-43-2 74-96-4 590-19-2 106-97-8 71-36-3 590-18-1 624-64-6 107-00-6 108-39-4 95-48-7 106-44-5 287-23-0 108-94-1 557-91-5 75-34-3 60-29-7 75-37-6 624-72-6 75-10-5 115-10-6 123-91-1 74-84-0 64-17-5 1640-89-7 75-08-1 353-36-6 110-00-9 7440-59-7 302-01-2 1333-74-0 75-31-0 67-56-1 74-99-7 96-37-7 540-67-0 74-93-1 75-28-5 75-65-0 115-11-7 98-83-9 91-20-3 7440-01-9 79-24-3 75-52-5 Mol. wt. 44.05256 26.03728 56.06326 39.948 78.11184 108.965 54.09044 58.1222 74.1216 56.10632 56.10632 54.09044 108.13782 108.13782 108.13782 56.10632 98.143 187.86116 98.95916 74.1216 66.04997 66.04997 52.02339 46.06844 88.10512 30.069 46.06844 98.18606 62.13404 48.0595 68.07396 4.0026 32.04516 2.01588 59.11026 32.04186 40.06386 84.15948 60.09502 48.10746 58.1222 74.1216 56.10632 118.1757 128.17052 20.1797 75.0666 61.04002 C1 29705 30800 30702 20786 35978 27112 27400 17330 25300 39760 20908 25300 29002 16192 29090 31863 32182 20560 19560 26040 29736 27581 33851 25940 28345 31742 32585 34710 23014 30358 40860 20786 32998 64979 23590 30270 30810 35465 23337 31520 21380 17080 24970 37735 29120 20786 33055 38782 C2 C3 127.43 -53.08 80.95 -0.21793 0.384 0.191 -101.69 117.99 177.6 458.16 371.2 108.8 324.73 183.2 158.79 469.81 166 37.226 116.87 285.2 249.01 388 72.364 169.88 -20.966 178.46 88.3 26.567 87.4 304.96 271.36 62.839 -160.3 0.939 -5.2147 -788.17 310.42 84.64 35.8 147.38 309.03 60.1 271.2 381.7 211.8 112.94 82.88 89.54 -48.39 C4 C5 -0.816 -0.461 -0.411 0.635 -0.479 0.616 0.23616 0.547 -0.332 -0.22187 -0.268 0.228 -0.1581 0.17584 -0.186 0.446 0.12927 0.05 -0.084 -0.4427 0.1067 0.87 0.21379 5.8287 -0.274 -0.188 0.27 0.242 -0.285 -0.092 -0.199 0.846 0.964 0.238 0.413 -0.018459 2.164E-05 Tmin, K 50 50 50 100 50 100 50 50 50 50 50 50 50 50 50 50 50 100 100 50 50 50 50 50 50 50 50 50 50 50 100 100 50 50 50 50 50 50 50 50 50 50 50 50 50 100 50 50 Cp at Tmin 3.553E+04 2.911E+04 3.523E+04 2.079E+04 3.324E+04 3.891E+04 3.628E+04 3.820E+04 4.271E+04 4.520E+04 3.612E+04 3.446E+04 3.853E+04 3.849E+04 3.893E+04 3.431E+04 3.939E+04 4.576E+04 4.224E+04 4.477E+04 3.392E+04 3.568E+04 3.324E+04 3.440E+04 3.388E+04 3.339E+04 3.708E+04 4.975E+04 3.548E+04 3.377E+04 3.353E+04 2.079E+04 3.327E+04 3.797E+04 3.843E+04 3.403E+04 3.328E+04 4.344E+04 3.808E+04 3.453E+04 3.471E+04 3.567E+04 3.556E+04 4.550E+04 3.567E+04 2.079E+04 3.813E+04 3.740E+04 Tmax, K Cp at Tmax 200 200 200 1500 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 200 1500 200 250 200 200 200 200 200 200 200 200 200 200 200 1500 200 200 4.647E+04 3.554E+04 5.453E+04 2.079E+04 5.320E+04 5.071E+04 6.292E+04 7.632E+04 8.110E+04 6.152E+04 6.941E+04 6.194E+04 8.616E+04 9.099E+04 8.693E+04 4.875E+04 7.744E+04 6.432E+04 6.049E+04 9.292E+04 5.333E+04 5.523E+04 3.669E+04 5.419E+04 6.385E+04 4.223E+04 5.207E+04 9.234E+04 5.958E+04 4.719E+04 4.360E+04 2.079E+04 4.051E+04 2.834E+04 7.471E+04 3.968E+04 4.877E+04 7.462E+04 7.374E+04 4.354E+04 7.194E+04 8.546E+04 6.733E+04 9.416E+04 8.426E+04 2.079E+04 6.048E+04 4.562E+04 2-147 (Continued) 2-148 TABLE 2-74 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to a Polynomial Cp [J/(kmol∙K)] (Continued ) Cmpd. no. Name 253 289 290 294 295 296 304 310 320 321 322 324 331 Nitric oxide 2-Pentyne Phenanthrene Propadiene Propane 1-Propanol Propylbenzene Quinone Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene Thiophene 1,2,4-Trimethylbenzene Formula NO C5H8 C14H10 C3H4 C3H8 C3H8O C9H12 C6H4O2 C4H8O C10H12 C4H8S C4H4S C9H12 CAS 10102-43-9 627-21-4 85-01-8 463-49-0 74-98-6 71-23-8 103-65-1 106-51-4 109-99-9 119-64-2 110-01-0 110-02-1 95-63-6 Mol. wt. 30.0061 68.11702 178.2292 40.06386 44.09562 60.09502 120.19158 108.09476 72.10572 132.20228 88.17132 84.13956 120.19158 C1 34980 24330 27700 31690 26675 28800 22880 29668 36970 28560 41195 36765 35652 C2 -35.32 335.7 210 17.1 147.04 257 538.46 129.07 -12.28 225.1 -88.3 -112.82 323.89 C3 0.07729 -0.37 1.24 0.282 -0.35 -0.546 0.53105 0.444 0.616 0.942 0.862 0.305 C4 C5 Tmin, K -5.7357E-05 1.4526E-08 100 50 50 50 50 50 50 50 50 50 50 50 50 Cp at Tmin 3.216E+04 4.019E+04 4.130E+04 3.325E+04 3.403E+04 4.078E+04 4.844E+04 3.745E+04 3.747E+04 4.136E+04 3.914E+04 3.328E+04 5.261E+04 Tmax, K Cp at Tmax 1500 200 200 200 200 200 200 200 200 200 200 200 200 3.586E+04 7.667E+04 1.193E+05 4.639E+04 5.608E+04 6.620E+04 1.087E+05 7.672E+04 5.227E+04 9.822E+04 6.122E+04 4.868E+04 1.126E+05 Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where C 0p is in J/(kmol∙K) and T is in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties AIChE New York NY (2016)”. TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CAS Mol. wt. 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 C1 × 1E-05 C2 × 1E-05 0.48251 1.06650 0.34200 1.29400 0.40200 1.36750 0.87998 1.66350 0.57040 1.63200 0.44346 0.84650 0.36921 0.31793 0.57019 0.91830 0.60590 1.37030 0.56303 1.09720 0.28958 0.09390 0.33427 0.48980 0.76370 2.93770 See Table 2-155 1.95810 1.70190 0.55238 1.73380 0.68950 2.32750 0.77594 2.64550 0.76820 2.26350 1.00990 4.48980 0.84115 3.14280 0.95210 2.88680 0.99192 2.96330 1.07590 4.21050 0.30113 0.08009 0.72100 2.06400 0.52310 0.89110 0.36241 0.69248 0.66964 1.09950 0.50950 1.70500 0.80154 1.62420 1.04780 2.54900 1.06600 2.57500 0.74540 2.59070 0.90878 2.55080 0.64257 2.06180 0.65121 1.43250 0.74296 1.34760 1.16840 3.76900 1.13800 4.45400 0.92478 2.77950 0.92367 2.51660 0.66492 1.07260 0.89240 1.56750 1.48800 1.35220 0.82142 1.32340 0.29370 0.34540 0.30100 0.33380 0.29108 0.08773 0.37582 0.70540 C3 × 1E-03 C4 × 1E-05 1.99290 1.07500 1.26200 0.80153 1.60700 1.63980 0.67805 0.76747 1.64750 0.91248 3.01200 2.03600 1.60510 0.78851 0.64000 0.70030 0.76076 0.96800 0.49487 0.33430 0.38554 1.04460 -0.44070 0.07580 0.22560 2.17000 1.32570 0.76425 1.51200 1.79250 0.74786 1.31100 1.95390 0.70207 1.55830 1.90410 0.75140 1.65040 0.81205 1.74540 0.83737 1.53240 0.84149 1.87760 1.96700 1.60730 1.89300 1.67680 0.85796 0.87025 1.95600 1.55070 1.68370 1.61090 0.79390 0.90190 1.14600 0.84021 1.42800 0.89600 3.08510 0.51210 -37.41700 0.72545 1.75160 2.23820 -0.67585 2.83950 2.57430 1.63850 2.21160 4.17850 0.10780 1.68700 0.67540 0.44781 0.68373 1.33700 1.05750 1.87500 1.95100 1.73200 1.85200 1.33240 0.89648 0.89116 2.81800 3.04970 1.59740 1.56410 0.74240 1.09840 -678.00000 0.67932 0.26400 0.28930 0.08455 0.48500 C5 Tmin, K Cp at Tmin × 1E-05 912.78 502 569.7 2310.1 731.5 761.47 3036.6 2375.4 751.49 1178.4 1484 882 751.2 298.15 100 50 298.15 200 298.15 298.15 298.15 250 298.15 50 100 300 0.54732 0.34481 0.40200 1.10440 0.60487 0.52233 0.44032 0.71326 0.69837 0.64356 0.28958 0.33427 1.13020 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1.29930 1.49970 1.57560 2.69700 1.88200 1.11990 0.75868 1.56240 1.74240 1.37940 0.34956 0.66465 3.02260 41.232 2445.7 697.9 835.9 896 627.4 850.06 2002.6 719.16 828.81 314.6 765.3 2809 793.32 2441.1 685.6 2476.1 833 860.5 712.4 832.13 757.06 2477.2 2463.4 811.2 708.86 758.68 739.2 -2458.4 2566 6.98 2313.7 588 374.7 1538.2 236.1 298.15 298.15 200 200 298 300 298.15 300 300 200 100 200 298.15 298.15 298.15 200 298.15 298.15 298.15 298.15 298.15 250 298.15 298.15 298.15 200 200 200 298.15 298.15 298.15 298.15 50 100 60 100 1.27450 0.82616 0.76894 0.81258 1.09070 1.80010 1.11980 1.55010 1.41560 1.14810 0.30901 0.76789 0.63800 0.42454 0.79668 0.57563 0.98586 1.26670 1.26790 1.07860 1.12570 0.75708 0.80241 0.87766 1.52810 1.26590 0.97140 0.97633 0.81441 1.02830 1.15330 0.97246 0.29370 0.31003 0.29108 0.47299 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500.1 1500.15 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 5000 1500 1500 1500 3.25010 2.41800 2.67390 2.97120 2.68100 4.93110 3.28800 4.34450 3.29570 4.55570 0.37938 2.46280 1.54570 0.90758 1.92080 1.95550 2.66050 3.02890 3.03110 2.85090 2.87300 2.28980 2.27180 2.28360 3.67240 4.84350 3.10080 2.96150 1.92210 2.67780 2.59050 2.28510 0.63346 0.61475 0.35208 1.06620 Tmax, K Cp at Tmax × 1E-05 2-149 (Continued) 2-150 TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 Name Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone Formula CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O CAS Mol. wt. C1 × 1E-05 C2 × 1E-05 C3 × 1E-03 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 0.92004 0.29142 0.80110 0.52590 0.39420 0.36220 0.64710 0.61809 0.90974 0.79880 0.92021 1.08100 0.45894 0.50835 0.43200 0.90430 0.85860 0.58171 0.41600 0.48074 0.33800 0.54305 1.94250 1.67200 0.24457 1.69840 1.71010 1.93100 1.50450 0.30290 0.66622 0.74906 0.39100 1.61220 0.70000 0.69480 0.69780 0.63412 0.65271 0.36280 0.71450 0.78658 1.20800 0.91020 0.99953 0.91273 0.55477 0.57793 0.37540 1.13840 1.09300 1.08690 0.16446 0.09176 2.31000 1.40200 0.65730 0.69810 1.79800 1.80230 2.13210 2.85300 2.11060 3.79320 0.41286 1.64870 3.73500 2.57710 2.57770 3.17170 3.01400 2.51590 1.68940 3.99620 5.14030 5.35300 6.54600 5.39200 5.20890 5.48150 4.37940 0.09750 0.81703 1.27250 0.64800 4.47770 2.07460 2.08040 2.07800 0.83862 1.12540 0.68040 1.73440 1.74290 3.06600 2.67400 1.70380 2.41000 1.23610 0.89811 0.53510 2.57470 3.68300 4.05400 1.07640 0.94900 2.15700 2.03700 0.92800 1.80500 1.67600 1.54380 0.76324 1.47650 0.76622 1.75050 1.38120 0.82849 1.19200 0.78820 0.84895 1.54350 1.46170 1.58030 1.61350 1.35750 1.89780 1.61410 1.08990 1.56800 1.72650 1.60850 1.32910 2.51500 0.76285 1.98100 1.19400 1.68310 1.36640 1.36320 1.36350 0.76898 1.73760 1.25600 1.52400 1.71570 2.08900 1.71900 0.87072 1.66860 0.83501 0.84727 0.86687 0.73840 1.60570 1.78020 C4 × 1E-05 -5083.80000 0.10030 2.04600 0.99820 0.49300 0.44470 1.23300 1.18930 0.93355 2.04200 0.95073 3.00270 0.33023 0.86658 1.63500 1.30680 0.77780 2.12730 1.80950 1.74540 1.17680 2.56230 4.17520 3.78200 4.86420 3.93800 3.59350 3.74000 2.55570 -0.02750 0.40941 0.94370 0.42000 2.91800 1.59830 1.59400 1.59650 0.44030 0.87800 0.42750 1.22300 1.26270 2.34300 1.79260 1.07460 1.65200 -0.40972 0.43249 0.22998 1.62000 2.34200 2.97860 C5 2.3486 425 897.6 861.18 399.6 844.27 755.78 685.93 2474.5 664.7 2464.6 794.8 559.94 2472.4 530.1 1952.2 2401.5 701.62 668.8 718.37 722.8 618.54 859.95 742 424 720.5 782.92 754.75 632.01 368 2488.3 845.2 501 781.6 620.16 619.2 619.37 2533.2 795.45 548 674.2 765.1 891 794.94 2471.3 771.08 1033.4 2424.2 2437.2 2143 699 791.6 Tmin, K Cp at Tmin × 1E-05 298 50 200 298.15 100 298.15 298.15 200 298.15 200 298.15 200 273.15 298.15 100 200 298.15 150 100 150 100 300 298.15 200 298.15 298.15 298.15 200 298 100 298.15 200 100 200 200 200 200 298.15 200 100 150 200 298.15 200 298.15 200 298.15 298.15 298.15 300 298.15 300 0.61055 0.29142 0.82193 0.62879 0.40484 0.41193 0.84674 0.67679 1.24780 0.91584 1.25080 1.14800 0.54968 0.70636 0.43657 0.96478 1.14170 0.59782 0.41650 0.49182 0.33813 1.26440 2.37630 1.79670 2.52320 2.43540 2.23040 2.04340 2.19380 0.30195 0.79599 0.76345 0.39288 1.68410 0.82450 0.81978 0.82283 0.76395 0.67221 0.36369 0.72683 0.82172 1.41970 0.95017 1.16950 0.95673 0.67988 0.67730 0.42969 1.59950 1.56690 1.51020 Tmax, K 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500.1 1500 1500 1500 1500 1500 1500 1500 1500 1500 Cp at Tmax × 1E-05 1.04650 0.37930 2.53270 1.55080 1.00630 0.90655 2.09750 2.10230 3.21580 3.21630 3.21320 4.18080 0.81268 2.32330 3.65160 3.82510 3.47740 3.21320 2.92980 2.56190 1.72130 3.72360 6.04070 6.09320 6.10990 6.21860 5.87450 6.46130 5.27940 0.34251 1.56840 1.70410 0.95987 5.21450 2.51610 2.51610 2.51750 1.56330 1.57430 0.95430 2.16090 2.18940 3.46740 3.05190 2.92630 2.87240 1.54560 1.55140 0.94201 4.19410 4.05350 4.30930 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 1.15560 1.01130 0.65340 0.55650 0.77720 1.07760 1.10390 1.09910 0.78430 0.57431 0.72200 0.85438 1.39600 0.61453 0.60370 0.69490 1.14025 0.68444 1.09850 1.21140 2.12950 3.24810 0.44256 0.49200 0.99810 0.59400 0.78440 1.09440 1.04550 1.11500 1.10590 0.93177 0.33380 0.72860 0.63012 0.34300 0.33460 0.53700 1.57770 1.63400 1.09530 1.24000 0.60436 0.93700 1.13200 0.96993 0.29122 0.73393 0.49090 0.35193 0.33503 0.38220 0.33810 0.43673 See Table 2-155 1.83050 3.23930 1.61790 1.63840 4.03200 4.67180 4.64450 4.64010 1.43640 0.94494 1.78300 4.57720 4.78000 1.74380 1.37470 1.52400 5.36801 1.98020 4.34120 2.61270 6.63300 11.09000 0.84737 1.45770 2.09310 1.61800 3.39900 4.17940 2.31480 3.39100 4.63060 2.79330 0.94790 1.84360 1.45840 1.42700 1.21160 1.88600 4.40170 4.51190 3.00320 3.20000 0.87524 2.82900 2.94000 1.08780 0.10132 2.37390 0.88880 0.65344 0.49394 0.93000 0.75930 1.28390 0.95919 1.56110 1.78370 1.73410 1.54400 1.65400 1.69430 1.66790 1.58360 0.89551 1.53200 1.51810 2.19000 1.34180 1.64100 1.65140 2.08860 0.82793 1.62220 0.78956 1.71550 1.63600 0.87224 1.66280 2.02260 1.81200 1.55900 0.88375 0.71000 1.67050 1.66280 0.78650 1.59600 1.68800 1.67300 1.63800 1.60840 1.20700 1.74940 1.75320 1.79880 1.96700 0.78662 1.64800 1.82700 0.70467 1.45300 2.30860 0.83107 1.13330 1.92800 1.84500 1.19250 0.74699 0.99605 2.15010 1.02420 1.08990 2.50800 3.33970 3.39490 3.37360 0.87100 0.65065 1.31000 2.97400 3.97050 1.01020 0.79880 1.06580 4.13440 0.90830 3.64550 1.69030 4.51610 7.45000 0.67130 0.93900 1.80300 1.07800 2.42600 -1.60900 1.47100 2.51800 3.29900 1.64590 0.55100 1.19900 0.97296 1.03700 0.82410 0.86400 3.23780 3.10320 2.13110 2.34600 0.62622 2.15500 2.05500 0.55556 0.09410 2.45890 0.54120 0.15240 0.29728 0.69000 0.31800 0.47541 2826.3 689.3 821.4 793.04 649.95 792.5 798.35 781.97 730.65 2467.4 762 641.01 900.6 592.09 743.5 722.2 809.837 2447.1 743.62 2394.4 777.5 726.27 2430.4 744.7 928.05 820 702 1183.1 2061.6 733.6 781.1 2303.3 740.8 767.3 773.65 744.7 737.3 496 792.34 809.75 817.35 896 –2190 724.7 852 2089.7 662.91 906.45 2446 5316.2 965.04 850 550 2500.6 298.15 298.15 200 200 200 200 200 200 200 298.15 200 200 300 200 200 200 298.15 298.15 300 300 200 200 298.15 273.15 200 200 200 300 300 298 200 298.15 60 300 300 150 50 100 298.15 298.15 298.15 298.15 298.15 300 298.15 298.15 50 200 298.15 100 298.15 150 50 298.15 1.27770 1.46380 0.67211 0.58115 0.93628 1.15350 1.17770 1.18200 0.81551 0.65866 0.75937 1.05500 1.74810 0.70950 0.62976 0.73547 1.67000 0.92284 1.72980 1.59000 2.24420 3.52350 0.52652 0.61172 1.01260 0.61390 0.89121 1.45980 1.51020 1.55830 1.18750 1.33350 0.33380 0.91775 0.77997 0.34798 0.33460 0.54118 2.02790 2.03600 1.36200 1.44790 0.73021 1.33770 1.35380 1.18910 0.29122 0.75730 0.59646 0.35193 0.35440 0.38326 0.33810 0.65450 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200.15 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1200 1200 1500 1200 1500 1500 1500 1500 1500 6000 1500 1500 1500 1500 3.06780 3.66690 1.91480 1.85850 4.03530 4.95430 4.92430 4.92750 1.95230 1.65840 2.25960 4.59830 4.47400 2.09440 1.69490 1.92550 4.97220 2.81860 4.51430 4.24840 7.43250 12.21100 1.45610 1.65760 2.65940 1.85280 3.61470 4.25400 3.63300 3.62130 4.91840 4.14000 1.09870 2.20160 1.80950 1.51780 1.32970 2.14850 5.12010 4.87440 3.22890 3.42340 1.66280 3.05690 3.45350 2.21700 0.38122 2.50800 1.49880 1.05710 0.71121 1.12030 0.99328 1.79520 2-151 (Continued) 2-152 TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 Name Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide Formula C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S CAS Mol. wt. C1 × 1E-05 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 2.78780 1.30930 1.20150 1.31350 1.22150 1.41060 1.27680 1.25070 1.18510 1.44200 1.07120 2.62830 1.18400 1.04400 1.16220 1.06250 1.26150 1.09400 1.12370 1.04340 0.93760 1.26620 0.91290 1.03600 0.41729 0.27617 0.29120 0.29157 0.30125 0.29134 0.33288 0.74694 0.79534 0.49522 0.72510 0.33298 0.39252 0.61160 0.55500 0.51734 0.12060 0.41000 0.93960 0.67100 0.74600 1.84580 0.92139 0.87026 0.81924 0.79060 0.82051 1.07850 C2 × 1E-05 9.52470 3.53810 4.00100 2.33170 3.99100 2.88580 3.38100 2.14800 3.63620 4.16030 3.02580 8.97330 3.07260 3.52300 2.07080 3.52100 3.59640 1.80700 2.93600 3.07490 3.01500 3.72940 2.55770 3.00900 0.54686 0.09560 0.09530 0.09048 0.31710 0.09325 0.26086 2.43560 1.44250 1.87180 2.08900 0.79933 0.87900 2.02900 1.78200 0.68157 2.37660 1.05780 2.55900 2.22200 3.26500 1.74300 3.33710 2.55560 2.60380 1.65600 3.08690 2.73880 C3 × 1E-03 C4 × 1E-05 C5 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 1.69350 1.52500 1.67660 0.67567 1.58000 0.80394 1.38310 0.69120 1.73590 1.66030 1.52730 1.69120 1.70770 1.69460 0.68661 1.58350 1.84450 0.68900 1.40100 1.74590 1.90570 1.65740 1.52900 2.11600 0.81130 2.46600 2.14200 2.09380 1.61020 2.90500 0.91340 1.71500 0.81831 1.29580 1.85160 2.08690 1.91650 1.76830 1.26000 0.80525 1.05430 1.70800 0.82500 1.42100 1.54500 1.22000 1.83610 1.77570 1.75930 1.69260 1.38640 1.58850 6.66510 2.23950 2.74000 1.82400 2.83500 1.49680 1.88800 1.61900 2.50480 2.65720 2.09750 6.26400 2.11740 2.36900 1.53550 2.46200 2.59400 1.47400 1.60100 2.07280 1.98600 2.30800 1.73700 2.10600 0.41755 0.03760 0.01570 -0.00107 0.21790 0.00195 -0.17979 1.84840 0.95493 1.48520 1.64830 0.41602 0.53654 1.33020 0.85300 0.51402 1.81860 0.68360 1.36000 1.19400 1.92300 -56.11000 2.46440 1.76360 1.71950 1.21670 1.78860 1.90670 744.57 740.37 756.4 1846 717.7 2456.1 650.3 1759.3 785.73 759.39 689.62 744.41 790.64 761.6 1932.5 715.75 819.17 1772 650.5 793.53 817 757.8 683 902.4 2639.2 567.6 1400 120 626 1326 949.4 757.75 2499.9 569.96 798.43 991.96 896.7 835.5 562 2463.8 418.8 735 3000 614.7 666.7 31.2 757.83 807.82 800.93 788.4 613.87 749.6 200 298.15 200 300 298.15 298.15 200 150 298.15 200 200 200 298.15 200 298.15 298.15 298.15 200 150 298 300 200 200 300 298.15 250 50 50 100 50 100 298.15 298.15 300 298.15 50 273.15 300 298 298.15 298.15 150 300 150 200 300 298.15 200 200 298.15 300 273.15 3.00340 1.70230 1.28280 1.84970 1.75720 1.79590 1.39680 1.26880 1.54340 1.51910 1.17210 2.83120 1.48160 1.11170 1.61070 1.53110 1.58290 1.18150 1.14430 1.33010 1.19090 1.33400 1.00040 1.22150 0.48803 0.28426 0.29120 0.29137 0.30137 0.29134 0.33288 1.04270 0.97640 0.97903 0.94749 0.33298 0.42513 0.76980 0.84891 0.60784 0.99083 0.41364 1.25860 0.69311 0.85462 1.27930 1.31350 0.90596 0.85589 0.96319 1.33000 1.31730 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1200.1 1500 1500 1500 1500 1500 1200.1 1500 1200 1500 1500 1500 1500 1500 1500 1500.15 1200 1200 10.41600 4.27590 4.42830 4.29410 4.53460 4.59900 4.13860 3.84460 4.08360 4.78310 3.59850 9.81820 3.66440 3.86200 3.76360 3.97260 4.06720 3.32070 3.58740 3.48190 3.18890 4.24830 3.03710 3.18940 1.05830 0.32248 0.34786 0.34063 0.55224 0.32243 0.51432 2.53830 2.45580 2.14970 2.20570 0.88904 1.05330 2.22090 2.07540 1.33000 2.16630 1.23880 3.35690 2.50280 3.37920 3.22620 3.48560 2.89230 2.87090 2.15020 3.19940 3.16870 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 0.82740 0.89400 0.59895 0.92270 0.79590 0.92279 0.92279 0.78439 0.69411 0.64220 0.72830 0.79188 0.78400 0.75083 0.50600 0.72840 1.22700 0.47400 0.89232 1.59140 0.99247 0.43697 0.86400 1.74830 0.90300 0.94326 0.76394 0.90658 0.73226 0.77650 0.92151 0.93775 0.46149 1.00010 0.98059 0.60865 0.89232 See Table 2-155 0.64084 0.29105 0.33284 0.47876 0.29338 See Table 2-155 3.10620 1.71190 1.51750 0.12660 1.54000 1.81180 1.53520 1.76460 1.62890 2.95020 2.13770 2.91000 1.16360 4.11500 2.59600 2.67090 2.67090 2.50070 3.02090 3.07110 1.03070 1.31660 2.10320 1.95770 1.21900 3.17130 2.19500 1.22600 2.47650 1.76400 2.72750 0.50387 1.81100 4.92880 3.80100 3.59650 1.68020 1.71370 1.36060 2.44200 2.39430 2.61780 1.27810 2.65370 3.08940 1.59650 2.67720 1.75500 1.57000 1.56500 1.65040 0.62130 0.68784 0.68784 0.81937 1.69030 1.63870 1.54290 0.87136 1.54880 1.64240 1.63700 1.35200 0.84200 2.18800 1.69600 1.20760 2.00300 0.80924 0.75430 1.73840 1.60200 1.35330 0.82654 0.80201 0.84872 1.71400 1.69360 1.72910 1.45650 0.77176 1.64560 1.61900 0.76122 1.51490 2.07300 0.81581 2.90060 2.28800 1.98470 1.98470 1.30010 2.12090 2.12980 0.78110 0.86597 1.18550 1.19490 0.89400 1.89480 1.19100 0.85983 1.55980 -407.40000 1.89740 0.42223 0.80000 3.58970 2.45300 2.05690 1.02850 1.04240 0.88667 1.81800 1.48960 1.62360 0.79115 1.11620 2.09850 0.93783 1.02010 782 678.3 690.39 779.48 1698.6 1732.4 1732.4 2416.4 781.56 750.25 668.94 2468 693 749.19 743 585.14 2460 1008.2 791.4 10.503 849.64 2192.4 2160 788.01 691.6 599.92 2483.1 2489.7 2499.8 716 797.79 783.23 643.23 2405.2 732.6 739.55 2435.5 200 298 200 200 300 300 300 298.15 200 200 200 298.15 200 273.16 250 300 298.15 298.15 200 300 273 298.15 298.15 298.15 200 300 298.15 298.15 298.15 300 298 298.15 200 298.15 298.15 300 298.15 0.86459 1.34610 0.63795 0.99530 1.53020 1.50990 1.50990 1.09680 0.74637 0.70833 0.77172 0.92283 0.83967 0.90040 0.58880 1.32000 1.47550 0.51946 0.92804 1.12910 1.13770 0.50277 1.16210 2.25670 1.01920 1.56000 0.96745 1.13730 0.88184 1.12420 1.12510 1.17280 0.51411 1.40620 1.35330 0.77480 1.32040 1500 1200 1500 1500 1200 1200 1200 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500.15 1500 1500 1500 1500 1500 1500 1500 1500 1200 1500 1500 1500 1200 1200 1500 1500 1500 1500 1500 1500 2.52550 3.07660 1.55930 4.31800 4.13590 4.14670 4.14670 3.54830 3.14960 3.15490 1.58930 2.29440 2.48160 2.31780 1.51090 3.19870 3.65320 1.35950 2.86960 2.99910 2.99520 1.06940 2.86370 5.71770 3.96170 3.74090 2.66680 2.85290 2.28420 2.52760 2.63910 2.99040 1.52530 3.86080 3.47810 1.88710 3.73860 1.16310 0.08615 0.49837 0.78357 0.32360 0.80970 1.70160 0.70930 0.82960 1.12380 0.59591 0.00103 0.23264 0.37215 0.21770 2425.6 909.79 372.91 2433.8 479.4 298.15 50 100 298.15 100 0.79235 0.29105 0.34036 0.57242 0.29475 1500 1500 1500 1500 1500 1.92450 0.34838 0.80919 1.32860 0.58278 10.57500 4.50580 4.91500 6.01100 4.93600 3.59270 4.68440 5.04400 3.97080 10.03400 0.76791 1.71000 1.64480 1.08150 1.57800 0.81841 1.72880 1.61820 1.89280 0.77107 -4.56610 3.36580 3.47000 4.59460 3.58800 2.17920 3.23040 3.38570 3.21360 -4.30120 912.03 807.38 749.6 418.2 721.11 2550.1 783.67 755.48 855.52 916.73 200 298.15 200 298.15 298.15 298.15 298.15 200 298.15 200 3.35330 2.15310 1.62570 2.29530 2.20920 2.26250 2.00140 1.86580 1.96930 3.18000 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 11.61300 5.42420 5.54070 5.52670 5.66060 5.85550 5.27760 5.90820 4.79240 11.01600 2-153 (Continued) 2-154 TABLE 2-75 Heat Capacity at Constant Pressure of Inorganic and Organic Compounds in the Ideal Gas State Fit to Hyperbolic Functions Cp [J/(kmol∙K)] (Continued ) Cmpd. no. 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 Name Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Formula C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 CAS Mol. wt. C1 × 1E-05 C2 × 1E-05 C3 × 1E-03 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 1.59550 1.35540 1.40820 1.38050 1.58030 1.39010 1.49520 1.35990 1.59810 1.23070 0.56777 0.29103 0.33483 2.46790 1.06000 0.88050 2.83600 0.90600 1.08530 0.90053 0.96896 0.82523 1.13270 1.09740 0.75300 0.82096 1.27200 0.43400 0.59683 0.73640 0.48308 0.59474 0.61900 0.73145 1.05630 0.71306 0.69590 0.52525 1.79940 0.76078 1.13460 0.43852 3.14670 4.43100 4.34360 4.45900 3.23480 3.80600 4.41030 4.16050 4.60630 3.49420 1.11940 0.10040 0.29577 8.42120 2.85000 3.01100 1.08000 3.06200 3.07470 2.70850 2.49070 2.59430 2.94700 3.29590 2.09050 1.46770 3.56890 2.44500 2.55330 2.54400 0.73665 1.26610 2.02130 2.03130 4.33970 1.16890 1.77780 1.46630 1.75300 2.10490 2.80980 1.50600 0.85788 1.63560 1.46620 1.57510 0.79814 1.37170 0.80211 1.73170 1.62950 1.52800 0.62070 2.52650 1.52170 1.68650 1.93000 1.65020 2.10700 1.60540 1.86720 1.65920 1.41770 1.72910 1.74180 1.67610 1.53070 0.84463 0.75021 1.15200 1.23970 1.08520 0.78152 0.84431 1.62930 1.93750 1.60980 0.92731 1.70980 1.54760 1.19600 1.72560 0.79504 1.39880 C4 × 1E-05 1.47130 3.05400 2.76870 3.20160 1.78820 2.25730 -2.09580 2.86750 3.03010 2.46170 -0.38079 0.09356 0.27151 5.85370 2.01000 1.89200 -3.56000 2.11500 2.22710 1.80120 1.30100 1.76800 2.09870 1.94860 1.37800 0.96258 1.32990 1.51200 1.55190 0.80800 0.48698 0.86165 1.29560 1.48150 3.18100 1.02100 1.26540 0.93033 -4.12000 1.39360 1.23760 0.74754 C5 Tmin, K Cp at Tmin × 1E-05 Tmax, K Cp at Tmax × 1E-05 2679.4 746.4 659.38 718.8 2434.3 660.96 981.95 784.47 756.28 694.81 676.72 1153.8 680.35 743.6 879.23 747.6 283 717.97 825.4 743.96 646.7 778.7 795.78 757.67 672.8 2452.3 2409.4 507 576.78 573 2480 2482.7 727.4 843.37 729.66 2512.8 763.78 674.15 108.2 789.03 2449.5 616.46 298.15 200 298.15 298.15 298.15 150 200 298.15 200 200 298.15 50 100 200 298.15 200 298.15 298.15 298.15 200 200 298.15 298 200 200 298.15 298.15 100 298.15 298.15 298.15 298.15 298.15 298.15 300 298.15 298.15 298.15 298.15 200 298.15 130 1.92770 1.45290 2.06520 1.98320 2.02310 1.41620 1.57750 1.77230 1.68810 1.34480 0.79711 0.29103 0.33489 2.65860 1.25200 0.94039 1.38240 1.30440 1.35390 0.95908 1.05360 1.08560 1.42020 1.15470 0.82759 0.98524 1.86940 0.44014 1.10540 1.07450 0.59127 0.73665 0.85428 0.89664 1.63920 0.80337 0.89382 0.73244 1.35940 0.79326 1.52430 0.44363 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1000.15 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 4.91940 4.97640 5.04110 5.09650 5.20600 4.65470 4.90670 4.68070 5.35490 4.16040 1.56180 0.36533 0.59282 9.22090 3.24590 3.29270 3.29520 3.41330 3.47010 3.07970 3.03580 2.88970 3.49940 3.69560 2.47540 2.50600 5.06820 2.60450 2.83900 2.67370 1.33810 2.05600 2.24580 2.27600 4.65270 2.11890 2.12480 1.72030 3.20240 2.43530 4.16280 1.68170 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 0.87100 0.73815 0.74740 2.01140 0.80992 0.36810 0.89300 0.71806 0.33375 0.35256 0.33408 1.00130 2.07190 2.30820 0.54850 1.05550 0.65341 1.13520 0.48694 0.58140 0.66554 2.14960 1.27660 0.71070 1.05200 1.22100 1.13900 0.98200 2.03670 2.15400 1.95290 1.85900 0.53600 0.55978 0.42364 0.84894 0.33363 0.75680 0.85210 0.75120 2.44700 1.95290 1.95230 0.80820 1.57510 0.71245 2.15030 2.26690 0.25864 1.22700 0.49677 2.61780 6.26680 7.86780 1.84910 3.21010 1.71150 5.63310 1.23760 2.86300 1.12570 7.30450 2.55590 1.50510 3.79000 2.68650 5.28600 5.40200 1.81810 2.44320 6.09980 5.86900 2.11900 1.21410 0.87350 1.14710 0.26790 3.39240 3.29540 3.39700 1.92540 1.59540 1.63100 1.86560 0.74707 0.65201 0.77200 1.27390 0.93280 0.67938 0.87322 0.87239 2.40440 1.68230 0.83310 0.78248 0.77705 1.62110 0.71271 1.44060 1.54540 1.66950 0.80937 0.79662 1.48140 0.82886 1.59400 1.53100 1.20890 1.11260 1.70870 1.57180 1.19800 1.61020 1.64920 1.38000 2.61050 1.49600 1.49440 1.49280 1.88800 1.23560 1.21120 -2.44040 0.60196 0.46721 0.99900 1.73420 0.10880 0.78407 0.28563 1.28310 6.34500 5.44860 0.89089 1.43950 0.91824 3.38290 0.47248 1.89800 0.97196 4.99980 1.48290 0.84537 2.33100 1.42030 3.35100 3.49300 0.79777 0.58651 4.13020 4.32600 1.14700 0.89079 0.65560 0.90000 0.08896 2.24700 2.11500 2.24700 821.3 730.5 750.92 279.98 2344.9 286.03 2442 537.65 423.7 351.27 393.74 3521.5 967.71 743.1 2458.5 2433 2432.6 681.9 2484.2 650.43 717.04 741.02 2231.7 2187.6 667.3 2443 677.94 639.9 1060.8 950.59 775.4 722.7 510 710.4 739.07 644.61 1169 675.9 675.8 675.1 298.15 200 200 298.15 298.15 100 100 300 100 100 100 298.15 298.15 200 298.15 298.15 298.15 200 298.15 200 298.15 200 200 200 200 298.15 200 200 298.15 298.15 200 298.15 100 200 200 298.15 100 200 200 200 1.10220 0.78247 0.78483 1.02180 1.07700 0.41815 0.89310 1.33700 0.33538 0.38719 0.34081 1.26040 2.47630 2.48640 0.76617 1.52510 0.90956 1.30690 0.72827 0.70157 0.84963 2.31560 1.32780 0.74387 1.18320 1.54310 1.31390 1.21940 2.10540 2.27260 2.05940 2.66140 0.54044 0.59670 0.44572 1.07540 0.33363 0.87588 0.96428 0.87096 1500 1500 1500 1000.15 1500 1500 1500 1200 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 2273.15 1500 1500 1500 2.74840 2.32870 2.32160 2.11750 2.49790 1.05370 3.24160 2.58230 0.56950 1.53970 0.79673 3.59670 6.69470 8.62250 2.55380 4.53700 2.56890 5.57840 1.81130 3.00290 1.64330 8.02510 4.20460 2.43220 4.19830 4.18780 5.37690 5.37540 3.75850 4.35600 6.83420 6.78340 2.37500 1.55900 1.14230 1.85950 0.52760 3.59200 3.59650 3.59230 Constants in this table can be used in the following equation to calculate the ideal gas heat capacity C0p. C0p = C1 + C2[C3/T/sinh(C3/T)]2 + C4[C5/T/cosh(C5/T)]2 where C0p is in J/(kmol∙K) and T is in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-155 2-156 PHYSICAL AnD CHEMICAL DATA TABLE 2-76 Cp/Cv: Ratios of Specific Heats of Gases at 1 atm Pressure* Compound Formula Acetaldehyde Acetic acid Acetylene C2H4O C2H4O2 C2H2 Air Ammonia Argon NH3 Ar Temperature, °C Ratio of specific heats, (γ) = Cp /Cv 30 136 15 -71 925 17 -78 -118 15 15 -180 0–100 1.14 1.15 1.26 1.31 1.36 1.403 1.408 1.415 1.320 1.670 1.715 1.67 Benzene Bromine C6H6 Br2 90 20–350 1.10 1.32 Carbon dioxide CO2 disulfide monoxide CS2 CO 1.299 1.37 1.21 1.402 1.433 1.355 1.15 1.256 1.315 Chlorine Chloroform Cyanogen Cyclohexane Cl2 CHCl3 (CN)2 C6H12 15 -75 100 15 -180 15 100 15 80 Dichlorodifluormethane CCl2F2 25 1.139 Ethane C2H6 Ethyl alcohol ether C2H6O C4H10O Ethylene C2H4 100 15 -82 90 35 80 100 15 -91 1.157 1.200 1.28 1.13 1.08 1.086 1.201 1.253 1.345 Helium Hexane (n-) Hydrogen He C6H14 H2 -180 80 15 -76 -181 20 15 100 65 140 210 1.667 1.066 1.407 1.441 1.607 1.42 1.41 1.40 1.31 1.28 1.24 bromide chloride HBr HCl cyanide HCN Compound Formula Hydrogen (Cont.) iodide sulfide HI H 2S Iodine Isobutane I2 C4H10 Krypton Kr Mercury Methane Hg CH4 Methyl acetate alcohol ether Methylal C3H6O2 CH4O C2H6O C3H8O2 Neon Nitric oxide Ne NO Nitrogen N2 Nitrous oxide N2O Oxygen O2 Pentane (n-) Phosphorus Potassium C5H12 P K Sodium Sulfur dioxide Na SO2 Xenon Xe Temperature, °C Ratio of specific heats, (γ) = Cp /Cv 20–100 15 -45 -57 1.40 1.332 1.350 1.356 185 15 1.30 1.110 19 1.672 360 600 300 15 -80 -115 15 77 6–30 13 40 1.67 1.113 1.196 1.310 1.339 1.347 1.14 1.237 1.11 1.06 1.09 19 15 -45 -80 15 -181 100 15 -30 -70 1.667 1.400 1.39 1.38 1.402 1.433 1.28 1.303 1.31 1.34 15 -76 -181 1.398 1.405 1.439 86 300 850 1.071 1.17 1.77 750–920 15 1.68 1.290 19 1.678 *For compounds that appear in Tables 2-109 to 2-122, values are from E. W. Lemmon, M. O. McLinden, and D. G. Friend, “Thermophysical Properties of Fluid Systems” in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P. J. Linstrom and W. G. Mallard, June 2005, National Institute of Standards and Technology, Gaithersburg, Md. (http://webbook.nist.gov). Values for other compounds are from International Critical Tables, vol. 5, pp. 80–82. SPECIFIC HEATS OF AQUEOUS SOLUTIOnS TABLE 2-79 Ethyl Alcohol Additional References Most of the tables below are from International Critical Tables, vol. 5, pp. 115–116, 122–125. Specific heats for other compounds in aqueous solution can also be found in the same reference. TABLE 2-77 Acetic Acid (at 38çC) Mole % acetic acid Cal/(g⋅°C) 0 1.0 6.98 0.911 30.9 0.73 54.5 0.631 100 0.535 Specific heat, cal/(g⋅°C) Mole % C2H5OH 3°C 23°C 41°C 4.16 11.5 37.0 61.0 100.0 1.05 1.02 0.805 0.67 0.54 1.02 1.03 0.86 0.727 0.577 1.02 1.03 0.875 0.748 0.621 TABLE 2-80 TABLE 2-78 Ammonia Glycerol Specific heat, cal/(g⋅°C) Specific heat, cal/(g⋅°C) Mole % NH3 2.4°C 20.6°C 41°C 61°C 0 10.5 20.9 31.2 41.4 1.01 0.98 0.96 0.956 0.985 1.0 0.995 0.99 1.0 0.995 1.06 1.03 1.0 1.02 Mole % C3H5(OH)3 15°C 32°C 2.12 4.66 11.5 22.7 43.9 100.0 0.961 0.929 0.851 0.765 0.67 0.555 0.960 0.924 0.841 0.758 0.672 0.576 SPECIFIC HEATS TABLE 2-81 Hydrochloric Acid TABLE 2-86 Potassium Hydroxide (at 19çC) Specific heat, cal/(g⋅°C) Mole % HCl 0.0 9.09 16.7 20.0 25.9 2-157 0°C 10°C 20°C 40°C 60°C 1.00 0.72 0.61 0.58 0.55 0.72 0.605 0.575 0.74 0.631 0.591 0.75 0.645 0.615 0.78 0.67 0.638 0.61 TABLE 2-82 Methyl Alcohol Specific heat, cal/(g⋅°C) Mole % CH3OH 5°C 20°C 40°C 5.88 12.3 27.3 45.8 69.6 100 1.02 0.975 0.877 0.776 0.681 0.576 1.0 0.982 0.917 0.811 0.708 0.60 0.995 0.98 0.92 0.83 0.726 0.617 Specific heat at 20°C, cal/(g⋅°C) 0 10 20 30 40 50 60 70 80 90 1.000 0.900 0.810 0.730 0.675 0.650 0.640 0.615 0.575 0.515 0 1.0 0.497 0.975 1.64 0.93 4.76 0.814 9.09 0.75 TABLE 2-87 normal Propyl Alcohol Specific heat, cal/(g⋅°C) Mole % C3H7OH 5°C 20°C 40°C 1.55 5.03 11.4 23.1 41.2 73.0 100.0 1.03 1.07 1.035 0.877 0.75 0.612 0.534 1.02 1.06 1.032 0.90 0.78 0.645 0.57 1.01 1.03 0.99 0.91 0.815 0.708 0.621 TABLE 2-88 Sodium Carbonate* Temperature, °C % Na2CO3 by weight 0.000 1.498 2.000 2.901 4.000 5.000 6.000 8.000 10.000 13.790 13.840 20.000 25.000 TABLE 2-83 nitric Acid % HNO3 by Weight Mole % KOH Cal/(g⋅°C) 17.6 30.0 76.6 98.0 0.9992 0.9807 0.9986 1.0098 1.0084 0.9786 0.9597 0.9594 0.9428 0.9761 0.9392 0.9183 0.9086 0.8924 0.9452 0.8881 0.8631 0.8936 0.8615 0.8911 *J. Chem. Soc. 3062–3079 (1931). TABLE 2-89 Sodium Chloride Specific heat, cal/(g⋅°C) TABLE 2-84 Phosphoric Acid* Mole % NaCl %H2PO4 Cp at 21.3°C cal/(g⋅°C) %H3PO4 Cp at 21.3°C cal/(g⋅°C) 2.50 3.80 5.33 8.81 10.27 14.39 16.23 19.99 22.10 24.56 25.98 28.15 29.96 32.09 33.95 36.26 38.10 40.10 42.08 44.11 46.22 48.16 49.79 0.9903 0.9970 0.9669 0.9389 0.9293 0.8958 0.8796 0.8489 0.8300 0.8125 0.8004 0.7856 0.7735 0.7590 0.7432 0.7270 0.7160 0.7024 0.6877 0.6748 0.6607 0.6475 0.6370 50.00 52.19 53.72 56.04 58.06 60.23 62.10 64.14 66.13 68.14 69.97 69.50 71.88 73.71 75.79 77.69 79.54 80.00 82.00 84.00 85.98 88.01 89.72 0.6350 0.6220 0.6113 0.5972 0.5831 0.5704 0.5603 0.5460 0.5349 0.5242 0.5157 0.5160 0.5046 0.4940 0.4847 0.4786 0.4680 0.4686 0.4593 0.4500 0.4419 0.4359 0.4206 *Z. Physik. Chem., A167, 42 (1933). TABLE 2-85 Potassium Chloride Specific heat, cal/(g⋅°C) Mole % KCl 6°C 20°C 33°C 40°C 0.99 3.85 5.66 7.41 0.945 0.828 0.77 0.947 0.831 0.775 0.727 0.947 0.835 0.778 0.947 0.837 0.775 0.249 0.99 2.44 9.09 6°C 20°C 33°C 57°C 0.96 0.91 0.805 0.99 0.97 0.915 0.81 0.97 0.915 0.81 0.923 0.82 TABLE 2-90 Sodium Hydroxide (at 20çC) Mole % NaOH Cal/(g . °C) 0 1.0 0.5 0.985 1.0 0.97 9.09 0.835 16.7 0.80 28.6 0.784 37.5 0.782 TABLE 2-91 Sulfuric Acid* %H2SO4 Cp at 20°C, cal/(g⋅°C) %H2SO4 Cp at 20°C, cal/(g⋅°C) 0.34 0.68 1.34 2.65 3.50 5.16 9.82 15.36 21.40 22.27 23.22 24.25 25.39 26.63 28.00 29.52 30.34 31.20 33.11 0.9968 0.9937 0.9877 0.9762 0.9688 0.9549 0.9177 0.8767 0.8339 0.8275 0.8205 0.8127 0.8041 0.7945 0.7837 0.7717 0.7647 0.7579 0.7422 35.25 37.69 40.49 43.75 47.57 52.13 57.65 64.47 73.13 77.91 81.33 82.49 84.48 85.48 89.36 91.81 94.82 97.44 100.00 0.7238 .7023 .6770 .6476 .6153 .5801 .5420 .5012 .4628 .4518 .4481 .4467 .4408 .4346 .4016 .3787 .3554 .3404 .3352 *Vinal and Craig, Bur. Standards J. Research, 24, 475 (1940). 2-158 PHYSICAL AnD CHEMICAL DATA SPECIFIC HEATS OF MISCELLAnEOUS MATERIALS TABLE 2-92 Specific Heats of Miscellaneous Liquids and Solids Material Alumina Alundum Asbestos Asphalt Bakelite Brickwork Carbon (gas retort) (see under Graphite) Cellulose Cement, Portland Clinker Charcoal (wood) Chrome brick Clay Coal tar oils Coal tars Coke Concrete Cryolite Diamond Fireclay brick Fluorspar Gasoline Glass (crown) ( flint) (pyrex) (silicate) wool Granite Graphite Gypsum Kerosene Limestone Litharge Magnesia Magnesite brick Marble Porcelain, fired Berlin Porcelain, green Berlin Porcelain, fired earthenware Porcelain, green earthenware Specific heat, cal/(g⋅°C) 0.2 (100°C); 0.274 (1500°C) 0.186 (100°C) 0.25 0.22 0.3 to 0.4 About 0.2 0.168 (26 to 76°C) 0.314 (40 to 892°C) 0.387 (56 to 1450°C) 0.204 0.32 0.186 0.242 0.17 0.224 0.26 to 0.37 0.34 (15 to 90°C) 0.35 (40°C); 0.45 (200°C) 0.265 (21 to 400°C) 0.359 (21 to 800°C) 0.403 (21 to 1300°C) 0.156 (70 to 312°F); 0.219 (72 to 1472°F) 0.253 (16 to 55°C) 0.147 0.198 (100°C); 0.298 (1500°C) 0.21 (30°C) 0.53 0.16 to 0.20 0.117 0.20 0.188 to 0.204 (0 to 100°C) 0.24 to 0.26 (0 to 700°C) 0.157 0.20 (20 to 100°C) 0.165 (26 to 76°C); 0.390 (56 to 1450°C) 0.259 (16 to 46°C) 0.47 0.217 0.055 0.234 (100°C); 0.188 (1500°C) 0.222 (100°C); 0.195 (1500°C) 0.21 (18°C) 0.189 (60°C) 0.185 (60°C) 0.186 (60°C) 0.181 (60°C) TABLE 2-92 Specific Heats of Miscellaneous Liquids and Solids (Continued ) Material Specific heat, cal/(g⋅°C) Pyrex glass Pyrites (copper) Pyrites (iron) Pyroxylin plastics Quartz Rubber (vulcanized) Sand Silica Silica brick Silicon carbide brick Silk Steel Stone Stoneware (common) Turpentine Wood (Oak) Woods, miscellaneous Wool Zirconium oxide 0.20 0.131 (30°C) 0.136 (30°C) 0.34 to 0.38 0.17 (0°C); 0.28 (350°C) 0.415 0.191 0.316 0.202 (100°C); 0.195 (1500°C) 0.202 (100°C) 0.33 0.12 about 0.2 0.188 (60°C) 0.42 (18°C) 0.570 0.45 to 0.65 0.325 0.11 (100°C); 0.179 (1500°C) TABLE 2-93 Oils (Animal, Vegetable, Mineral Oils) Cp[cal/(g⋅°C)] = A / d 415 + B(t - 15) where d = density, g/cm3. °F = 9⁄5°C + 32; to convert calories per gram-degree Celsius to British thermal units per pound-degree Fahrenheit, multiply by 1.0; to convert grams per cubic centimeter to pounds per cubic foot, multiply by 62.43. Oils A Castor Citron Fatty drying nondrying semidrying oils (except castor) Naphthene base Olive Paraffin base Petroleum oils 0.500 0.440 0.450 0.445 0.450 0.405 0.425 0.415 B 0.0007 (0.438 at 54°C) 0.0007 0.0007 0.0007 0.0007 0.0009 (0.47 at 7°C) 0.0009 0.0009 PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS Unit Conversions °F = 9⁄5°C + 32; to convert kilocalories per gram-mole to British thermal units per pound-mole, multiply by 1.799 × 10-3. PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS 2-159 TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds* The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from (a) Bichowsky and Rossini, “Thermochemistry of the Chemical Substances,” Reinhold, New York, 1936; (b) Latimer, “Oxidation States of the Elements and Their Potentials in Aqueous Solution,” Prentice-Hall, New York, 1938; (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards; and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. State† Compound Aluminum Al AlBr3 Al4C3 AlCl3 AlF3 AlI3 AlN Al(NH4)(SO4)2 Al(NH4)(SO4)2⋅12H2O Al(NO3)3⋅6H2O Al(NO3)3⋅9H2O Al2O3 Al(OH)3 Al2O3⋅SiO2 Al2O3⋅SiO2 Al2O3⋅SiO2 3Al2O3⋅2SiO2 Al2S3 Al2(SO4)3 Al2(SO4)3⋅6H2O Al2(SO4)3⋅18H2O Antimony Sb SbBr3 SbCl3 SbCl5 SbF3 SbI3 Sb2O3 Sb2O4 Sb2O5 Sb2S3 Arsenic As AsBr3 AsCl3 AsF3 AsH3 AsI3 As2O3 As2O5 As2S3 Barium Ba BaBr2 BaCl2 Ba(ClO3)2 Ba(ClO4)2 Ba(CN)2 Ba(CNO)2 BaCN2 BaCO3 BaCrO4 BaF2 BaH2 Ba(HCO3)2 BaI2 c c aq c c aq, 600 c aq c aq c c c c c c, corundum c c, sillimanite c, disthene c, andalusite c, mullite c c aq c c Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -123.4 -209.5 -30.8 -163.8 -243.9 -329 -360.8 -72.8 -163.4 -57.7 -561.19 -1419.36 -680.89 -897.59 -399.09 -304.8 -648.7 -642.4 -642.0 -1874 -121.6 -820.99 -893.9 -1268.15 -2120 c c c l c c c, I, orthorhombic c, II, octahedral c c c, black 0.00 -59.9 -91.3 -104.8 -216.6 -22.8 -165.4 -166.6 -213.0 -230.0 -38.2 c c l l g c c c c amorphous 0.00 -45.9 -80.2 -223.76 43.6 -13.6 -154.1 -217.9 -20 -34.76 c c aq, 400 c aq, 300 c aq, 1600 c aq, 800 c c aq c c, witherite c c aq, 1600 c aq c aq, 400 0.00 -180.38 -185.67 -205.25 -207.92 -176.6 -170.0 -210.2 *For footnotes see end of table. Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 -189.2 -29.0 -209.5 -312.6 -152.5 -50.4 -486.17 -1179.26 -526.32 -376.87 -272.9 -739.53 -759.3 -1103.39 0.00 -77.8 -146.0 -186.6 -196.1 -36.9 0.00 -70.5 -212.27 37.7 -134.8 -183.9 -20 0.00 -183.0 -196.5 -134.4 -155.3 -63.6 -284.2 -342.2 -287.9 -284.6 -40.8 -459 -144.6 -155.17 BaMoO4 Ba3N2 Ba(NO2)2 Ba(NO3)2 BaO Ba(OH)2 BaO⋅SiO2 Ba3(PO4)2 BaPtCl6 BaS BaSO3 BaSO4 BaWO4 Beryllium Be BeBr2 BeCl2 BeI2 Be3N2 BeO Be(OH)2 BeS BeSO4 Bismuth Bi BiCl3 BiI3 BiO Bi2O3 Bi(OH)3 Bi2S3 Bi2(SO4)3 Boron B BBr3 BCl3 BF3 B2H6 BN B2O3 B(OH)3 B2S3 Bromine Br2 -180.7 BrCl Cadmium Cd CdBr2 -271.4 CdCl2 -48 -212.1 -265.3 -31.5 -414.4 -158.52 State† Compound Barium (Cont.) Ba(IO3)2 Cd(CN)2 CdCO3 CdI2 Cd3N2 Cd(NO3)2 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol c aq c c c aq c aq, 600 c c aq, 400 c c c c c c c -264.5 -237.50 -370 -90.7 -184.5 -179.05 -236.99 -227.74 -133.0 -225.9 -237.76 -363 -992 -284.9 -111.2 -282.5 -340.2 -402 c c aq c aq c aq c c c c c aq 0.00 -79.4 -142 -112.6 -163.9 -39.4 -112 -134.5 -145.3 -215.6 -56.1 -281 c c aq c aq c c c c c 0.00 -90.5 -101.6 -24 -27 -49.5 -137.1 -171.1 -43.9 -607.1 c l g g g g c c gls c c 0.00 -52.7 -44.6 -94.5 -265.2 7.5 -32.1 -302.0 -297.6 -260.0 -56.6 l g g c c aq, 400 c aq, 400 c c c aq, 400 c aq, 400 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -198.35 -150.75 -189.94 -209.02 -313.4 0.00 -127.9 -141.4 -103.4 -122.4 -138.3 -254.8 0.00 7.47 3.06 0.00 -75.8 -76.6 -92.149 -96.44 36.2 -178.2 -48.40 -47.46 39.8 -115.67 0.00 -76.4 -43.2 -117.9 -39.1 0.00 -50.9 -90.8 -261.0 19.9 -27.2 -282.9 -280.3 -229.4 0.00 0.931 -0.63 0.00 -70.7 -67.6 -81.889 -81.2 -163.2 -43.22 -71.05 (Continued) 2-160 PHYSICAL AnD CHEMICAL DATA TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) State† Compound Cadmium (Cont.) CdO Cd(OH)2 CdS CdSO4 Calcium Ca CaBr2 CaC2 CaCl2 CaCN2 Ca(CN)2 CaCO3 CaCO3⋅MgCO3 CaC2O4 Ca(C2H3O2)2 CaF2 CaH2 CaI2 Ca3N2 Ca(NO3)2 Ca(NO3)2⋅2H2O Ca(NO3)2⋅3H2O Ca(NO3)2⋅4H2O CaO Ca(OH)2 CaO⋅SiO2 CaS CaSO4 CaSO4⋅½H2O CaSO4⋅2H2O CaWO4 Carbon C CO CO2 Cerium Ce CeN Cesium Cs CsBr CsCl Cs2CO3 CsF CsH CsHCO3 CsI CsNH2 CsNO3 Cs2O CsOH Cs2S Cs2SO4 c c c c aq, 400 c c aq, 400 c c aq c c aq c, calcite c, aragonite c c c aq c aq c c aq, 400 c c aq, 400 c c c c c aq, 800 c, II, wollastonite c, I, pseudowollastonite c c, insoluble form c, soluble form α c, soluble form β c c c Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol -62.35 -135.0 -34.5 -222.23 -232.635 0.00 -162.20 -187.19 -14.8 -190.6 -209.15 -85 -43.3 -289.5 -289.54 -558.8 -332.2 -356.3 -364.1 -290.2 -286.5 -46 -128.49 -156.63 -103.2 -224.05 -228.29 -367.95 -439.05 -509.43 -151.7 -235.58 -239.2 -377.9 -376.6 -114.3 -338.73 -336.58 -335.52 -376.13 -479.33 -387 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -55.28 -113.7 -33.6 -194.65 0.00 -181.86 -16.0 -179.8 -195.36 -54.0 -270.8 -270.57 -311.3 -264.1 -35.7 -157.37 -88.2 -177.38 -293.57 -351.58 -409.32 -144.3 -213.9 -207.9 -357.5 -356.6 -113.1 -311.9 -309.8 -308.8 -425.47 c, graphite c, diamond g g 0.00 0.453 -26.416 -94.052 0.00 0.685 -32.808 -94.260 c c 0.00 -78.2 0.00 -70.8 c c aq, 500 c aq, 400 c c aq, 400 c c aq, 2000 c aq, 400 c c aq, 400 c c aq, 200 c c aq 0.00 -97.64 -91.39 -106.31 -102.01 -271.88 -131.67 -140.48 -12 -230.6 -226.6 -83.91 -75.74 -28.2 -121.14 -111.54 -82.1 -100.2 -117.0 -87 -344.86 -340.12 0.00 -94.86 Chlorine Cl2 ClF ClO ClO2 ClO3 Cl2O Cl2O7 Chromium Cr CrBr3 Cr3C2 Cr4C CrCl2 CrF2 CrF3 CrI2 CrO3 Cr2O3 Cr2(SO4)3 Cobalt Co CoBr2 Co3C CoCl2 CoCO3 CoF2 CoI2 Co(NO3)2 CoO Co3O4 Co(OH)2 Co(OH)3 CoS Co2S3 CoSO4 Columbium Cb Cb2O5 Copper Cu CuBr CuBr2 CuCl CuCl2 CuClO4 Cu(ClO3)2 Cu(ClO4)2 CuI CuI2 -101.61 Cu3N Cu(NO3)2 -135.98 -7.30 CuO Cu2O Cu(OH)2 CuS Cu2S CuSO4 -210.56 -82.61 -96.53 -107.87 -316.66 State† Compound Cu2SO4 Erbium Er Er(OH)3 Fluorine F2 F2O g g g g g g g c aq c c c aq c c c aq c c aq Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -25.7 33 24.7 37 18.20 63 0.00 -21.008 -16.378 -103.1 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 29.5 22.40 0.00 -122.7 -21.20 -16.74 -93.8 -102.1 -152 -231 -63.7 -64.1 -139.3 -268.8 -249.3 -626.3 c c aq c c aq, 400 c aq c aq c aq c c c c c c c aq, 400 0.00 -55.0 -73.61 9.49 -76.9 -95.58 -172.39 -172.98 -24.2 -43.15 -102.8 -114.9 -57.5 -196.5 -131.5 -177.0 -22.3 -40.0 -216.6 c c 0.00 -462.96 0.00 0.00 -26.7 -34.0 -42.4 -31.4 -48.83 -64.7 -28.3 0.00 -23.8 c c c aq c c aq, 400 aq aq, 400 aq c c aq c c aq, 200 c c c c c c aq, 800 c aq 0.00 -61.96 7.08 -66.6 -75.46 -155.36 -144.2 -37.4 -65.3 -108.9 -142.0 -19.8 -188.9 -17.8 -4.8 -11.9 17.78 -73.1 -83.6 -38.5 -43.00 -108.9 -11.6 -18.97 -184.7 -200.78 -179.6 -33.25 -24.13 1.34 15.4 -5.5 -16.66 -8.76 -36.6 -31.9 -38.13 -85.5 -11.69 -20.56 -158.3 -160.19 -152.0 c c 0.00 -326.8 0.00 g g 0.00 5.5 0.00 9.7 PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS 2-161 TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) State† Compound Gallium Ga GaBr3 GaCl3 GaN Ga2O Ga2O3 Germanium Ge Ge3N4 GeO2 Gold Au AuBr AuBr3 AuCl AuCl3 AuI Au2O3 Au(OH)3 Hafnium Hf HfO2 Hydrogen H3AsO3 H3AsO4 HBr HBrO HBrO3 HCl HCN HClO HClO3 HClO4 HC2H3O2 H2C2O4 HCOOH H2CO3 HF HI HIO HIO3 HN3 HNO3 HNO3⋅H2O HNO3⋅3H2O H2O H2O2 H3PO2 H3PO3 H3PO4 H2S H2S2 H2SO3 H2SO4 H2Se Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol c c c c c c 0.00 -92.4 -125.4 -26.2 -84.3 -259.9 0.00 c c c 0.00 -15.7 -128.6 0.00 c c c aq c c aq c c c 0.00 -3.4 -14.5 -11.0 -8.3 -28.3 -32.96 0.2 11.0 -100.6 0.00 c c 0.00 -271.1 0.00 -258.2 aq c aq g aq, 400 aq aq g aq, 400 g aq, 100 aq, 400 aq aq, 660 l aq, 400 c aq, 300 l aq, 200 aq g aq, 200 g aq, 400 aq c aq g g l aq, 400 l l g l l aq, 200 c aq c aq c aq, 400 g aq, 2000 l aq, 200 l aq, 400 g aq -175.6 -214.9 -214.8 -8.66 -28.80 -25.4 -11.51 -22.063 -39.85 31.1 24.2 -28.18 -23.4 -31.4 -116.2 -116.74 -196.7 -194.6 -97.8 -98.0 -167.19 -64.2 -75.75 6.27 -13.47 -38 -56.77 -54.8 70.3 -31.99 -41.35 -49.210 -112.91 -252.15 -57.7979 -68.3174 -45.16 -45.80 -145.5 -145.6 -232.2 -232.2 -306.2 -309.32 -4.77 -9.38 -3.6 -146.88 -193.69 -212.03 20.5 18.1 -153.04 Hydrogen (Cont.) H2SeO3 H2SeO4 24.47 H2SiO3 H4SiO4 H2Te H2TeO3 H2TeO4 Indium In InBr3 InCl3 InI3 4.21 -0.76 18.71 -183.93 -12.72 -24.58 -19.90 5.00 -22.778 -31.330 27.94 26.55 -19.11 -0.25 -10.70 -93.56 -96.8 -165.64 -82.7 -85.1 -149.0 -64.7 0.365 -12.35 -23.33 -32.25 78.50 -17.57 -19.05 -78.36 -193.70 -54.6351 -56.6899 -28.23 -31.47 -120.0 -204.0 -270.0 -7.85 -128.54 17.0 18.4 State† Compound InN In2O3 Iodine I2 IBr ICl ICl3 I 2 O5 Iridium Ir IrCl IrCl2 IrCl3 IrF6 IrO2 Iron Fe FeBr2 FeBr3 Fe3C Fe(CO)5 FeCO3 FeCl2 FeCl3 FeF2 FeI2 FeI3 Fe4N Fe(NO3)2 Fe(NO3)3 FeO Fe2O3 Fe3O4 Fe(OH)2 Fe(OH)3 FeO⋅SiO2 Fe2P FeSi FeS FeS2 FeSO4 Fe2(SO4)3 FeTiO3 Lanthanum La LaCl3 La3H8 LaN La2O3 LaS2 La2S3 La2(SO4)3 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol c aq c aq, 400 c c g c aq aq -126.5 -122.4 -130.23 -143.4 -267.8 -340.6 36.9 -145.0 -145.0 -165.6 c c aq c aq c aq c c 0.00 -97.2 -112.9 -128.5 -145.6 -56.5 -67.2 -4.8 -222.47 c g g g c c 0.00 14.88 10.05 4.20 -21.8 -42.5 0.00 4.63 1.24 -1.32 -6.05 c c c c l c 0.00 -20.5 -40.6 -60.5 -130 -40.14 0.00 -16.9 -32.0 -46.5 c, α c aq, 540 aq c l c, siderite c aq c aq, 2000 aq, 1200 c aq aq c aq aq, 800 c c c c c c c c c c, pyrites c, marcasite c aq, 400 aq, 400 c, ilmenite 0.00 -57.15 -78.7 -95.5 5.69 -187.6 -172.4 -81.9 -100.0 -96.4 -128.5 -177.2 -24.2 -47.7 -49.7 -2.55 -118.9 -156.5 -64.62 -198.5 -266.9 -135.9 -197.3 -273.5 -13 -19.0 -22.64 -38.62 -33.0 -221.3 -236.2 -653.3 -295.51 0.00 c c aq c c c c c aq 0.00 -253.1 -284.7 -160 -72.0 -539 -148.3 -351.4 -972 -101.36 -247.9 33.1 -115.7 0.00 -97.2 -117.5 -60.5 -69.47 -76.26 4.24 -154.8 -72.6 -83.0 -96.5 -151.7 -45 -39.5 0.862 -72.8 -81.3 -59.38 -179.1 -242.3 -115.7 -166.3 -23.23 -35.93 -195.5 -196.4 -533.4 -277.06 0.00 -64.6 (Continued) 2-162 PHYSICAL AnD CHEMICAL DATA TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) Compound Lead Pb PbBr2 PbCO3 Pb(C2H3O2)2 PbC2O4 PbCl2 PbF2 PbI2 Pb(NO3)2 PbO PbO2 Pb3O4 Pb(OH)2 PbS PbSO4 Lithium Li LiBr LiBrO3 Li2C2 LiCN LiCNO LiC2H3O2 Li2CO3 LiCl LiClO3 LiClO4 LiF LiH LiHCO3 LiI LiIO3 Li3N LiNO3 Li2O Li2O2 LiOH LiOH⋅H2O Li2O⋅SiO2 Li2Se Li2SO4 Li2SO4⋅H2O Magnesium Mg Mg(AsO4)2 MgBr2 Mg(CN)2 MgCN2 Mg(C2H3O2)2 MgCO3 MgCl2 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol c c aq c, cerussite c aq, 400 c c aq c c c aq, 400 c, red c, yellow c c c c c 0.00 -66.24 -56.4 -167.6 -232.6 -234.2 -205.3 -85.68 -82.5 -159.5 -41.77 -106.88 -99.46 -51.72 -50.86 -65.0 -172.4 -123.0 -22.38 -218.5 0.00 -62.06 -54.97 -150.0 c c aq, 400 aq c aq aq aq c aq, 1900 c aq, 278 aq aq c aq, 400 c aq, 2000 c aq, 400 aq c c aq, 400 c c aq c aq, 400 c gls c aq c aq, 400 c 0.00 -83.75 -95.40 -77.9 -13.0 -31.4 -101.2 -183.9 -289.7 -293.1 -97.63 -106.45 -87.5 -106.3 -145.57 -144.85 -22.9 -231.1 -65.07 -80.09 -121.3 -47.45 -115.350 -115.88 -142.3 -151.9 -159 -116.58 -121.47 -188.92 -374 -84.9 -95.5 -340.23 -347.02 -411.57 c c aq c aq, 400 aq c aq c c aq, 400 0.00 -731.3 -749 -123.9 -167.33 -39.7 -61 -344.6 -261.7 -153.220 -189.76 State† -184.40 -75.04 -68.47 -148.1 -41.47 -58.3 -45.53 -43.88 -52.0 -142.2 -102.2 -21.98 -192.9 0.00 -95.28 -65.70 -31.35 -94.12 -160.00 -269.8 -267.58 -102.03 -70.95 -81.4 Compound Magnesium (Cont.) MgCl2⋅H2O MgCl2⋅2H2O MgCl2⋅4H2O MgCl2⋅6H2O MgF2 MgI2 MgMoO4 Mg3N2 Mg(NO3)2 Mg(NO3)2⋅2H2O Mg(NO3)2⋅6H2O MgO MgO⋅SiO2 Mg(OH)2 MgS MgSO4 MgTe MgWO4 Manganese Mn MnBr2 Mn3C Mn(C2H3O2)2 MnCO3 MnC2O4 MnCl2 MnF2 MnI2 -136.40 -210.98 -83.03 -102.95 -37.33 -96.95 -138.0 -106.44 -108.29 -105.64 -314.66 -375.07 0.00 Mn5N2 Mn(NO3)2 Mn(NO3)2.6H2O MnO MnO2 Mn2O3 Mn3O4 MnO.SiO2 Mn(OH)2 Mn(OH)3 Mn3(PO4)2 MnSe MnS MnSO4 Mn2(SO4)3 Mercury Hg HgBr HgBr2 -630.14 Hg(C2H3O2)2 -156.94 -29.08 HgCl2 -286.38 -241.7 -143.77 HgCl Hg2Cl2 Hg(CN)2 HgC2O4 State† Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol c c c c c c aq, 400 c c c aq, 400 c c c c c, ppt. c, brucite c aq c aq, 400 c c -230.970 -305.810 -453.820 -597.240 -263.8 -86.8 -136.79 -329.9 -115.2 -188.770 -209.927 -336.625 -624.48 -143.84 -347.5 -221.90 -223.9 -84.2 -108 -304.94 -325.4 -25 -345.2 c, α c aq c c aq c c c aq, 400 aq, 1200 c aq c c aq, 400 c c c c c c c c c c c, green c aq, 400 c aq 0.00 -91 -106 1.1 -270.3 -282.7 -211 -240.9 -112.0 -128.9 -206.1 -49.8 -76.2 -57.77 -134.9 -148.0 -557.07 -92.04 -124.58 -229.5 -331.65 -301.3 -163.4 -221 -736 -26.3 -47.0 -254.18 -265.2 -635 -657 l g c aq c aq c aq g c c aq, 1110 c 0.00 23 -40.68 -38.4 -196.3 -192.5 -53.4 -50.3 19 -63.13 62.8 66.25 -159.3 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -205.93 -267.20 -387.98 -505.45 -132.45 -100.8 -140.66 -160.28 -496.03 -136.17 -326.7 -200.17 -193.3 -277.7 -283.88 0.00 -97.8 1.26 -227.2 -192.5 -102.2 -180.0 -73.3 -46.49 -101.1 -441.2 -86.77 -111.49 -209.9 -306.22 -282.1 -143.1 -190 -27.5 -48.0 -228.41 0.00 18 -38.8 -9.74 -139.2 -42.2 -23.25 14 PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS 2-163 TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol g c, red g c aq aq c, red c, yellow ppt. c c, black c c 57.1 -25.3 33 -28.88 -56.8 -58.5 -21.6 -20.8 -21.6 -10.7 -166.6 -177.34 52.25 -24.0 23 -26.53 -13.09 -15.65 -13.94 c c c c c c c 0.00 4.36 -8.3 -130 -180.39 -56.27 -61.48 c c aq c aq aq c aq, 400 c aq c aq c aq, 200 c c c c c aq, 200 0.00 -53.4 -72.6 9.2 -249.6 230.9 -75.0 -94.34 -157.5 -171.6 -22.4 -42.0 -101.5 -113.5 -58.4 -129.8 -163.2 -20.4 -216 -231.3 g g g aq, 200 c aq c aq, 400 c aq c aq aq c aq c aq, 400 c aq c aq c aq c aq c aq, 500 0.00 -27 -10.96 -19.27 -64.57 -60.27 -148.1 -148.58 -0.7 3.6 -17.8 -12.3 -223.4 -266.3 -260.6 -75.23 -71.20 -69.4 -63.2 -276.9 -271.3 -111.6 -110.2 -48.43 -44.97 -87.40 -80.89 State† Compound Mercury (Cont.) HgH HgI2 HgI Hg2I2 Hg(NO3)2 Hg2(NO3)2 HgO Hg2O HgS HgSO4 Hg2SO4 Molybdenum Mo Mo2C Mo2N MoO2 MoO3 MoS2 MoS3 Nickel Ni NiBr2 Ni3C Ni(C2H3O2)2 Ni(CN)2 NiCl2 NiF2 NiI2 Ni(NO3)2 NiO Ni(OH)2 Ni(OH)3 NiS NiSO4 Nitrogen N2 NF3 NH3 NH4Br NH4C2H3O2 NH4CN NH4CNS (NH4)2CO3 (NH4)2C2O4 NH4Cl NH4ClO4 (NH4)2CrO4 NH4F NH4I NH4NO3 -12.80 -8.80 -149.12 0.00 2.91 -118.0 -162.01 -54.19 -57.38 0.00 -60.7 8.88 -190.1 66.3 -74.19 -142.9 -36.2 -64.0 -51.7 -105.6 -187.6 Nitrogen (Cont.) NH4OH (NH4)2S (NH4)2SO4 N2H4 N2H4⋅H2O N2H4⋅H2SO4 N2O NO NO2 N2O4 N2O5 NOBr NOCl Osmium Os OsO4 Oxygen O2 O3 Palladium Pd PdO Phosphorus P P P2 P4 PBr3 PBr5 PCl3 PCl5 PH3 PI3 P2O5 POCl3 Platinum Pt PtBr4 0.00 -3.903 -43.54 -108.26 20.4 4.4 -164.1 -196.2 -48.59 -21.1 PtCl2 PtCl4 PtI4 Pt(OH)2 PtS PtS2 Potassium K K3AsO3 K3AsO4 KH2AsO4 KBr KBrO3 KC2H3O2 KCl -209.3 -84.7 -31.3 State† Compound KClO3 KClO4 KCN aq aq, 400 c aq, 400 l l c g g g g c l g Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol -87.59 -55.21 -281.74 -279.33 12.06 -57.96 -232.2 19.55 21.600 7.96 2.23 -10.0 11.6 12.8 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -14.50 -215.06 -214.02 24.82 20.719 12.26 23.41 19.26 16.1 c c g 0.00 -93.6 -80.1 0.00 -70.9 -68.1 g g 0.00 33.88 0.00 38.86 c c 0.00 -20.40 0.00 0.00 -4.22 150.35 33.82 13.2 -45 -60.6 -70.0 -76.8 -91.0 2.21 -10.9 -360.0 -138.4 0.00 -1.80 141.88 24.60 5.89 c, white (“yellow”) c, red (“violet”) g g g l c g l g g c c g c c aq c c aq c c c c c aq aq c c aq, 400 c aq, 1667 c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 400 0.00 -40.6 -50.7 -34 -62.6 -82.3 -18 -87.5 -20.18 -26.64 0.00 -323.0 -390.3 -271.2 -94.06 -89.19 -81.58 -71.68 -173.80 -177.38 -104.348 -100.164 -93.5 -81.34 -103.8 -101.14 -28.1 -25.3 -65.2 -63.3 -73.2 -1.45 -127.2 0.00 -67.9 -18.55 -24.28 0.00 -355.7 -236.7 -90.8 -92.0 -60.30 -156.73 -97.76 -98.76 -69.30 -72.86 -28.08 (Continued) 2-164 PHYSICAL AnD CHEMICAL DATA TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) State† Compound Potassium (Cont.) KCNO KCNS K2CO3 K2C2O4 K2CrO4 K2Cr2O7 KF K3Fe(CN)6 K4Fe(CN)6 KH KHCO3 KI KIO3 KIO4 KMnO4 K2MoO4 KNH2 KNO2 KNO3 K2O K2O⋅Al2O3⋅SiO2 K2O⋅Al2O3⋅SiO2 KOH K3PO3 K3PO4 KH2PO4 K2PtCl4 K2PtCl6 K2Se K2SeO4 K2S K2SO3 K2SO4 K2SO4⋅Al2(SO4)3 K2SO4⋅Al2(SO4)3· 24H2O K2S2O6 Rhenium Re ReF6 Rhodium Rh RhO Rh2O Rh2O3 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol c aq c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 400 c aq, 180 c aq c aq c c aq, 2000 c aq, 500 c aq, 400 aq c aq, 400 aq, 880 c aq c aq, 400 c c, leucite gls c, adularia c, microcline gls c aq, 400 aq aq c c aq c aq, 9400 c aq aq c aq, 400 c aq c aq, 400 c -99.6 -94.5 -47.0 -41.07 -274.01 -280.90 -319.9 -315.5 -333.4 -328.2 -488.5 -472.1 -134.50 -138.36 -48.4 -34.5 -131.8 -119.9 -10 -229.8 -224.85 -78.88 -73.95 -121.69 -115.18 -98.1 -192.9 -182.5 -364.2 -28.25 -86.0 -118.08 -109.79 -86.2 -1379.6 -1368.2 -1784.5 -1784.5 -1747 -102.02 -114.96 -397.5 -478.7 -362.7 -254.7 -242.6 -299.5 -286.1 -74.4 -83.4 -267.1 -121.5 -110.75 -267.7 -269.7 -342.65 -336.48 -1178.38 c c -2895.44 -418.62 -2455.68 c g 0.00 -274 0.00 c c c c 0.00 -21.7 -22.7 -68.3 0.00 -90.85 Rubidium Rb RbBr -44.08 -264.04 RbCN Rb2CO3 -293.1 RbCl -306.3 RbF -440.9 -133.13 RbHCO3 RbI -5.3 -207.71 -77.37 -79.76 -101.87 -99.68 -169.1 -168.0 -342.9 -75.9 -94.29 -93.68 -105.0 -443.3 -326.1 -226.5 -263.6 -99.10 -240.0 -111.44 -251.3 -314.62 -310.96 -1068.48 State† Compound RbNH2 RbNO3 Rb2O Rb2O2 RbOH Ruthenium Ru RuS2 Selenium Se Se2Cl2 SeF6 SeO2 Silicon Si SiBr4 SiC SiCl4 SiF4 SiH4 SiI4 Si3N4 SiO2 Silver Ag AgBr Ag2C2 AgC2H3O2 AgCN Ag2CO3 Ag2C2O4 AgCl AgF AgI AgIO3 AgNO2 AgNO3 Ag2O c c g aq, 500 aq c aq, 220 c g aq, ∞ c aq, 400 c aq, 2000 c g aq, 400 c c aq, 400 c c c aq, 200 c c c, I, hexagonal c, II, red, monoclinic l g c Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol 0.00 -95.82 -45.0 -90.54 -25.9 -273.22 -282.61 -105.06 -53.6 -101.06 -133.23 -139.31 -230.01 -225.59 -81.04 -31.2 -74.57 -27.74 -119.22 -110.52 -82.9 -107 -101.3 -115.8 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol 0.00 -52.50 -93.38 -263.78 -98.48 -57.9 -100.13 -134.5 -209.07 -40.5 -81.13 -95.05 -106.39 0.00 -46.99 0.00 -44.11 0.00 0.2 0.00 -22.06 -246 -56.33 -13.73 -222 0.00 -93.0 -28 -150.0 -142.5 -370 -14.8 -29.8 -179.25 -202.62 0.00 c l c l g g g c c c, cristobalite, 1600° form c, cristobalite, 1100° form c, quartz c, tridymite -203.35 -203.23 c c c c aq c c c c c aq, 400 c c c aq c aq, 6500 c 0.00 -23.90 84.5 -95.9 -91.7 33.8 -119.5 -158.7 -30.11 -48.7 -53.1 -15.14 -42.02 -11.6 -2.9 -29.4 -24.02 -6.95 -27.4 -133.9 -133.0 -360 -9.4 -154.74 -202.46 -190.4 0.00 -23.02 -70.86 38.70 -103.0 -25.98 -47.26 -16.17 -24.08 3.76 9.99 -7.66 -7.81 -2.23 PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS 2-165 TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) State† Compound Silver (Cont.) Ag2S Ag2SO4 Sodium Na Na3AsO3 Na3AsO4 NaBr NaBrO NaBrO3 NaC2H3O2 NaCN NaCNO NaCNS Na2CO3 NaCO2NH2 Na2C2O4 NaCl NaClO3 NaClO4 Na2CrO4 Na2Cr2O7 NaF NaH NaHCO3 NaI NaIO3 Na2MoO4 NaNO2 NaNO3 Na2O Na2O2 Na2O⋅SiO2 Na2O⋅Al2O3⋅3SiO2 Na2O⋅Al2O3⋅4SiO2 NaOH Na3PO3 Na3PO4 Na2PtCl4 Na2PtCl6 Na2Se Na2SeO4 Na2S Na2SO3 Na2SO4 c c aq c aq, 500 c aq, 500 c aq, 400 aq aq, 400 c aq, 400 c aq, 200 c aq c aq, 400 c aq, 1000 c c aq, 600 c aq, 400 c aq, 400 c aq, 476 c aq, 800 aq, 1200 c aq, 400 c c aq c aq, ∞ aq, 400 c aq c aq c aq, 400 c c c c, natrolite c c aq, 400 aq, 1000 c aq, 400 aq c aq c aq, 440 c aq, 800 c aq, 400 c aq, 800 c aq, 1100 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -5.5 -170.1 -165.8 -7.6 -146.8 -139.22 0.00 -314.61 -366 -381.97 -86.72 -86.33 -78.9 -68.89 -170.45 -175.450 -22.47 -22.29 -96.3 -91.7 -39.94 -38.23 -269.46 -275.13 -142.17 -313.8 -309.92 -98.321 -97.324 -83.59 -78.42 -101.12 -97.66 -319.8 -323.0 -465.9 -135.94 -135.711 -14 -226.0 -222.1 -69.28 -71.10 -112.300 -364 -358.7 -86.6 -83.1 -111.71 -106.880 -99.45 -119.2 -383.91 -1180 -1366 -101.96 -112.193 -389.1 -457 -471.9 -237.2 -272.1 -280.9 -59.1 -78.1 -254 -261.5 -89.8 -105.17 -261.2 -264.1 -330.50 -330.82 0.00 -341.17 -87.17 -57.59 -152.31 -23.24 -86.00 -39.24 -249.55 -251.36 -283.42 -91.894 -93.92 Sodium (Cont.) Na2SO4⋅10H2O Na2WO4 Strontium Sr SrBr2 Sr(C2H3O2)2 Sr(CN)2 SrCO3 SrCl2 SrF2 Sr(HCO3)2 SrI2 Sr3N2 Sr(NO3)2 SrO SrO⋅SiO2 SrO2 Sr2O Sr(OH)2 Sr3(PO4)2 -62.84 SrS -73.29 SrSO4 -296.58 -431.18 -129.0 -128.29 -9.30 -202.66 -202.87 SrWO4 Sulfur S -74.92 -94.84 -333.18 -71.04 -87.62 -88.84 -90.06 -105.0 -361.49 -90.60 -100.18 -428.74 -216.78 -89.42 -230.30 -101.76 -240.14 -241.58 -302.38 -301.28 State† Compound S2 S6 S8 S2Br2 SCl4 S2Cl2 S2Cl4 SF6 SO SO2 SO3 SO2Cl2 Tantalum Ta TaN Ta2O5 Tellurium Te TeBr4 TeCl4 TeF6 TeO2 Thallium Tl TlBr TlCl c c aq c c aq, 400 c aq aq c c aq, 400 c aq c aq, 400 c c aq, 400 c gls c c c aq, 800 c aq c aq c aq, 400 c Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -1033.85 -391 -381.5 -870.52 0.00 -171.0 -187.24 -358.0 -364.4 -59.5 -290.9 -197.84 -209.20 -289.0 -459.1 -136.1 -156.70 -91.4 -233.2 -228.73 -140.8 -364 -153.3 -153.6 -228.7 -239.4 -980 -985 -113.1 -120.4 -345.3 -345.0 -393 0.00 -0.071 0.257 -345.18 0.00 -182.36 -311.80 -54.50 -271.9 -195.86 -413.76 -157.87 -76.5 -185.70 -133.7 -139.0 -208.27 -881.54 -109.78 -309.30 c, rhombic c, monoclinic l, λ l, λµ equilibrium g g g g l l l l g g g g l c, α c, β c, γ g l 0.00 0.023 0.072 0.071 43.57 19.36 13.97 12.770 53.25 31.02 27.78 27.090 -4 -13.7 -14.2 -24.1 -262 19.02 -70.94 -94.39 -103.03 -105.09 -105.92 -109.34 -82.04 -89.80 -237 12.75 -71.68 -88.59 -88.28 -88.22 -88.34 -88.98 -74.06 -75.06 c c c 0.00 -51.2 -486.0 0.00 -45.11 -453.7 c c c g c 0.00 -49.3 -77.4 -315 -77.56 0.00 -57.4 -292 -64.66 c c aq c aq 0.00 -41.5 -28.0 -49.37 -38.4 0.00 -39.43 -32.34 -44.46 -39.09 -5.90 (Continued) 2-166 PHYSICAL AnD CHEMICAL DATA TABLE 2-94 Heats and Free Energies of Formation of Inorganic Compounds (Continued ) Compound Thallium (Cont.) TlCl3 TlF TlI TlNO3 Tl2O Tl2O3 TlOH Tl2S Tl2SO4 Thorium Th ThBr4 ThC2 ThCl4 ThI4 Th3N4 ThO2 Th(OH)4 Th(SO4)2 Tin Sn SnBr2 SnBr4 SnCl2 SnCl4 SnI2 SnO SnO2 Sn(OH)2 Sn(OH)4 SnS Titanium Ti TiC TiCl4 TiN TiO2 † State† Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol c aq aq c aq c aq c c c aq c c aq, 800 -82.4 -91.0 -77.6 -31.1 -12.7 -58.2 -48.4 -43.18 -120 -57.44 -53.9 -22 -222.8 -214.1 c c aq c c aq aq c c c, “soluble” c aq 0.00 -281.5 -352.0 -45.1 -335 -392 -292.0 -309.0 -291.6 -336.1 -632 -668.1 c, II, tetragonal c, III, “gray,” cubic c aq c aq c aq l aq c aq c c c c c 0.00 0.6 -61.4 -60.0 -94.8 -110.6 -83.6 -81.7 -127.3 -157.6 -38.9 -33.3 -67.7 -138.1 -136.2 -268.9 -18.61 c c l c c, III, rutil amorphous 0.00 -110 -181.4 -80.0 -225.0 -214.1 Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol -44.25 -73.46 -31.3 -20.09 -36.32 -34.01 -45.54 -45.35 -197.79 -191.62 0.00 -295.31 -322.32 -246.33 -282.3 -280.1 -549.2 0.00 1.1 -55.43 -97.66 -68.94 -110.4 -124.67 -30.95 -60.75 -123.6 -115.95 -226.00 0.00 -109.2 -165.5 -73.17 -211.9 -201.4 Heat of formation‡§ ΔH ( formation) at 25°C, kcal/mol Free energy of formation∙¶ ΔF ( formation) at 25°C, kcal/mol c c c c 0.00 -130.5 -195.7 -84 0.00 -118.3 -177.3 c c c c c c c c c 0.00 -29 -213 -251 -274 -256.6 -756.8 -291.6 -845.1 0.00 c c l l c c c c c 0.00 -147 -187 -165 -41.43 -195 -296 -342 -373 c c c aq, 400 c aq, 400 c c c aq, 400 aq c aq aq, 400 c, hexagonal c c, rhombic c, wurtzite c aq, 400 0.00 -3.6 -77.0 -93.6 -259.4 -269.4 17.06 -192.9 -99.9 -115.44 -192.9 -50.50 -61.6 -134.9 -83.36 -282.6 -153.66 -45.3 -233.4 -252.12 c c c c c, monoclinic c c 0.00 -29.8 -268.9 -82.5 -258.5 -411.0 -337 State† Compound Tungsten W WO2 WO3 WS2 Uranium U UC2 UCl3 UCl4 U3N4 UO2 UO2(NO3)2⋅6H2O UO3 U3O8 Vanadium V VCl2 VCl3 VCl4 VN V2O2 V2O3 V2O4 V2O5 Zinc Zn ZnSb ZnBr2 Zn(C2H3O2)2 Zn(CN)2 ZnCO3 ZnCl2 ZnF2 ZnI2 Zn(NO3)2 ZnO ZnO⋅SiO2 Zn(OH)2 ZnS ZnSO4 Zirconium Zr ZrC ZrCl4 ZrN ZrO2 Zr(OH)4 ZrO(OH)2 -249.6 -242.2 -617.8 0.00 -35.08 -277 -316 -342 0.00 -3.88 -72.9 -214.4 -173.5 -88.8 -166.6 -49.93 -87.7 -76.19 -44.2 -211.28 0.00 -34.6 -75.9 -244.6 -307.6 The physical state is indicated as follows: c, crystal (solid); l, liquid; g, gas; gls, glass or solid supercooled liquid; aq, in aqueous solution. A number following the symbol aq applies only to the values of the heats of formation (not to those of free energies of formation); and indicates the number of moles of water per mole of solute; when no number is given, the solution is understood to be dilute. For the free energy of formation of a substance in aqueous solution, the concentration is always that of the hypothetical solution of unit molality. ‡ The increment in heat content, ΔH, is the reaction of forming the given substance from its elements in their standard states. When ΔH is negative, heat is evolved in the process, and, when positive, heat is absorbed. § The heat of solution in water of a given solid, liquid, or gaseous compound is given by the difference in the value for the heat of formation of the given compound in the solid, liquid, or gaseous state and its heat of formation in aqueous solution. The following two examples serve as an illustration of the procedure: (1) For NaCl(c) and NaCl(aq, 400H2O), the values of ΔH( formation) are, respectively, -98.321 and -97.324 kcal/mol. Subtraction of the first value from the second gives ΔH = 0.998 kcal/mol for the reaction of dissolving crystalline sodium chloride in 400 mol of water. When this process occurs at a constant pressure of 1 atm, 0.998 kg-cal of energy are absorbed. (2) For HCl(g) and HCl(aq, 400H2O), the values for ΔH( formation) are, respectively, -22.06 and -39.85 kcal/mol. Subtraction of the first from the second gives ΔH = -17.79 kcal/mol for the reaction of dissolving gaseous hydrogen chloride in 400 mol of water. At a constant pressure of 1 atm, 17.79 kcal of energy are evolved in this process. ∙The increment in the free energy, ΔF, is the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are: for a gas, fugacity (approximately equal to the pressure) of 1 atm; for a pure liquid or solid, the substance at a pressure of 1 atm; for a substance in aqueous solution, the hypothetical solution of unit molality, which has all the properties of the infinitely dilute solution except the property of concentration. ¶ The free energy of solution of a given substance from its normal standard state as a solid, liquid, or gas to the hypothetical one molal state in aqueous solution may be calculated in a manner similar to that described in footnote § for calculating the heat of solution. TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K Cmpd. no. 2-167 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 Ideal gas enthalpy of formation, J/kmol × 1E-07 -17.1 -23.83 -43.28 -57.55 -21.57 6.467 22.82 -8.18 -35.591 17.97 0 -4.5898 -6.79 0 -10.09 8.288 11.15 -29.41 21.57 5.68 -9.025 -11.5 9.33 17.849 3.091 10.5018 -6.36 -3.77 16.23 10.924 -12.579 -44.58 -43.32 -27.51 -29.29 -0.05 -0.74 -1.1 -48.56 -1.314 -8.78 -9.66 16.52 -20.62 -47.58 3.342 -39.351 11.69 -11.053 Ideal gas Gibbs energy of formation, J/kmol × 1E-07 -13.78 -15.96 -37.45 -47.6 -15.13 8.241 21.068 -5.68 -30.6 18.92 0 -1.64 2.27 0 -0.211 12.96 14.76 -21.42 25.8 17.3 -0.254 3.37 16.3 27.63 0.314 13.8532 -2.574 -2.7037 19.86 14.972 -1.67 -30.44 -29.18 -15.07 -16.7 7.041 6.536 6.32 -31.26 14.54 1.139 0.512 20.225 -11.48 -36 10.57 -39.437 6.68 -13.715 Ideal gas entropy, J/(kmol∙K) × 1E-05 Standard net enthalpy of combustion, J/kmol × 1E-09 2.6384 2.722 2.825 3.899 2.954 2.438 2.0081 2.97 3.15 2.77267 1.94452 1.9266 3.61 1.54845 3.641 2.693 3.369 3.69 3.21 4.4 3.713 4.39 3.607 3.9367 2.4535 3.24386 2.873 2.421 2.93 2.7889 3.0991 4.065 4.065 3.618 3.566 3.074 3.012 2.965 4.425 4.3949 3.752 3.667 2.9039 3.418 3.601 3.337 2.13677 2.379 1.97556 -1.1046 -1.0741 -0.7866 -1.675 -1.659 -1.18118 -1.257 -1.5468 -1.32717 -1.71238 0 -0.31683 -3.6072 0 -3.39877 -3.136 -3.4474 -3.0951 -3.524 -6.2876 -3.56 -4.83 -4.06 -6.248 0 -3.01917 -1.301 -0.7185 -2.4617 -2.409 -2.65732 -2.2678 -2.2824 -2.454 -2.446 -2.5408 -2.5339 -2.53 -3.28 -5.5644 -2.9554 -2.949 -2.4647 -2.301 -2.008 -2.4146 -1.0769 -0.283 (Continued) 2-168 TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 Name Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Formula CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CAS 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 Mol. wt. 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 Ideal gas enthalpy of formation, J/kmol × 1E-07 Ideal gas Gibbs energy of formation, J/kmol × 1E-07 -9.581 -92.21 0 5.109 -11.23 -10.29 -8.57 -13.32 -14.477 -13.23 -12.857 -12.535 0.4 30.894 2.85 -12.33 -28.62 -22.61 -0.46 -7.703 3.23 5.33 -9.602 -33.17 -24.946 -59.43 -39.85 -12.47 -21.09 4.1 0 -4.08 -3.89 -5.354 -87.76 0 9.829 -6.045 -7.01 -6.209 -5.251 -6.136 -4.019 -3.543 -3.166 13.79 29.76 11.22 3.191 -10.95 -9.028 10.77 3.885 11.05 10.44 4.886 -6.349 3.318 -30.5 -10.02 12.27 6.165 25.16 0 -1.181 -1.054 -33.34 2.57 3.02 2.25 -12.941 -12.979 -9.552 -15.08 -16.28 -40.847 -7.142 -25.21 -8.356 -49.7 -44.77 -8.827 7.79 8.29 7.67 -7.259 -7.3945 -6.896 -6.52 -8.018 -22.574 7.308 -12.21 1.774 -43.9485 -39.19 Ideal gas entropy, J/(kmol∙K) × 1E-05 Standard net enthalpy of combustion, J/kmol × 1E-09 3.0991 2.62 2.23079 3.1403 2.758 2.956 2.341 3.155 3.0594 3.5604 3.5259 3.5075 3.86 2.4117 2.64396 2.97276 3.277 3.3426 3.10518 2.929 2.91267 2.37378 3.646 5.672 5.457 5.99 5.971 5.433 6.116 5.263 1.4486 3.276 3.297 2.92964 5.014 3.4353 3.4185 3.3674 3.0501 3.0828 2.7018 3.448 3.548 4.29 3.522 3.423 3.681 2.824 2.88194 -0.2653 0.5286 0 -2.976 -1.279 -0.38 -0.6705 -1.864 -1.863 -3.52783 -3.528 -3.52256 -4.951 -1.096 -2.5678 -3.656 -3.4639 -3.299 -3.532 -3.0709 -2.9393 -1.9593 -3.968 -5.958 -6.29422 -5.72 -6.116 -6.1809 -6.6161 -6.1037 -0.24625 -1.16 -1.1769 -4.94691 -2.825 -2.826 -2.802 -1.1104 -1.105 -0.51388 -1.72 -1.707 -2.4105 -2.8003 -2.5035 -2.9607 -0.773662 -0.823 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 -45.23 -14.38 -31.92 -31.14 -38.97 -38.42 14.57 -1.845 -17.68 -18.1 -17.2172 -17.9996 -2.42 -18.41 -19.17 -19.41 -60.5 -9.47 -3.724 -15.046 -62.742 -31.58 5.2 -11.6 -29.072 -45.646 -8.382 -23.495 -44.45 -4.715 2.992 -32.6 -53.78 -48.55 -17.15 -12.69 5.251 -1.73 -39.22 12.3428 -5.263 -38.83 -55.95 -33.37 -28.58 -28.61 -4.63 -46.36 -27.22 -59.15 0 -11.6566 -42.4747 6.42 -12.48 -12.37 -23.8 -20.11 18.49 6.839 -0.3125 3.52293 4.12124 3.44761 1.516 -11.28 -8.84 0.5717 -46.7749 -1.925 0.7302 -8.1441 -41.97 -18.16 17.5 11.96 4.981 11.57 -3.192 -16.785 -32.8 3.616 13.073 -19.05 -35.9 -31.22 3.955 4.48 6.844 10.3 -30.18 17.7987 -1.323 -30.31 -32.49 -9.042 -12.64 -13.3 -0.4814 -31.93 -11.52 -50.66 0 -6.9036 2.4658 4.12 3.989 4.27 3.726 4.038 2.833 2.7296 3.6592 3.65012 3.7451 3.70912 3.35291 2.667 3.26 4.1455 6.6 2.9953 2.8585 3.0627 4.245 3.0012 4.13 3.2 6.2415 9.3787 2.2912 2.8064 3.597 2.848 3.6063 4.55 4.23 4.417 3.826 3.783 2.192 3.21833 3.04891 2.5062 2.4299 3.282 5.097 5.076 3.8 4.069 2.961 4.025 3.881 4.07 2.02789 3.02629 -0.183031 -3.99 -3.70261 -4.095 -2.394 -2.996 -2.4189 -1.6146 -3.84761 -4.8639 -4.87084 -4.86436 -2.0441 -1.3284 -1.78871 -4.46075 -4.4662 -2.569 -1.7443 -1.6054 -4.41057 -2.1863 -5.8939 -4.0189 -7.51368 -12.3908 -1.42864 -1.235 -2.061 -1.5874 -4.3448 -4.41 -3.21203 -3.284 -4.87051 -4.2839 -1.323 -1.691 -1.0527 -1.481 -1.218 -1.50696 -4.448 -4.943 -3.103 -3.4863 -1.7366 -2.674 -3.12 -1.67471 -2.81451 2-169 (Continued) 2-170 TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 Name Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Formula C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N CAS 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 Mol. wt. Ideal gas enthalpy of formation, J/kmol × 1E-07 Ideal gas Gibbs energy of formation, J/kmol × 1E-07 Ideal gas entropy, J/(kmol∙K) × 1E-05 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 -26.44 -23.43 -10.86 -19.22 -37.88 -3.48 0 -39.445 -26.48 -18.765 -53.62 -33.68 -35.3 -30.1 -30.0453 -6.289 -14.95 10.3 -37.417 -24.8 -16.694 -51.19 -31.62 -33.46 -27.9826 -27.76 -4.167 10.6 -12.92 12.37 10.5 9.5353 0 -3.629 -9.231 13.5143 -27.33 -2.063 -48.41 -8.38 -77.89 -36.8 -7.452 -20.094 -24 -41.19 18.49 -33.3 -2.297 -21.23 -21.03 -10.26 -14.71 -35.11 0.08225 0 9.083 -8.367 0.8165 -33.4 -12.55 -13.7 -12.25 -11.96 9.482 3.622 22.7 8.216 -9.92 -0.006634 -33.8 -13.39 -15.06 -13.0081 -12.6 8.7 19.9 2.759 21.85 19.9 15.917 0 -5.334 -9.53 12.4725 -27.54 -3.344 -36.21 3.192 -69.29 -28.8 -5.049 -16.232 -13.5 -32.42 19.384 -25.7 3.207 2.644 2.22734 2.19 2.4857 2.487 2.6714 1.26152 8.2023 4.5 4.2798 4.8 4.795 4.66 4.58 4.486 4.252 4.939 4.085 7.8102 4.22 3.8874 4.41 4.402 4.349 4.17856 4.092 3.863 3.76 4.546 3.694 3.72 2.3861 1.30571 1.98591 1.86786 2.01719 1.7367 2.056 3.412 3.124 4.003 3.5 1.8627 2.3988 3.2 3.198 2.4836 3.66 2.433 Standard net enthalpy of combustion, J/kmol × 1E-09 -1.127 -0.5219 -0.5268 -0.5021 -0.2115 -1.9959 0 -10.5618 -4.136 -4.46473 -3.839 -4.285 -4.27 -4.098 -4.09952 -4.3499 -4.7865 -4.2717 -9.95145 -3.524 -3.8551 -3.23 -3.675 -3.67 -3.49 -3.492 -3.7397 -3.64 -4.1762 -3.661 -3.64 -0.5342 -0.24182 -0.06904 -0.0286 -0.62329 0.1524 -0.518 -2.0004 -2.1566 -0.7732 -1.93 -0.80262 -0.6382 -1.71 -1.461 -1.8487 -1.9303 -0.97508 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.0019096 -28.79 12.908 -15.37 -49.8 -30.3 -3.53 -4.18 26 -25.81 -10.2 13.8 -45.07 -21.5 -15.48 -33.2 -32.7 -35.26 -10.62 -0.38 0.74 -40.2 -21.64 -23.9 -5.96 -35.24 -26.6 -28.64 -6.24 -25.2 -26.26 -8.96 -2.29 -36 -57.95 -17.455 -27.8 -13.499 -31.24 -1.71 -42.75 -23.82 -8.23 -2.91 11.83 -28.3 -10.8 15.058 0 -10.21 0 -13.2089 -18.1 19.75 -1.405 -34.99 -14.54 6.668 6.045 30.25 -10.17 2.691 20.72 -30.53 -16.61 2.733 -12.9 -12.68 -15.24 3.63 10.38 11.38 -34.83 -11.71 -14.7 1.147 -29.5 -10.7 -13.51 0.0244 -12.18 -13.93 1.4509 -0.98 -25.4 -31.8 -0.5338 -9.321 -2.144 -17.76 5.808 -31.1 -11.1 1.793 1.853 21.73 -11.7 -4.73 22.408 0 -0.6125 0 -9.063 4.14 3.2151 3.4374 3.9 3.869 3.395 3.386 2.78 3.901 4.118 3.189 3.988 2.98277 3.433 3.75 3.853 3.853 3.399 3.264 3.305 3.287 3.0881 3.394 3.332 2.852 3.81 4.129 1.955 3.416 3.699 3.59 2.55 4.01 5.533 3.8089 4.32 2.955 3.263 2.9309 3.596 3.52 3.717 2.565 3.725 3.58 3.08 3.3315 1.46327 3.168 1.91609 2.60773 -3.772 -3.032 -3.23954 -2.622 -3.062 -3.1159 -3.1088 -2.93 -3.12818 -3.5723 -3.046 -2.686 -1.693 -4.25714 -4.058 -4.0574 -4.0318 -3.6741 -3.534 -3.5464 -1.357 -1.9314 -2.268 -2.354 -0.8924 -3.122 -3.4762 -1.06 -2.5311 -2.877 -2.957 -1.1517 -2.54 -5.056 -3.84915 -3.739 -2.64812 -2.4239 -2.5242 -2.078 -2.51739 -2.962 -1.999 -4.8214 -3.11 -1.77431 -4.9809 0 -1.25 2-171 (Continued) 2-172 TABLE 2-95 Enthalpies and Gibbs Energies of Formation, Entropies, and net Enthalpies of Combustion of Inorganic and Organic Compounds at 298.15 K (Continued ) Cmpd. no. 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 Name Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Formula CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O CAS 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 Mol. wt. 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 Ideal gas enthalpy of formation, J/kmol × 1E-07 Ideal gas Gibbs energy of formation, J/kmol × 1E-07 Ideal gas entropy, J/(kmol∙K) × 1E-05 Standard net enthalpy of combustion, J/kmol × 1E-09 -7.47 8.205 9.025 -43.579 -31.09 -22.874 -57.73 -37.79 -39.71 -10.35 -19.08 6.17 -41.512 -29.02 -20.875 -55.6 -35.73 -37.62 -32.16 -33.9 -8.194 -17.01 8.23 -71.95 0 14.2671 -35.311 -22.78 -14.676 -49.13 -29.57 -31.37 -25.92 -25.79 -2.162 -11.3 -10.84 14.44 12.89 20.12 -9.6399 -1.454 -37.14 19.05 -10.468 -25.46 -27.21 4.677 -18.49 -0.6934 10.416 8.657 10.74 -7.136 2.498 -31.7 -10.86 -12.61 11.23 5.28 24.34 9.91 -8 1.6 -32.5 -11.7 -13.43 -11.38 -12.81 10.57 4.457 23.5 -66.24 0 16.3164 7.426 -10.67 -0.8813 -34.7 -14.23 -15.88 -13.83 -13.44 7.837 1.814 1.94408 21.03 19.45 30.219 -3.2637 4.87212 -30.7001 20.08 -2.439 -15.99 -17.52 20.85 -12.37 2.751 2.1985 2.106 8.9866 5.266 5.064 5.59 5.579 5.523 5.041 5.724 4.8699 8.5945 4.896 4.6723 5.2 5.187 5.132 4.962 4.879 4.637 5.331 4.478 3.608 2.05147 2.38823 7.4181 3.777 3.4945 4.02 4.01 3.958 3.786 3.7 3.462 4.05 4.154 3.298 3.3084 3.945 3.1481 3.527 3.995 2.439 2.702 3.226 3.175 4.233 3.065 -0.6432 -0.0820482 -0.0902489 -11.7812 -5.35 -5.68455 -5.061 -5.506 -5.506 -5.5716 -6.006 -5.493 -11.1715 -4.74 -5.07415 -4.448 -4.895 -4.894 -4.6984 -4.711 -4.961 -5.3962 -4.88145 -0.1989 0 -0.142671 -9.34237 -2.91 -3.24494 -2.617 -3.064 -3.058 -2.87956 -2.8804 -3.13037 -3.564 -3.5641 -3.051 -3.0291 -6.8282 -2.921 -3.298 -3.1715 -1.8563 -2.04311 -1.844 -1.834 -5.232 -1.684 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.0791128 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 -45.35 5.155 -46.48 -7.05 0.79 2.023 -40.76 -7.59 -6.75 -42.15 -12.29 -161.494 14.74 -81.6 -29.684 -122.047 -39.572 -66.94 27.66 -33.244 -18.418 2.661 -3.376 -22.56 11.544 5.017 -14.2 -31.177 -9.58 -2.431 -0.95 -1.38 -22.401 -21.845 6.24 4.34 -27.043 -41.9 -31.49 30.46 2.845 -48.116 -24.1818 1.732 1.908 1.803 -35.82 9.688 -32.04 4.17 13.76 6.264 -29.36 -0.218 0.2583 -30.4 -6.92 -157.27 21.39 -70.11 -30.012 -111.653 -37.095 -55.01 42.3 6.599 -7.969 16.71 4.59 2.239 12.67 12.22 -8.097 5.771 11.41 9.899 12.61 11.71 1.394 1.828 26.79 28.44 4.116 -9.177 -22.79 30.6 4.195 -42.5514 -22.8572 11.876 12.2 12.14 2.949 2.877 4.023 3.242 4.0014 2.67 3.678 3.243 3.365 3.52 3.205 2.82651 3.451 4.398 2.481 2.91625 2.5651 4.48 5.263 7.0259 2.9729 3.6964 3.1 3.893 2.784 3.2099 3.371 6.6337 4.054 2.87 3.805 3.961 4.2296 4.2702 4.435 4.607 5.8493 6.363 3.28 2.794 2.7354 3.73966 1.88825 3.5854 3.5383 3.52165 -1.395 -1.80056 -2.672 -2.165 -4.95415 -1.9262 -2.041 -2.3398 -2.3458 -1.6476 -2.658 0.7055 -4.219 -1.3591 0.924 0.1422 -3.19 -9.053 -8.73282 -2.325 -5.3575 -2.76549 -5.0639 -2.4352 -3.734 -0.9685 -8.1229 -4.0405 -2.2449 -4.934 -4.9307 -5.06528 -5.06876 -2.6867 -3.2959 -6.9036 -6.726 -1.95 -2.362 -1.178 -1.544 -4.3318 -4.333 -4.333 The compounds are considered to be formed from the elements in their standard states at 298.15 K and 1 bar. These include C (graphite) and S (rhombic). Enthalpy of combustion is the net value for the compound in its standard state at 298.15 K and 1 bar. Products of combustion are taken to be CO2 (gas), H2O (gas), F2(gas), Cl2 (gas), Br2 (gas), I2 (gas), SO2 (gas), N2 (gas), P4O10 (crystalline), SiO2 (crystobalite), and Al2O3 (crystal, alpha). Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-173 2-174 PHYSICAL AnD CHEMICAL DATA TABLE 2-96 Ideal Gas Sensible Enthalpies, hT – h298 (kJ/kmol), of Combustion Products Temperature, K CO CO2 H OH H2 N NO NO2 N2 N2O O O2 SO2 H2O -2858 -1692 -1110 -529 0 -3414 -2079 -1383 -665 0 -2040 -1209 -793 -377 0 -2976 -1756 -1150 -546 0 -2774 -1656 -1091 -522 0 -2040 -1209 -793 -378 0 -2951 -1743 -1142 -543 0 -3495 -2104 -1392 -672 0 -2857 -1692 -1110 -528 0 -3553 -2164 -1438 -692 0 -2186 -1285 -840 -398 0 -2868 -1703 -1118 -533 0 -3736 -2258 -1496 -718 0 -3282 -1948 -1279 -609 0 300 320 340 360 380 54 638 1221 1805 2389 69 823 1594 2382 3184 38 454 870 1285 1701 55 654 1251 1847 2442 53 630 1209 1791 2373 38 454 870 1286 1701 55 652 1248 1845 2442 68 816 1571 2347 3130 54 636 1219 1802 2386 72 854 1654 2470 3302 41 478 913 1346 1777 54 643 1234 1828 2425 74 881 1702 2538 3387 62 735 1410 2088 2769 400 420 440 460 480 2975 3563 4153 4643 5335 4003 4835 5683 6544 7416 2117 2532 2948 3364 3779 3035 3627 4219 4810 5401 2959 3544 4131 4715 5298 2117 2533 2949 3364 3780 3040 3638 4240 4844 5450 3927 4735 5557 6392 7239 2971 3557 4143 4731 5320 4149 5010 5884 6771 7670 2207 2635 3063 3490 3918 3025 3629 4236 4847 5463 4250 5126 6015 6917 7831 3452 4139 4829 5523 6222 500 550 600 650 700 5931 7428 8942 10477 12023 8305 10572 12907 15303 17754 4196 5235 6274 7314 8353 5992 7385 8943 10423 11902 5882 6760 8811 10278 11749 4196 5235 6274 7314 8353 6059 7592 9144 10716 12307 8099 10340 12555 14882 17250 5911 7395 8894 10407 11937 8580 10897 13295 15744 18243 4343 5402 6462 7515 8570 6084 7653 9244 10859 12499 8758 11123 13544 16022 18548 6925 8699 10501 12321 14192 750 800 850 900 950 13592 15177 16781 18401 20031 20260 22806 25398 28030 30689 9392 10431 11471 12510 13550 13391 14880 16384 17888 19412 13223 14702 16186 17676 19175 9329 10431 11471 12510 13550 13919 15548 17195 18858 20537 19671 22136 24641 27179 29749 13481 15046 16624 18223 19834 20791 23383 26014 28681 31381 9620 10671 11718 12767 13812 14158 15835 17531 19241 20965 21117 23721 26369 29023 31714 16082 18002 19954 21938 23954 1000 1100 1200 1300 1400 21690 25035 28430 31868 35343 33397 38884 44473 50148 55896 14589 16667 18746 20824 22903 20935 24024 27160 30342 33569 20680 23719 26797 29918 33082 14589 16667 18746 20824 22903 22229 25653 29120 32626 36164 32344 37605 42946 48351 53808 21463 24760 28109 31503 34936 34110 39647 45274 50976 56740 14860 16950 19039 21126 23212 22703 26212 29761 33344 36957 34428 39914 45464 51069 56718 26000 30191 34506 38942 43493 1500 1600 1700 1800 1900 38850 42385 45945 49526 53126 61705 67569 73480 79431 85419 24982 27060 29139 31217 33296 36839 40151 43502 46889 50310 36290 39541 42835 46169 49541 24982 27060 29139 31218 33296 39729 43319 46929 50557 54201 59309 64846 70414 76007 81624 38405 41904 45429 48978 52548 62557 68420 74320 80254 86216 25296 27381 29464 31547 33630 40599 44266 47958 51673 55413 62404 68123 73870 79642 85436 48151 52908 57758 62693 67706 2000 2100 2200 2300 2400 56744 60376 64021 67683 71324 91439 97488 103562 109660 115779 35375 37453 39532 41610 43689 53762 57243 60752 64285 67841 52951 56397 59876 63387 66928 35375 37454 39534 41614 43695 57859 61530 65212 68904 72606 87259 92911 98577 104257 109947 56137 59742 63361 66995 70640 92203 98212 104240 110284 116344 35713 37796 39878 41962 44045 59175 62961 66769 70600 74453 91250 97081 102929 108792 114669 72790 77941 83153 88421 93741 2500 2600 2700 2800 2900 74985 78673 82369 86074 89786 121917 128073 134246 140433 146636 45768 47846 49925 52004 54082 71419 75017 78633 82267 85918 70498 74096 77720 81369 85043 45777 47860 49945 52033 54124 76316 80034 83759 87491 91229 115648 121357 127075 132799 138530 74296 77963 81639 85323 89015 122417 128501 134596 140701 146814 46130 48216 50303 52391 54481 78328 82224 86141 90079 94036 120559 126462 132376 138302 144238 99108 104520 109973 115464 120990 3000 3500 4000 4500 5000 93504 112185 130989 149895 168890 152852 184109 215622 247354 279283 56161 66554 75947 87340 97733 89584 108119 126939 145991 165246 88740 107555 126874 146660 166876 56218 66769 77532 88614 100111 94973 113768 132671 151662 170730 144267 173020 201859 230756 259692 92715 111306 130027 148850 167763 152935 183636 214453 245348 276299 56574 67079 77675 88386 99222 98013 118165 188705 159572 180749 150184 180057 210145 240427 270893 126549 154768 183552 212764 242313 200 240 260 280 298.15 Converted and usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.). PROPERTIES OF FORMATIOn AnD COMBUSTIOn REACTIOnS 2-175 TABLE 2-97 Ideal Gas Entropies s°, kJ/(kmol· K), of Combustion Products Temperature, K CO CO2 H OH H2 N NO NO2 N2 N2O O O2 SO2 H2O 200 240 260 280 298.15 186.0 191.3 193.7 195.3 197.7 200.0 206.0 208.8 211.5 213.8 106.4 110.1 111.8 113.3 114.7 171.6 177.1 179.5 181.8 183.7 119.4 124.5 126.8 129.2 130.7 145.0 148.7 150.4 151.9 153.3 198.7 204.1 206.6 208.8 210.8 225.9 232.2 235.0 237.7 240.0 180.0 185.2 187.6 189.8 191.6 205.6 211.9 214.8 217.5 220.0 152.2 156.2 158.0 159.7 161.1 193.5 198.7 201.1 203.3 205.1 233.0 239.9 242.8 245.8 248.2 175.5 181.4 184.1 186.6 188.8 300 320 340 360 380 197.8 199.7 201.5 203.2 204.7 214.0 216.5 218.8 221.0 223.2 114.8 116.2 117.4 118.6 119.7 183.9 185.9 187.7 189.4 191.0 130.9 132.8 134.5 136.2 137.7 153.4 154.8 156.0 157.2 158.3 210.9 212.9 214.7 216.4 218.0 240.3 242.7 245.0 247.2 249.3 191.8 193.7 195.5 197.2 198.7 220.2 222.7 225.2 227.5 229.7 161.2 162.6 163.9 165.2 166.3 205.3 207.2 209.0 210.7 212.5 248.5 251.1 253.6 256.0 258.2 189.0 191.2 193.3 195.2 197.1 400 420 440 460 480 206.2 207.7 209.0 210.4 211.6 225.3 227.3 229.3 231.2 233.1 120.8 121.8 122.8 123.7 124.6 192.5 194.0 195.3 196.6 197.9 139.2 140.6 141.9 143.2 144.5 159.4 160.4 161.4 162.3 163.1 219.5 221.0 222.3 223.7 225.0 251.3 253.2 255.1 257.0 258.8 200.2 201.5 202.9 204.2 205.5 231.9 234.0 236.0 238.0 239.9 167.4 168.4 169.4 170.4 171.3 213.8 215.3 216.7 218.0 219.4 260.4 262.5 264.6 266.6 268.5 198.8 200.5 202.0 203.6 205.1 500 550 600 650 700 212.8 215.7 218.3 220.8 223.1 234.9 239.2 243.3 247.1 250.8 125.5 127.5 129.3 131.0 132.5 199.1 201.8 204.4 206.8 209.0 145.7 148.6 151.1 153.4 155.6 164.0 166.0 167.8 169.4 171.0 226.3 229.1 231.9 234.4 236.8 260.6 264.7 268.8 272.6 276.0 206.7 209.4 212.2 214.6 216.9 241.8 246.2 250.4 254.3 258.0 172.2 174.2 176.1 177.7 179.3 220.7 223.7 226.5 229.1 231.5 270.5 274.9 279.2 283.1 286.9 206.5 210.5 213.1 215.9 218.7 750 800 850 900 950 225.2 227.3 229.2 231.1 232.8 255.4 257.5 260.6 263.6 266.5 133.9 135.2 136.4 137.7 138.8 211.1 213.0 214.8 216.5 218.1 157.6 159.5 161.4 163.1 164.7 172.5 173.8 175.1 176.3 177.4 239.0 241.1 243.0 245.0 246.8 279.3 282.5 285.5 288.4 291.3 219.0 221.0 223.0 224.8 226.5 261.5 264.8 268.0 271.1 274.0 180.7 182.1 183.4 184.6 185.7 233.7 235.9 237.9 239.9 241.8 290.4 293.8 297.0 300.1 303.0 221.3 223.8 226.2 228.5 230.6 1000 1100 1200 1300 1400 234.5 237.7 240.7 243.4 246.0 269.3 274.5 279.4 283.9 288.2 139.9 141.9 143.7 145.3 146.9 219.7 222.7 225.4 228.0 230.3 166.2 169.1 171.8 174.3 176.6 178.5 180.4 182.2 183.9 185.4 248.4 251.8 254.8 257.6 260.2 293.9 298.9 303.6 307.9 311.9 228.2 231.3 234.2 236.9 239.5 276.8 282.1 287.0 291.5 295.8 186.8 188.8 190.6 192.3 193.8 243.6 246.9 250.0 252.9 255.6 305.8 311.0 315.8 320.3 324.5 232.7 236.7 240.5 244.0 247.4 1500 1600 1700 1800 1900 248.4 250.7 252.9 254.9 256.8 292.2 296.0 299.6 303.0 306.2 148.3 149.6 150.9 152.1 153.2 232.6 234.7 236.8 238.7 240.6 178.8 180.9 182.9 184.8 186.7 186.9 188.2 189.5 190.7 191.8 262.7 265.0 267.2 269.3 271.3 315.7 319.3 322.7 325.9 328.9 241.9 244.1 246.3 248.3 250.2 299.8 303.6 307.2 310.6 313.8 195.3 196.6 197.9 199.1 200.2 258.1 260.4 262.7 264.8 266.8 328.4 332.1 335.6 338.9 342.0 250.6 253.7 256.6 259.5 262.2 2000 2100 2200 2300 2400 258.7 260.5 262.2 263.8 265.4 309.3 312.2 315.1 317.8 320.4 154.3 155.3 156.3 157.2 158.1 242.3 244.0 245.7 247.2 248.7 188.4 190.1 191.7 193.3 194.8 192.9 193.9 194.8 195.8 196.7 273.1 274.9 276.6 278.3 279.8 331.8 334.5 337.2 339.7 342.1 252.1 253.8 255.5 257.1 258.7 316.9 319.8 322.6 325.3 327.9 201.3 202.3 203.2 204.2 205.0 268.7 270.6 272.4 274.1 275.7 345.0 347.9 350.6 353.2 355.7 264.8 267.3 269.7 272.0 274.3 2500 2600 2700 2800 2900 266.9 268.3 269.7 271.0 272.3 322.9 325.3 327.6 329.9 332.1 158.9 159.7 160.5 161.3 162.0 250.2 251.6 253.0 254.3 255.6 196.2 197.7 199.0 200.3 201.6 197.5 198.3 199.1 199.9 200.6 281.4 282.8 284.2 285.6 286.9 344.5 346.7 348.9 350.9 352.9 260.2 261.6 263.0 264.3 265.6 330.4 332.7 335.0 337.3 339.4 205.9 206.7 207.5 208.3 209.0 277.3 278.8 280.3 281.7 283.1 358.1 360.4 362.6 364.8 366.9 276.5 278.6 380.7 282.7 284.6 3000 3500 4000 4500 5000 273.6 279.4 284.4 288.8 292.8 334.2 343.8 352.2 359.7 366.4 162.7 165.9 168.7 171.1 173.3 256.8 262.5 267.6 272.1 276.1 202.9 208.7 213.8 218.5 222.8 201.3 204.6 207.4 210.1 212.5 288.2 294.0 299.0 303.5 307.5 354.9 363.8 371.5 378.3 384.4 266.9 272.6 277.6 282.1 286.0 341.5 350.9 359.2 366.5 373.0 209.7 212.9 215.8 218.3 220.6 284.4 290.7 296.2 301.1 305.5 368.9 378.1 386.1 393.3 399.7 286.5 295.2 302.9 309.8 316.0 Usually rounded off from JANAF Thermochemical Tables, NSRDS-NBS-37, 1971 (1141 pp.). Equilibrium constants can be calculated by combining Δhf° values from Table 2-95, hT - h298 from Table 2-96, and s° values from the above, using the formula ln kp = -ΔG/(RT), where ΔG = Δhf° + (hT - h298) - T s°. 2-176 PHYSICAL AnD CHEMICAL DATA HEATS OF SOLUTIOn TABLE 2-98 Heats of Solution of Inorganic Compounds in Water Heat evolved, in kilocalories per gram formula weight, on solution in water at 18°C. Computed from data in Bichowsky and Rossini, Thermochemistry of Chemical Substances, Reinhold, New York, 1936. Substance Dilution* Formula Heat, kcal/mol Aluminum bromide chloride aq 600 600 aq aq aq aq aq aq aq aq ∞ aq 600 aq ∞ aq ∞ 800 aq aq aq aq aq AlBr3 AlCl3 AlCl3⋅6H2O AlF3 AlF3⋅½H2O AlF3⋅3½H2O AlI3 Al2(SO4)3 Al2(SO4)3⋅6H2O Al2(SO4)3⋅18H2O NH4Br NH4Cl (NH4)2CrO4 (NH4)2Cr2O7 NH4I NH4NO3 NH4BO3⋅H2O (NH4)2SO4 NH4HSO4 (NH4)2SO3 (NH4)2SO3⋅H2O SbF3 SbI3 H3AsO4 +85.3 +77.9 +13.2 +31 +19.0 -1.7 +89.0 +126 +56.2 +6.7 -4.45 -3.82 -5.82 -12.9 -3.56 -6.47 -9.0 -2.75 +0.56 -1.2 -4.13 -1.7 -0.8 -0.4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq aq aq aq aq aq aq Ba(BrO3)2⋅H2O BaBr2 BaBr2⋅H2O BaBr2⋅2H2O Ba(ClO3)2 Ba(ClO3)2⋅H2O BaCl2 BaCl2⋅H2O BaCl2.2H2O Ba(CN)2 Ba(CN)2⋅H2O Ba(CN)2⋅2H2O Ba(IO3)2 Ba(IO3)2⋅H2O BaI2 BaI2⋅H2O BaI2⋅2H2O BaI2⋅2½H2O BaI2⋅7H2O Ba(NO3)2 Ba(ClO4)2 Ba(ClO4)2⋅3H2O BaS BeBr2 BeCl2 BeI2 BeSO4 BeSO4⋅H2O BeSO4⋅2H2O BeSO4⋅4H2O BiI3 H3BO3 -15.9 +5.3 -0.8 -3.87 -6.7 -10.6 +2.4 -2.17 -4.5 +1.5 -2.4 -4.9 -9.1 -11.3 +10.5 +2.7 +0.14 -0.58 -6.61 -10.2 -2.8 -10.5 +7.2 +62.6 +51.1 +72.6 +18.1 +13.5 +7.9 +1.1 +3 -5.4 400 400 400 400 400 400 400 400 400 400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ CdBr2 CdBr2⋅4H2O CdCl2 CdCl2⋅H2O CdCl2⋅2½H2O Cd(NO3)2⋅H2O Cd(NO3)2⋅4H2O CdSO4 CdSO4⋅H2O CdSO4⋅2⅔H2O Ca(C2H3O2)2 Ca(C2H3O2)2⋅H2O CaBr2 CaBr2⋅6H2O CaCl2 CaCl2⋅H2O CaCl2⋅2H2O CaCl2⋅4H2O CaCl2⋅6H2O +0.4 -7.3 +3.1 +0.6 -3.00 +4.17 -5.08 +10.69 +6.05 +2.51 +7.6 +6.5 +24.86 -0.9 +4.9 +12.3 +12.5 +2.4 -4.11 fluoride iodide sulfate Ammonium bromide chloride chromate dichromate iodide nitrate perborate sulfate sulfate, acid sulfite Antimony fluoride iodide Arsenic acid Barium bromate bromide chlorate chloride cyanide iodate iodide nitrate perchlorate sulfide Beryllium bromide chloride iodide sulfate Bismuth iodide Boric acid Cadmium bromide chloride nitrate sulfate Calcium acetate bromide chloride Substance Calcium—(Cont.) formate iodide Dilution* Formula Heat, kcal/mol 400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq ∞ ∞ ∞ aq +0.7 +28.0 +1.8 +4.1 +0.7 -3.2 -4.2 -7.99 -0.6 -1 +5.1 +3.6 -0.18 +18.6 +5.3 +2.0 +5.7 +18.4 -1.25 +18.5 +9.8 -2.9 +18.8 +15.0 -1.4 -3.6 +2.4 +0.5 +10.3 -2.6 -10.7 +15.9 +9.3 +3.65 -2.85 +11.6 Cuprous sulfate aq Ca(CHO2)2 CaI2 CaI2⋅8H2O Ca(NO3)2 Ca(NO3)2⋅H2O Ca(NO3)2⋅2H2O Ca(NO3)2⋅3H2O Ca(NO3)2⋅4H2O Ca(H2PO4)2⋅H2O CaHPO4⋅2H2O CaSO4 CaSO4⋅½H2O CaSO4⋅2H2O CrCl2 CrCl2⋅3H2O CrCl2⋅4H2O CrI2 CoBr2 CoBr2⋅6H2O CoCl2 CoCl2⋅2H2O CoCl2⋅6H2O CoI2 CoSO4 CoSO4⋅6H2O CoSO4⋅7H2O Cu(C2H3O2)2 Cu(CHO2)2 Cu(NO3)2 Cu(NO3)2⋅3H2O Cu(NO3)2⋅6H2O CuSO4 CuSO4⋅H2O CuSO4⋅3H2O CuSO4⋅5H2O Cu2SO4 Ferric chloride 1000 1000 1000 800 aq 400 400 400 aq 400 400 400 400 FeCl3 FeCl3⋅2½H2O FeCl3⋅6H2O Fe(NO3)3⋅9H2O FeBr2 FeCl2 FeCl2⋅2H2O FeCl2⋅4H2O FeI2 FeSO4 FeSO4⋅H2O FeSO4⋅4H2O FeSO4⋅7H2O +31.7 +21.0 +5.6 -9.1 +18.0 +17.9 +8.7 +2.7 +23.3 +14.7 +7.35 +1.4 -4.4 400 400 aq aq aq 400 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ Pb(C2H3O2)2 Pb(C2H3O2)2⋅3H2O PbBr2 PbCl2 Pb(CHO2)2 Pb(NO3)2 LiBr LiBr⋅H2O LiBr⋅2H2O LiBr⋅3H2O LiCl LiCl⋅H2O LiCl⋅2H2O LiCl⋅3H2O LiF LiOH LiOH⋅⅛H2O LiOH⋅H2O LiI LiI⋅½H2O LiI⋅H2O LiI⋅2H2O LiI⋅3H2O LiNO3 LiNO3⋅3H2O +1.4 -5.9 -10.1 -3.4 -6.9 -7.61 +11.54 +5.30 +2.05 -1.59 +8.66 +4.45 +1.07 -1.98 -0.74 +4.74 +4.39 +9.6 +14.92 +10.08 +6.93 +3.43 -0.17 +0.466 -7.87 nitrate phosphate, monodibasic sulfate Chromous chloride iodide Cobaltous bromide chloride iodide sulfate Cupric acetate formate nitrate sulfate nitrate Ferrous bromide chloride iodide sulfate Lead acetate bromide chloride formate nitrate Lithium bromide chloride fluoride hydroxide iodide nitrate aq aq aq 400 400 400 aq 400 400 400 aq aq 200 200 200 800 *The numbers represent moles of water used to dissolve 1 g formula weight of substance; ∞ means “infinite dilution”; and aq means “aqueous solution of unspecified dilution.” HEATS OF SOLUTIOn 2-177 TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued ) Dilution* Substance Lithium—(Cont.) sulfate Magnesium bromide chloride iodide nitrate phosphate sulfate sulfide Manganic nitrate sulfate Manganous acetate bromide chloride formate iodide sulfate Mercuric acetate bromide chloride nitrate Mercurous nitrate Nickel bromide Nickel chloride iodide nitrate sulfate Phosphoric acid, orthopyroPotassium acetate aluminum sulfate Formula Heat, kcal/mol +6.71 +3.77 ∞ ∞ Li2SO4 Li2SO4⋅H2O ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq ∞ ∞ ∞ ∞ ∞ ∞ aq 400 400 400 aq aq aq aq aq aq 400 400 400 aq aq aq aq aq aq aq 400 400 400 aq aq aq aq aq MgBr2 MgBr2⋅H2O MgBr2⋅6H2O MgCl2 MgCl2⋅2H2O MgCl2⋅4H2O MgCl2⋅6H2O MgI2 Mg(NO3)2⋅6H2O Mg3(PO4)2 MgSO4 MgSO4⋅H2O MgSO4⋅2H2O MgSO4⋅4H2O MgSO4⋅6H2O MgSO4⋅7H2O MgS Mn(NO3)2 Mn(NO3)2⋅3H2O Mn(NO3)2⋅6H2O Mn2(SO4)3 Mn(C2H3O2)2 Mn(C2H3O2)2⋅4H2O MnBr2 MnBr2⋅H2O MnBr2⋅4H2O MnCl2 MnCl2⋅2H2O MnCl2⋅4H2O Mn(CHO2)2 Mn(CHO2)2⋅2H2O MnI2 MnI2⋅H2O MnI2⋅2H2O MnI2⋅4H2O MnI2⋅6H2O MnSO4 MnSO4⋅H2O MnSO4⋅7H2O Hg(C2H3O2)2 HgBr2 HgCl2 Hg(NO3)2⋅½H2O Hg2(NO3)2⋅2H2O +43.7 +35.9 +19.8 +36.3 +20.8 +10.5 +3.4 +50.2 -3.7 +10.2 +21.1 +14.0 +11.7 +4.9 +0.55 -3.18 +25.8 +12.9 -3.9 -6.2 +22 +12.2 +1.6 +15 +14.4 +16.1 +16.0 +8.2 +1.5 +4.3 -2.9 +26.2 +24.1 +22.7 +19.9 +21.2 +13.8 +11.9 -1.7 -4.0 -2.4 -3.3 -0.7 -11.5 aq aq 800 800 800 800 aq 200 200 200 200 400 400 aq aq ∞ 600 600 NiBr2 NiBr2⋅3H2O NiCl2 NiCl2⋅2H2O NiCl2⋅4H2O NiCl2⋅6H2O NiI2 Ni(NO3)2 Ni(NO3)2⋅6H2O NiSO4 NiSO4⋅7H2O H3PO4 H3PO4⋅½H2O H4P2O7 H4P2O7⋅1½H2O KC2H3O2 KAl(SO4)2 KAl(SO4)2⋅3H2O KAl(SO4)2⋅12H2O KHCO3 KBrO3 KBr K2CO3 K2CO3⋅½H2O K2CO3⋅1½H2O KClO3 KCl K2CrO4 KCr(SO4)2 KCr(SO4)2⋅H2O KCr(SO4)2⋅2H2O KCr(SO4)2⋅6H2O KCr(SO4)2⋅12H2O +19.0 +0.2 +19.23 +10.4 +4.2 -1.15 +19.4 +11.8 -7.5 +15.1 -4.2 +2.79 -0.1 +25.9 +4.65 +3.55 +48.5 +26.6 -10.1 -5.1 -10.13 -5.13 +6.58 +4.25 -0.43 -10.31 -4.404 -4.9 +55 +42 +33 +7 -9.5 bicarbonate bromate bromide carbonate 2000 ∞ ∞ ∞ chlorate chloride chromate chrome sulfate ∞ ∞ 2185 600 Substance Potassium—(Cont.) cyanide dichromate fluoride hydrosulfide hydroxide iodate iodide nitrate oxalate perchlorate permanganate phosphate, dihydrogen pyrosulfite sulfate sulfate, acid sulfide sulfite thiocyanate thionate, dithiosulfate Silver acetate nitrate Sodium acetate arsenate bicarbonate borate, tetrabromide carbonate chlorate chloride chromate cyanide fluoride hydrosulfide Sodium hydroxide iodide metaphosphate nitrate nitrite perchlorate phosphate di triphosphate di diphosphite, monodipyrophosphate di- Dilution* Formula Heat, kcal/mol ∞ 400 aq aq aq ∞ 800 ∞ aq aq ∞ aq ∞ KCN K2Cr2O7 KF KF⋅2H2O KF⋅4H2O KHS KHS⋅¼H2O KOH KOH⋅¾H2O KOH⋅H2O KOH⋅7H2O KIO3 KI KNO3 K2C2O4 K2C2O4⋅H2O KClO4 KMnO4 KH2PO4 K2S2O5 K2S2O5⋅½H2O K2SO4 KHSO4 K2S K2SO3 K2SO3⋅H2O KCNS K2S2O6 K2S2O3 -3.0 -17.8 +3.96 -1.85 -6.05 +0.86 +1.21 +12.91 +4.27 +3.48 +0.86 -6.93 -5.23 -8.633 -4.6 -7.5 -12.94 -10.4 +4.7 -11.0 -10.22 -6.32 -3.10 -11.0 +1.8 +1.37 -6.08 -13.0 -4.5 aq 200 ∞ ∞ 500 500 1800 900 900 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 800 800 800 200 200 200 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 600 ∞ aq ∞ 1600 1600 1600 1600 1600 1600 600 600 800 800 1600 1600 1200 1200 AgC2H3O2 AgNO3 NaC2H3O2 NaC2H3O2⋅3H2O Na3AsO4 Na3AsO4⋅12H2O NaHCO3 Na2B4O7 Na2B4O7⋅10H2O NaBr NaBr⋅2H2O Na2CO3 Na2CO3⋅H2O Na2CO3⋅7H2O Na2CO3⋅10H2O NaClO3 NaCl Na2CrO4 Na2CrO4⋅4H2O Na2CrO4⋅10H2O NaCN NaCN⋅½H2O NaCN⋅2H2O NaF NaHS NaHS⋅2H2O NaOH NaOH⋅½H2O NaOH⋅⅔H2O NaOH⋅¾H2O NaOH⋅H2O NaI NaI⋅2H2O NaPO3 NaNO3 NaNO2 NaClO4 Na2HPO4 Na3PO4 Na3PO4⋅12H2O Na2HPO4⋅2H2O Na2HPO4⋅7H2O Na2HPO4⋅12H2O NaH2PO3 NaH2PO3⋅2½H2O Na2HPO3 Na2HPO3⋅5H2O Na4P2O7 Na4P2O7⋅10H2O Na2H2P2O7 Na2H2P2O7⋅6H2O -5.4 -4.4 +4.085 -4.665 +15.6 -12.61 -4.1 +10.0 -16.8 -0.58 -4.57 +5.57 +2.19 -10.81 -16.22 -5.37 -1.164 +2.50 -7.52 -16.0 -0.37 -0.92 -4.41 -0.27 +4.62 -1.49 +10.18 +8.17 +7.08 +6.48 +5.17 +1.57 -3.89 +3.97 -5.05 -3.6 -4.15 +5.21 +13 -15.3 -0.82 -12.04 -23.18 +0.90 -5.29 +9.30 -4.54 +11.9 -11.7 -2.2 -14.0 200 1600 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 400 (Continued) 2-178 PHYSICAL AnD CHEMICAL DATA TABLE 2-98 Heats of Solution of Inorganic Compounds in Water (Continued ) Substance Sodium—(Cont.) sulfate sulfate, acid sulfide sulfite thiocyanate thionate, diSodium thiosulfate Stannic bromide Stannous bromide iodide Strontium acetate bromide Dilution* Formula Heat, kcal/mol ∞ ∞ 800 800 ∞ ∞ ∞ ∞ ∞ ∞ ∞ aq aq aq aq aq aq aq ∞ ∞ ∞ ∞ ∞ ∞ ∞ Na2SO4 Na2SO4⋅10H2O NaHSO4 NaHSO4⋅H2O Na2S Na2S⋅4½H2O Na2S⋅5H2O Na2S⋅9H2O Na2SO3 Na2SO3⋅7H2O NaCNS Na2S2O6 Na2S2O6⋅2H2O Na2S2O3 Na2S2O3⋅5H2O SnBr4 SnBr2 SnI2 Sr(C2H3O2)2 Sr(C2H3O2)2⋅½H2O SrBr2 SrBr2⋅H2O SrBr2⋅2H2O SrBr2⋅4H2O SrBr2⋅6H2O +0.28 -18.74 +1.74 +0.15 +15.2 +0.09 -6.54 -16.65 +2.8 -11.1 -1.83 -5.80 -11.86 +2.0 -11.30 +15.5 -1.6 -5.8 +6.2 +5.9 +16.4 +9.25 +6.5 +0.4 -6.1 Substance Dilution* Strontium—(Cont.) chloride iodide nitrate sulfate Sulfuric acid, pyroZinc acetate bromide chloride iodide nitrate sulfate Formula ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ SrCl2 SrCl2⋅H2O SrCl2⋅2H2O SrCl2⋅6H2O SrI2 SrI2⋅H2O SrI2⋅2H2O SrI2⋅6H2O Sr(NO3)2 Sr(NO3)2⋅4H2O SrSO4 H2S2O7 +11.54 +6.4 +2.95 -7.1 +20.7 +12.65 +10.4 -4.5 -4.8 -12.4 +0.5 -18.08 400 400 400 400 400 aq 400 400 400 400 400 400 Zn(C2H3O2)2 Zn(C2H3O2)2⋅H2O Zn(C2H3O2)2⋅2H2O ZnBr2 ZnCl2 ZnI2 Zn(NO3)2⋅3H2O Zn(NO3)2⋅6H2O ZnSO4 ZnSO4⋅H2O ZnSO4⋅6H2O ZnSO4⋅7H2O +9.8 +7.0 +3.9 +15.0 +15.72 +11.6 -5 -6.0 +18.5 +10.0 -0.8 -4.3 note: To convert kilocalories per mole to British thermal units per pound-mole, multiply by 1.799 × 10-3. TABLE 2-99 Heats of Solution of Organic Compounds in Water (at Infinite Dilution and Approximately Room Temperature) Recalculated and rearranged from International Critical Tables, vol. 5, pp. 148–150. cal/mol = Btu/(lb⋅mol) × 1.799. Solute Acetic acid (solid), C2H4O2 Acetylacetone, C5H8O2 Acetylurea, C3H6N2O2 Aconitic acid, C6H6O6 Ammonium benzoate, C7H9NO2 picrate succinate (n-) Aniline, hydrochloride, C6H8ClN Barium picrate Benzoic acid, C7H6O2 Camphoric acid, C10H16O4 Citric acid, C6H8O7 Dextrin, C12H20O10 Fumaric acid, C4H4O4 Hexamethylenetetramine, C6H12N4 Hydroxybenzamide (m-), C7H7NO2 (m-), (HCl) (o-), C7H7NO2 (p-) Hydroxybenzoic acid (o-), C7H6O3 (p-), C7H6O3 Hydroxybenzyl alcohol (o-), C7H8O2 Inulin, C36H62O31 Isosuccinic acid, C4H6O4 Itaconic acid, C5H6O4 Lactose, C12H22O11⋅H2O Lead picrate (2H2O) Magnesium picrate (8H2O) Maleic acid, C4H4O4 Malic acid, C4H6O5 Malonic acid, C3H4O4 Mandelic acid, C8H2O3 Mannitol, C6H14O6 Menthol, C10H20O Nicotine dihydrochloride, C10H16Cl2N2 Nitrobenzoic acid (m-), C7H5NO4 (o-), C7H5NO4 (p-), C7H5NO4 Nitrophenol (m-), C6H5NO3 (o-), C6H5NO3 (p-), C6H5NO3 Heat of solution, cal/mol solute* -2,251 -641 -6,812 -4,206 -2,700 -8,700 -3,489 -2,732 -4,708 -6,501 -502 -5,401 268 -5,903 4,780 -4,161 -7,003 -4,340 -5,392 -6,350 -5,781 -3,203 -96 -3,420 -5,922 -3,705 -7,098 -13,193 14,699 -15,894 -4,441 -3,150 -4,493 -3,090 -5,260 0 6,561 -5,593 -5,306 -8,891 -5,210 -6,310 -4,493 Solute Oxalic acid, C2H2O4 (2H2O) Phenol (solid), C6H6O Phthalic acid, C8H6O4 Picric acid, C6H3N3O7 Piperic acid, C12H10O4 Piperonylic acid, C8H6O4 Potassium benzoate citrate tartrate (n-) (0.5 H2O) Pyrogallol, C6H6O3 Pyrotartaric acid Quinone Raffinose, C18H32O16 (5H2O) Resorcinol, C6H6O2 Silver malonate (n-) Sodium citrate (tri-) picrate potassium tartrate (4H2O) succinate (n-) (6H2O) tartrate (n-) (2H2O) Strontium picrate (6H2O) Succinic acid, C4H6O4 Succinimide, C4H5NO2 Sucrose, C12H22O11 Tartaric acid (d-) Thiourea, CH4N2S Urea, CH4N2O acetate formate nitrate oxalate Vanillic acid Vanillin Zinc picrate (8H2O) Heat, kcal/mol Heat of solution, cal/mol solute* -2,290 -8,485 -2,605 -4,871 -7,098 -10,492 -9,106 -1,506 2,820 -5,562 -3,705 -5,019 -3,991 -9,703 -3,960 -9,799 5,270 -6,441 -1,817 -12,342 2,390 -10,994 -1,121 -5,882 7,887 -14,412 -6,405 -4,302 -1,319 -3,451 -5,330 -3,609 -8,795 -7,194 -10,803 -17,806 -5,160 -5,210 -11,496 -15,894 *+ denotes heat evolved, and - denotes heat absorbed. The data in the International Critical Tables were calculated by E. Anderson. THERMAL EXPAnSIOn AnD COMPRESSIBILITY 2-179 THERMAL EXPAnSIOn AnD COMPRESSIBILITY Unit Conversion For this subsection, the following unit conversion is applicable: °F = 9⁄5°C + 32. Additional References Some of the tables given under this subject are reprinted by permission from the Smithsonian Tables. For other data on thermal expansion, see International Critical Tables. The tabular index is in volume 3, and the data are in volume 2. Thermal Expansion of Gases No tables of coefficients of thermal expansion of gases are given in this edition. The coefficient at constant pressure, 1/u (∂u/∂T)p, for an ideal gas is merely the reciprocal of the absolute temperature. For a real gas or liquid, both it and the coefficient at constant volume 1/p (∂p/∂T)v should be calculated either from the equation of state or from tabulated PVT data. For expansion of liquids and solids, see the following tables. TABLE 2-100 Linear Expansion of the Solid Elements* C is the true expansion coefficient at the given temperature; M is the mean coefficient between given temperatures; where one temperature is given, the true coefficient at that temperature is indicated; α and β are coefficients in formula lt = l0(1 + αt + βt2); l0 is length at 0°C (unless otherwise indicated, when, if x is the reference temperature, lt = lx[1 + α(t - tx) + β(t - tx)2]; lt is length at t °C). Element Temp., °C C × 104 Aluminum Aluminum Antimony Arsenic Bismuth Cadmium Cadmium Carbon, diamond graphite Chromium Cobalt Copper Copper Gold Gold Indium Iodine Iridium Iridium Iron, soft cast wrought steel Lead (99.9) 20 300 20 20 20 0 0 50 50 0.224 0.284 0.136∙ 0.05 0.014∙ 0.54∙ 0.20⊥ 0.012 0.06 20 20 200 20 0.123 0.162 0.170 0.140 40 0.417 20 0.065 40 20 20 20 0.1210 0.118 0.119 0.114 100 280 20 0.291 0.343 0.254 20 0.233 Molybdenum 20 0.053 Nickel 20 0.126 Osmium Palladium 40 20 0.066 0.1173 Platinum 20 20 0.0887 0.0893 40 40 0 40 20 20 0.0850 0.0963 0.439 0.0763 0.1846 0.195 Magnesium Manganese † Potassium Rhodium Ruthenium Selenium Silicon Silver Sodium Steel, 36.4Ni Tantalum† 20 0.065 Tellurium Thallium Tin 20 40 20 20 27 20‡ 20‡ 20 0.016∙ 0.302 0.214 0.305∙ 0.0444 0.643∙ 0.125⊥ 0.358 † Tungsten Zinc Temp. range, °C M × 104 100 500 20 0.235 0.311 0.080⊥ 20 -180, -140 -180, -140 0.103⊥ 0.59∙ 0.117⊥ 20, 100 0.068 17, -191, 100 300 100 17 0.166 0.175 0.143 0.132 -190, 17 0.837 α × 104 β × 106 0, 500 0.22 0.009 20, 20, 100 100 0.526∙ 0.214⊥ 20, 6, 0, 500 121 625 0.086 0.121 0.161 0.0064 0.0040 0, 520 0.142 0.0022 0.0636 0.0679 0.0032 0.0011 Temp. range, °C 0, 80 1070, 1720 0, 20, 20, 100 0.11 100 200 0.291 0.300 -100, + 20 20, 100 0, 100 -190, 0 0, 100 25, 100 25, 500 0, 100 0.240 0.260 0.228 0.159 0.052 0.049 0.055 0.130 0, 6, 50 21 0.83 0.0876 0, 100 -3, +18 0, 100 0.660 0.0249 0.197 -190, -17 20, 260 20, 340 -78, 0 0, 100 20 0.622 0.031 0.055 0.059 0.0655 0.272⊥ 20 100 -100 100 100 0.154⊥ 0.045 0.656∙ 0.639∙ 0.141⊥ 0, -140, +20, +20, 0, 0, 0, 100, 750 750 750 240 0.1158 0.1170 0.1118 0.269 0.0053 0.0053 0.0053 0.011 + 20, 500 0.2480 0.0096 20, 300 -142, 19 19, +305 0.216 0.0515 0.0501 0.0121 0.0057 0.0014 -190, + 20 + 20, +300 500, 1000 0.1308 0.1236 0.1346 0.0166 0.0066 0.0033 -190, 0, -190, 0, 0, +100 1000 -100 + 80 1000 0.1152 0.1167 0.0875 0.0890 0.0887 0.00517 0.0022 0.00314 0.00121 0.00132 -75, -112 0.0746 -75, 0, 20, 0, 260, 340, 20, -67 875 500 50 500 500 400 0.0182 0.1827 0.1939 0.72 0.144 0.136 0.0646 0.0009 8, 95 0.2033 0.0263 -105, +502 + 0, 400 0.0428 0.354 0.00058 0.010 0.00479 0.00295 *Smithsonian Tables. For more complete tabulations see Table 142, Smithsonian Physical Tables, 9th ed., 1954; Handbook of Chemistry and Physics, 40th ed., pp. 2239–2245. Chemical Rubber Publishing Co.; Goldsmith, and Waterman, WADC-TR-58-476, 1959; Johnson (ed.), WADD-TR-60-56, 1960, etc. † Molybdenum, 300 to 2500°C; lt = l300[1 + 5.00 × 10-6(t - 300) + 10.5 × 10-10(t - 300)2] Tantalum, 300 to 2800°C; lt = l300[1 + 6.60 × 10-6(t - 300) + 5.2 × 10-10(t - 300)2] Tungsten, 300 to 2700°C; lt = l300[1 + 4.44 × 10-6(t - 300) + 4.5 × 10-10(t - 300)2] Beryllium, 20 to 100°C; 12.3 × 10-6 per °C. Columbium, 0 to 100°C; 7.2 × 10-6 per °C. Tantalum, 20 to 100°C; 6.6 × 10-6 per °C. ‡ These values for zinc were taken from Grüneisen and Goens, Z. Physik., 29:141 (1924). 2-180 PHYSICAL AnD CHEMICAL DATA TABLE 2-101 Linear Expansion of Miscellaneous Substances* The coefficient of cubical expansion may be taken as three times the linear coefficient. In the following table, t is the temperature or range of temperature, and C, the coefficient of expansion. t, °C Substance Amber Bakelite, bleached Brass: Cast Wire Wire 71.5 Cu + 27.7 Zn + 0.3 Sn + 0.5 Pb 71 Cu + 29 Zn Bronze: 3 Cu + 1 Sn 3 Cu + 1 Sn 3 Cu + 1 Sn 86.3 Cu + 9.7 Sn + 4 Zn 97.6 Cu + hard 2.2 Sn + soft 0.2 P Caoutchouc Caoutchouc Celluloid Constantan Duralumin, 94Al { 0–30 0–09 20–60 C × 104 0.50 0.61 0.22 0–100 0–100 0–100 0.1875 0.1930 0.1783–0.193 40 0–100 0.1859 0.1906 16.6–100 16.6–350 16.6–957 40 0–80 0–80 0.1844 0.2116 0.1737 0.1782 0.1713 0.1708 16.7–25.3 20–70 4–29 20–100 20–300 25.3–35.4 0–100 0–100 0–100 0–100 0.657–0.686 0.770 1.00 0.1523 0.23 0.25 0.842 0.1950 0.1836 0.1523 0.1552 Substance Jena thermometer 59III Jena thermometer 59III Gutta percha Ice Iceland spar: Parallel to axis Perpendicular to axis Lead tin (solder) 2 Pb + 1 Sn Limestone Magnalium Manganin Marble Monel metal Paraffin Paraffin Paraffin Platinum-iridium, 10 Pt + 1 Ir Platinum-silver, 1 Pt + 2 Ag Porcelain Porcelain Bayeux Quartz: Parallel to axis Parallel to axis Perpend. to axis Quartz glass Quartz glass Quartz glass Rock salt Rubber, hard Rubber, hard Speculum metal Steel, 0.14 C, 34.5 Ni t, °C 0–100 −191–+16 20 −20–−1 C × 104 Substance 0.058 0.424 1.983 0.51 Topas: Parallel to lesser horizontal axis Parallel to greater horizontal axis Parallel to vertical axis Tourmaline: Parallel to longitudinal axis Parallel to horizontal axis Type metal Vulcanite Wedgwood ware Wood: Parallel to fiber: Ash Beech Chestnut Elm Mahogany Maple Oak Pine Walnut Across the fiber: Beech Chestnut Elm Mahogany Maple Oak Pine Walnut Wax white Wax white Wax white Wax white 0–80 0–80 0.2631 0.0544 0–100 25–100 12–39 15–100 25–100 25–600 0–16 16–38 38–49 0.2508 0.09 0.238 0.181 0.117 0.14 0.16 1.0662 1.3030 4.7707 40 0.0884 0–100 20–790 1000–1400 0.1523 0.0413 0.0553 t, °C C × 104 0−100 0.0832 0−100 0−100 0.0836 0.0472 0−100 0.0937 0−100 16.6−254 0−18 0−100 0.0773 0.1952 0.6360 0.0890 0−100 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 0.0951 0.0257 0.0649 0.0565 0.0361 0.0638 0.0492 0.0541 0.0658 Ebonite Fluorspar, CaF2 0–80 0.0797 German silver −190 to + 16 0.0521 2.34 0.614 Gold-platinum, 2 Au + 1 Pt 0–80 0.1337 2.34 0.325 Gold-copper, 2 Au + 1 Cu –190 to + 16 −0.0026 2.34 0.443 Glass: 16 to 500 0.0057 2.34 0.404 Tube 0–100 0.0833 16 to 1000 0.0058 2.34 0.484 Tube 0–100 0.0828 40 0.4040 2.34 0.544 Plate 0–100 0.0891 0 0.691 2.34 0.341 Crown (mean) 0–100 0.0897 –160 0.300 2.34 0.484 Crown (mean) 50–60 0.0954 0–100 0.1933 10−26 2.300 Flint 50–60 0.0788 25–100 0.037 26−31 3.120 III Jena ther- 16 0–100 0.081 25–600 0.136 31−43 4.860 mometer normal 43−57 15.227 *Smithsonian Tables. For a more complete tabulation see Tables 143, 144. Smithsonian Physical Tables. 9th ed., 1954, also reprinted in American Institute of Physics Handbook, McGraw-Hill, New York, 1957; Handbook of Chemistry and Physics, 40th ed., pp. 2239–2245, Chemical Rubber Publishing Co. For data on many solids prior to 1926, see Gruneisen, Handbuch der Physik, vol. 10, pp. 1–52, 1926, translation available as N.A.S.A. RE 2-18-59W, 1959. For eight plastic solids below 300 K, see Scott, Cryogenic Engineering, p. 331, Van Nostrand, Princeton, NJ, 1959. For 11 other materials to 300 K, see Scott, loc. cit., p. 333. For quartz and silica, see Cook, Brit. J. Appl. Phys., 7, 285 (1956). } THERMAL EXPAnSIOn AnD COMPRESSIBILITY TABLE 2-102 Volume Expansion of Liquids* TABLE 2-103 If V0 is the volume at 0°, then at t° the expansion formula is Vt = V0(1 + αt + βt2 + γ t3). The table gives values of α, β, and γ, and of C, the true coefficient of volume expansion at 20° for some liquids and solutions. The temperature range of the observation is ∆t. Values for the coefficient of volume expansion of liquids can be derived from the tables of specific volumes of the saturated liquid given as a function of temperature later in this section. C = (dV/dt)/V0 Liquid Range α × 103 β × 106 γ × 108 C × 103 at 20° Acetic acid 16−107 1.0630 0.12636 1.0876 1.071 Acetone 0−54 1.3240 3.8090 −0.87983 1.487 Alcohol: Amyl −15–80 0.9001 0.6573 1.18458 0.902 Ethyl, 30% by volume 18−39 0.2928 10.790 −11.87 Ethyl, 50% by volume 0−39 0.7450 1.85 0.730 Ethyl, 99.3% by volume 27−46 1.012 2.20 1.12 Ethyl, 500 atm pressure 0−40 0.866 Ethyl, 3000 atm pressure 0−40 0.524 Methyl 0−61 1.1342 1.3635 0.8741 1.199 Benzene 11−81 1.17626 1.27776 0.80648 1.237 Bromine 0−59 1.06218 1.87714 −0.30854 1.132 Calcium chloride: 5.8% solution 18−25 0.07878 4.2742 0.250 40.9% solution 17−24 0.42383 0.8571 0.458 Carbon disulfide −34–60 1.13980 1.37065 1.91225 1.218 500 atm pressure 0−50 0.940 3000 atm pressure 0−50 0.581 Carbon tetrachloride 0−76 1.18384 0.89881 1.35135 1.236 Chloroform 0−63 1.10715 4.66473 −1.74328 1.273 Ether −15–38 1.51324 2.35918 4.00512 1.656 Glycerin 0.4853 0.4895 0.505 Hydrochloric acid, 33.2% solution 0−33 0.4460 0.215 0.455 Mercury 0−100 0.18182 0.0078 0.18186 Olive oil 0.6821 1.1405 −0.539 0.721 Pentane 0−33 1.4646 3.09319 1.6084 1.608 Potassium chloride, 24.3% solution 16−25 0.2695 2.080 0.353 Phenol 36−157 0.8340 0.10732 0.4446 1.090 Petroleum, 0.8467 density 24−120 0.8994 1.396 0.955 Sodium chloride, 20.6% solution 0−29 0.3640 1.237 0.414 Sodium sulfate, 24% solution 11−40 0.3599 1.258 0.410 Sulfuric acid: 10.9% solution 0−30 0.2835 2.580 0.387 100.0% 0−30 0.5758 −0.432 0.558 Turpentine −9−106 0.9003 1.9595 −0.44998 0.973 Water 0−33 −0.06427 8.5053 −6.7900 0.207 *Smithsonian Tables, Table 269. For a detailed discussion of mercury data, see Cook, Brit. J. Appl. Phys., 7, 285 (1956). For data on nitrogen and argon, see Johnson (ed.), WADD-TR-60-56, 1960. Bromoform1 7.7 − 50°C. Vt = 0.34204[1 + 0.00090411(t − 7.7) + 0.0000006766(t − 7.7)2] 0.34204 is the specific volume of bromoform at 7.7°C. Glycerin2 −62 to 0°C. Vt = V0(1 + 4.83 × 10−4t − 0.49 × 10−6t2) 0 − 80°C. Vt = V0(1 + 4.83 × 10−4t + 0.49 × 10−6t2) 3 Mercury 0 − 300°C. Vt − V0[1 + 10−8(18,153.8t + 0.7548t2 + 0.001533t2 + 0.00000536t4)] 1 Sherman and Sherman, J. Am. Chem. Soc., 50, 1119 (1928). (An obvious error in their equation has been corrected.) 2 Samsoen, Ann. phys., (10) 9, 91 (1928). 3 Harlow, Phil. Mag., (7) 7, 674 (1929). 2-181 Volume Expansion of Solids* If v2 and v1 are the volumes at t2 and t1, respectively, then v2 = v1(1 + C∆t), C being the coefficient of cubical expansion and ∆t the temperature interval. Where only a single temperature is stated, C represents the true coefficient of volume expansion at that temperature. Substance t or ∆t C × 104 Antimony Beryl Bismuth Copper† Diamond Emerald Galena Glass, common tube hard Jena, borosilicate 59 III pure silica Gold Ice Iron Lead† Paraffin Platinum Porcelain, Berlin chloride nitrate sulfate Quartz Rock salt Rubber Silver Sodium Stearic acid Sulfur, native Tin Zinc† 0−100 0−100 0−100 0−100 40 40 0−100 0−100 0−100 20−100 0−80 0−100 −20 to −1 0−100 0−100 20 0−100 20 0−100 0−100 20 0−100 50−60 20 0−100 20 33.8−45.4 13.2−50.3 0−100 0−100 0.3167 0.0105 0.3948 0.4998 0.0354 0.0168 0.558 0.276 0.214 0.156 0.0129 0.4411 1.1250 0.3550 0.8399 5.88 0.265 0.0814 1.094 1.967 1.0754 0.3840 1.2120 4.87 0.5831 2.13 8.1 2.23 0.6889 0.8928 *Smithsonian Tables, Table 268. † See additional data below. Aluminum1 100 − 530°C. V = V0(1 + 2.16 × 10−5t + 0.95 × 10−8t2) 1 Cadmium 130 − 270°C. V = V0(1 + 8.04 × 10−5t + 5.9 × 10−8t2) 1 Copper 110 − 300°C. V = V0(1 + 1.62 × 10−5t + 0.20 × 10−8t2) Colophony2 0 − 34°C. V = V0(1 + 2.21 × 10−4t + 0.31 × 10−6t2) 34 − 150°C. V = V34[1 + 7.40 × 10−4(t − 34) + 5.91 × 10−6(t − 34)2] 1 Lead 100 − 280°C. V = V0(1 + 1.60 × 10−5t + 3.2 × 10−8t2) 2 Shellac 0 − 46°C. V = V0(1 + 2.73 × 10−4t + 0.39 × 10−6t2) 46 − 100°C. V = V46[1 + 13.10 × 10−4(t − 46) + 0.62 × 10−6(t − 46)2] Silica (vitreous)3 0 − 300°C. Vt = V0[1 + 10−8(93.6t + 0.7776t2 − 0.003315t2 + 0.000005244t4) Sugar (cane, amorphous)2 0 − 67°C. Vt = V0(1 + 2.34 × 10−4t + 0.14 × 10−6t2) 67 − 160°C. Vt = V67[1 + 5.02 × 10−4(t − 67) + 0.43 × 10−6(t − 67)2] Zinc1 120 − 360°C. Vt = V0(1 + 8.50 × 10−5t + 3.9 × 10−8t2) 1 2 3 Uffelmann, Phil. Mag., (7) 10, 633 (1930). Samsoen, Ann. phys., (10) 9, 83 (1928). Harlow, Phil. Mag., (7) 7, 674 (1929). 2-182 PHYSICAL AnD CHEMICAL DATA GAS EXPAnSIOn: JOULE-THOMSOn EFFECT Introduction The Joule-Thomson coefficient, (∂T/∂P)H , is the change in gas temperature with pressure during an adiabatic expansion (a throttling process, at constant enthalpy H). The temperature at which the Joule-Thomson coefficient changes sign is called the Joule-Thomson inversion temperature. Joule-Thomson coefficients for substances listed in Table 2-104 are given in tables in the Thermodynamic Properties section. Unit Conversions To convert the Joule-Thomson coefficient µ, in degrees Celsius per atmosphere to degrees Fahrenheit per atmosphere, multiply by 1.8. Temperature conversion: °F = 9⁄5°C + 32; °R = 9⁄5 K. To convert bars to pounds-force per square inch, multiply by 14.504; to convert bars to kilopascals, multiply by 100. TABLE 2-104 Additional References Available for the Joule-Thomson Coefficient Temp. range, °C Pressure range, atm Gas 0–10 10–50 50–200 12, 15, 19 35 15, 19, 35 Ammonia Argon Benzene Butane Carbon dioxide 12, 15, 16 19, 35 28 39 31 26 7, 8, 28 37 17 Air Carbon monoxide Deuterium Dowtherm A Ethane Ethylene Helium Hydrogen 46 45 1, 38 24, 30 39 31 26 7, 8, 37 17 22, 24, 25 1∗ 46 45 >200 <0 0–300 19, 35 12, 15, 16 19, 35 28 39 31 26 7, 8, 9, 10 37 17 39 31 39 7, 8, 37 7, 8, 37 1,∗ 22, 24 25 17 1,∗ 22, 24, 25 1, 38 22, 24, 25 30 6 38 24, 30 6 Methane Mixtures Natural gas Nitrogen 13, 28, 40 13, 40 33 13, 40 Nitrous oxide Pentane Propane Steam 26, 34, 44 41 28, 29, 42 34 43 29, 42, 47 42, 47 1, 38 22, 24, 25 30 33 13 34 33 13, 40 46 45 9, 10 38 24 6 9, 11 33 9, 10, 13 28, 40 9, 10 26, 34, 44 43 28, 29, 42 45 >300 Other references 3, 4, 18 2, 3 31 46 48 13 19 29, 42, 47 29, 47 ∗See also 14 (generalized chart); 18 (review, to 1919); 20–22; 23 (review, to 1948); 27 (review, to 1905); 32, 36, 41, 50. References: 1. Baehr. Z. Elektrochem., 60, 515 (1956). 2. Beattie, J. Math. Phys., 9, 11 (1930). 3. Beattie, Phys. Rev., 35, 643 (1930). 4. Bradley and Hale, Phys. Rev., 29, 258 (1909). 5. Brown and Dean, Bur. Stand. J. Res., 60, 161 (1958). 6. Budenholzer, Sage, et al., Ind. Eng. Chem., 29, 658 (1937). 7. Burnett, Phys. Rev., 22, 590 (1923). 8. Burnett, Univ. Wisconsin Bull. 9(6), 1926. 9. Charnley, Ph.D. thesis. University of Manchester, 1952. 10. Charnley, Isles, et al., Proc. R. Soc. (London), A217, 133 (1953). 11. Charnley, Rowlinson, et al., Proc. R. Soc. (London), A230, 354 (1955). 12. Dalton, Commun. Phys. Lab. Univ. Leiden, no. 109c, 1909. 13. Deming and Deming, Phys. Rev., 48, 448 (1935). 14. Edmister, Pet. Refiner, 28, 128 (1949). 15. Eucken, Clusius, et al., Z. Tech. Phys., 13, 267 (1932). 16. Eumorfopoulos and Rai, Phil. Mag., 7, 961 (1926). 17. Huang, Lin, et al., Z. Phys., 100, 594 (1936). 18. Hoxton, Phys. Rev., 13, 438 (1919). 19. Ishkin and Kaganev, J. Tech. Phys. U.S.S.R., 26, 2323 (1956). 20. Isles, Ph.D. thesis, Leeds University. 21. Jenkin and Pye, Phil. Trans. R. Soc. (London), A213, 67 (1914); A215, 353 (1915). 22. Johnston, J. Am. Chem. Soc., 68, 2362 (1946). 23. Johnston, Trans. Am. Soc. Mech. Eng., 70, 651 (1948). 24. Johnston, Bezman, et al., J. Am. Chem. Soc., 68, 2367 (1946). 25. Johnston, Swanson, et al., J. Am. Chem. Soc., 68, 2373 (1946). 26. Kennedy, Sage, et al., Ind. Eng. Chem., 28, 718 (1936). 27. Kester, Phys. Rev., 21, 260 (1905). 28. Keyes and Collins, Proc. Nat. Acad. Sci., 18, 328 (1932). 29. Kleinschmidt, Mech. Eng., 45, 165 (1923); 48, 155 (1926). 30. Koeppe, Kältetechnik, 8, 275 (1956). 31. Lindsay and Brown, Ind. Eng. Chem., 27, 817 (1935). 32. Noell, dissertation, Munich, 1914, Forschungsdienst, 184, p. 1, 1916. 33. Palienko, Tr. Inst. Ispol’ z. Gaza, Akad. Nauk Ukr. SSR, no. 4, p. 87, 1956. 34. Pattee and Brown, Ind. Eng. Chem., 26, 511, (1934). 35. Roebuck, Proc. Am. Acad. Arts Sci., 60, 537 (1925); 64, 287 (1930). 36. Roebuck, see 49 below, 37. Roebuck and Murrell, Phys. Rev., 55, 240 (1939). 38. Roebuck and Osterberg, Phys. Rev., 37, 110 (1931); 43, 60 (1933). 39. Roebuck and Osterberg, Phys. Rev., 46, 785 (1934). 40. Roebuck and Osterberg, Phys. Rev., 48, 450 (1935). 41. Roebuck, Murrell, et al., J. Am. Chem. Soc., 64, 400 (1942). 42. Sage, unpublished data, California Institute of Technology, 1959. 43. Sage and Lacy, Ind. Eng. Chem., 27, 1484 (1934). 44. Sage, Kennedy, et al., Ind. Eng. Chem., 28, 601 (1936). 45. Sage, Webster, et al., Ind. Eng. Chem., 29, 658 (1937). 46. Ullock, Gaffert, et al., Trans. Am. Inst. Chem. Eng., 32, 73 (1936). 47. Yang, Ind. Eng. Chem., 45, 786 (1953). 48. Zelmanov, J. Phys. U.S.S.R., 3, 43 (1940). 49. Roebuck, recalculated data. 50. Michels et al., van der Waals laboratory publications. Gunn, Cheuh, and Prausnitz, Cryogenics, 6, 324 (1966), review equations relating the inversion temperatures and pressures. The ability of various equations of state to relate these was also discussed by Miller, Ind. Eng. Chem. Fundam., 9, 585 (1970); and Juris and Wenzel, Am. Inst. Chem. Eng. J., 18, 684 (1972). Perhaps the most detailed review is that of Hendricks, Peller, and Baron. NASA Tech. Note D 6807, 1972. CRITICAL COnSTAnTS TABLE 2-105 Approximate Inversion-Curve Locus in Reduced Coordinates (Tr = T/Tc ; Pr = P/Pc)* Pr 0 0.5 1 1.5 2 2.5 3 4 TrL TrU 0.782 4.984 0.800 4.916 0.818 4.847 0.838 4.777 0.859 4.706 0.880 4.633 0.903 4.550 0.953 4.401 Pr 5 6 7 8 9 10 11 11.79 TrL 1.01 1.08 1.16 1.25 1.35 1.50 1.73 2.24 TrU 4.23 4.06 3.88 3.68 3.45 3.18 2.86 2.24 ∗Calculated from the best three-constant equation recommended by Miller, Ind. Eng. Chem. Fundam., 9, 585 (1970). TrL refers to the lower curve, and TrU, to the upper curve. Additional References For other inorganic substances see Mathews, Chem. Rev., 72 (1972):71–100. For other organics see Kudchaker, Alani, and Zwolinski, Chem. Rev., 68 (1968): 659–735. TABLE 2-106 Cmpd. no. 2-183 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Critical Constants and Acentric Factors of Inorganic and Organic Compounds Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 Cl2 CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 Mol. wt. TC, K 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 70.906 466 761 591.95 606 508.2 545.5 308.3 506 615 540 132.45 405.65 645.6 150.86 824 562.05 689 751 702.3 830 720.15 662 718 773 584.15 670.15 503.8 464 452 425 425.12 680 676 563.1 535.9 419.5 435.5 428.6 575.4 660.5 570.1 554 440 537.2 615.7 585.4 304.21 552 132.92 556.35 227.51 417.15 PC, MPa 5.57 6.6 5.786 4 4.701 4.85 6.138 5 5.66 4.66 3.774 11.28 4.25 4.898 5.05 4.895 4.74 4.47 4.215 3.352 4.374 3.11 4.06 3.38 10.3 4.5191 5.565 6.929 4.36 4.32 3.796 5.21 4.02 4.414 4.1885 4.02 4.21 4.1 3.09 2.89 3.97 4.06 4.6 4.41 4.06 3.88 7.383 7.9 3.499 4.56 3.745 7.71 VC, m3/kmol 0.154 0.215 0.177 0.304 0.209 0.193 0.112 0.197 0.208 0.216 0.09147 0.07247 0.337 0.07459 0.346 0.256 0.315 0.344 0.3132 0.5677 0.382 0.442 0.367 0.497 0.135 0.324 0.204 0.152 0.22 0.221 0.255 0.303 0.305 0.273 0.27 0.241 0.234 0.238 0.389 0.497 0.307 0.307 0.208 0.258 0.293 0.291 0.094 0.16 0.0944 0.276 0.143 0.124 ZC 0.221 0.224 0.208 0.241 0.233 0.206 0.268 0.234 0.23 0.224 0.313 0.242 0.267 0.291 0.255 0.268 0.261 0.246 0.226 0.276 0.279 0.25 0.25 0.261 0.286 0.263 0.271 0.273 0.255 0.27 0.274 0.279 0.218 0.258 0.254 0.278 0.272 0.274 0.251 0.262 0.257 0.271 0.262 0.255 0.232 0.232 0.274 0.275 0.299 0.272 0.283 0.276 Acentric factor 0.262493 0.421044 0.466521 0.455328 0.306527 0.341926 0.191185 0.319832 0.538324 0.310664 0 0.252608 0.350169 0 0.5585 0.2103 0.262789 0.602794 0.343214 0.501941 0.363116 0.433236 0.312604 0.402873 0.128997 0.250575 0.205275 0.153426 0.165877 0.195032 0.200164 0.630463 0.704256 0.58828 0.580832 0.184495 0.201877 0.217592 0.439393 0.394149 0.271361 0.25059 0.246976 0.282553 0.675003 0.3601 0.223621 0.110697 0.0481621 0.192552 0.178981 0.0688183 (Continued) 2-184 TABLE 2-106 Cmpd. no. 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–isopropyl amine Di–isopropyl ether Di–isopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Formula C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 CAS 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 Mol. wt. 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 TC, K PC, MPa VC, m3/kmol 632.35 460.35 536.4 416.25 503.15 489 705.85 697.55 704.65 631 400.15 459.93 553.8 650.1 653 560.4 511.7 507 398 664 674 617.7 722.1 688 616.6 696 619.85 38.35 628 650.15 611 584.1 683.95 705 684.75 523 561.6 510 560 572 736.6 496.6 466.7 557.15 386.44 445 351.255 523.1 500.05 576 507.8 543 473.2 4.5191 5.27 5.472 6.68 4.425 4.54 4.56 5.01 5.15 3.209 5.924 4.98 4.08 4.26 4 4.35 4.51 4.8 5.54 3.97 2.6 2.11 2.28 2.308 2.223 2.13 2.37 1.6617 6.03 5.4769 7.17 2.46 4.07 4.07 4.07 5.07 5.37 6.08 4.24 4.24 4.27 3.71 3.64 3.96 4.5198 4.34 5.784 3.2 2.88 3.02 3.773 3.446 4.87 0.308 0.192 0.239 0.141 0.243 0.247 0.312 0.282 0.277 0.434 0.151 0.21 0.308 0.322 0.311 0.291 0.26 0.245 0.162 0.355 0.575 0.617 0.639 0.645 0.584 0.624 0.552 0.060263 0.276 0.2616 0.223 0.487 0.351 0.351 0.351 0.24 0.22 0.185 0.291 0.291 0.349 0.301 0.28 0.318 0.179 0.195 0.123 0.418 0.386 0.416 0.297 0.35 0.221 ZC 0.265 0.264 0.293 0.272 0.257 0.276 0.242 0.244 0.244 0.265 0.269 0.273 0.273 0.254 0.229 0.272 0.276 0.279 0.271 0.255 0.267 0.254 0.243 0.26 0.253 0.23 0.254 0.314 0.319 0.265 0.315 0.247 0.251 0.244 0.251 0.28 0.253 0.265 0.265 0.259 0.243 0.27 0.263 0.272 0.252 0.229 0.244 0.308 0.267 0.262 0.265 0.267 0.274 Acentric factor 0.249857 0.188591 0.221902 0.151 0.215047 0.198553 0.448034 0.43385 0.50721 0.327406 0.275605 0.18474 0.208054 0.369047 0.299006 0.212302 0.194874 0.19611 0.127829 0.264134 0.520066 0.492328 0.813724 0.606986 0.480456 0.587421 0.51783 −0.14486 0.125025 0.206724 0.20945 0.447646 0.27898 0.219189 0.284638 0.233943 0.286595 0.198622 0.252928 0.256391 0.952882 0.303856 0.281065 0.29002 0.275052 0.222428 0.277138 0.388315 0.338683 0.404427 0.32768 0.352222 0.238542 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane 2-185 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 437.2 500 591.15 606.15 596.15 615 400.1 649.6 537.3 766 402 503.04 729 777.4 587 766.8 550 658 768 305.32 514 523.3 456.15 617.15 698 655 571 609.15 569.5 282.34 593 720 537 469.15 508.4 674.6 583 489 567 499.15 546 500.23 559.95 144.12 560.09 375.31 317.42 420 771 588 490.15 5.2 736 620 540.2 5.34 3.15 2.93843 2.93843 2.93843 5.36 5.37 4.42 2.91 2.78 3.56 5.53 5.65 2.76 5.2081 3.08 3.14 1.82 1.16 4.872 6.137 3.88 5.62 3.609 3.18 3.41 2.95 3.04 3.4 5.041 6.29 8.2 6.85 7.19 4.74 2.778 2.46 3.41 3.32 5.49 3.362 3.37007 3.33 5.1724 4.55051 5.028 5.87511 6.59 7.8 5.81 5.5 0.2275 1.34 3.16 2.74 0.18 0.361 0.45 0.46 0.46 0.252 0.17 0.26199 0.393 0.53 0.258 0.201 0.227 0.529 0.238 0.503 0.402 0.755 1.34 0.1455 0.168 0.286 0.207 0.374 0.489 0.389 0.403 0.43 0.375 0.131 0.264 0.191 0.173 0.140296 0.229 0.528 0.487 0.329 0.369 0.207 0.345 0.339 0.403 0.066547 0.269 0.159 0.113 0.0851 0.163 0.125 0.218 0.0573 1.11 0.434 0.428 0.264 0.274 0.269 0.268 0.273 0.264 0.2744 0.214 0.256 0.231 0.275 0.266 0.212 0.226 0.254 0.243 0.276 0.251 0.243 0.279 0.241 0.255 0.307 0.263 0.268 0.244 0.25 0.258 0.269 0.281 0.337 0.262 0.265 0.25876 0.257 0.262 0.247 0.276 0.26 0.274 0.256 0.275 0.288 0.287 0.263 0.256 0.252 0.161 0.198 0.149 0.294 0.302 0.244 0.266 0.261 0.299885 0.249251 0.232569 0.232443 0.237864 0.205916 0.200221 0.31771 0.296407 0.656848 0.129957 0.194256 0.280551 0.580691 0.279262 0.43889 0.449684 0.576385 0.906878 0.099493 0.643558 0.366409 0.284788 0.30347 0.477055 0.632579 0.401075 0.245525 0.270095 0.0862484 0.472367 0.506776 0.200735 0.197447 0.284736 0.801289 0.494378 0.305629 0.389061 0.187751 0.394373 0.347328 0.269778 0.0530336 0.247183 0.217903 0.194721 0.167887 0.412381 0.312521 0.201538 −0.390032 0.769688 0.405751 0.349469 (Continued) 2-186 TABLE 2-106 Cmpd. no. 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane Formula C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 CAS Mol. wt. TC, K PC, MPa VC, m3/kmol 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 677.3 632.3 608.3 606.6 611.4 537.4 645 547 723 594 507.6 660.2 611.3 585.3 587.61 582.82 504 544 623 516.2 549 653.15 33.19 363.15 324.65 456.65 461.15 373.53 605 471.85 834 662 190.564 512.5 718 506.55 402.4 536 430.05 693 490 460.4 643 577.2 465 470 492 512.74 593 463.2 554.5 442 572.1 3.043 3.085 3 2.92 2.94 2.92 2.77 3.21 1.4 3.46 3.025 3.308 3.446 3.311 3.287 3.32 3.21 3.53 3.08 3.62 3.53 14.7 1.313 8.552 8.31 5.39 6.48 8.96291 3.7 4.54 6.1 4.79 4.599 8.084 4.98 4.75 5.63 4.25 7.46 3.59 3.83 3.38 3.89 3.93 3.447 3.42 4.38 3.371 3.47 4.2 3.473 4.17 3.48 0.466 0.444 0.447 0.433 0.434 0.402 0.465 0.387 1.04 0.378 0.371 0.408 0.382 0.385 0.378 0.378 0.348 0.331 0.412 0.322 0.331 0.158 0.064147 0.1 0.081 0.139 0.069 0.0985 0.292 0.221 0.279 0.28 0.0986 0.117 0.267 0.228 0.164 0.27 0.154 0.436 0.291 0.306 0.347 0.329 0.292 0.292 0.248 0.329 0.36 0.275 0.34 0.246 0.369 ZC 0.252 0.261 0.265 0.251 0.251 0.263 0.24 0.273 0.243 0.266 0.266 0.246 0.259 0.262 0.254 0.259 0.267 0.258 0.245 0.272 0.256 0.428 0.305 0.283 0.249 0.197 0.117 0.284 0.215 0.256 0.245 0.244 0.286 0.222 0.223 0.257 0.276 0.258 0.321 0.272 0.274 0.27 0.252 0.269 0.26 0.256 0.266 0.26 0.253 0.3 0.256 0.279 0.27 Acentric factor 0.759934 0.562105 0.567733 0.407565 0.418982 0.343194 0.422568 0.377799 0.717404 0.361818 0.301261 0.733019 0.558598 0.553 0.384626 0.380086 0.285121 0.218301 0.368101 0.332699 0.221387 0.314282 −0.215993 0.073409 0.131544 0.409913 0.382283 0.0941677 0.61405 0.275913 0.738273 0.331817 0.0115478 0.565831 0.435111 0.331255 0.211537 0.342296 0.281417 0.420541 0.187439 0.227875 0.589443 0.59002 0.234056 0.28703 0.137046 0.313008 0.3229 0.308085 0.377519 0.225204 0.236055 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-187 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F 3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 686 614 617 532.7 542 526 483 437.8 535.5 533 487.2 497 574.6 488 464.48 553.4 553.1 469.95 566 694 497.7 546.49 407.8 506.2 417.9 530.6 476.25 565 352.5 654 497.1 437 748.4 44.4 593 126.2 234 588.15 309.57 180.15 758 658.5 594.6 710.7 670.9 649.5 593.1 681 598.05 747 638.9 568.7 694.26 652.3 629.8 4 3.79 3.79 3.79 4.13 4.13 3.95 4.4 4.15 4.26 6 3.41 3.27 5.48 3.762 3.8 4.021 7.23 3.68 2.54 3.04 3.042 3.64 3.972 4 4.004 3.801 3.97 4.7 3.36 3.286 4.67 4.05 2.653 5.16 3.4 4.4607 6.31 7.245 6.48 1.21 2.68 2.29 2.514 2.527 2.5408 2.428 2.31 2.61 1.27 2.96 2.49 2.779 2.783 2.749 0.374 0.374 0.374 0.319 0.303 0.303 0.289 0.221 0.267 0.254 0.172 0.329 0.369 0.202 0.276 0.31 0.328 0.145 0.323 0.572 0.368 0.38 0.259 0.275 0.239 0.282 0.276 0.307 0.205 0.399 0.329 0.21 0.407 0.0417 0.236 0.08921 0.11875 0.173 0.0974 0.058 1.26 0.543 0.551 0.584 0.576 0.577 0.524 0.571 0.497 1.19 0.488 0.486 0.523 0.509 0.512 0.262 0.278 0.276 0.273 0.278 0.286 0.284 0.267 0.249 0.244 0.255 0.272 0.253 0.273 0.269 0.256 0.28718 0.268 0.253 0.252 0.27 0.254 0.278 0.26 0.275 0.256 0.265 0.259 0.329 0.247 0.262 0.27 0.265 0.3 0.247 0.289 0.272 0.223 0.274 0.251 0.242 0.266 0.255 0.248 0.261 0.271 0.258 0.233 0.261 0.243 0.272 0.256 0.252 0.261 0.269 0.221299 0.68049 0.67904 0.228759 0.23179 0.229606 0.275755 0.231374 0.323369 0.209108 0.255551 0.307786 0.355671 0.300694 0.26555 0.320845 0.24611 0.158174 0.280233 0.791271 0.279149 0.344201 0.183521 0.615203 0.19484 0.346586 0.276999 0.273669 0.131449 0.32297 0.246542 0.241564 0.302034 −0.0395988 0.380324 0.0377215 0.119984 0.348026 0.140894 0.582944 0.852231 0.473309 0.44346 0.778706 0.584074 0.6092 0.436736 0.52604 0.470974 0.811359 0.441993 0.399552 0.773427 0.569694 0.58814 (Continued) 2-188 TABLE 2-106 Cmpd. no. 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 Critical Constants and Acentric Factors of Inorganic and Organic Compounds (Continued ) Name 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan Formula C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S CAS 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 Mol. wt. TC, K 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 632.7 627.7 566.9 667.3 574 828 154.58 261 708 566.1 469.7 639.16 588.1 561 561.08 560.95 464.8 584.3 598 481.2 519 869 694.25 653 791 394 369.83 536.8 508.3 636 503.6 600.81 561.3 549.73 496.95 638.35 364.85 538 517 536.6 PC, MPa 2.64 2.704 2.663 2.52 2.88 8.2 5.043 5.57 1.48 3.845 3.37 3.63 3.897 3.7 3.694 3.74 3.56 3.536 3.47 4.17 4.03 2.9 6.13 4.06 4.72 5.25 4.248 5.169 4.765 3.12 5.038 4.668 4.26 3.36 4.74 3.2 4.6 4.02 4.75 4.63 VC, m3/kmol 0.497 0.496953 0.464 0.518 0.442 0.227 0.0734 0.089 0.969 0.313 0.313 0.35 0.326 0.326 0.301 0.336 0.2934 0.385 0.359 0.277 0.276 0.554 0.229 0.37 0.421 0.165 0.2 0.219 0.222 0.437 0.204 0.235 0.242 0.345 0.26 0.44 0.185 0.285 0.254 0.254 ZC 0.249 0.257 0.262 0.235 0.267 0.27 0.288 0.228 0.244 0.256 0.27 0.239 0.258 0.259 0.238 0.269 0.27 0.28 0.251 0.289 0.258 0.222 0.243 0.277 0.302 0.264 0.276 0.254 0.25 0.258 0.246 0.22 0.221 0.254 0.298 0.265 0.281 0.256 0.281 0.264 Acentric factor 0.454874 0.440561 0.392149 0.449744 0.42329 0.286278 0.0221798 0.211896 0.68632 0.313152 0.251506 0.706632 0.57483 0.554979 0.343288 0.344846 0.237218 0.26853 0.320705 0.289925 0.175199 0.470716 0.44346 0.412323 0.702495 0.104121 0.152291 0.6209 0.663 0.341975 0.281254 0.579579 0.350057 0.388902 0.279839 0.344391 0.137588 0.308779 0.21381 0.231789 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F 6S O 3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 626 683 259 636 838 430.75 318.69 490.85 883.6 857 693 540.15 720 631.95 568 579.35 591.75 602 675 535.15 433.25 664.5 649.1 543.8 573.5 846 828 639 703.9 519.13 454 432 543.15 647.096 617 630.3 616.2 6.1 5.96 3.72 3.84 5 7.8841 3.76 8.21 3.486 2.99 1.57 5.19 3.65 5.16 2.87 5.69 4.108 4.48 1.68 3.04 4.07 3.454 3.232 2.57 2.82 3.39 3.04 1.95 2.119 3.958 4.86 5.67 3.06 22.064 3.541 3.732 3.511 0.239 0.291 0.202 0.352 0.33 0.122 0.19852 0.127 0.424 0.731 0.897 0.224 0.408 0.249 0.461 0.219 0.316 0.281 0.826 0.39 0.254 0.414 0.43 0.468 0.455 0.479 0.572 0.685 0.715 0.27 0.205 0.179 0.408 0.0559472 0.375 0.37 0.378 0.28 0.305 0.349 0.256 0.237 0.269 0.282 0.255 0.201 0.307 0.244 0.259 0.249 0.245 0.28 0.259 0.264 0.252 0.247 0.266 0.287 0.259 0.258 0.266 0.269 0.231 0.253 0.252 0.259 0.248 0.264 0.283 0.276 0.229 0.259 0.264 0.259 1.10651 0.494515 0.38584 0.297097 0.743044 0.245381 0.215146 0.42396 0.94695 0.551265 0.643017 0.225354 0.335255 0.199551 0.244953 0.196972 0.264012 0.259135 0.617397 0.316193 0.206243 0.366553 0.37871 0.303455 0.2903 0.862257 0.897249 0.530316 0.623622 0.351307 0.106852 0.100107 0.281543 0.344861 0.326485 0.31013 0.321839 Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-189 2-190 PHYSICAL AnD CHEMICAL DATA COMPRESSIBILITIES Introduction The compressibility factor Z can be calculated by using the defining equation Z = PV/(RT), where P is pressure, V is molar volume, R is the gas constant, and T is absolute temperature. Values of P, V, and T for substances listed in Table 2-109 are given in tables in the Thermodynamic Properties section. For the units used in these tables, R is 0.008314472 MPadm3/(mol ⋅ K). Values at temperatures and pressures other than those in the tables can be generated for many of the substances in Table 2-109 by TABLE 2-107 going to http://webbook.nist.gov and selecting NIST Chemistry WebBook, then Thermophysical Properties of Fluid Systems High Accuracy Data. Results can be pasted into a spreadsheet to facilitate calculation of the compressibility factor. Unit Conversions For this subsection, the following unit conversion is applicable: °R = 9⁄5 K. To convert bars to pounds-force per cubic inch, multiply by 14.504. To convert bars to kilopascals, multiply by 100. Compressibilities of Liquids* At the constant temperature T, the compressibility β = (1/ V0 )(dV/dP). In general as P increases, β decreases rapidly at first and then slowly; the change of β with T is large at low pressures but very small at pressures above 1000 to 2000 megabars. 1 megabar = 0.987 atm = 106 dynes/cm2 based upon the older usage, 1 bar = 1 dyne/cm2. Substance Temp., °C Pressure, megabars Compressibility per megabar β × 106 Substance Temp., °C Pressure, megabars Compressibility per megabar β × 106 Substance Temp., °C Pressure, megabars Compressibility per megabar β × 106 Acetone 14 23 111 Ethyl acetate 20 400 75 Methyl alcohol 15 23 103 Acetone 20 500 61 alcohol 14 23 100 alcohol 20 200 95 Acetone 20 1,000 52 alcohol 20 500 63 alcohol 20 400 80 Acetone 40 12,000 9 alcohol 20 1,000 54 alcohol 20 500 65 Amyl alcohol 14 23 88 alcohol 20 12,000 8 alcohol 20 1,000 54 alcohol, iso. 20 200 84 bromide 20 200 100 alcohol 20 12,000 8 alcohol, iso. 20 400 70 bromide 20 400 82 Nitric acid 0 17 32 alcohol, n 20 500 61 bromide 20 500 70 Oils: alcohol, n 20 1,000 46 bromide 20 1,000 54 Almond 15 5 53 alcohol, n 20 12,000 8 bromide 20 12,000 8 Castor 15 5 46 alcohol, n 40 12,000 8 chloride 15 23 151 Linseed 15 5 51 Benzene 17 5 89 chloride 20 500 102 Olive 15 5 55 Benzene 20 200 77 chloride 20 1,000 66 Rapeseed 20 59 Benzene 20 400 67 chloride 20 12,000 8 Phosphorus trichloride 10 250 71 Bromine 20 200 56 ether 25 23 188 trichloride 20 500 63 Bromine 20 400 51 ether 20 500 84 trichloride 20 1,000 47 Butyl alcohol, iso 18 8 97 ether 20 1,000 61 trichloride 20 12,000 8 alcohol, iso 20 200 81 ether 20 12,000 10 Propyl alcohol (n) 20 200 77 alcohol, iso 20 400 64 iodide 20 200 81 alcohol (n) 20 400 67 alcohol, iso 20 500 56 iodide 20 400 69 alcohol (n?) 20 500 65 alcohol, iso 20 1,000 46 iodide 20 500 64 alcohol (n?) 20 1,000 47 alcohol, iso 20 12,000 8 iodide 20 1,000 50 alcohol (n?) 20 12,000 7 Carbon bisulfide 16 21 86 iodide 20 12,000 8 Toluene 20 200 74 bisulfide 20 500 57 Gallium 30 300 3.97 Toluene 20 400 64 bisulfide 20 1,000 48 Glycerol 15 5 22 Turpentine 20 74 bisulfide 20 12,000 6 Hexane 20 200 117 Water 20 13 49 tetrachloride 20 200 86 Hexane 20 400 91 Water 20 200 43 tetrachloride 20 400 73 Kerosene 20 500 55 Water 20 400 41 Chloroform 20 200 83 Kerosene 20 1,000 45 Water 20 500 39 Chloroform 20 400 70 Kerosene 20 12,000 8 Water 40 500 38 Dichloroethylsulfide 32 1,000 34 Mercury 20 300 3.95 Water 40 1,000 33 Dichloroethylsulfide 32 2,000 24 Mercury 22 500 3.97 Water 40 12,000 9 Ethyl acetate 13 23 103 Mercury 22 1,000 3.91 Xylene, meta 20 200 69 acetate 20 200 90 Mercury 22 12,000 2.37 meta 20 400 60 * Smithsonian Tables, Table 106. Scott (Cryogenic Engineering, Van Nostrand, Princeton, N.J., 1959) gives data for liquid nitrogen (p. 283), oxygen (p. 276), and hydrogen (p. 303). For a convenient index to the high-pressure work of Bridgman, see American Institute of Physics Handbook, p. 2-163, McGraw-Hill, New York, 1957. TABLE 2-108 Compressibilities of Solids Many data on the compressibility of solids obtained prior to 1926 are contained in Gruneisen, Handbuch der Physik, vol. 10, Springer, Berlin, 1926, pp. 1–52; also available as translation, NASA RE 2-18-59W, 1959. See also Tables 271, 273, 276, 278, and other material in Smithsonian Physical Tables, 9th ed., 1954. For a review of high-pressure work to 1946, see Bridgman, Rev. Mod. Phys., 18, 1 (1946). THERMODYnAMIC PROPERTIES 2-191 THERMODYnAMIC PROPERTIES Explanation of Tables The following subsection presents thermodynamic properties of a number of fluids. In some cases, transport properties are also included. Property tables generated from the NIST database (Lemmon, E. W., M. O. McLinden, and M. L. Huber, NIST Standard Reference Database 23) are listed in Table 2-109. The number of digits provided in these tables was chosen for uniformity of appearance and formatting and does not represent the uncertainties of the physical quantities: They are the result of calculations from the standard thermophysical property formulations within a fixed format. They were generated using REFPROP software (Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). Megan Friend helped produce these tables initially for Perry’s 8th edition. Because properties for many compounds also can be generated by the user at the NIST website, only more commonly used compounds’ properties are given here. For other compounds, go to http://webbook.nist.gov and select NIST Chemistry WebBook > Thermophysical Properties of Fluid Systems High Accuracy Data. After selecting the desired unit system and temperature and/or pressure increments for which properties are to be generated, the resulting table can be copied into a spreadsheet. Notation cp = isobaric specific heat cv = isochoric specific heat e = specific internal energy h = enthalpy k = thermal conductivity p = pressure s = specific entropy t = temperature T = absolute temperature u = specific internal energy µ = viscosity v = specific volume f = subscript denoting saturated liquid g = subscript denoting saturated vapor Unit Conversions For this subsection, the following unit conversions are applicable: cp, specific heat: To convert kilojoules per kilogram-kelvin to British thermal units (Btu) per pound–degree Fahrenheit, multiply by 0.23885. e, internal energy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992. g, gravity acceleration: To convert meters per second squared to feet per second squared, multiply by 3.2808. h, enthalpy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992. k, thermal conductivity: To convert watts per meter-kelvin to Btu–feet per hour–square foot–degree Fahrenheit, multiply by 0.57779. p, pressure: To convert bars to kilopascals, multiply by 100; to convert bars to pounds-force per square inch, multiply by 14.504; and to convert millimeters of mercury to pounds-force per square inch, multiply by 0.01934. s, entropy: To convert kilojoules per kilogram-kelvin to Btu per pound– degree Rankine, multiply by 0.23885. t, temperature: °F = 9⁄ 5°C + 32. T, absolute temperature: °R = 9⁄ 5 K. u, internal energy: To convert kilojoules per kilogram to Btu per pound, multiply by 0.42992. µ, viscosity: To convert pascal-seconds to pound-force–seconds per square foot, multiply by 0.020885; to convert pascal-seconds to cp, multiply by 1000. v, specific volume: To convert cubic meters per kilogram to cubic feet per pound, multiply by 16.018. r, density: To convert kilograms per cubic meter to pounds per cubic foot, multiply by 0.062428. Additional References Bretsznajder, Prediction of Transport and Other Physical Properties of Fluids, Pergamon, New York, 1971. D’Ans and Lax, Handbook for Chemists and Physicists (in German), 3 vols., SpringerVerlag, Berlin. Engineering Data Book, 12th ed., 2004, Natural Gas Processors Suppliers Association, Tulsa, Okla. Ganic, Hartnett, and Rohsenow, Handbook of Heat Transfer, 2nd ed., McGraw-Hill, New York, 1984. Gray, American Institute of Physics Handbook, 3d ed., McGraw-Hill, New York, 1972. Kay and Laby, Tables of Physical and Chemical Constants, Longman, London, various editions and dates. Landolt-Börnstein Tables, many volumes and dates, Springer-Verlag, Berlin. Partington, Advanced Treatise on Physical Chemistry, Longman, London, 1950. Raznjevic, Handbook of Thermodynamic Tables and Charts, McGraw-Hill, New York, 1976 and other editions. Reynolds, Thermodynamic Properties in SI, Department of Mechanical Engineering, Stanford University, 1979. Stephan and Lucas, Viscosity of Dense Fluids, Plenum, New York and London, 1979. Vargaftik, Tables of the Thermophysical Properties of Gases and Liquids, Wiley, New York, 1975. Vargaftik, Filippov, Tarzimanov, and Totskiy, Thermal Conductivity of Liquids and Gases (in Russian), Standartov, Moscow, 1978. Weast, Handbook of Chemistry and Physics, Chemical Rubber Co., Boca Raton, FL, 97th print edition (2016) and online. 2-192 PHYSICAL AnD CHEMICAL DATA TABLE 2-109 Thermodynamic Properties of Acetone Temperature K Pressure MPa 178.50 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 508.10 2.3265E-06 2.8743E-06 1.9454E-05 9.6588E-05 0.00037556 0.0012008 0.0032765 0.0078514 0.016899 0.033259 0.060720 0.10404 0.16891 0.26188 0.39033 0.56235 0.78681 1.0733 1.4324 1.8759 2.4172 3.0725 3.8632 4.6924 178.50 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 508.10 2.3265E-06 2.8743E-06 1.9454E-05 9.6588E-05 0.00037556 0.0012008 0.0032765 0.0078514 0.016899 0.033259 0.060720 0.10404 0.16891 0.26188 0.39033 0.56235 0.78681 1.0733 1.4324 1.8759 2.4172 3.0725 3.8632 4.6924 200.00 250.00 300.00 328.84 0.10000 0.10000 0.10000 0.10000 328.84 350.00 400.00 450.00 500.00 550.00 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 200.00 250.00 300.00 350.00 400.00 416.48 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 416.48 450.00 500.00 550.00 1.0000 1.0000 1.0000 1.0000 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol 0.063601 0.063715 0.064868 0.066048 0.067264 0.068525 0.069840 0.071218 0.072673 0.074217 0.075867 0.077643 0.079569 0.081677 0.084008 0.086616 0.089578 0.093001 0.097051 0.10200 0.10832 0.11706 0.13145 0.21277 0.47366 0.64687 2.3835 4.1282 5.8823 7.6487 9.4311 11.234 13.060 14.915 16.802 18.725 20.687 22.693 24.746 26.852 29.015 31.243 33.546 35.938 38.445 41.117 44.096 49.249 0.47366 0.64687 2.3835 4.1282 5.8823 7.6488 9.4314 11.234 13.062 14.918 16.807 18.733 20.701 22.714 24.779 26.900 29.085 31.343 33.685 36.130 38.707 41.476 44.604 50.247 0.0080825 0.0090488 0.018316 0.026935 0.035003 0.042602 0.049806 0.056674 0.063259 0.069601 0.075739 0.081702 0.087517 0.093209 0.098798 0.10431 0.10975 0.11516 0.12056 0.12599 0.13150 0.13720 0.14341 0.15437 0.082500 0.082598 0.083407 0.084076 0.084758 0.085541 0.086468 0.087553 0.088794 0.090180 0.091697 0.093329 0.095063 0.096886 0.098794 0.10078 0.10286 0.10504 0.10736 0.10986 0.11265 0.11600 0.12077 0.11544 0.11550 0.11604 0.11660 0.11731 0.11825 0.11946 0.12094 0.12270 0.12474 0.12704 0.12962 0.13249 0.13568 0.13924 0.14328 0.14794 0.15350 0.16042 0.16967 0.18350 0.20893 0.28551 1765.7 1757.0 1672.3 1591.8 1514.4 1439.4 1366.3 1294.8 1224.5 1155.2 1086.7 1018.8 951.24 883.84 816.36 748.57 680.21 610.99 540.51 468.19 392.99 312.66 221.66 0 637,900. 520,660. 83,324. 18,065. 4,973.1 1,656.0 642.89 282.74 137.74 72.996 41.482 24.979 15.782 10.377 7.0503 4.9192 3.5050 2.5368 1.8547 1.3611 0.99393 0.71168 0.48154 0.21277 36.689 36.764 37.528 38.314 39.121 39.947 40.790 41.649 42.522 43.406 44.302 45.207 46.119 47.033 47.946 48.849 49.733 50.582 51.376 52.083 52.648 52.968 52.771 49.249 38.173 38.260 39.149 40.059 40.989 41.936 42.897 43.869 44.849 45.834 46.821 47.806 48.784 49.751 50.698 51.615 52.490 53.305 54.033 54.636 55.050 55.154 54.631 50.247 0.21928 0.21801 0.20686 0.19803 0.19103 0.18546 0.18104 0.17754 0.17479 0.17266 0.17102 0.16980 0.16892 0.16831 0.16791 0.16768 0.16754 0.16745 0.16734 0.16711 0.16664 0.16569 0.16367 0.15437 0.050120 0.050280 0.051928 0.053740 0.055800 0.058169 0.060883 0.063945 0.067329 0.070988 0.074863 0.078895 0.083030 0.087227 0.091459 0.095718 0.10001 0.10438 0.10887 0.11357 0.11865 0.12436 0.13126 0.058440 0.058600 0.060265 0.062119 0.064267 0.066795 0.069763 0.073198 0.077094 0.081429 0.086172 0.091302 0.096822 0.10277 0.10927 0.11649 0.12481 0.13483 0.14772 0.16583 0.19480 0.25197 0.42947 172.60 173.29 179.95 186.29 192.29 197.94 203.19 207.99 212.26 215.93 218.90 221.08 222.35 222.60 221.70 219.53 215.94 210.76 203.80 194.82 183.50 169.39 151.36 0 0.065254 0.069389 0.074210 0.077500 2.9626 8.8328 14.913 18.575 2.9691 8.8397 14.921 18.583 0.021248 0.047436 0.069594 0.081247 0.083638 0.086143 0.090180 0.093199 0.11621 0.11902 0.12473 0.12941 45.137 46.843 50.998 55.474 60.316 65.522 47.730 49.643 54.255 59.166 64.436 70.066 0.16988 0.17552 0.18783 0.19939 0.21049 0.22122 0.078579 0.079533 0.085418 0.092823 0.10033 0.10753 0.090892 0.090386 0.094849 0.10175 0.10903 0.11612 220.94 229.44 246.85 262.23 276.40 289.72 2.9486 8.8130 14.885 21.312 28.263 30.714 3.0138 8.8824 14.959 21.392 28.351 30.806 0.021178 0.047357 0.069499 0.089316 0.10788 0.11389 0.083649 0.086152 0.090182 0.095644 0.10213 0.10452 0.11619 0.11896 0.12460 0.13326 0.14605 0.15210 1649.7 1396.0 1162.0 936.35 707.25 627.32 50.387 54.081 59.388 64.832 53.120 57.281 63.156 69.107 0.16747 0.17709 0.18947 0.20081 0.10335 0.10087 0.10402 0.10950 0.13228 0.11921 0.11743 0.12100 212.13 233.76 256.99 275.55 Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s JouleThomson K/MPa Saturated Properties 15.723 15.695 15.416 15.141 14.867 14.593 14.319 14.041 13.760 13.474 13.181 12.880 12.568 12.243 11.904 11.545 11.163 10.753 10.304 9.8043 9.2319 8.5423 7.6072 4.7000 1.5677E-06 1.9207E-06 1.2001E-05 5.5355E-05 0.00020108 0.00060385 0.0015555 0.0035368 0.0072603 0.013699 0.024107 0.040034 0.063362 0.096367 0.14184 0.20329 0.28530 0.39420 0.53918 0.73472 1.0061 1.4051 2.0767 4.7000 −0.43351 −0.43308 −0.42849 −0.42274 −0.41520 −0.40545 −0.39322 −0.37827 −0.36033 −0.33907 −0.31399 −0.28437 −0.24915 −0.20678 −0.15495 −0.090162 −0.0069455 0.10371 0.25760 0.48516 0.85357 1.5474 3.3240 14.310 3845.4 3637.4 2139.7 1312.0 834.10 547.82 370.79 258.27 184.97 136.14 102.93 79.878 63.590 51.884 43.343 37.032 32.325 28.797 26.154 24.184 22.717 21.551 20.240 14.310 Single-Phase Properties 15.325 14.411 13.475 12.903 0.038565 0.035712 0.030709 0.027083 0.024272 0.022008 15.333 14.423 13.491 12.483 11.308 10.852 0.36582 0.31254 0.26538 0.23391 25.930 28.002 32.563 36.923 41.200 45.437 0.065220 0.069336 0.074123 0.080107 0.088431 0.092149 2.7336 3.1996 3.7681 4.2751 1645.6 1391.1 1155.7 1024.0 −0.42678 −0.39768 −0.33922 −0.28685 81.384 58.339 30.192 18.173 12.201 8.8355 −0.42708 −0.39848 −0.34115 −0.24033 −0.042437 0.074613 29.536 20.211 12.984 9.1542 THERMODYnAMIC PROPERTIES 2-193 TABLE 2-109 Thermodynamic Properties of Acetone (Continued ) Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol 15.367 14.471 13.560 12.588 11.490 10.123 7.8139 1.7344 0.065073 0.069106 0.073747 0.079439 0.087035 0.098782 0.12798 0.57657 2.8871 8.7271 14.762 21.128 27.958 35.450 44.435 60.563 3.2125 9.0726 15.130 21.525 28.393 35.944 45.075 63.446 15.410 14.528 13.641 12.709 11.683 10.491 8.9733 6.6600 0.064894 0.068831 0.073307 0.078687 0.085592 0.095320 0.11144 0.15015 2.8125 8.6237 14.616 20.916 27.629 34.864 42.815 52.079 Enthalpy kJ/mol Entropy kJ/(mol⋅K) JouleThomson K/MPa Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s 0.020868 0.047011 0.069085 0.088784 0.10711 0.12488 0.14406 0.17943 0.083704 0.086197 0.090197 0.095584 0.10186 0.10898 0.11961 0.12191 0.11609 0.11871 0.12408 0.13214 0.14320 0.16059 0.23343 0.17820 1667.9 1417.7 1189.0 972.15 759.27 538.79 262.33 205.69 −0.42837 −0.40187 −0.34909 −0.25988 −0.10136 0.26123 2.3418 10.650 3.4614 9.3120 15.349 21.703 28.485 35.818 43.930 53.581 0.020488 0.046589 0.068589 0.088163 0.10626 0.12352 0.14060 0.15896 0.083781 0.086264 0.090234 0.095554 0.10166 0.10827 0.11552 0.12442 0.11598 0.11843 0.12351 0.13100 0.14066 0.15332 0.17314 0.22174 1689.9 1443.6 1220.9 1013.1 815.03 622.74 433.48 255.34 −0.42983 −0.40569 −0.35775 −0.27983 −0.15336 0.080235 0.63674 2.7218 Single-Phase Properties (Cont.) 200.00 250.00 300.00 350.00 400.00 450.00 500.00 550.00 200.00 250.00 300.00 350.00 400.00 450.00 500.00 550.00 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 250.00 300.00 350.00 400.00 450.00 500.00 550.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 15.320 14.657 14.023 13.409 12.813 12.234 11.674 0.065276 0.068228 0.071312 0.074574 0.078044 0.081739 0.085664 7.2620 12.852 18.631 24.654 30.941 37.489 44.286 13.790 19.675 25.763 32.112 38.745 45.663 52.852 0.040421 0.061873 0.080632 0.097579 0.11320 0.12777 0.14147 0.088285 0.092127 0.097243 0.10299 0.10892 0.11478 0.12045 0.11631 0.11946 0.12424 0.12980 0.13553 0.14112 0.14639 1791.8 1616.6 1466.4 1337.4 1226.9 1133.0 1053.8 −0.43634 −0.42000 −0.39555 −0.36734 −0.33807 −0.30922 −0.28171 450.00 500.00 550.00 500.00 500.00 500.00 15.616 15.306 15.012 0.064037 0.065335 0.066615 27.237 33.413 39.856 59.256 66.081 73.163 0.097266 0.11164 0.12514 0.11562 0.12123 0.12669 0.13393 0.13909 0.14416 2201.1 2129.8 2067.5 −0.39010 −0.37710 −0.36510 The values in this table were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in the equation of state are 0.1% in the saturated liquid density between 280 and 310 K, 0.5% in density in the liquid phase below 380 K, and 1% in density elsewhere, including all states at pressures above 100 MPa. The uncertainties in vapor pressure are 0.5% above 270 K (0.25% between 290 and 390 K), and the uncertainties in heat capacities and speeds of sound are 1%. These uncertainties (in caloric properties and sound speeds) may be higher at pressures above the saturation pressure and at temperatures above 320 K in the liquid phase and at supercritical conditions. 2-194 TABLE 2-110 Thermodynamic Properties of Air Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol 59.75 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 0.005265 0.005546 0.006797 0.008270 0.009994 0.012000 0.014320 0.016988 0.020042 0.023520 0.027461 0.031908 0.036905 0.042498 0.048733 0.055659 0.063326 0.071786 0.081091 0.091294 0.10245 0.11462 0.12785 0.14221 0.15775 0.17453 0.19262 0.21207 0.23295 0.25531 0.27922 0.30475 0.33196 0.36091 0.39166 0.42429 0.45886 0.49543 0.53408 0.57486 0.61786 0.66313 0.71074 0.76077 0.81329 0.86836 0.92606 0.98645 1.0496 1.1156 1.1845 1.2564 1.3314 1.4095 1.4908 1.5753 33.067 33.031 32.888 32.745 32.601 32.457 32.312 32.166 32.020 31.873 31.725 31.576 31.427 31.277 31.126 30.974 30.821 30.668 30.513 30.357 30.200 30.042 29.883 29.722 29.560 29.397 29.232 29.066 28.898 28.729 28.558 28.385 28.210 28.033 27.854 27.673 27.489 27.304 27.115 26.924 26.730 26.533 26.333 26.130 25.923 25.713 25.499 25.281 25.058 24.831 24.598 24.361 24.118 23.868 23.613 23.350 0.030242 0.030275 0.030406 0.030539 0.030674 0.030810 0.030949 0.031089 0.031231 0.031375 0.031521 0.031669 0.031820 0.031972 0.032127 0.032285 0.032445 0.032608 0.032773 0.032941 0.033112 0.033287 0.033464 0.033645 0.033829 0.034017 0.034209 0.034404 0.034604 0.034808 0.035017 0.035230 0.035449 0.035672 0.035901 0.036137 0.036378 0.036625 0.036880 0.037142 0.037411 0.037688 0.037975 0.038270 0.038575 0.038891 0.039217 0.039556 0.039908 0.040273 0.040653 0.041050 0.041464 0.041896 0.042350 0.042826 −1.0619 −1.0481 −0.99308 −0.93803 −0.88298 −0.82792 −0.77286 −0.71777 −0.66267 −0.60755 −0.55239 −0.49720 −0.44196 −0.38669 −0.33135 −0.27597 −0.22051 −0.16499 −0.10939 −0.05371 0.002063 0.057934 0.11391 0.17000 0.22621 0.28255 0.33903 0.39566 0.45245 0.50940 0.56653 0.62386 0.68138 0.73912 0.79709 0.85529 0.91375 0.97248 1.0315 1.0908 1.1505 1.2104 1.2708 1.3315 1.3926 1.4542 1.5162 1.5787 1.6417 1.7053 1.7695 1.8343 1.8997 1.9659 2.0329 2.1007 −1.0617 −1.0480 −0.99287 −0.93778 −0.88267 −0.82755 −0.77241 −0.71725 −0.66205 −0.60681 −0.55152 −0.49619 −0.44079 −0.38533 −0.32979 −0.27417 −0.21846 −0.16265 −0.10673 −0.05070 0.005456 0.061749 0.11819 0.17478 0.23155 0.28849 0.34562 0.40296 0.46051 0.51829 0.57631 0.63459 0.69315 0.75199 0.81115 0.87062 0.93044 0.99063 1.0512 1.1122 1.1736 1.2354 1.2978 1.3606 1.4240 1.4880 1.5525 1.6177 1.6836 1.7502 1.8176 1.8858 1.9549 2.0250 2.0960 2.1682 Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s JouleThomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.034011 0.033955 0.033731 0.033512 0.033298 0.033089 0.032884 0.032683 0.032486 0.032294 0.032105 0.031920 0.031739 0.031562 0.031388 0.031217 0.031050 0.030886 0.030725 0.030568 0.030413 0.030262 0.030113 0.029968 0.029826 0.029686 0.029550 0.029417 0.029286 0.029158 0.029033 0.028911 0.028792 0.028676 0.028563 0.028453 0.028346 0.028241 0.028140 0.028042 0.027948 0.027856 0.027768 0.027684 0.027603 0.027525 0.027452 0.027383 0.027317 0.027256 0.027200 0.027149 0.027103 0.027062 0.027028 0.027000 0.055064 0.055062 0.055060 0.055062 0.055069 0.055081 0.055098 0.055120 0.055148 0.055181 0.055220 0.055266 0.055317 0.055376 0.055441 0.055514 0.055594 0.055682 0.055779 0.055884 0.055998 0.056122 0.056256 0.056400 0.056556 0.056723 0.056902 0.057094 0.057300 0.057521 0.057757 0.058009 0.058278 0.058566 0.058874 0.059202 0.059553 0.059928 0.060329 0.060757 0.061216 0.061707 0.062232 0.062796 0.063401 0.064052 0.064753 0.065508 0.066323 0.067206 0.068163 0.069205 0.070341 0.071585 0.072951 0.074459 1030.3 1028.3 1020.3 1012.2 1004.0 995.77 987.48 979.13 970.72 962.24 953.70 945.10 936.43 927.70 918.90 910.04 901.11 892.11 883.05 873.91 864.71 855.44 846.09 836.67 827.18 817.61 807.96 798.24 788.44 778.56 768.59 758.55 748.42 738.20 727.90 717.51 707.03 696.46 685.80 675.05 664.20 653.26 642.22 631.08 619.84 608.50 597.06 585.51 573.85 562.09 550.21 538.21 526.10 513.86 501.48 488.97 −0.40785 −0.40743 −0.40565 −0.40375 −0.40173 −0.39958 −0.39729 −0.39485 −0.39227 −0.38952 −0.38660 −0.38352 −0.38024 −0.37677 −0.37310 −0.36922 −0.36511 −0.36076 −0.35616 −0.35130 −0.34616 −0.34074 −0.33500 −0.32894 −0.32254 −0.31577 −0.30862 −0.30107 −0.29308 −0.28464 −0.27572 −0.26628 −0.25629 −0.24573 −0.23455 −0.22270 −0.21016 −0.19686 −0.18275 −0.16779 −0.15189 −0.13501 −0.11705 −0.09794 −0.07758 −0.05588 −0.03271 −0.00795 0.018543 0.046927 0.077386 0.11012 0.14538 0.18342 0.22456 0.26917 171.43 171.02 169.40 167.78 166.16 164.53 162.91 161.28 159.65 158.01 156.37 154.73 153.09 151.44 149.79 148.14 146.49 144.83 143.16 141.50 139.83 138.15 136.48 134.80 133.11 131.42 129.78 128.11 126.44 124.76 123.07 121.38 119.69 118.00 116.30 114.61 112.91 111.21 109.51 107.81 106.11 104.41 102.71 101.01 99.316 97.623 95.933 94.247 92.565 90.888 89.216 87.551 85.893 84.242 82.599 80.965 376.64 371.92 353.83 336.91 321.09 306.27 292.39 279.38 267.17 255.71 244.94 234.81 225.28 216.31 207.85 199.88 192.35 185.23 178.51 172.14 166.11 160.39 154.96 149.80 144.90 140.23 135.78 131.54 127.50 123.63 119.93 116.38 112.98 109.72 106.59 103.58 100.68 97.879 95.179 92.571 90.048 87.605 85.236 82.937 80.703 78.529 76.412 74.347 72.331 70.361 68.432 66.542 64.688 62.867 61.075 59.311 Saturated Properties −0.01536 −0.01513 −0.01422 −0.01333 −0.01245 −0.01158 −0.01073 −0.00989 −0.00906 −0.00824 −0.00744 −0.00664 −0.00586 −0.00508 −0.00432 −0.00357 −0.00282 −0.00209 −0.00136 −0.00064 6.86E-05 0.000772 0.001467 0.002156 0.002838 0.003513 0.004181 0.004844 0.005501 0.006153 0.006799 0.007440 0.008077 0.008708 0.009336 0.009960 0.010579 0.011195 0.011808 0.012418 0.013025 0.013630 0.014232 0.014833 0.015431 0.016029 0.016625 0.017221 0.017816 0.018411 0.019006 0.019602 0.020200 0.020799 0.021400 0.022004 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 132.63 1.6633 1.7546 1.8495 1.9479 2.0499 2.1557 2.2653 2.3787 2.4960 2.6173 2.7427 2.8721 3.0055 3.1431 3.2845 3.4295 3.5770 3.7228 3.7858 59.75 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 0.002432 0.002584 0.003274 0.004111 0.005120 0.006325 0.007756 0.009442 0.011416 0.013713 0.016372 0.019431 0.022933 0.026921 0.031443 0.036547 0.042282 0.048702 0.055859 0.063810 0.072611 0.082321 0.093001 0.10471 0.11751 0.13147 0.14665 0.16312 0.18094 0.20018 0.22091 0.24320 0.26712 0.29273 0.32011 0.34934 0.38047 0.41359 0.44878 0.48609 0.52562 0.56742 0.61159 23.080 22.801 22.514 22.217 21.908 21.588 21.253 20.903 20.534 20.144 19.727 19.278 18.788 18.242 17.616 16.863 15.869 14.198 10.448 0.004907 0.005192 0.006475 0.008005 0.009817 0.011948 0.014438 0.017326 0.020659 0.024481 0.028841 0.033789 0.039379 0.045664 0.052702 0.060550 0.069268 0.078918 0.089564 0.10127 0.11410 0.12813 0.14343 0.16006 0.17811 0.19765 0.21875 0.24150 0.26598 0.29228 0.32048 0.35068 0.38298 0.41747 0.45426 0.49345 0.53517 0.57953 0.62667 0.67671 0.72980 0.78609 0.84575 0.043328 0.043857 0.044417 0.045011 0.045645 0.046323 0.047052 0.047841 0.048700 0.049643 0.050691 0.051871 0.053225 0.054818 0.056765 0.059300 0.063015 0.070432 0.095715 203.80 192.59 154.45 124.93 101.86 83.693 69.263 57.715 48.406 40.849 34.673 29.595 25.394 21.899 18.975 16.515 14.437 12.671 11.165 9.8746 8.7639 7.8043 6.9721 6.2475 5.6145 5.0595 4.5715 4.1408 3.7597 3.4214 3.1203 2.8516 2.6111 2.3954 2.2014 2.0265 1.8686 1.7255 1.5957 1.4777 1.3702 1.2721 1.1824 2.1695 2.2392 2.3100 2.3821 2.4554 2.5303 2.6069 2.6854 2.7662 2.8496 2.9363 3.0269 3.1227 3.2253 3.3379 3.4661 3.6243 3.8680 4.4004 2.2415 2.3161 2.3922 2.4697 2.5490 2.6302 2.7135 2.7992 2.8878 2.9796 3.0753 3.1759 3.2827 3.3976 3.5243 3.6695 3.8497 4.1302 4.7627 0.022611 0.023223 0.023840 0.024462 0.025092 0.025731 0.026380 0.027041 0.027717 0.028412 0.029131 0.029880 0.030668 0.031512 0.032436 0.033492 0.034804 0.036863 0.041603 0.026979 0.026965 0.026961 0.026966 0.026982 0.027010 0.027053 0.027113 0.027194 0.027300 0.027438 0.027618 0.027855 0.028171 0.028607 0.029242 0.030266 0.032343 0.076131 0.077996 0.080090 0.082459 0.085163 0.088280 0.091919 0.096227 0.10142 0.10781 0.11589 0.12645 0.14089 0.16186 0.19519 0.25624 0.40151 1.0148 476.31 463.48 450.49 437.29 423.88 410.23 396.30 382.04 367.40 352.31 336.67 320.36 303.21 285.00 265.37 243.75 219.07 189.12 0 4.8774 4.8825 4.9025 4.9225 4.9424 4.9621 4.9817 5.0012 5.0205 5.0397 5.0587 5.0774 5.0960 5.1144 5.1326 5.1505 5.1682 5.1856 5.2028 5.2196 5.2362 5.2525 5.2684 5.2841 5.2994 5.3143 5.3289 5.3431 5.3569 5.3703 5.3832 5.3958 5.4079 5.4195 5.4307 5.4413 5.4514 5.4610 5.4701 5.4785 5.4864 5.4936 5.5002 5.3730 5.3800 5.4081 5.4361 5.4639 5.4915 5.5189 5.5461 5.5731 5.5998 5.6263 5.6525 5.6784 5.7040 5.7292 5.7541 5.7786 5.8027 5.8264 5.8497 5.8726 5.8949 5.9169 5.9383 5.9591 5.9795 5.9993 6.0185 6.0372 6.0552 6.0726 6.0893 6.1054 6.1207 6.1354 6.1492 6.1624 6.1747 6.1862 6.1968 6.2066 6.2154 6.2233 0.096708 0.096323 0.094825 0.093392 0.092020 0.090705 0.089445 0.088235 0.087074 0.085959 0.084887 0.083855 0.082862 0.081906 0.080983 0.080094 0.079235 0.078406 0.077604 0.076828 0.076076 0.075348 0.074643 0.073957 0.073292 0.072645 0.072016 0.071403 0.070806 0.070224 0.069655 0.069099 0.068556 0.068024 0.067503 0.066991 0.066489 0.065995 0.065510 0.065031 0.064560 0.064094 0.063633 0.020805 0.020809 0.020825 0.020843 0.020864 0.020886 0.020911 0.020938 0.020968 0.021000 0.021035 0.021072 0.021113 0.021156 0.021201 0.021250 0.021302 0.021356 0.021414 0.021474 0.021538 0.021605 0.021674 0.021747 0.021822 0.021901 0.021983 0.022068 0.022155 0.022246 0.022340 0.022436 0.022536 0.022638 0.022744 0.022852 0.022964 0.023078 0.023196 0.023317 0.023441 0.023568 0.023698 0.029217 0.029225 0.029261 0.029302 0.029348 0.029399 0.029455 0.029518 0.029587 0.029663 0.029746 0.029836 0.029934 0.030040 0.030155 0.030278 0.030410 0.030552 0.030703 0.030865 0.031037 0.031220 0.031415 0.031621 0.031840 0.032072 0.032317 0.032577 0.032851 0.033141 0.033447 0.033770 0.034111 0.034472 0.034853 0.035256 0.035681 0.036132 0.036610 0.037116 0.037654 0.038225 0.038834 154.83 155.14 156.38 157.60 158.81 159.99 161.16 162.30 163.42 164.53 165.60 166.66 167.69 168.70 169.69 170.65 171.58 172.49 173.37 174.23 175.05 175.85 176.62 177.36 178.07 178.75 179.40 180.02 180.61 181.17 181.69 182.19 182.65 183.08 183.47 183.84 184.17 184.46 184.72 184.95 185.14 185.30 185.42 0.31767 0.37057 0.42848 0.49214 0.56243 0.64047 0.72765 0.82574 0.93703 1.0646 1.2125 1.3865 1.5951 1.8510 2.1752 2.6058 3.2246 4.2808 6.3978 58.283 57.634 55.151 52.832 50.666 48.640 46.742 44.963 43.293 41.724 40.248 38.858 37.548 36.313 35.146 34.043 32.999 32.010 31.072 30.183 29.337 28.534 27.769 27.041 26.346 25.684 25.051 24.447 23.869 23.316 22.786 22.278 21.791 21.324 20.876 20.445 20.031 19.632 19.249 18.879 18.523 18.180 17.848 79.340 77.724 76.119 74.523 72.938 71.363 69.798 68.243 66.700 65.170 63.658 62.176 60.751 59.445 58.409 58.054 59.591 67.802 57.571 55.852 54.152 52.467 50.794 49.130 47.469 45.809 44.141 42.460 40.755 39.013 37.215 35.332 33.316 31.072 28.384 24.467 5.2938 5.3199 5.4244 5.5291 5.6340 5.7391 5.8444 5.9500 6.0559 6.1621 6.2688 6.3759 6.4835 6.5917 6.7005 6.8099 6.9202 7.0312 7.1431 7.2560 7.3700 7.4851 7.6014 7.7192 7.8384 7.9591 8.0817 8.2060 8.3324 8.4610 8.5919 8.7254 8.8616 9.0008 9.1433 9.2893 9.4390 9.5929 9.7513 9.9145 10.083 10.257 10.438 4.2197 4.2382 4.3119 4.3855 4.4590 4.5324 4.6057 4.6788 4.7519 4.8248 4.8976 4.9703 5.0429 5.1154 5.1878 5.2602 5.3325 5.4048 5.4771 5.5494 5.6217 5.6940 5.7664 5.8389 5.9116 5.9844 6.0574 6.1307 6.2043 6.2781 6.3524 6.4272 6.5024 6.5782 6.6547 6.7318 6.8098 6.8887 6.9686 7.0495 7.1317 7.2153 7.3003 2-195 (Continued) 2-196 TABLE 2-110 Thermodynamic Properties of Air (Continued ) Temperature K 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 132.63 Pressure MPa Density mol/dm3 0.65820 0.70732 0.75903 0.81341 0.87055 0.93052 0.9934 1.0593 1.1282 1.2004 1.2757 1.3545 1.4366 1.5223 1.6115 1.7045 1.8013 1.9020 2.0067 2.1156 2.2287 2.3462 2.4682 2.5949 2.7266 2.8633 3.0055 3.1536 3.3084 3.4712 3.6462 3.7858 0.90895 0.97587 1.0467 1.1217 1.2011 1.2852 1.3742 1.4684 1.5682 1.6740 1.7862 1.9053 2.0318 2.1664 2.3097 2.4625 2.6259 2.8009 2.9889 3.1913 3.4103 3.6481 3.9078 4.1934 4.5101 4.8653 5.2697 5.7405 6.3074 7.0343 8.1273 10.448 Volume dm3/mol 1.1002 1.0247 0.95535 0.89147 0.83254 0.77810 0.72772 0.68102 0.63767 0.59737 0.55985 0.52486 0.49217 0.46160 0.43296 0.40608 0.38082 0.35702 0.33457 0.31335 0.29323 0.27412 0.25590 0.23847 0.22173 0.20554 0.18976 0.17420 0.15854 0.14216 0.12304 0.095715 Sound speed m/s JouleThomson K/MPa Therm. cond. mW/(m⋅K) Viscosity mPa⋅s 0.039483 0.040176 0.040918 0.041714 0.042570 0.043492 0.044490 0.045573 0.046751 0.048038 0.049450 0.051005 0.052727 0.054644 0.056790 0.059209 0.061956 0.065102 0.068738 0.072988 0.078015 0.084052 0.091426 0.10063 0.11241 0.12801 0.14959 0.18134 0.23261 0.32992 0.59804 185.51 185.55 185.57 185.54 185.48 185.38 185.24 185.07 184.85 184.60 184.30 183.97 183.59 183.17 182.71 182.21 181.66 181.08 180.45 179.78 179.06 178.31 177.51 176.68 175.81 174.91 173.96 172.98 171.93 170.79 169.40 0 17.528 17.218 16.918 16.628 16.346 16.072 15.805 15.546 15.292 15.044 14.800 14.561 14.324 14.090 13.856 13.623 13.388 13.151 12.909 12.661 12.405 12.137 11.854 11.553 11.229 10.874 10.480 10.033 9.5119 8.8740 7.9854 6.3978 10.626 10.821 11.024 11.237 11.459 11.693 11.939 12.198 12.473 12.764 13.074 13.406 13.762 14.145 14.559 15.008 15.499 16.039 16.635 17.298 18.042 18.884 19.849 20.968 22.288 23.877 25.841 28.367 31.807 37.001 46.996 7.3870 7.4755 7.5659 7.6586 7.7537 7.8514 7.9521 8.0560 8.1634 8.2749 8.3907 8.5114 8.6375 8.7696 8.9086 9.0552 9.2104 9.3755 9.5518 9.7412 9.9456 10.168 10.411 10.681 10.982 11.324 11.720 12.191 12.775 13.553 14.798 0.021087 0.020796 0.021504 0.022817 0.024150 0.025246 0.026091 0.026734 0.027229 0.027619 0.030116 0.029149 0.029830 0.031137 0.032467 0.033562 0.034406 0.035049 0.035544 0.035934 198.24 347.36 446.40 523.89 589.60 648.15 701.76 751.59 798.38 842.62 17.423 2.2510 0.50305 −0.12430 −0.41124 −0.56194 −0.64963 −0.70457 −0.74078 −0.76547 9.4692 26.384 39.944 51.755 62.543 72.680 82.381 91.781 100.97 110.01 7.1068 18.537 27.090 34.176 40.394 46.051 51.325 56.325 61.127 65.783 0.013532 0.017351 0.027868 0.027368 0.061355 0.065680 658.25 582.97 −0.14308 −0.00232 104.97 93.879 88.326 73.903 6.2479 12.289 18.218 24.326 30.698 37.311 44.114 51.065 58.128 65.278 0.060461 0.093372 0.10851 0.11877 0.12677 0.13340 0.13908 0.14405 0.14847 0.15245 0.024739 0.020859 0.021526 0.022830 0.024159 0.025253 0.026096 0.026738 0.027233 0.027622 0.044597 0.029563 0.029954 0.031194 0.032498 0.033582 0.034419 0.035057 0.035550 0.035939 185.23 348.45 448.46 525.96 591.54 649.96 703.44 753.17 799.86 844.02 15.779 2.1789 0.47425 −0.13809 −0.41899 −0.56686 −0.65304 −0.70711 −0.74278 −0.76711 11.965 26.684 40.110 51.868 62.628 72.748 82.438 91.830 101.01 110.05 7.9625 18.672 27.179 34.242 40.446 46.094 51.361 56.357 61.155 65.808 1.2820 12.042 0.012483 0.079244 0.028034 0.021131 0.058181 0.031423 710.56 355.63 −0.21837 1.8817 111.13 28.389 96.436 19.420 Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) 5.5060 5.5112 5.5156 5.5193 5.5221 5.5240 5.5250 5.5251 5.5241 5.5221 5.5188 5.5143 5.5085 5.5012 5.4924 5.4819 5.4695 5.4550 5.4383 5.4190 5.3969 5.3715 5.3424 5.3089 5.2701 5.2248 5.1713 5.1069 5.0268 4.9209 4.7566 4.4004 6.2302 6.2360 6.2408 6.2444 6.2469 6.2481 6.2480 6.2465 6.2436 6.2391 6.2330 6.2252 6.2156 6.2039 6.1901 6.1740 6.1554 6.1341 6.1097 6.0819 6.0504 6.0147 5.9740 5.9277 5.8746 5.8133 5.7417 5.6563 5.5513 5.4143 5.2053 4.7627 0.063177 0.062726 0.062277 0.061832 0.061389 0.060947 0.060506 0.060065 0.059623 0.059180 0.058735 0.058286 0.057833 0.057375 0.056910 0.056437 0.055955 0.055461 0.054954 0.054432 0.053890 0.053326 0.052735 0.052112 0.051448 0.050732 0.049950 0.049076 0.048067 0.046830 0.045064 0.041603 0.023833 0.023970 0.024112 0.024258 0.024408 0.024563 0.024722 0.024887 0.025058 0.025234 0.025418 0.025608 0.025807 0.026015 0.026232 0.026461 0.026701 0.026956 0.027226 0.027514 0.027823 0.028155 0.028516 0.028910 0.029344 0.029827 0.030371 0.030994 0.031726 0.032619 0.033814 5.6800 9.8544 14.072 18.500 23.201 28.145 33.282 38.568 43.966 49.453 6.4941 12.348 18.231 24.323 30.686 37.293 44.094 51.042 58.104 65.253 0.080463 0.11269 0.12770 0.13794 0.14593 0.15255 0.15823 0.16320 0.16762 0.17160 1.2007 1.5924 1.2383 1.6321 5.5251 9.8022 14.046 18.485 23.190 28.138 33.278 38.565 43.964 49.451 1.0983 9.5710 Single-Phase Properties 100 300 500 700 900 1100 1300 1500 1700 1900 100 106.22 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1 1 108.1 300 500 700 900 1100 1300 1500 1700 1900 1 1 1 1 1 1 1 1 1 1 100 300 5 5 0.12283 0.040103 0.024046 0.017175 0.013359 0.010931 0.009249 0.008016 0.007073 0.006329 26.593 25.232 1.3836 0.40205 0.23974 0.17119 0.13319 0.10902 0.092279 0.079999 0.070604 0.063185 27.222 2.0232 8.1414 24.936 41.586 58.223 74.855 91.486 108.12 124.75 141.38 158.00 0.037604 0.039632 0.72278 2.4873 4.1711 5.8415 7.5079 9.1727 10.837 12.500 14.163 15.827 0.036735 0.49426 500 700 900 1100 1300 1500 1700 1900 5 5 5 5 5 5 5 5 1.1814 0.84321 0.65711 0.53874 0.45667 0.39636 0.35015 0.31361 0.84642 1.1859 1.5218 1.8562 2.1898 2.5229 2.8559 3.1887 13.935 18.417 23.146 28.107 33.256 38.550 43.954 49.445 18.167 24.347 30.755 37.388 44.205 51.165 58.234 65.389 0.094907 0.10529 0.11334 0.11999 0.12568 0.13066 0.13509 0.13907 0.021621 0.022885 0.024197 0.025282 0.026119 0.026757 0.027249 0.027636 0.030478 0.031434 0.032632 0.033664 0.034473 0.035095 0.035577 0.035958 458.30 535.45 600.34 658.10 711.01 760.23 806.49 850.28 0.36370 −0.19118 −0.44905 −0.58606 −0.66646 −0.71716 −0.75073 −0.77366 40.969 52.433 63.045 73.076 82.707 92.057 101.21 110.22 27.606 34.545 40.682 46.287 51.523 56.497 61.278 65.917 100 300 500 700 900 1100 1300 1500 1700 1900 10 10 10 10 10 10 10 10 10 10 27.863 4.0370 2.3157 1.6542 1.2922 1.0618 0.90165 0.78374 0.69321 0.62149 0.035889 0.24771 0.43183 0.60452 0.77388 0.94184 1.1091 1.2759 1.4426 1.6090 0.99444 9.2885 13.802 18.336 23.092 28.070 33.231 38.532 43.943 49.438 1.3533 11.766 18.120 24.382 30.831 37.489 44.321 51.292 58.368 65.528 0.011382 0.072612 0.088894 0.099422 0.10752 0.11420 0.11990 0.12489 0.12932 0.13330 0.028284 0.021441 0.021733 0.022952 0.024243 0.025317 0.026146 0.026780 0.027268 0.027653 0.055716 0.033664 0.031078 0.031710 0.032786 0.033760 0.034537 0.035139 0.035608 0.035981 763.47 369.50 471.81 547.83 611.64 668.47 720.60 769.17 814.87 858.18 −0.27969 1.5212 0.25100 −0.24405 −0.47890 −0.60517 −0.67990 −0.72730 −0.75881 −0.78039 117.77 31.116 42.260 53.257 63.641 73.538 83.082 92.372 101.48 110.45 105.78 20.637 28.194 34.944 40.985 46.531 51.728 56.673 61.432 66.054 100 300 500 700 900 1100 1300 1500 1700 1900 100 100 100 100 100 100 100 100 100 100 33.161 21.138 15.089 11.803 9.7481 8.3307 7.2877 6.4847 5.8456 5.3239 0.030156 0.047309 0.066273 0.084722 0.10258 0.12004 0.13722 0.15421 0.17107 0.18783 0.24746 7.0356 12.371 17.367 22.408 27.580 32.880 38.287 43.779 49.340 3.2631 11.767 18.999 25.840 32.667 39.584 46.602 53.708 60.886 68.123 0.001378 0.049067 0.067619 0.079134 0.087711 0.09465 0.10051 0.10559 0.11009 0.11411 0.031980 0.023981 0.023117 0.023855 0.024903 0.025831 0.026565 0.027131 0.027569 0.027915 0.048218 0.038366 0.034686 0.034011 0.034331 0.034845 0.035323 0.035723 0.036049 0.036317 1192.4 818.47 772.41 790.14 821.78 857.40 894.00 930.40 966.13 1001.0 −0.47290 −0.49747 −0.55640 −0.62591 −0.67702 −0.71435 −0.74281 −0.76506 −0.78264 −0.79653 179.20 86.312 71.549 73.572 79.057 85.797 93.151 100.84 108.75 116.78 252.46 53.642 42.159 43.339 46.948 51.158 55.511 59.875 64.208 68.504 300 500 700 900 1100 1300 1500 1700 1900 500 500 500 500 500 500 500 500 500 34.106 29.826 26.714 24.283 22.305 20.651 19.243 18.027 16.963 0.029320 0.033528 0.037433 0.041180 0.044833 0.048423 0.051966 0.055473 0.058952 6.2145 11.583 16.768 22.008 27.358 32.814 38.354 43.961 49.623 20.875 28.348 35.484 42.598 49.775 57.025 64.337 71.698 79.098 0.033155 0.052311 0.064323 0.073261 0.080460 0.086515 0.091746 0.096353 0.10047 0.028875 0.026614 0.026496 0.026991 0.027539 0.028000 0.02836 0.02864 0.02886 0.039265 0.036111 0.035494 0.035702 0.036073 0.036415 0.036693 0.036911 0.037085 1678.8 1573.6 1514.8 1482.8 1468.3 1465.1 1469.3 1478.5 1491.1 −0.57656 −0.65015 −0.67879 −0.68796 −0.69130 −0.69354 −0.69594 −0.69875 −0.70188 208.23 178.50 161.67 151.95 146.88 144.95 145.84 148.48 152.39 181.12 120.62 97.470 86.531 81.387 79.411 79.312 80.393 82.251 300 500 700 900 1100 1300 1500 1700 1900 1000 1000 1000 1000 1000 1000 1000 1000 1000 40.130 36.567 33.895 31.736 29.916 28.338 26.946 25.701 24.577 0.024919 0.027347 0.029503 0.031510 0.033427 0.035288 0.037111 0.038909 0.040688 6.8286 12.271 17.554 22.890 28.327 33.857 39.461 45.123 50.830 31.747 39.618 47.057 54.399 61.754 69.145 76.573 84.032 91.519 0.024761 0.044944 0.057468 0.066695 0.074073 0.080246 0.085561 0.090229 0.094392 0.032271 0.029334 0.028754 0.028917 0.029215 0.029476 0.029675 0.029821 0.029928 0.041510 0.037843 0.036801 0.036702 0.036858 0.037051 0.037224 0.037369 0.037491 2208.5 2104.7 2033.9 1984.7 1951.3 1929.3 1915.7 1908.3 1905.8 −0.50493 −0.57316 −0.60504 −0.61882 −0.62560 −0.62968 −0.63251 −0.63465 −0.63632 274.96 247.30 230.60 219.72 212.46 207.70 204.81 203.41 203.25 337.76 219.41 174.51 149.43 133.76 123.58 116.94 112.74 110.27 This table was generated for a standard three-component dry air containing mole fractions 0.7812 nitrogen, 0.2096 oxygen, and 0.0092 argon. The values in this table were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., Jacobsen, R. T, Penoncello, S. G., and Friend, D. G., “Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa,” J. Phys. Chem. Ref. Data 29(3):331–385, 2000. The source for viscosity and thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the freezing point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated speed of sound values is 0.2% and that for calculated heat capacities is 1%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is 0.5%, increasing to 1.0% at 2000 K and 2000 MPa. For viscosity, the uncertainty is 1% in the dilute gas. The uncertainty is around 2% between 270 and 300 K and increases to 5% outside of this region. There are very few measurements between 130 and 270 K for air to validate this claim, and the uncertainties may be even higher in this supercritical region. For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple points. The uncertainties range from 3% between 140 and 300 K to 5% at the triple point and at high temperatures. The uncertainties above 100 MPa are not known due to a lack of experimental data. 2-197 2-198 FIG. 2-3 Pressure-enthalpy diagram for dry air. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of E. W. Lemmon, R. T. Jacobsen,, S. G. Penoncello, and D. G. Friend. THERMODYnAMIC PROPERTIES TABLE 2-111 Air Other tables include Stewart, R. B., S. G. Penoncello, et al., University of Idaho CATS report, 85-5, 1985 (0.1-700 bar, 85-750 K), and Lemmon, E. W., Jacobsen, R. T., Penoncello, S. G., and Friend, D. G., Thermodynamic Properties of Air and Mixtures of Nitrogen, Argon, and Oxygen from 60 to 2000 K at Pressures to 2000 MPa, J. Phys. Chem. Ref. Data, 29(3): 331-385, 2000. Tables including reactions with hydrocarbons include Gordon, S., NASA Techn. Paper 1907, 4 vols., 1982. See also Gupta, R. N., K-P. Lee, et al., NASA RP 1232, 1990 (89 pp.) and RP 1260, 1991 (75 pp.). Analytic expressions for high temperatures were given by Matsuzaki, R., Jap. J. Appl. Phys., 21, 7 (1982): 1009-1013 and Japanese National Aerospace Laboratory report NAL TR 671, 1981 (45 pp.). Functions from 1500 to 15,000 K were tabulated by Hilsenrath, J. and M. Klein, AEDC-TR-65-58 = AD 612 301, 1965 (333 pp.). Tables from 10000 to 10,000,000 K were authored by Gilmore, F. R., Lockheed rept. 3-27-67-1, vol 1., 1967 (340 pp.), also published as Radiative Properties of Air, IFI/Plenum, New York, 1969 (648 pp.). Saturation and superheat tables and a chart to 7000 psia, 660°R appear in Stewart, R. B., R. T. Jacobsen, et al., Thermodynamic Properties of Refrigerants, ASHRAE, Atlanta, Ga, 1986 (521 pp.). For specific heat, thermal conductivity, and viscosity see Thermophysical Properties of Refrigerants, ASHRAE, 1993. Air, Moist For other data in this handbook, please see Figure 2-2 and the psychrometric tables, figures and descriptions in Section 12. An ASHRAE publication, Thermodynamic Properties of Dry Air and Water and S. I. Psychrometric Charts, 1983 (360 pp.), extensively reviews moist air properties. Gandiduson, P., Chem. Eng., Oct. 29, 1984 gives on page 118 a nomograph from 50 to 120°F, while equations in SI units were given by Nelson, B., Chem. Eng. Progr. 76, 5 (May 1980): 83–85. Liley, P. E., 2000 Solved Problems in M.E. Thermodynamics, McGraw-Hill, New York, 1989, gives four simple equations with which most calculations can be made. Devres, Y.O., Appl. Energy 48 (1994): 1–18 gives equations with which three known properties can be used to determine four others. Klappert, M. T. and G. F. Schilling, Rand RM-4244-PR = AD 604 856, 1984 (40 pp.) gives tables from 100 to 270 K, while programs from −60 to 2°F are given by Sando, F. A., ASHRAE Trans., 96, 2 (1990): 299–308. Viscosity references include Kestin, J. and J. H. Whitelaw, Int. J. Ht. Mass Transf. 7, 11 (1964): 1245–1255; Studnokov, E. L., Inz.-Fiz. Zhur. 19, 2 (1970): 338–340; Hochramer, D. and F. Munczak, Setzb. Ost. Acad. Wiss II 175, 10 (1966): 540–550. For thermal conductivity see, for instance, Mason, E. A. and L. Monchick, Humidity and Moisture Control in Science and Industry, Reinhold, New York, 1965 (257–272). 2-199 2-200 TABLE 2-112 Thermodynamic Properties of Ammonia Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol 0.00000 0.32333 1.0480 1.7825 2.5265 3.2793 4.0403 4.8093 5.5862 6.3712 7.1651 7.9691 8.7850 9.6153 10.463 11.333 12.232 13.169 14.158 15.224 16.424 17.969 20.640 0.00014154 0.32353 1.0484 1.7833 2.5279 3.2818 4.0445 4.8160 5.5963 6.3861 7.1866 7.9993 8.8265 9.6714 10.538 11.432 12.361 13.335 14.373 15.503 16.790 18.478 21.499 23.661 23.770 24.006 24.233 24.450 24.655 24.846 25.021 25.179 25.317 25.435 25.528 25.595 25.632 25.634 25.595 25.505 25.350 25.107 24.734 24.144 23.047 20.640 25.279 25.424 25.737 26.038 26.325 26.596 26.847 27.077 27.281 27.459 27.606 27.720 27.796 27.830 27.816 27.746 27.606 27.381 27.042 26.539 25.768 24.386 21.499 Entropy kJ/(mol⋅K) Sound speed m/s Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) 0.00000 0.0016351 0.0051707 0.0085874 0.011894 0.015098 0.018205 0.021222 0.024154 0.027010 0.029797 0.032525 0.035203 0.037843 0.040458 0.043065 0.045682 0.048339 0.051075 0.053961 0.057149 0.061223 0.068559 0.049972 0.049837 0.049521 0.049207 0.048906 0.048613 0.048327 0.048047 0.047774 0.047511 0.047266 0.047044 0.046856 0.046715 0.046636 0.046642 0.046767 0.047064 0.047619 0.048589 0.050319 0.054109 0.071565 0.071988 0.072971 0.073950 0.074883 0.075764 0.076608 0.077448 0.078328 0.079296 0.080412 0.081747 0.083390 0.085465 0.088145 0.091701 0.096576 0.10357 0.11435 0.13314 0.17550 0.38707 2124.2 2080.2 1992.7 1913.7 1839.2 1766.9 1695.6 1624.5 1553.1 1481.0 1407.8 1333.2 1256.7 1177.9 1096.5 1011.8 923.38 830.62 732.78 628.75 515.88 384.58 0 0.12931 0.12714 0.12273 0.11884 0.11536 0.11224 0.10942 0.10684 0.10447 0.10227 0.10021 0.098259 0.096395 0.094589 0.092817 0.091046 0.089242 0.087355 0.085316 0.083003 0.080169 0.075992 0.068559 0.026510 0.026650 0.027053 0.027583 0.028245 0.029043 0.029978 0.031050 0.032253 0.033581 0.035028 0.036584 0.038244 0.040004 0.041868 0.043844 0.045954 0.048233 0.050744 0.053589 0.056957 0.061281 0.035130 0.035345 0.035961 0.036783 0.037836 0.039142 0.040728 0.042623 0.044859 0.047476 0.050530 0.054099 0.058302 0.063320 0.069443 0.077150 0.087280 0.10141 0.12286 0.16000 0.24170 0.59477 354.12 357.91 365.94 373.38 380.19 386.30 391.66 396.20 399.86 402.59 404.30 404.95 404.45 402.70 399.61 395.05 388.86 380.83 370.69 357.96 341.67 318.22 0 Therm. Joule-Thomson cond. K/MPa mW/(m⋅K) Viscosity µPa⋅s Saturated Properties 195.50 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.00 390.00 400.00 405.40 0.0060912 0.0086509 0.017739 0.033790 0.060407 0.10223 0.16494 0.25531 0.38107 0.55092 0.77436 1.0617 1.4240 1.8728 2.4205 3.0802 3.8660 4.7929 5.8778 7.1402 8.6045 10.305 11.339 43.035 42.754 42.111 41.442 40.748 40.032 39.293 38.533 37.748 36.939 36.101 35.230 34.320 33.363 32.350 31.264 30.087 28.788 27.321 25.606 23.465 20.232 13.212 195.50 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 380.00 390.00 400.00 405.40 0.0060912 0.0086509 0.017739 0.033790 0.060407 0.10223 0.16494 0.25531 0.38107 0.55092 0.77436 1.0617 1.4240 1.8728 2.4205 3.0802 3.8660 4.7929 5.8778 7.1402 8.6045 10.305 11.339 0.0037635 0.0052305 0.010249 0.018721 0.032214 0.052667 0.082417 0.12421 0.18126 0.25729 0.35664 0.48448 0.64702 0.85202 1.1094 1.4325 1.8399 2.3598 3.0375 3.9558 5.2979 7.6973 13.212 0.023237 0.023389 0.023747 0.024130 0.024541 0.024980 0.025450 0.025952 0.026491 0.027072 0.027700 0.028385 0.029138 0.029973 0.030912 0.031986 0.033237 0.034737 0.036602 0.039054 0.042616 0.049426 0.075690 265.71 191.19 97.573 53.415 31.043 18.987 12.133 8.0506 5.5168 3.8867 2.8040 2.0641 1.5455 1.1737 0.90139 0.69810 0.54350 0.42377 0.32922 0.25279 0.18875 0.12992 0.075690 −0.23362 −0.22917 −0.21883 −0.20813 −0.19712 −0.18561 −0.17327 −0.15963 −0.14414 −0.12612 −0.10470 −0.078790 −0.046923 −0.0070718 0.043673 0.10967 0.19774 0.31928 0.49497 0.76738 1.2455 2.3557 5.0513 171.13 152.55 120.01 96.215 78.430 64.852 54.280 45.905 39.175 33.701 29.207 25.489 22.391 19.794 17.599 15.728 14.112 12.690 11.400 10.172 8.9038 7.3513 5.0513 818.99 803.14 768.02 733.17 698.80 665.09 632.16 600.07 568.85 538.50 508.99 480.25 452.23 424.83 397.96 371.51 345.32 319.25 293.07 266.57 239.65 216.00 19.636 19.684 19.860 20.132 20.503 20.978 21.560 22.258 23.079 24.034 25.138 26.408 27.872 29.568 31.559 33.945 36.900 40.752 46.149 54.556 70.114 113.54 559.57 507.28 414.98 346.68 294.94 254.85 223.08 197.34 176.06 158.12 142.74 129.33 117.49 106.91 97.325 88.555 80.430 72.796 65.493 58.315 50.877 41.802 6.8396 6.9515 7.2115 7.4846 7.7679 8.0587 8.3552 8.6558 8.9595 9.2664 9.5771 9.8938 10.220 10.561 10.927 11.330 11.792 12.346 13.053 14.025 15.527 18.529 Single-Phase Properties 200.00 239.56 239.56 300.00 400.00 500.00 600.00 700.00 200.00 298.05 298.05 300.00 400.00 500.00 600.00 700.00 200.00 300.00 362.03 362.03 400.00 500.00 600.00 700.00 200.00 300.00 398.32 398.32 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00 300.00 400.00 500.00 600.00 700.00 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 10.000 100.00 100.00 100.00 100.00 100.00 500.00 500.00 500.00 500.00 500.00 1000.0 1000.0 1000.0 1000.0 1000.0 42.756 40.064 0.051595 0.040502 0.030171 0.024091 0.020060 0.017188 42.774 35.403 0.45697 0.45215 0.31157 0.24426 0.20197 0.17248 42.852 35.450 28.505 2.4828 1.8706 1.3046 1.0412 0.87563 42.947 35.714 20.945 7.1390 6.5455 2.8656 2.1650 1.7835 38.995 33.105 27.067 21.518 17.303 45.670 42.416 39.515 36.909 34.550 49.944 47.551 45.362 43.378 41.556 0.023388 0.024960 19.382 24.690 33.144 41.509 49.849 58.179 0.023379 0.028246 2.1883 2.2117 3.2095 4.0940 4.9513 5.7977 0.023336 0.028209 0.035081 0.40277 0.53459 0.76650 0.96040 1.1420 0.023284 0.028000 0.047744 0.14008 0.15278 0.34897 0.46190 0.56069 0.025644 0.030207 0.036945 0.046473 0.057794 0.021896 0.023576 0.025307 0.027094 0.028943 0.020022 0.021030 0.022045 0.023053 0.024064 0.32270 3.2461 24.646 26.378 29.297 32.514 36.096 40.068 0.31651 7.8111 25.512 25.592 29.019 32.359 35.994 39.994 0.28942 7.8852 13.365 25.309 27.540 31.630 35.527 39.662 0.25644 7.7848 17.655 23.303 23.801 30.616 34.920 39.241 6.5830 13.432 20.212 26.825 33.074 4.7114 10.633 16.367 22.007 27.680 4.1818 9.8612 15.432 20.911 26.418 0.32504 3.2486 26.584 28.847 32.612 36.665 41.081 45.885 0.33989 7.8393 27.700 27.804 32.229 36.453 40.945 45.792 0.40611 8.0263 13.540 27.323 30.213 35.462 40.329 45.373 0.48928 8.0648 18.132 24.704 25.329 34.106 39.539 44.848 9.1474 16.453 23.907 31.472 38.854 15.660 22.421 29.021 35.554 42.152 24.204 30.891 37.477 43.964 50.481 0.0016320 0.014960 0.11237 0.12080 0.13162 0.14065 0.14869 0.15609 0.0016010 0.031996 0.098633 0.098979 0.11177 0.12119 0.12937 0.13684 0.0014649 0.032243 0.048887 0.086956 0.094581 0.10634 0.11521 0.12298 0.0012980 0.031903 0.060394 0.076892 0.078458 0.098525 0.10844 0.11663 0.027511 0.048523 0.065147 0.078942 0.090326 0.018023 0.037482 0.052215 0.064127 0.074295 0.011750 0.030984 0.045686 0.057514 0.067559 0.049842 0.048626 0.029005 0.028021 0.030417 0.033897 0.037731 0.041678 0.049890 0.047085 0.036271 0.035866 0.031641 0.034312 0.037928 0.041791 0.050097 0.047090 0.047152 0.048722 0.038466 0.036193 0.038798 0.042289 0.050342 0.047164 0.053149 0.060447 0.057611 0.038603 0.039862 0.042896 0.048894 0.046636 0.045999 0.046723 0.048331 0.052877 0.051527 0.050431 0.050614 0.051816 0.055176 0.054864 0.053323 0.052940 0.053649 0.071983 0.075726 0.039079 0.036849 0.038883 0.042280 0.046083 0.050015 0.071938 0.081465 0.053356 0.052493 0.041627 0.043338 0.046628 0.050341 0.071739 0.080899 0.10538 0.10501 0.061581 0.048779 0.049210 0.051836 0.071495 0.079960 0.30653 0.46915 0.30552 0.057806 0.052806 0.053796 0.072740 0.073557 0.075495 0.075193 0.072317 0.067831 0.066802 0.065418 0.065476 0.066615 0.065784 0.066677 0.065150 0.064819 0.065697 2080.3 1770.0 386.05 434.39 497.93 550.96 597.69 640.16 2081.5 1347.9 404.91 407.16 488.94 546.79 595.60 639.15 2086.8 1361.2 811.17 378.95 441.81 528.14 586.79 635.17 2093.5 1394.2 409.04 323.12 336.28 505.64 577.38 631.50 1774.7 1378.2 1081.8 918.11 861.52 2597.1 2353.2 2176.9 2044.6 1943.8 3230.2 2997.6 2842.8 2728.6 2639.0 −0.22921 −0.18613 65.377 27.493 10.681 5.5276 3.2702 2.0841 −0.22959 −0.084271 26.163 25.620 10.494 5.4884 3.2544 2.0746 −0.23126 −0.089577 0.34968 12.419 9.6373 5.2830 3.1693 2.0254 −0.23328 −0.10159 2.0704 7.6606 7.7633 4.9335 3.0278 1.9491 −0.19551 −0.11309 0.049919 0.23722 0.32753 −0.25055 −0.25064 −0.25260 −0.24722 −0.23682 −0.25989 −0.25431 −0.26084 −0.26235 −0.25820 803.24 666.56 20.955 25.100 37.215 53.119 68.607 78.312 804.23 485.81 26.145 26.308 38.087 53.750 69.123 78.751 808.60 487.57 313.94 41.693 45.730 57.294 71.791 80.941 814.02 496.50 218.73 101.04 95.455 63.922 76.053 84.235 622.86 431.98 305.65 234.79 196.04 989.00 804.05 674.00 582.63 511.57 1324.0 1138.9 996.49 887.73 797.25 507.47 256.42 8.0459 10.161 13.971 17.863 21.682 25.391 509.28 131.82 9.8313 9.9115 13.927 17.877 21.717 25.434 517.30 132.49 71.291 12.475 14.036 18.073 21.941 25.662 527.29 136.36 43.632 17.793 17.230 18.722 22.393 26.035 193.71 96.237 60.386 46.188 41.237 376.31 188.46 120.77 91.251 77.538 554.62 274.91 174.11 129.02 107.14 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., Harms-Watzenberg, F., and Baehr, H. D., “Eine neue Fundamentalgleichung fuer Ammoniak,” DKV-Tagungsbericht, 20:167–181, 1993. The source for viscosity is Fenghour, A., Wakeham, W. A., Vesovic, V., Watson, J. T. R., Millat, J., and Vogel, E., “The Viscosity of Ammonia,” J. Phys. Chem. Ref. Data 24:1649–1667, 1995. The source for thermal conductivity is Tufeu, R., Ivanov, D. Y., Garrabos, Y., and Le Neindre, B., “Thermal Conductivity of Ammonia in a Large Temperature and Pressure Range Including the Critical Region,” Ber. Bunsenges. Phys. Chem. 88:422–427, 1984. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.2% in density, 2% in heat capacity, and 2% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. The uncertainty varies from 0.5% for the viscosity of the dilute gas phase at moderate temperatures to about 5% for the viscosity at high pressures and temperatures. The uncertainty in thermal conductivity is 2%. 2-201 2-202 TABLE 2-113 Temperature K Thermodynamic Properties of Carbon Dioxide Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 180.63 176.15 169.67 163.28 156.98 150.75 144.58 138.47 132.40 126.35 120.31 114.25 108.17 102.03 95.810 89.546 83.558 80.593 256.70 242.01 222.19 204.23 187.88 172.96 159.30 146.74 135.14 124.40 114.40 105.02 96.174 87.731 79.548 71.409 62.936 53.107 11.014 11.301 11.745 12.221 12.736 13.297 13.917 14.610 15.396 16.306 17.381 18.687 20.325 22.468 25.424 29.821 37.215 53.689 10.951 11.135 11.409 11.689 11.976 12.272 12.579 12.902 13.245 13.614 14.017 14.469 14.987 15.601 16.361 17.357 18.792 21.306 Saturated Properties 216.59 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 304.13 0.51796 0.59913 0.73509 0.89291 1.0747 1.2825 1.5185 1.7850 2.0843 2.4188 2.7909 3.2033 3.6589 4.1607 4.7123 5.3177 5.9822 6.7131 7.3773 26.777 26.497 26.078 25.646 25.201 24.742 24.264 23.767 23.246 22.697 22.114 21.491 20.817 20.077 19.247 18.284 17.100 15.434 10.625 0.037345 0.037740 0.038347 0.038992 0.039680 0.040418 0.041213 0.042075 0.043018 0.044059 0.045219 0.046531 0.048037 0.049808 0.051957 0.054693 0.058480 0.064793 0.094118 3.5030 3.7943 4.2235 4.6554 5.0908 5.5303 5.9749 6.4256 6.8836 7.3505 7.8282 8.3190 8.8266 9.3560 9.9154 10.519 11.197 12.036 13.928 3.5223 3.8169 4.2517 4.6902 5.1334 5.5821 6.0375 6.5007 6.9733 7.4571 7.9544 8.4681 9.0024 9.5633 10.160 10.810 11.547 12.471 14.622 0.022943 0.024279 0.026209 0.028110 0.029986 0.031840 0.033678 0.035505 0.037326 0.039148 0.040979 0.042829 0.044711 0.046643 0.048657 0.050805 0.053196 0.056151 0.063094 0.042895 0.042682 0.042383 0.042103 0.041843 0.041605 0.041393 0.041212 0.041079 0.041029 0.041109 0.041351 0.041750 0.042270 0.042900 0.043734 0.045175 0.049288 0.085960 0.086338 0.087024 0.087886 0.088954 0.090263 0.091866 0.093831 0.096251 0.099258 0.10306 0.10798 0.11457 0.12385 0.13790 0.16176 0.21098 0.38279 975.85 951.21 915.16 879.09 842.88 806.38 769.44 731.78 693.01 652.58 610.07 565.46 519.14 471.54 422.75 371.95 315.91 245.67 0 −0.14430 −0.13180 −0.11104 −0.086994 −0.059053 −0.026454 0.011808 0.057087 0.11121 0.17663 0.25672 0.35639 0.48324 0.64959 0.87650 1.2037 1.7218 2.7258 5.8665 216.59 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 304.13 0.51796 0.59913 0.73509 0.89291 1.0747 1.2825 1.5185 1.7850 2.0843 2.4188 2.7909 3.2033 3.6589 4.1607 4.7123 5.3177 5.9822 6.7131 7.3773 0.31268 0.35941 0.43766 0.52878 0.63442 0.75654 0.89743 1.0599 1.2472 1.4637 1.7149 2.0080 2.3535 2.7663 3.2702 3.9074 4.7654 6.1028 10.625 3.1982 2.7824 2.2849 1.8912 1.5762 1.3218 1.1143 0.94353 0.80180 0.68320 0.58314 0.49800 0.42490 0.36150 0.30579 0.25593 0.20985 0.16386 0.094118 17.286 17.329 17.387 17.438 17.481 17.515 17.538 17.550 17.549 17.532 17.498 17.441 17.359 17.241 17.078 16.848 16.509 15.935 13.928 18.943 18.996 19.067 19.127 19.175 19.210 19.230 19.234 19.220 19.185 19.125 19.037 18.913 18.746 18.519 18.209 17.764 17.035 14.622 0.094138 0.093276 0.092055 0.090878 0.089736 0.088622 0.087526 0.086439 0.085352 0.084254 0.083133 0.081972 0.080750 0.079437 0.077987 0.076319 0.074270 0.071364 0.063094 0.027691 0.028120 0.028782 0.029488 0.030241 0.031042 0.031899 0.032827 0.033844 0.034955 0.036164 0.037482 0.038949 0.040628 0.042629 0.045155 0.048677 0.054908 0.039992 0.040943 0.042489 0.044244 0.046248 0.048555 0.051242 0.054421 0.058244 0.062912 0.068721 0.076168 0.086123 0.10020 0.12177 0.15906 0.23904 0.52463 222.78 223.15 223.49 223.57 223.40 222.96 222.24 221.22 219.87 218.19 216.15 213.75 210.96 207.72 203.94 199.45 193.84 185.33 0 26.174 25.084 23.617 22.288 21.077 19.969 18.950 18.005 17.117 16.277 15.476 14.704 13.947 13.185 12.387 11.509 10.459 9.0093 5.8665 Single-Phase Properties 250.00 450.00 650.00 850.00 1050.0 0.10000 0.10000 0.10000 0.10000 0.10000 0.048542 0.026758 0.018506 0.014148 0.011452 250.00 450.00 650.00 850.00 1050.0 1.0000 1.0000 1.0000 1.0000 1.0000 0.53250 0.27038 0.18527 0.14131 0.11430 250.00 287.43 5.0000 5.0000 287.43 450.00 650.00 850.00 1050.0 5.0000 5.0000 5.0000 5.0000 5.0000 250.00 450.00 650.00 850.00 1050.0 10.000 10.000 10.000 10.000 10.000 18.448 24.664 32.199 40.636 49.704 20.509 28.401 37.602 47.705 58.436 0.11415 0.13712 0.15397 0.16750 0.17883 0.026766 0.034775 0.040192 0.043944 0.046573 0.035428 0.043148 0.048529 0.052271 0.054895 247.79 324.41 385.01 437.11 483.65 17.399 4.0212 1.6551 0.78058 0.34646 12.950 29.346 45.466 60.295 73.843 12.565 21.901 29.873 36.707 42.692 1.8779 3.6985 5.3976 7.0767 8.7487 18.023 24.546 32.133 40.591 49.671 19.901 28.244 37.530 47.668 58.419 0.093263 0.11771 0.13473 0.14830 0.15965 0.029361 0.034954 0.040239 0.043965 0.046585 0.042504 0.043866 0.048779 0.052397 0.054970 235.08 322.89 385.36 438.06 484.84 17.606 3.9880 1.6311 0.76632 0.33777 13.584 29.620 45.651 60.435 73.956 12.691 21.954 29.907 36.732 42.712 0.041563 0.053196 6.2824 10.202 6.4902 10.468 0.034925 0.049681 0.041321 0.043268 0.090937 0.14775 762.21 398.39 142.22 92.760 153.15 75.598 0.28090 0.70647 1.0755 1.4237 1.7650 16.977 24.000 31.842 40.395 49.524 18.381 27.533 37.219 47.513 58.349 0.077209 0.10313 0.12091 0.13469 0.14613 0.043774 0.035769 0.040445 0.044055 0.046637 0.13705 0.047478 0.049898 0.052945 0.055297 201.86 317.50 387.59 442.64 490.31 11.974 3.8034 1.5263 0.70611 0.30129 27.323 31.164 46.589 61.117 74.494 16.808 22.429 30.157 36.899 42.836 24.459 2.9910 1.8632 1.3930 1.1205 0.040885 0.33433 0.53671 0.71790 0.89248 6.0862 23.276 31.482 40.155 49.347 6.4950 26.619 36.849 47.334 58.271 0.034120 0.095787 0.11461 0.12866 0.14021 0.041488 0.036785 0.040693 0.044164 0.046701 0.087624 0.052935 0.051293 0.053603 0.055685 804.05 314.60 391.91 449.04 497.48 −0.034849 3.4705 1.3965 0.63635 0.25964 147.52 33.917 48.005 62.093 75.242 162.47 23.679 30.687 37.224 43.066 24.060 18.798 3.5600 1.4155 0.92982 0.70241 0.56658 20.601 37.372 54.037 70.683 87.321 0.015208 1.0195 250.00 450.00 650.00 850.00 1050.0 100.00 100.00 100.00 100.00 100.00 28.075 19.246 13.677 10.636 8.7929 0.035619 0.051959 0.073117 0.094022 0.11373 4.3002 16.560 27.132 37.076 46.995 7.8621 21.756 34.444 46.478 58.368 0.026023 0.067062 0.090445 0.10660 0.11916 0.043569 0.040841 0.043108 0.045620 0.047676 0.073521 0.066107 0.061252 0.059534 0.059512 1227.6 753.30 646.36 646.61 668.90 −0.27302 −0.11128 −0.054084 −0.13292 −0.21482 206.28 106.65 86.093 87.259 94.022 287.05 83.996 58.868 54.445 55.058 450.00 650.00 850.00 1050.0 500.00 500.00 500.00 500.00 28.922 25.661 23.144 21.126 0.034576 0.038969 0.043208 0.047334 13.014 23.302 33.551 43.903 30.302 42.786 55.155 67.570 0.050604 0.073576 0.090166 0.10328 0.047702 0.048419 0.049676 0.050818 0.063434 0.061885 0.061912 0.062247 1576.4 1404.7 1320.1 1278.7 −0.38514 −0.40369 −0.41098 −0.41674 239.59 197.25 177.31 168.50 303.64 191.14 145.07 123.33 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span, R., and Wagner, W., “A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa,” J. Phys. Chem. Ref. Data 25(6):1509–1596, 1996. The source for viscosity is Fenghour, A., Wakeham, W. A., and Vesovic, V., “The Viscosity of Carbon Dioxide,” J. Phys. Chem. Ref. Data 27:31–44, 1998. The source for thermal conductivity is Vesovic, V., Wakeham, W. A., Olchowy, G. A., Sengers, J. V., Watson, J. T. R., and Millat, J., “The Transport Properties of Carbon Dioxide,” J. Phys. Chem. Ref. Data 19:763–808, 1990. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. At pressures up to 30 MPa and temperatures up to 523 K, the estimated uncertainty ranges from 0.03% to 0.05% in density, 0.03% (in the vapor) to 1% in the speed of sound (0.5% in the liquid), and 0.15% (in the vapor) to 1.5% (in the liquid) in heat capacity. Special interest has been focused on the description of the critical region and the extrapolation behavior of the formulation (to the limits of chemical stability). The uncertainty in viscosity ranges from 0.3% in the dilute gas near room temperature to 5% at the highest pressures. The uncertainty in thermal conductivity is less than 5%. 2-203 2-204 TABLE 2-114 Thermodynamic Properties of Carbon Monoxide Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 30.330 30.064 29.773 29.478 29.180 28.878 28.573 28.262 27.947 27.626 27.300 26.967 26.627 26.280 25.924 25.559 25.184 24.798 24.399 23.987 23.560 23.114 22.649 22.161 21.646 21.099 20.513 19.878 19.179 18.390 17.464 16.288 10.850 0.032971 0.033262 0.033588 0.033924 0.034270 0.034628 0.034999 0.035383 0.035782 0.036197 0.036630 0.037082 0.037556 0.038052 0.038574 0.039125 0.039708 0.040326 0.040985 0.041689 0.042446 0.043263 0.044151 0.045124 0.046197 0.047395 0.048749 0.050307 0.052141 0.054377 0.057259 0.061393 0.092166 −0.81158 −0.70065 −0.58046 −0.46058 −0.34088 −0.22127 −0.10165 0.018099 0.13806 0.25835 0.37906 0.50030 0.62218 0.74482 0.86835 0.99289 1.1186 1.2457 1.3742 1.5045 1.6368 1.7713 1.9085 2.0487 2.1925 2.3405 2.4938 2.6536 2.8221 3.0024 3.2010 3.4328 4.2912 −0.81106 −0.69995 −0.57950 −0.45927 −0.33915 −0.21900 −0.098716 0.021834 0.14277 0.26421 0.38629 0.50915 0.63291 0.75773 0.88377 1.0112 1.1402 1.2710 1.4039 1.5390 1.6768 1.8175 1.9616 2.1097 2.2624 2.4205 2.5853 2.7583 2.9420 3.1403 3.3608 3.6210 4.6137 −0.010820 −0.0092140 −0.0075210 −0.0058785 −0.0042823 −0.0027285 −0.0012138 0.00026503 0.0017110 0.0031269 0.0045153 0.0058787 0.0072195 0.0085399 0.0098422 0.011129 0.012402 0.013663 0.014916 0.016162 0.017404 0.018646 0.019891 0.021142 0.022406 0.023688 0.024996 0.026343 0.027744 0.029230 0.030854 0.032745 0.040039 5.1252 5.1600 5.1971 5.2334 5.2688 5.3031 5.3363 5.3682 5.3988 5.4280 5.4556 5.4816 5.5058 5.5280 5.5482 5.5661 5.5816 5.5945 5.6044 5.6112 5.6145 5.6138 5.6088 5.6859 5.7343 5.7859 5.8361 5.8849 5.9320 5.9775 6.0210 6.0625 6.1019 6.1388 6.1733 6.2050 6.2338 6.2595 6.2819 6.3007 6.3157 6.3265 6.3327 6.3339 6.3295 6.3191 0.084499 0.082704 0.080887 0.079194 0.077613 0.076131 0.074739 0.073426 0.072185 0.071007 0.069885 0.068813 0.067785 0.066796 0.065840 0.064912 0.064007 0.063120 0.062248 0.061385 0.060526 0.059665 0.058797 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.035351 0.034805 0.034248 0.033724 0.033232 0.032768 0.032329 0.031915 0.031522 0.031150 0.030798 0.030463 0.030146 0.029846 0.029562 0.029294 0.029043 0.028809 0.028592 0.028395 0.028218 0.028066 0.027941 0.027850 0.027800 0.027803 0.027874 0.028038 0.028333 0.028826 0.029646 0.031097 0.060430 0.060226 0.060064 0.059961 0.059917 0.059930 0.060002 0.060132 0.060324 0.060578 0.060899 0.061291 0.061760 0.062314 0.062962 0.063716 0.064590 0.065604 0.066781 0.068153 0.069759 0.071656 0.073916 0.076648 0.080005 0.084225 0.089692 0.097070 0.10762 0.12411 0.15392 0.22603 998.20 980.50 961.22 941.89 922.49 903.01 883.44 863.76 843.95 824.00 803.89 783.60 763.12 742.41 721.45 700.22 678.68 656.78 634.50 611.77 588.54 564.73 540.25 515.01 488.86 461.63 433.11 403.00 370.88 336.15 297.82 254.03 0 −0.36906 −0.36553 −0.36074 −0.35489 −0.34794 −0.33981 −0.33041 −0.31966 −0.30742 −0.29356 −0.27794 −0.26034 −0.24056 −0.21834 −0.19335 −0.16523 −0.13353 −0.097704 −0.057078 −0.010824 0.042104 0.10304 0.17371 0.25641 0.35427 0.47167 0.61495 0.79382 1.0239 1.3325 1.7728 2.4703 6.1475 180.28 175.49 170.45 165.55 160.76 156.06 151.45 146.89 142.40 137.96 133.57 129.23 124.94 120.69 116.51 112.38 108.31 104.30 100.36 96.482 92.679 88.948 85.290 81.702 78.180 74.716 71.296 67.896 64.476 60.972 57.261 53.107 274.18 252.15 232.14 215.32 201.01 188.69 177.96 168.52 160.13 152.60 145.77 139.52 133.75 128.38 123.34 118.57 114.02 109.66 105.45 101.35 97.342 93.404 89.510 85.641 81.774 77.888 73.954 69.940 65.797 61.448 56.748 51.348 0.021089 0.021155 0.021238 0.021333 0.021441 0.021563 0.021699 0.021850 0.022017 0.022199 0.022397 0.022611 0.022842 0.023089 0.023352 0.023633 0.023931 0.024248 0.024586 0.024945 0.025329 0.025741 0.026186 0.029785 0.029947 0.030153 0.030394 0.030672 0.030993 0.031360 0.031777 0.032250 0.032783 0.033383 0.034057 0.034813 0.035661 0.036615 0.037690 0.038906 0.040288 0.041869 0.043694 0.045820 0.048326 0.051322 167.25 169.22 171.27 173.22 175.07 176.80 178.42 179.92 181.29 182.54 183.66 184.65 185.51 186.22 186.80 187.23 187.52 187.67 187.66 187.51 187.20 186.73 186.11 40.804 38.426 36.126 34.080 32.250 30.604 29.116 27.763 26.527 25.392 24.345 23.377 22.477 21.638 20.853 20.118 19.426 18.773 18.154 17.565 17.001 16.458 15.930 Cv kJ/(mol⋅K) Saturated Properties 68.160 70.000 72.000 74.000 76.000 78.000 80.000 82.000 84.000 86.000 88.000 90.000 92.000 94.000 96.000 98.000 100.00 102.00 104.00 106.00 108.00 110.00 112.00 114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00 130.00 132.86 0.015537 0.021053 0.028718 0.038447 0.050599 0.065559 0.083738 0.10556 0.13148 0.16196 0.19748 0.23852 0.28559 0.33919 0.39983 0.46805 0.54438 0.62934 0.72348 0.82736 0.94154 1.0666 1.2031 1.3517 1.5130 1.6877 1.8765 2.0802 2.2997 2.5360 2.7904 3.0647 3.4982 68.160 70.000 72.000 74.000 76.000 78.000 80.000 82.000 84.000 86.000 88.000 90.000 92.000 94.000 96.000 98.000 100.00 102.00 104.00 106.00 108.00 110.00 112.00 0.015537 0.021053 0.028718 0.038447 0.050599 0.065559 0.083738 0.10556 0.13148 0.16196 0.19748 0.23852 0.28559 0.33919 0.39983 0.46805 0.54438 0.62934 0.72348 0.82736 0.94154 1.0666 1.2031 0.027707 0.036656 0.048780 0.063796 0.082130 0.10424 0.13059 0.16171 0.19810 0.24036 0.28906 0.34486 0.40845 0.48058 0.56209 0.65388 0.75700 0.87260 1.0020 1.1468 1.3088 1.4903 1.6938 36.091 27.281 20.500 15.675 12.176 9.5935 7.6573 6.1841 5.0478 4.1605 3.4595 2.8997 2.4483 2.0808 1.7791 1.5293 1.3210 1.1460 0.99799 0.87198 0.76404 0.67102 0.59039 6.6865 6.8845 7.1009 7.3188 7.5382 7.7592 7.9820 8.2067 8.4335 8.6627 8.8944 9.1291 9.3672 9.6091 9.8555 10.107 10.366 10.632 10.909 11.198 11.502 11.828 12.181 4.6366 4.7768 4.9329 5.0934 5.2589 5.4300 5.6076 5.7922 5.9847 6.1860 6.3968 6.6182 6.8512 7.0969 7.3566 7.6317 7.9239 8.2350 8.5675 8.9238 9.3073 9.7221 10.173 114.00 116.00 118.00 120.00 122.00 124.00 126.00 128.00 130.00 132.86 1.3517 1.5130 1.6877 1.8765 2.0802 2.2997 2.5360 2.7904 3.0647 3.4982 100.00 200.00 300.00 400.00 500.00 0.10000 0.10000 0.10000 0.10000 0.10000 100.00 108.96 1.0000 1.0000 108.96 200.00 300.00 400.00 500.00 1.0000 1.0000 1.0000 1.0000 1.0000 100.00 200.00 300.00 400.00 500.00 5.0000 5.0000 5.0000 5.0000 5.0000 1.9228 2.1815 2.4754 2.8123 3.2027 3.6629 4.2194 4.9212 5.8832 10.850 0.52008 0.45841 0.40397 0.35558 0.31224 0.27301 0.23700 0.20320 0.16998 0.092166 5.5986 5.5827 5.5598 5.5286 5.4872 5.4324 5.3595 5.2594 5.1113 4.2912 6.3016 6.2762 6.2416 6.1959 6.1367 6.0602 5.9605 5.8264 5.6322 4.6137 0.057914 0.057008 0.056070 0.055084 0.054034 0.052892 0.051613 0.050117 0.048216 0.040039 5.7653 7.8674 9.9522 12.045 14.169 6.5785 9.5259 12.446 15.371 18.328 0.080014 0.10048 0.11231 0.12073 0.12733 0.039586 0.042829 1.1047 1.7009 1.1443 1.7437 0.71782 1.6200 2.4867 3.3334 4.1732 5.6147 7.7647 9.8936 12.005 14.140 25.864 3.4130 2.0232 1.4824 1.1786 0.038663 0.29299 0.49426 0.67458 0.84845 0.026671 0.027203 0.027794 0.028462 0.029229 0.030133 0.031233 0.032636 0.034579 0.054966 0.059493 0.065263 0.072864 0.083320 0.098585 0.12291 0.16759 0.27599 185.33 184.38 183.27 181.99 180.52 178.84 176.93 174.68 171.86 0 15.411 14.894 14.372 13.833 13.265 12.648 11.956 11.140 10.100 6.1475 12.569 13.005 13.507 14.101 14.826 15.747 16.981 18.777 21.845 10.667 11.213 11.821 12.509 13.301 14.234 15.373 16.840 18.936 0.021118 0.020812 0.020833 0.021028 0.021479 0.030153 0.029239 0.029191 0.029364 0.029807 201.29 288.05 353.12 407.29 454.00 17.820 5.3111 2.5186 1.2653 0.56244 10.075 19.227 26.605 33.106 39.272 6.9147 12.897 17.731 21.870 25.540 0.012262 0.017998 0.029062 0.028142 0.064114 0.070627 685.44 577.22 −0.14414 0.070176 112.87 90.884 6.3325 9.3847 12.380 15.338 18.313 0.060114 0.080819 0.092976 0.10149 0.10812 0.025522 0.020996 0.020895 0.021064 0.021505 0.046966 0.030510 0.029646 0.029598 0.029948 186.99 286.20 354.42 409.43 456.39 16.739 5.1924 2.4256 1.2088 0.52786 11.655 19.474 26.760 33.222 39.364 0.99666 7.2656 9.6364 11.834 14.015 1.1900 8.7305 12.108 15.207 18.258 0.011154 0.064994 0.078767 0.087691 0.094498 0.029263 0.021878 0.021174 0.021224 0.021618 0.060925 0.038000 0.031673 0.030585 0.030535 737.92 285.27 362.95 420.15 467.56 −0.21740 4.3757 2.0288 0.98413 0.39254 152.30 22.190 27.812 33.871 39.837 112.19 15.094 18.716 22.588 26.139 Single-Phase Properties 0.12298 0.060293 0.040104 0.030062 0.024045 25.261 23.349 1.3931 0.61727 0.40214 0.29999 0.23962 8.1315 16.586 24.935 33.265 41.588 113.83 95.450 9.5017 13.192 17.918 22.024 25.676 100.00 200.00 300.00 400.00 500.00 10.000 10.000 10.000 10.000 10.000 26.482 7.4298 4.0263 2.9079 2.3052 0.037761 0.13459 0.24837 0.34389 0.43381 0.88669 6.5960 9.3290 11.634 13.870 1.2643 7.9419 11.813 15.073 18.208 0.0099878 0.056188 0.072068 0.081462 0.088461 0.029539 0.022832 0.021511 0.021420 0.021755 0.058409 0.048831 0.034036 0.031689 0.031188 792.04 307.84 379.01 435.68 482.48 −0.27800 2.8854 1.5731 0.74980 0.25486 200.46 34.772 30.972 35.414 40.797 110.33 19.114 19.862 23.298 26.682 100.00 200.00 300.00 400.00 500.00 50.000 50.000 50.000 50.000 50.000 29.422 20.591 14.766 11.439 9.3865 0.033988 0.048566 0.067725 0.087418 0.10654 0.39153 4.5424 7.7949 10.518 13.024 2.0910 6.9707 11.181 14.889 18.350 0.0040257 0.038097 0.055259 0.065951 0.073681 0.031398 0.025036 0.023212 0.022620 0.022659 0.052094 0.045541 0.039083 0.035519 0.033937 1066.8 706.01 609.73 604.51 622.30 −0.43831 −0.28689 −0.21242 −0.27153 −0.36911 567.46 256.88 139.18 94.476 76.899 99.463 50.929 34.086 31.319 32.167 31.474 24.888 20.200 16.970 14.662 0.031772 0.040181 0.049505 0.058928 0.068206 0.095937 3.9022 7.0625 9.8487 12.449 3.2732 7.9203 12.013 15.741 19.269 −0.00053857 0.031951 0.048608 0.059353 0.067230 0.033037 0.026437 0.024358 0.023555 0.023434 0.050530 0.043352 0.038799 0.036051 0.034683 1282.4 987.69 866.60 822.33 808.91 −0.47725 −0.50923 −0.54516 −0.59581 −0.64123 100.00 200.00 300.00 400.00 500.00 100.00 100.00 100.00 100.00 100.00 1005.7 536.84 331.69 229.18 173.58 90.560 73.380 54.648 45.748 42.504 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data, 51(3):785–850, 2006. The source for viscosity and thermal conductivity is Version 9.08 of the NIST14 database. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The equation of state is valid from the triple point to 500 K with pressures to 100 MPa. At higher pressures, the deviations from the equation increase rapidly, and it is not recommended to use the equation above 100 MPa. The uncertainties in the equation are 0.3% in density (approaching 1% near the critical point), 0.2% in vapor pressure, and 2% in heat capacities. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4–6%. 2-205 2-206 PHYSICAL AnD CHEMICAL DATA FIG. 2-4 Temperature-entropy diagram for carbon monoxide. Pressure P, in atmospheres; density r, in grams per cubic centimeter; enthalpy H, in joules per gram. (From J.G. Hust and R.B. Stewart, NBS Tech. Note 202, 1963.) TABLE 2-115 Thermodynamic Properties of Ethanol Temperature K Pressure MPa 250.00 265.00 280.00 295.00 310.00 325.00 340.00 355.00 370.00 385.00 400.00 415.00 430.00 445.00 460.00 475.00 490.00 505.00 513.90 0.00027007 0.00089527 0.0025823 0.0066146 0.015298 0.032394 0.063544 0.11663 0.20205 0.33279 0.52446 0.79509 1.1649 1.6559 2.2916 3.0963 4.0954 5.3159 6.1480 250.00 265.00 280.00 295.00 310.00 325.00 340.00 355.00 370.00 385.00 400.00 415.00 430.00 445.00 460.00 475.00 490.00 505.00 513.90 0.00027007 0.00089527 0.0025823 0.0066146 0.015298 0.032394 0.063544 0.11663 0.20205 0.33279 0.52446 0.79509 1.1649 1.6559 2.2916 3.0963 4.0954 5.3159 6.1480 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 6.9274 8.3792 9.9424 11.630 13.445 15.385 17.444 19.615 21.892 24.268 26.740 29.307 31.970 34.737 37.629 40.684 44.002 47.926 53.880 6.9275 8.3793 9.9426 11.631 13.446 15.387 17.448 19.622 21.905 24.290 26.775 29.362 32.054 34.862 37.810 40.943 44.374 48.480 54.906 0.037330 0.042968 0.048704 0.054574 0.060574 0.066684 0.072875 0.079123 0.085403 0.091699 0.098000 0.10430 0.11061 0.11695 0.12335 0.12991 0.13684 0.14485 0.15723 49.039 49.932 50.851 51.792 52.749 53.717 54.684 55.640 56.573 57.469 58.312 59.087 59.774 60.348 60.777 61.004 60.916 60.144 53.880 51.116 52.134 53.174 54.234 55.307 56.383 57.450 58.494 59.500 60.451 61.329 62.115 62.785 63.312 63.654 63.747 63.453 62.328 54.906 0.21409 0.20808 0.20310 0.19899 0.19561 0.19282 0.19053 0.18862 0.18701 0.18562 0.18438 0.18322 0.18208 0.18088 0.17954 0.17792 0.17578 0.17228 0.15723 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.076657 0.083798 0.091653 0.099433 0.10670 0.11322 0.11893 0.12381 0.12792 0.13130 0.13405 0.13625 0.13798 0.13934 0.14041 0.14134 0.14234 0.14382 0.093612 0.10028 0.10829 0.11678 0.12524 0.13340 0.14115 0.14847 0.15543 0.16215 0.16883 0.17576 0.18341 0.19262 0.20504 0.22469 0.26508 0.41790 1325.0 1260.8 1202.8 1149.2 1098.1 1048.0 997.94 947.31 895.56 842.31 787.16 729.67 669.25 605.07 535.80 459.19 371.03 264.74 0 −0.44553 −0.41423 −0.37872 −0.34323 −0.30910 −0.27615 −0.24356 −0.21011 −0.17428 −0.13410 −0.086812 −0.028333 0.047976 0.15384 0.31228 0.57597 1.0976 2.5369 8.6373 178.12 173.58 169.56 165.87 162.38 159.01 155.69 152.39 149.09 145.78 142.47 139.18 135.93 132.78 129.85 127.41 126.33 129.43 3140.9 2182.0 1564.4 1152.5 869.40 669.49 524.87 417.88 337.04 274.76 225.91 186.93 155.35 129.37 107.62 88.972 72.213 55.104 0.058885 0.060795 0.062753 0.064753 0.066816 0.068988 0.071336 0.073932 0.076838 0.080106 0.083774 0.087876 0.092450 0.097544 0.10323 0.10966 0.11709 0.12644 0.067215 0.069146 0.071149 0.073238 0.075464 0.077921 0.080736 0.084059 0.088058 0.092930 0.098936 0.10646 0.11610 0.12898 0.14727 0.17612 0.23200 0.42053 226.86 233.03 238.89 244.41 249.49 254.02 257.88 260.92 263.02 264.03 263.82 262.27 259.21 254.44 247.61 238.10 224.59 203.70 0 Cv kJ/(mol⋅K) Saturated Properties 17.911 17.642 17.376 17.106 16.828 16.537 16.231 15.905 15.557 15.181 14.774 14.331 13.843 13.298 12.676 11.941 11.007 9.5842 5.9910 0.00012998 0.00040670 0.0011115 0.0027080 0.0059814 0.012150 0.022975 0.040873 0.069039 0.11160 0.17385 0.26261 0.38683 0.55876 0.79629 1.1286 1.6143 2.4339 5.9910 0.055831 0.056681 0.057551 0.058460 0.059426 0.060469 0.061610 0.062872 0.064281 0.065871 0.067684 0.069779 0.072241 0.075202 0.078889 0.083745 0.090848 0.10434 0.16692 7693.7 2458.8 899.69 369.28 167.18 82.305 43.525 24.466 14.485 8.9606 5.7521 3.8080 2.5851 1.7897 1.2558 0.88602 0.61945 0.41086 0.16692 149.30 111.11 87.283 71.858 61.180 53.164 46.697 41.226 36.486 32.353 28.756 25.644 22.967 20.681 18.747 17.136 15.831 14.728 8.6373 14.936 15.737 16.612 17.566 18.602 19.731 20.969 22.341 23.886 25.659 27.741 30.251 33.369 37.377 42.735 50.248 61.578 82.512 7.2715 7.7433 8.2114 8.6756 9.1353 9.5902 10.040 10.486 10.929 11.372 11.820 12.283 12.774 13.318 13.961 14.786 15.982 18.148 (Continued) 2-207 2-208 TABLE 2-115 Thermodynamic Properties of Ethanol (Continued ) Temperature K Pressure MPa Entropy kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 164.74 153.26 1047.2 443.11 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol 17.016 15.993 0.058768 0.062527 12.219 19.033 12.225 19.040 0.056554 0.077475 0.10193 0.12261 0.11962 0.14658 1132.5 960.72 −0.33179 −0.21908 55.390 59.207 67.925 77.796 58.222 62.477 72.058 82.775 0.18909 0.20043 0.22176 0.24127 0.073221 0.080640 0.092910 0.10403 0.083127 0.089997 0.10162 0.11252 260.21 279.09 312.39 341.55 42.587 28.685 11.830 5.6356 0.058707 0.067589 0.071181 12.202 26.715 30.866 12.261 26.783 30.938 0.056497 0.097937 0.10802 0.10191 0.13400 0.13732 0.11954 0.16857 0.18015 1137.9 791.85 694.41 3.0216 3.9114 4.8846 59.504 67.014 77.311 62.526 70.925 82.195 0.18255 0.20078 0.22131 0.090516 0.096953 0.10581 0.11184 0.11008 0.11605 260.65 300.64 337.33 24.014 12.007 5.6301 0.058443 0.066842 0.097846 0.099875 12.129 26.516 46.419 46.876 12.421 26.851 46.908 47.375 0.056249 0.097435 0.14179 0.14272 0.10185 0.13359 0.14311 0.14340 0.11922 0.16658 0.32410 0.35152 1161.4 829.44 308.88 292.31 −0.33665 −0.11211 1.7596 2.0063 2.1809 1.1372 0.45852 0.87939 60.445 74.966 62.737 79.363 0.17336 0.20395 0.12389 0.11419 0.34099 0.13659 209.80 314.06 15.000 5.6703 75.676 61.725 17.454 18.972 17.203 15.147 11.521 2.8001 0.058131 0.066020 0.086800 0.35713 12.041 26.293 44.752 71.266 12.623 26.953 45.620 74.837 0.055950 0.096860 0.13830 0.19172 0.10179 0.13313 0.14031 0.12599 0.11885 0.16456 0.22204 0.18744 1189.5 872.36 464.50 273.66 −0.34096 −0.13414 0.60618 5.6926 170.07 149.80 130.15 84.190 1111.8 252.40 80.680 23.411 Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Single-Phase Properties 300.00 351.05 0.10000 0.10000 351.05 400.00 500.00 600.00 0.10000 0.10000 0.10000 0.10000 300.00 400.00 423.85 1.0000 1.0000 1.0000 423.85 500.00 600.00 1.0000 1.0000 1.0000 300.00 400.00 500.00 501.39 5.0000 5.0000 5.0000 5.0000 501.39 600.00 5.0000 5.0000 300.00 400.00 500.00 600.00 10.000 10.000 10.000 10.000 0.035314 0.030577 0.024191 0.020086 17.034 14.795 14.049 0.33095 0.25567 0.20473 17.111 14.961 10.220 10.013 28.317 32.704 41.338 49.786 −0.33273 −0.089821 0.013963 21.965 26.374 37.865 52.622 165.24 142.87 137.25 32.003 39.539 53.583 167.43 146.07 127.42 128.00 10.369 11.853 14.768 17.543 1053.2 227.32 167.52 12.568 14.859 17.678 1079.6 238.82 61.882 59.510 300.00 400.00 500.00 600.00 100.00 100.00 100.00 100.00 18.389 17.030 15.408 13.601 0.054380 0.058722 0.064899 0.073523 10.984 24.075 39.356 55.055 16.422 29.947 45.846 62.407 0.051802 0.090466 0.12589 0.15608 0.10149 0.12901 0.13221 0.12575 0.11571 0.15081 0.16433 0.16553 1558.1 1348.2 1166.1 1015.1 −0.37198 −0.25352 −0.17199 −0.082822 207.54 195.29 188.35 187.31 1611.3 435.09 192.15 109.49 300.00 400.00 500.00 600.00 200.00 200.00 200.00 200.00 19.244 18.138 16.878 15.505 0.051963 0.055134 0.059250 0.064494 10.349 22.905 37.295 51.902 20.742 33.931 49.145 64.801 0.048505 0.086238 0.12014 0.14869 0.10196 0.12678 0.12868 0.12066 0.11495 0.14539 0.15623 0.15566 1830.4 1660.3 1525.6 1422.7 −0.37578 −0.28090 −0.22946 −0.19099 238.67 228.57 224.49 226.40 2085.4 591.02 269.30 148.43 The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Dillon, H.E., and Penoncello, S.G., “A Fundamental Equation for Calculation of the Thermodynamic Properties of Ethanol,” Int. J. Thermophys., 25(2):321–335, 2004. The source for viscosity is Kiselev, S. B., Ely, J. F., Abdulagatov, I. M., and Huber, M. L., “Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols,” Ind. Eng. Chem. Res., 44:6916–6927, 2005. The source for thermal conductivity is unpublished, 2004; however, the fit uses functional form found in Marsh, K., Perkins, R., and Ramires, M.L.V., “Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data, 47(4):932–940, 2002. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in the equation of state are 0.2% in density, 3% in heat capacities, 1% in speed of sound, and 0.5% in vapor pressure and saturation densities. The estimated uncertainty in the liquid phase along the saturation boundary is approximately 3%, increasing to 10% at pressures to 100 MPa, and is estimated at 10% in the vapor phase. The estimated uncertainty in the liquid phase is approximately 5% and is estimated as 10% in the vapor phase. THERMODYnAMIC PROPERTIES FIG. 2-5 Enthalpy-concentration diagram for aqueous ethyl alcohol. Reference states: Enthalpies of liquid water and ethyl alcohol at 0°C are zero. Note: In order to interpolate equilibrium compositions, a vertical may be erected from any liquid composition on the boiling line and its intersection with the auxiliary line determined. A horizontal from this intersection will establish the equilibrium vapor composition on the dew line. (F. Bosnjakovic, Technische Thermodynamik, T. Steinkopff, Leipzig, 1935.) 2-209 2-210 TABLE 2-116 Thermodynamic Properties of normal Hydrogen Temperature K Pressure MPa 13.957 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.190 13.957 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000 26.000 27.000 28.000 29.000 30.000 31.000 32.000 33.190 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 0.0077031 0.0078936 0.013436 0.021534 0.032848 0.048078 0.067960 0.093249 0.12472 0.16314 0.20932 0.26406 0.32818 0.40250 0.48788 0.58524 0.69554 0.81989 0.95964 1.1168 1.3301 38.148 38.129 37.701 37.261 36.802 36.321 35.812 35.274 34.702 34.092 33.439 32.738 31.979 31.152 30.242 29.225 28.067 26.706 25.017 22.637 14.940 0.026214 0.026226 0.026524 0.026838 0.027172 0.027533 0.027923 0.028350 0.028817 0.029333 0.029905 0.030546 0.031271 0.032101 0.033067 0.034217 0.035629 0.037444 0.039973 0.044175 0.066934 −0.10434 −0.10367 −0.088896 −0.074446 −0.059414 −0.043440 −0.026375 −0.0081516 0.011274 0.031947 0.053929 0.077308 0.10222 0.12884 0.15744 0.18843 0.22245 0.26061 0.30524 0.36302 0.53004 −0.10414 −0.10346 −0.088539 −0.073868 −0.058521 −0.042116 −0.024477 −0.0055080 0.014868 0.036732 0.060188 0.085375 0.11248 0.14176 0.17357 0.20846 0.24723 0.29132 0.34360 0.41236 0.61907 −0.0059480 −0.0059000 −0.0048799 −0.0039471 −0.0030355 −0.0021219 −0.0011983 −0.00026211 0.00068790 0.0016528 0.0026344 0.0036357 0.0046610 0.0057167 0.0068122 0.0079614 0.0091865 0.010527 0.012063 0.014035 0.020012 0.0077031 0.0078936 0.013436 0.021534 0.032848 0.048078 0.067960 0.093249 0.12472 0.16314 0.20932 0.26406 0.32818 0.40250 0.48788 0.58524 0.69554 0.81989 0.95964 1.1168 1.3301 0.067540 0.069018 0.11050 0.16764 0.24349 0.34126 0.46437 0.61652 0.80187 1.0251 1.2919 1.6089 1.9848 2.4307 2.9618 3.6003 4.3810 5.3643 6.6763 8.6823 14.940 14.806 14.489 9.0494 5.9651 4.1069 2.9303 2.1535 1.6220 1.2471 0.97549 0.77406 0.62153 0.50383 0.41141 0.33763 0.27775 0.22826 0.18642 0.14978 0.11518 0.066934 0.68715 0.68764 0.69864 0.70899 0.71875 0.72783 0.73614 0.74359 0.75005 0.75541 0.75951 0.76218 0.76318 0.76224 0.75895 0.75276 0.74277 0.72747 0.70374 0.66274 0.53004 0.80120 0.80201 0.82024 0.83745 0.85365 0.86871 0.88249 0.89484 0.90558 0.91455 0.92154 0.92630 0.92853 0.92783 0.92368 0.91531 0.90154 0.88031 0.84748 0.79136 0.61907 0.058918 0.058777 0.055705 0.053010 0.050622 0.048480 0.046537 0.044755 0.043103 0.041554 0.040085 0.038674 0.037303 0.035950 0.034594 0.033206 0.031749 0.030160 0.028317 0.025879 0.020012 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.011064 0.010957 0.0096961 0.0096482 0.010003 0.010462 0.010915 0.011323 0.011677 0.011978 0.012235 0.012457 0.012655 0.012840 0.013025 0.013224 0.013460 0.013764 0.014198 0.014926 0.015654 0.015547 0.014420 0.014709 0.015557 0.016642 0.017842 0.019120 0.020476 0.021935 0.023539 0.025351 0.027465 0.030024 0.033265 0.037610 0.043909 0.054194 0.074872 0.14185 1361.1 1359.6 1318.5 1271.6 1226.6 1185.5 1147.3 1110.7 1074.7 1038.2 1000.5 960.99 919.10 874.29 826.00 773.58 716.22 652.73 581.16 497.24 0 −1.4137 −1.4230 −1.5204 −1.4695 −1.3623 −1.2409 −1.1194 −1.0003 −0.88232 −0.76268 −0.63795 −0.50414 −0.35648 −0.18882 0.0073109 0.24446 0.54283 0.93827 1.5038 2.4292 5.3208 76.293 76.650 84.106 90.079 94.784 98.405 101.10 103.01 104.24 104.87 104.98 104.60 103.79 102.53 100.83 98.654 95.935 92.547 88.221 82.176 25.463 25.310 22.215 19.784 17.815 16.182 14.799 13.607 12.565 11.641 10.811 10.057 9.3625 8.7151 8.1034 7.5160 6.9409 6.3620 5.7518 5.0391 0.013157 0.013129 0.012872 0.012907 0.012992 0.013083 0.013178 0.013280 0.013392 0.013514 0.013650 0.013802 0.013973 0.014167 0.014392 0.014655 0.014971 0.015358 0.015854 0.016535 0.021964 0.021944 0.021898 0.022199 0.022618 0.023121 0.023724 0.024449 0.025329 0.026401 0.027724 0.029376 0.031482 0.034234 0.037960 0.043253 0.051322 0.065054 0.093486 0.18606 304.61 305.17 316.15 325.05 333.00 340.22 346.75 352.59 357.75 362.25 366.11 369.34 371.95 373.96 375.38 376.19 376.39 375.97 374.91 373.31 0 Cv kJ/(mol⋅K) Saturated Properties 31.943 31.808 28.572 25.724 23.407 21.522 19.961 18.642 17.507 16.513 15.629 14.829 14.091 13.396 12.726 12.061 11.374 10.624 9.7362 8.5059 5.3208 10.375 10.431 11.624 12.681 13.681 14.669 15.675 16.716 17.806 18.956 20.180 21.493 22.916 24.477 26.218 28.202 30.535 33.407 37.226 43.200 0.66345 0.66695 0.74268 0.81064 0.87421 0.93555 0.99611 1.0569 1.1186 1.1819 1.2472 1.3151 1.3863 1.4619 1.5433 1.6331 1.7362 1.8628 2.0375 2.3378 Single-Phase Properties 25.000 100.00 175.00 250.00 325.00 400.00 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 25.000 31.268 1.0000 1.0000 31.268 100.00 175.00 250.00 325.00 400.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 25.000 100.00 175.00 250.00 325.00 400.00 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 0.50823 0.12030 0.068680 0.048077 0.036986 0.030054 1.9676 8.3127 14.560 20.800 27.037 33.273 0.81207 1.7949 3.0224 4.4642 5.9947 7.5545 1.0088 2.6261 4.4785 6.5442 8.6984 10.882 0.049309 0.079163 0.092882 0.10269 0.11022 0.11626 0.012734 0.014263 0.018150 0.020003 0.020681 0.020865 0.022519 0.022637 0.026480 0.028323 0.028998 0.029180 403.66 808.92 1026.9 1209.1 1371.7 1519.7 12.894 1.4058 0.13575 −0.22980 −0.38965 −0.47650 20.761 68.334 117.11 160.59 197.72 234.06 1.3142 4.1896 6.1845 7.9025 9.4561 10.892 0.030538 0.040861 0.089693 0.31894 0.12023 0.35980 0.0041410 0.012531 0.012580 0.014353 0.025394 0.084709 985.14 560.14 −0.51115 1.7031 106.80 86.829 9.9923 5.5759 0.14049 0.83027 1.4653 2.0926 2.7176 3.3418 0.69511 1.7679 3.0101 4.4576 5.9910 7.5525 0.83559 2.5982 4.4754 6.5501 8.7086 10.894 0.027747 0.059751 0.073667 0.083515 0.091062 0.097113 0.016014 0.014331 0.018190 0.020028 0.020699 0.020878 0.10713 0.023244 0.026659 0.028401 0.029039 0.029204 374.52 817.03 1035.8 1217.3 1379.1 1526.4 9.4548 1.3036 0.11718 −0.23428 −0.39039 −0.47605 38.524 70.413 118.31 161.46 198.43 234.65 2.0997 4.2550 6.2213 7.9283 9.4759 10.908 35.661 5.9683 3.3132 2.3268 1.7990 1.4680 0.028042 0.16755 0.30183 0.42978 0.55587 0.68120 0.046611 1.6549 2.9582 4.4292 5.9750 7.5440 0.18682 2.4927 4.4673 6.5781 8.7543 10.950 0.0021443 0.045314 0.059998 0.070022 0.077631 0.083710 0.012376 0.014583 0.018352 0.020136 0.020776 0.020937 0.020610 0.025613 0.027370 0.028723 0.029211 0.029304 1223.4 865.94 1077.3 1254.0 1412.0 1556.2 −0.90198 0.86369 0.032971 −0.25678 −0.39563 −0.47537 119.36 80.395 123.58 165.19 201.36 237.09 13.101 4.5875 6.3871 8.0420 9.5631 10.979 32.746 24.474 7.1182 1.2044 0.68243 0.47788 0.36797 0.29924 25.000 100.00 175.00 250.00 325.00 400.00 10.000 10.000 10.000 10.000 10.000 10.000 37.930 11.417 6.3697 4.5028 3.5006 2.8687 0.026364 0.087588 0.15699 0.22209 0.28567 0.34859 0.020221 1.5346 2.9000 4.3966 5.9563 7.5339 0.28386 2.4105 4.4699 6.6175 8.8130 11.020 0.00059913 0.038585 0.053931 0.064133 0.071811 0.077921 0.012222 0.014838 0.018532 0.020260 0.020867 0.021006 0.018499 0.027423 0.028063 0.029065 0.029402 0.029419 1402.1 955.43 1133.3 1300.6 1453.0 1593.1 −1.0762 0.39679 −0.068718 −0.28786 −0.40519 −0.47687 131.12 94.196 130.39 169.92 205.05 240.15 16.625 5.1692 6.6199 8.1898 9.6733 11.067 100.00 175.00 250.00 325.00 400.00 50.000 50.000 50.000 50.000 50.000 31.993 22.700 17.524 14.304 12.107 0.031257 0.044053 0.057066 0.069911 0.082595 1.1768 2.6415 4.2297 5.8539 7.4773 2.7397 4.8442 7.0830 9.3494 11.607 0.023964 0.039587 0.050225 0.058153 0.064404 0.016349 0.019545 0.020999 0.021434 0.021458 0.026254 0.029321 0.030163 0.030202 0.029985 1710.1 1632.6 1690.7 1784.8 1887.2 −0.57213 −0.46415 −0.46214 −0.48443 −0.51016 192.47 189.52 211.67 237.63 267.11 10.534 9.1377 9.7772 10.827 11.965 33.019 27.257 23.228 20.261 0.030286 0.036688 0.043051 0.049356 2.5589 4.1604 5.8083 7.4555 5.5875 7.8292 10.113 12.391 0.033643 0.044291 0.052281 0.058588 0.020316 0.021603 0.021923 0.021864 0.029140 0.030346 0.030469 0.030246 2128.4 2125.4 2170.6 2235.8 −0.52750 −0.50698 −0.51215 −0.52481 282.17 303.19 327.83 356.83 13.079 12.218 12.546 13.289 175.00 250.00 325.00 400.00 100.00 100.00 100.00 100.00 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Younglove, B. A., “Thermophysical Properties of Fluids. I. Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen,” J. Phys. Chem. Ref. Data, Suppl. 1, 11: 1–11, 1982. The source for viscosity is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972. The source for thermal conductivity is McCarty, R. D., and Weber, L. A., “Thermophysical Properties of Parahydrogen from the Freezing Liquid Line to 5000 R for Pressures to 10,000 psia,” N.B.S. Tech. Note 617, 1972. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.1% in the liquid phase, 0.25% in the vapor phase, and 0.2% in the supercritical region. The uncertainty in heat capacity is 3%, and the uncertainty in speed of sound is 2% in the liquid phase and 1% elsewhere. The uncertainty in viscosity ranges from 4% to 15%. The uncertainty in thermal conductivity below 100 K is estimated to be 3% below 150 atm and up to 10% below 700 atm. For temperatures around 100 K at low densities, the uncertainty is about 1%. Above 100 K, the uncertainty is estimated to be on the order of 10%. 2-211 2-212 TABLE 2-117 T, K 273 300 350 400 450 Saturated Hydrogen Peroxide* P, bar vf , m3/kg vg , m3/kg hf , kJ/kg hg, kJ/kg sf , kJ/(kg⋅K) sg , kJ/(kg⋅K) cpf , kJ/(kg⋅K) µf , 10−4 Pa⋅s kf , W/(m⋅K) 0.0004 0.0031 0.0564 0.4521 2.143 0.00068 0.00069 0.00072 0.00076 0.00081 1672 235 15.1 2.12 0.487 −5577 −5510 −5376 −5238 −5091 −4027 −3995 −3933 −3878 −3820 2.990 3.224 3.631 4.032 4.346 8.662 8.269 7.758 7.440 7.172 1.45 1.48 1.54 1.61 1.68 18.0 11.3 4.3 2.2 1.3 0.483 0.481 0.474 0.464 0.453 1.75 1.82 1.90 500 550 600 650 700 7.126 18.56 40.75 79.27 141.7 0.00088 0.00095 0.00107 0.00125 0.00171 0.155 0.0605 0.0268 0.0125 0.0048 −4945 −4794 −4635 −4463 −4195 −3777 −3745 −3731 −3746 −3860 4.656 4.941 5.209 5.485 5.682 6.992 6.846 6.720 6.582 6.339 708.5c 155.3 0.00284 0.0028 −4012 −4012 5.732 5.732 0.89 0.65 0.50 0.443 0.431 0.416 *Values reproduced or converted from a tabulation by Tsykalo and Tabachnikov in V. A. Rabinovich (ed.), Thermophysical Properties of Gases and Liquids, Standartov, Moscow, 1968; NBS-NSF transl. TT 69-55091, 1970. The reader may be reminded that very pure hydrogen peroxide is very difficult to obtain owing to its decomposition or instability. c = critical point. The FMC Corp., Philadelphia, PA tech. bull. 67, 1969 (100 pp.) contains an enthalpy-pressure diagram to 3000 psia, 1100 K. TABLE 2-118 Temperature K Thermodynamic Properties of Hydrogen Sulfide Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol 0.034345 0.034479 0.035082 0.035717 0.036390 0.037107 0.037875 0.038702 0.039599 0.040580 0.041662 0.042868 0.044230 0.045791 0.047618 0.049818 0.052573 0.056256 0.061837 0.074429 0.098135 −1.7210 −1.5628 −0.87841 −0.19759 0.48138 1.1602 1.8406 2.5245 3.2135 3.9100 4.6161 5.3348 6.0696 6.8248 7.6068 8.4246 9.2932 10.241 11.335 12.903 14.470 −1.7202 −1.5619 −0.87664 −0.19446 0.48661 1.1686 1.8534 2.5434 3.2408 3.9481 4.6685 5.4053 6.1629 6.9469 7.7650 8.6283 9.5548 10.578 11.779 13.538 15.353 16.328 16.382 16.611 16.832 17.043 17.244 17.431 17.604 17.761 17.899 18.016 18.108 18.171 18.199 18.183 18.109 17.957 17.684 17.192 16.046 14.470 17.876 17.947 18.250 18.541 18.818 19.079 19.320 19.539 19.735 19.902 20.039 20.139 20.198 20.207 20.156 20.027 19.793 19.403 18.736 17.266 15.353 Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s −0.34039 −0.33923 −0.33253 −0.32287 −0.30988 −0.29305 −0.27174 −0.24509 −0.21197 −0.17084 −0.11959 −0.055218 0.026636 0.13260 0.27324 0.46655 0.74618 1.1841 1.9714 3.9324 6.3885 254.24 251.74 240.93 230.26 219.81 209.52 199.43 189.56 179.91 170.48 161.26 152.24 143.40 134.71 126.16 117.71 109.36 101.19 93.864 92.754 439.13 428.67 385.68 346.75 311.74 280.37 252.29 227.14 204.60 184.32 166.02 149.44 134.32 120.43 107.58 95.533 84.050 72.784 61.060 46.102 Saturated Properties 187.70 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.10 0.023259 0.027106 0.050340 0.087474 0.14366 0.22485 0.33767 0.48934 0.68751 0.94022 1.2558 1.6429 2.1103 2.6672 3.3233 4.0889 4.9755 5.9969 7.1713 8.5294 8.9987 29.116 29.003 28.505 27.998 27.480 26.949 26.403 25.838 25.253 24.642 24.002 23.327 22.609 21.838 21.000 20.073 19.021 17.776 16.172 13.436 10.190 187.70 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 373.10 0.023259 0.027106 0.050340 0.087474 0.14366 0.22485 0.33767 0.48934 0.68751 0.94022 1.2558 1.6429 2.1103 2.6672 3.3233 4.0889 4.9755 5.9969 7.1713 8.5294 8.9987 0.015024 0.017314 0.030704 0.051165 0.080932 0.12253 0.17879 0.25286 0.34834 0.46937 0.62086 0.80887 1.0411 1.3280 1.6843 2.1323 2.7096 3.4881 4.6442 6.9933 10.190 66.559 57.758 32.569 19.545 12.356 8.1613 5.5933 3.9547 2.8707 2.1305 1.6107 1.2363 0.96050 0.75300 0.59373 0.46898 0.36906 0.28669 0.21532 0.14299 0.098135 −0.0085877 −0.0077504 −0.0042394 −0.00091743 0.0022415 0.0052596 0.0081564 0.010949 0.013654 0.016285 0.018857 0.021385 0.023885 0.026373 0.028873 0.031414 0.034044 0.036848 0.040035 0.044599 0.049374 0.044390 0.044124 0.043042 0.042067 0.041188 0.040393 0.039677 0.039030 0.038449 0.037930 0.037470 0.037070 0.036732 0.036462 0.036273 0.036191 0.036265 0.036600 0.037471 0.040079 0.068835 0.068707 0.068273 0.068029 0.067975 0.068115 0.068461 0.069032 0.069859 0.070989 0.072490 0.074466 0.077082 0.080603 0.085498 0.092666 0.10410 0.12534 0.17963 0.63367 1437.8 1425.8 1373.4 1321.0 1268.4 1215.6 1162.3 1108.5 1053.9 998.54 942.08 884.34 825.04 763.84 700.23 633.51 562.59 485.59 398.86 292.76 0 0.095815 0.094930 0.091395 0.088301 0.085567 0.083129 0.080933 0.078934 0.077092 0.075375 0.073752 0.072193 0.070669 0.069149 0.067594 0.065956 0.064157 0.062064 0.059360 0.054674 0.049374 0.025347 0.025386 0.025586 0.025837 0.026142 0.026502 0.026917 0.027388 0.027914 0.028496 0.029136 0.029838 0.030608 0.031458 0.032407 0.033485 0.034746 0.036293 0.038364 0.041755 0.034000 0.034078 0.034487 0.035021 0.035698 0.036537 0.037563 0.038807 0.040312 0.042139 0.044378 0.047166 0.050723 0.055410 0.061879 0.071400 0.086837 0.11617 0.19265 0.80649 245.84 247.20 252.82 257.96 262.58 266.64 270.10 272.91 275.05 276.47 277.15 277.05 276.12 274.34 271.64 268.00 263.35 257.65 250.84 242.80 0 55.730 53.868 46.796 41.090 36.435 32.601 29.412 26.737 24.476 22.550 20.897 19.466 18.212 17.097 16.081 15.116 14.142 13.053 11.629 9.0701 6.3885 10.628 10.775 11.429 12.107 12.816 13.566 14.365 15.227 16.166 17.202 18.360 19.675 21.197 22.997 25.187 27.946 31.600 36.820 45.513 70.939 8.0025 8.1053 8.5566 9.0159 9.4844 9.9634 10.455 10.961 11.485 12.031 12.604 13.213 13.867 14.582 15.380 16.300 17.405 18.833 20.940 25.604 (Continued) 2-213 2-214 TABLE 2-118 Thermodynamic Properties of Hydrogen Sulfide (Continued ) Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol 28.506 27.865 0.035080 0.035888 −0.87902 −0.021243 −0.87551 −0.017654 16.888 19.164 21.830 24.642 27.626 30.789 18.615 21.640 25.146 28.794 32.611 36.607 0.035053 0.040795 −0.89011 4.0550 −0.85506 4.0958 2.0080 2.2968 3.2255 4.0993 4.9547 5.8015 17.925 18.775 21.626 24.507 27.525 30.710 19.933 21.072 24.852 28.606 32.480 36.511 0.034935 0.043749 0.052654 −0.93837 5.9433 9.3164 −0.76369 6.1620 9.5797 0.36675 0.55412 0.77288 0.96476 1.1466 17.952 20.549 23.863 27.065 30.353 19.786 23.319 27.728 31.889 36.086 Cp kJ/(mol⋅K) Sound speed m/s 0.043042 0.041830 0.068269 0.067997 1373.6 1307.4 0.087559 0.099486 0.10956 0.11770 0.12465 0.13081 0.025911 0.025979 0.027268 0.028923 0.030708 0.032534 0.035183 0.034563 0.035693 0.037297 0.039059 0.040873 259.21 309.73 356.35 396.06 431.20 463.05 39.791 16.968 8.9467 5.5432 3.7250 2.6185 −0.0042980 0.016821 0.043058 0.037830 0.068210 0.071266 1377.6 986.97 −0.33351 −0.16116 0.075033 0.079019 0.089907 0.098281 0.10534 0.11155 0.028623 0.027626 0.027708 0.029100 0.030799 0.032589 0.042564 0.039427 0.037234 0.038036 0.039492 0.041157 276.67 296.60 351.09 393.73 430.30 462.94 22.188 17.369 9.0111 5.5366 3.7023 2.5947 −0.0045411 0.023458 0.034113 0.043127 0.036740 0.036269 0.067957 0.075047 0.10449 1394.7 855.61 560.70 0.064108 0.073747 0.083609 0.091196 0.097665 0.034782 0.030043 0.029940 0.031216 0.032838 0.087361 0.048271 0.041996 0.041590 0.042472 263.22 325.86 384.33 427.30 463.26 Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s Single-Phase Properties 200.00 212.60 0.10000 0.10000 212.60 300.00 400.00 500.00 600.00 700.00 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 200.00 272.07 1.0000 1.0000 272.07 300.00 400.00 500.00 600.00 700.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 200.00 300.00 340.26 5.0000 5.0000 5.0000 340.26 400.00 500.00 600.00 700.00 5.0000 5.0000 5.0000 5.0000 5.0000 0.057900 0.040389 0.030157 0.024088 0.020059 0.017187 28.528 24.513 0.49800 0.43539 0.31003 0.24394 0.20183 0.17237 28.625 22.858 18.992 2.7266 1.8047 1.2939 1.0365 0.87211 17.271 24.759 33.160 41.515 49.853 58.182 −0.0042425 −0.000082766 −0.33258 −0.31984 −0.33745 −0.017492 0.75500 14.116 9.1749 5.4471 3.5816 2.4840 240.95 227.54 12.288 17.999 24.990 32.218 39.592 47.091 241.31 168.56 17.430 19.015 25.609 32.691 39.980 47.423 242.90 146.15 109.14 385.79 337.30 9.1366 12.954 17.172 21.094 24.714 28.082 387.91 180.39 12.147 13.337 17.465 21.319 24.893 28.227 397.26 139.57 83.760 31.710 29.786 35.063 41.773 48.924 17.437 19.070 22.459 25.773 28.935 200.00 300.00 400.00 500.00 600.00 700.00 10.000 10.000 10.000 10.000 10.000 10.000 28.741 23.238 5.0473 2.8037 2.1399 1.7663 0.034793 0.043033 0.19812 0.35667 0.46730 0.56617 −0.99643 5.7496 18.370 22.959 26.466 29.903 −0.64850 6.1800 20.351 26.526 31.139 35.564 −0.0048367 0.022795 0.062081 0.076030 0.084452 0.091275 0.043212 0.036779 0.034651 0.031080 0.031755 0.033155 0.067668 0.072377 0.10189 0.048875 0.044597 0.044212 1415.5 902.78 291.29 375.68 426.01 465.45 −0.34197 −0.077399 8.2243 5.1487 3.3812 2.3347 244.82 150.49 44.719 38.963 44.210 50.878 408.90 148.08 23.639 24.438 27.165 30.013 300.00 400.00 500.00 600.00 700.00 75.000 75.000 75.000 75.000 75.000 26.050 21.973 17.947 14.519 11.974 0.038388 0.045510 0.055720 0.068874 0.083511 4.3332 9.9713 15.404 20.474 25.148 7.2123 13.384 19.583 25.640 31.412 0.017506 0.035260 0.049092 0.060142 0.069045 0.037754 0.035381 0.034762 0.034994 0.035721 0.061705 0.061962 0.061649 0.059227 0.056291 1276.9 983.51 786.35 688.11 654.55 −0.33612 −0.18247 0.057516 0.27314 0.36585 187.18 134.39 103.90 87.712 82.684 232.59 124.22 81.074 62.531 54.563 27.794 24.751 21.937 19.449 17.335 0.035979 0.040403 0.045585 0.051416 0.057687 3.5100 8.6429 13.539 18.248 22.811 8.9069 14.703 20.377 25.960 31.464 0.013888 0.030575 0.043238 0.053420 0.061906 0.038777 0.036402 0.035779 0.036044 0.036804 0.058983 0.057226 0.056273 0.055409 0.054711 1538.4 1302.6 1132.1 1019.1 949.06 −0.40376 −0.37006 −0.31802 −0.26874 −0.23292 214.24 165.64 135.75 118.38 110.03 311.25 174.85 119.57 93.323 79.581 300.00 400.00 500.00 600.00 700.00 150.00 150.00 150.00 150.00 150.00 The values in these tables were generated from the NIST REFPROP software (Lemmon, E.W., McLinden, M.O., and Huber, M.L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Span, R., “Short Fundamental Equations of State for 20 Industrial Fluids,” J. Chem. Eng. Data 51(3): 785–850, 2006. The source for viscosity and thermal conductivity is NIST14, Version 9.08. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.1% in the liquid phase below the critical temperature, 0.4% in the vapor phase, 1% at supercritical temperatures up to 500 K, and 2.5% at higher temperatures. Uncertainties will be higher near the critical point, and may be lower than 0.5% between 400 and 500 K. The uncertainty in vapor pressure is 0.25%, and the uncertainty in heat capacities is estimated to be 1%. For viscosity, estimated uncertainty is 2%. For thermal conductivity, estimated uncertainty, except near the critical region, is 4–6%. THERMODYnAMIC PROPERTIES FIG. 2-6 Enthalpy-concentration diagram for aqueous hydrogen chloride at 1 atm. Reference states: enthalpy of liquid water at 0°C is zero; enthalpy of pure saturated HCl vapor at 1 atm (–85.03°C) is 8000 kcal/mol. Note: It should be observed that the weight basis includes the vapor, which is particularly important in the two-phase region. Saturation values may be read at the ends of the tie lines [C.C. Van Nuys, Trans. Am. Inst. Chem. Eng 39: 663 (1943)]. 2-215 2-216 TABLE 2-119 Temperature K Thermodynamic Properties of Methane Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 0.035534 0.036554 0.037143 0.037768 0.038431 0.039138 0.039896 0.040714 0.041600 0.042569 0.043636 0.044825 0.046165 0.047702 0.049500 0.051667 0.054394 0.058078 0.063825 0.079902 0.098628 −1.1526 −0.64728 −0.37306 −0.096585 0.18242 0.46425 0.74927 1.0379 1.3307 1.6284 1.9317 2.2418 2.5602 2.8887 3.2304 3.5895 3.9734 4.3965 4.8955 5.7074 6.2136 −1.1522 −0.64602 −0.37097 −0.093257 0.18750 0.47174 0.75999 1.0529 1.3511 1.6557 1.9676 2.2884 2.6199 2.9647 3.3262 3.7098 4.1244 4.5873 5.1420 6.0685 6.6672 −0.011389 −0.0060856 −0.0034096 −0.00083691 0.0016441 0.0040439 0.0063722 0.0086383 0.010851 0.013020 0.015154 0.017264 0.019362 0.021462 0.023584 0.025755 0.028021 0.030467 0.033313 0.038000 0.041109 63.981 23.782 15.116 10.038 6.9171 4.9183 3.5915 2.6825 2.0424 1.5803 1.2393 0.98256 0.78568 0.63206 0.51014 0.41163 0.33038 0.26139 0.19945 0.12816 0.098628 6.8310 7.0469 7.1582 7.2654 7.3680 7.4652 7.5562 7.6403 7.7165 7.7837 7.8406 7.8856 7.9166 7.9306 7.9238 7.8898 7.8184 7.6893 7.4515 6.7850 6.2136 7.5793 7.8644 8.0104 8.1501 8.2825 8.4067 8.5215 8.6257 8.7180 8.7970 8.8608 8.9074 8.9340 8.9369 8.9109 8.8482 8.7357 8.5480 8.2217 7.3641 6.6672 0.084885 0.079019 0.076413 0.074103 0.072036 0.070168 0.068464 0.066891 0.065421 0.064029 0.062694 0.061391 0.060098 0.058789 0.057431 0.055982 0.054371 0.052471 0.049961 0.044819 0.041109 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.034776 0.033908 0.033500 0.033115 0.032749 0.032400 0.032069 0.031757 0.031469 0.031206 0.030974 0.030780 0.030631 0.030541 0.030531 0.030634 0.030920 0.031554 0.033085 0.041746 0.054029 0.054681 0.055135 0.055656 0.056253 0.056941 0.057741 0.058684 0.059809 0.061169 0.062840 0.064932 0.067613 0.071156 0.076044 0.083218 0.094816 0.11699 0.17822 1.5082 1538.6 1452.0 1403.9 1354.7 1304.6 1253.5 1201.3 1148.1 1093.6 1037.7 980.17 920.85 859.39 795.43 728.42 657.52 581.27 497.01 398.59 250.31 0 −0.48191 −0.45812 −0.44202 −0.42328 −0.40145 −0.37589 −0.34578 −0.31006 −0.26735 −0.21579 −0.15286 −0.075032 0.022798 0.14836 0.31398 0.54087 0.86918 1.3866 2.3397 5.2488 6.8877 211.24 199.67 193.03 186.18 179.21 172.15 165.04 157.91 150.78 143.65 136.54 129.43 122.32 115.19 108.01 100.73 93.324 85.799 78.733 96.970 204.52 155.78 136.86 121.34 108.39 97.432 88.031 79.868 72.699 66.333 60.620 55.437 50.682 46.266 42.105 38.115 34.196 30.193 25.773 18.982 0.025243 0.025487 0.025652 0.025842 0.026056 0.026295 0.026560 0.026854 0.027182 0.027549 0.027965 0.028439 0.028989 0.029636 0.030412 0.031374 0.032615 0.034338 0.037087 0.045796 0.033851 0.034425 0.034853 0.035378 0.036016 0.036786 0.037714 0.038836 0.040203 0.041885 0.043985 0.046657 0.050144 0.054849 0.061496 0.071527 0.088273 0.12151 0.21701 2.2590 249.13 260.09 265.31 270.01 274.17 277.76 280.76 283.13 284.86 285.93 286.31 285.97 284.88 283.01 280.30 276.66 271.99 266.04 258.03 238.55 0 47.921 37.826 33.883 30.662 28.004 25.790 23.928 22.347 20.993 19.819 18.789 17.870 17.035 16.255 15.500 14.732 13.896 12.892 11.492 8.4951 6.8877 8.8517 10.015 10.669 11.350 12.062 12.811 13.604 14.449 15.355 16.334 17.402 18.581 19.904 21.423 23.225 25.477 28.545 33.392 43.706 119.40 Cv kJ/(mol⋅K) Saturated Properties 90.694 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 155.00 160.00 165.00 170.00 175.00 180.00 185.00 190.00 190.56 0.011696 0.034376 0.056377 0.088130 0.13221 0.19143 0.26876 0.36732 0.49035 0.64118 0.82322 1.0400 1.2950 1.5921 1.9351 2.3283 2.7765 3.2852 3.8617 4.5186 4.5992 28.142 27.357 26.923 26.478 26.021 25.551 25.065 24.562 24.038 23.491 22.917 22.309 21.661 20.964 20.202 19.355 18.384 17.218 15.668 12.515 10.139 90.694 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 155.00 160.00 165.00 170.00 175.00 180.00 185.00 190.00 190.56 0.011696 0.034376 0.056377 0.088130 0.13221 0.19143 0.26876 0.36732 0.49035 0.64118 0.82322 1.0400 1.2950 1.5921 1.9351 2.3283 2.7765 3.2852 3.8617 4.5186 4.5992 0.015630 0.042048 0.066154 0.099622 0.14457 0.20332 0.27844 0.37278 0.48962 0.63279 0.80691 1.0177 1.2728 1.5821 1.9603 2.4294 3.0268 3.8257 5.0137 7.8027 10.139 3.6388 3.9976 4.1951 4.3964 4.6019 4.8123 5.0285 5.2517 5.4833 5.7254 5.9806 6.2526 6.5462 6.8688 7.2313 7.6515 8.1609 8.8251 9.8238 12.455 Single-Phase Properties −0.64803 −0.012738 −0.64438 −0.0089413 7.2969 9.5570 12.175 15.151 18.673 22.795 8.1908 11.209 14.665 18.475 22.831 27.784 0.036493 0.044610 −0.65829 2.1878 1.0220 1.5537 2.4524 3.3108 4.1567 4.9971 27.586 5.4706 2.1799 1.5333 1.2013 0.99281 100.00 111.51 0.10000 0.10000 111.51 200.00 300.00 400.00 500.00 600.00 0.10000 0.10000 0.10000 0.10000 0.10000 0.10000 100.00 149.14 1.0000 1.0000 149.14 200.00 300.00 400.00 500.00 600.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.97852 0.64363 0.40776 0.30205 0.24058 0.20012 100.00 200.00 300.00 400.00 500.00 600.00 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 100.00 200.00 300.00 400.00 500.00 600.00 10.000 10.000 10.000 10.000 10.000 10.000 27.360 26.341 −0.0060931 −0.000079677 0.054672 0.055828 0.073456 0.093427 0.10741 0.11834 0.12803 0.13705 0.025904 0.025259 0.027479 0.032300 0.038196 0.044179 0.035558 0.033784 0.035869 0.040652 0.046533 0.052509 271.33 369.98 449.74 510.56 561.86 608.04 29.808 9.2893 4.3216 2.2395 1.2245 0.68722 −0.62179 2.2325 −0.0061960 0.016902 0.033950 0.030810 0.054562 0.064535 1459.6 931.21 −0.46060 −0.089695 7.8788 9.3582 12.072 15.083 18.623 22.755 8.9007 10.912 14.524 18.393 22.780 27.752 0.061614 0.073276 0.087922 0.099023 0.10879 0.11784 0.028353 0.025879 0.027621 0.032360 0.038227 0.044198 0.046147 0.036730 0.036721 0.041056 0.046766 0.052659 286.08 357.81 447.04 510.57 562.99 609.73 18.022 9.5001 4.2699 2.2001 1.1998 0.67124 18.368 23.028 35.152 50.558 68.902 89.200 0.036250 0.18279 0.45874 0.65221 0.83240 1.0072 −0.70190 7.8197 11.590 14.779 18.401 22.581 −0.52065 8.7337 13.884 18.040 22.563 27.617 −0.0066393 0.051495 0.072954 0.084897 0.094971 0.10417 0.034116 0.032029 0.028262 0.032614 0.038361 0.044277 0.054117 0.11667 0.041234 0.042903 0.047789 0.053309 1490.0 291.29 439.25 513.11 569.49 618.13 −0.46993 8.9784 3.9428 2.0089 1.0870 0.60013 204.45 40.612 38.480 52.693 70.509 90.498 165.28 10.828 12.194 14.872 17.410 19.768 27.802 16.593 4.6859 3.1002 2.3887 1.9619 0.035969 0.060268 0.21340 0.32256 0.41863 0.50971 −0.75239 5.1551 10.942 14.401 18.132 22.371 −0.39270 5.7578 13.077 17.627 22.318 27.468 −0.0071652 0.034542 0.065137 0.078246 0.088698 0.098073 0.034314 0.030129 0.028995 0.032902 0.038516 0.044371 0.053642 0.085085 0.048165 0.045220 0.049007 0.054070 1525.7 567.92 444.53 522.58 580.99 630.63 −0.47979 1.0266 3.2606 1.7355 0.94125 0.51200 209.07 84.234 44.730 55.941 72.781 92.268 174.83 29.399 13.896 15.766 18.011 20.217 27.403 22.416 8.9395 16.524 24.901 33.243 41.572 49.895 1452.6 1339.7 −0.45829 −0.41705 0.033911 0.033003 0.11186 0.060518 0.040158 0.030082 0.024055 0.020042 0.036549 0.037963 199.74 184.09 11.561 21.941 34.552 50.127 68.564 88.921 200.62 130.66 155.91 117.20 4.4579 7.8096 11.245 14.272 16.976 19.431 157.63 56.297 6.2043 8.0145 11.367 14.357 17.040 19.483 200.00 300.00 400.00 500.00 600.00 100.00 100.00 100.00 100.00 100.00 25.496 21.266 17.881 15.305 13.357 0.039222 0.047024 0.055926 0.065340 0.074869 3.0510 7.0865 11.121 15.405 20.074 6.9732 11.789 16.713 21.939 27.561 0.020596 0.040126 0.054276 0.065922 0.076160 0.032058 0.031823 0.035273 0.040312 0.045724 0.048512 0.048281 0.050523 0.054139 0.058364 1541.0 1267.5 1115.8 1044.8 1018.4 −0.51619 −0.44889 −0.37484 −0.32811 −0.30439 188.05 137.68 120.38 120.87 130.36 80.392 47.835 37.584 33.590 32.111 200.00 300.00 400.00 500.00 600.00 500.00 500.00 500.00 500.00 500.00 33.003 30.786 28.929 27.331 25.934 0.030301 0.032482 0.034567 0.036588 0.038559 2.3322 5.9505 9.7401 13.934 18.612 17.482 22.192 27.024 32.228 37.892 0.0061671 0.025271 0.039152 0.050747 0.061061 0.037832 0.037006 0.039890 0.044407 0.049344 0.047821 0.047114 0.049933 0.054280 0.059017 2664.2 2500.0 2360.3 2250.3 2168.1 −0.53926 −0.55416 −0.52806 −0.49035 −0.45514 429.60 358.93 312.36 285.41 272.14 205.24 106.90 78.768 66.669 60.413 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Setzmann, U., and Wagner, W., “A New Equation of State and Tables of Thermodynamic Properties for Methane Covering the Range from the Melting Line to 625 K at Pressures up to 1000 MPa,” J. Phys. Chem. Ref. Data 20(6):1061–1151, 1991. The source for viscosity is Younglove, B. A., and Ely, J. F., “Thermophysical Properties of Fluids. II. Methane, Ethane, Propane, Isobutane and Normal Butane,” J. Phys. Chem. Ref. Data 16:577–798, 1987. The source for thermal conductivity is Friend, D. G., Ely, J. F., and Ingham, H., “Tables for the Thermophysical Properties of Methane,” NIST Tech. Note 1325, 1989. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties in density are 0.03% for pressures below 12 MPa and temperatures below 350 K and up to 0.07% for pressures less than 50 MPa. For the speed of sound, the uncertainty ranges from 0.03% (in the vapor phase) to 0.3% depending on temperature and pressure. Heat capacities may be generally calculated within an uncertainty of 1%. The uncertainty in viscosity is 2%, except in the critical region which is 5%. The uncertainty in thermal conductivity of the dilute gas between 130 and 625 K is 2.5%. For temperatures below 130 K, the uncertainty is less than 10%. Excluding the dilute gas, the uncertainty is 2% between 110 and 725 K at pressures up to 70 MPa, except near the critical point which has an uncertainty of 5% or greater. For the vapor at lower temperatures and the dense liquid near the triple point, an uncertainty of 10% is possible. 2-217 2-218 TABLE 2-120 Temperature K Thermodynamic Properties of Methanol Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Saturated Properties 175.61 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 510.00 513.38 1.8635E-07 3.7619E-07 3.2175E-06 1.9841E-05 9.4330E-05 0.00036348 0.0011791 0.0033166 0.0082787 0.018682 0.038692 0.074453 0.13447 0.22992 0.37483 0.58617 0.88399 1.2914 1.8349 2.5433 3.4456 4.5713 5.9794 7.7496 8.2159 175.61 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 375.00 390.00 405.00 420.00 435.00 450.00 465.00 480.00 495.00 510.00 513.38 1.8635E-07 3.7619E-07 3.2175E-06 1.9841E-05 9.4330E-05 0.00036348 0.0011791 0.0033166 0.0082787 0.018682 0.038692 0.074453 0.13447 0.22992 0.37483 0.58617 0.88399 1.2914 1.8349 2.5433 3.4456 4.5713 5.9794 7.7496 8.2159 28.230 28.096 27.629 27.163 26.703 26.250 25.802 25.360 24.922 24.484 24.041 23.590 23.124 22.638 22.123 21.571 20.973 20.315 19.579 18.741 17.759 16.553 14.880 11.689 8.7852 1.2764E-07 2.5140E-07 1.9855E-06 1.1378E-05 5.0556E-05 0.00018304 0.00056065 0.0014959 0.0035581 0.0076845 0.015300 0.028438 0.049870 0.083267 0.13344 0.20674 0.31179 0.46071 0.67055 0.96219 1.3555 1.9102 2.9050 5.1706 8.7852 0.035423 0.035592 0.036194 0.036815 0.037449 0.038096 0.038756 0.039432 0.040125 0.040844 0.041595 0.042390 0.043244 0.044174 0.045203 0.046358 0.047681 0.049226 0.051075 0.053360 0.056310 0.060411 0.067203 0.085547 0.11383 7,834,400. 3,977,700. 503,660. 87,892. 19,780. 5,463.4 1,783.7 668.48 281.05 130.13 65.359 35.164 20.052 12.009 7.4940 4.8370 3.2073 2.1706 1.4913 1.0393 0.73775 0.52352 0.34423 0.19340 0.11383 −12.440 −12.130 −11.067 −10.001 −8.9277 −7.8395 −6.7318 −5.5991 −4.4351 −3.2329 −1.9858 −0.68700 0.66961 2.0901 3.5806 5.1475 6.7983 8.5423 10.392 12.364 14.488 16.820 19.521 23.297 25.917 −12.440 −12.130 −11.067 −10.001 −8.9277 −7.8395 −6.7318 −5.5990 −4.4347 −3.2322 −1.9842 −0.68385 0.67543 2.1003 3.5975 5.1746 6.8404 8.6058 10.485 12.500 14.682 17.096 19.923 23.960 26.852 −0.049524 −0.047781 −0.042108 −0.036846 −0.031908 −0.027226 −0.022750 −0.018434 −0.014239 −0.010129 −0.0060725 −0.0020451 0.0019747 0.0060049 0.010061 0.014159 0.018314 0.022546 0.026879 0.031347 0.036009 0.040977 0.046590 0.054351 0.059911 0.056728 0.056689 0.056604 0.057072 0.057992 0.059275 0.060916 0.062917 0.065250 0.067864 0.070693 0.073674 0.076752 0.079881 0.083033 0.086189 0.089346 0.092514 0.095722 0.099032 0.10257 0.10666 0.11250 0.12653 0.070390 0.070750 0.070897 0.071215 0.072004 0.073141 0.074617 0.076487 0.078803 0.081584 0.084823 0.088505 0.092616 0.097164 0.10219 0.10776 0.11405 0.12133 0.13007 0.14120 0.15679 0.18345 0.25717 1.1088 1625.1 1590.2 1496.4 1425.3 1363.2 1304.6 1248.2 1194.1 1142.6 1093.5 1046.3 1000.2 954.32 907.64 859.31 808.48 754.41 696.47 634.17 567.09 494.36 412.12 308.94 192.83 0 28.219 28.353 28.810 29.259 29.698 30.123 30.534 30.932 31.321 31.703 32.077 32.442 32.789 33.108 33.385 33.601 33.736 33.767 33.687 33.541 33.439 33.258 32.267 29.688 25.917 29.679 29.850 30.430 31.003 31.564 32.109 32.637 33.149 33.648 34.134 34.606 35.060 35.485 35.869 36.194 36.436 36.571 36.570 36.423 36.184 35.981 35.652 34.325 31.187 26.852 0.19032 0.18544 0.17069 0.15841 0.14806 0.13923 0.13164 0.12508 0.11938 0.11442 0.11009 0.10627 0.10287 0.099808 0.096984 0.094317 0.091723 0.089128 0.086505 0.083978 0.081813 0.079634 0.075685 0.068520 0.059911 0.031874 0.032397 0.035224 0.040104 0.047248 0.056324 0.066572 0.077055 0.086920 0.095581 0.10279 0.10860 0.11331 0.11736 0.12125 0.12546 0.13033 0.13587 0.14101 0.14238 0.13589 0.12618 0.12608 0.13259 0.040287 0.040854 0.043954 0.049389 0.057480 0.067973 0.080135 0.093000 0.10564 0.11740 0.12798 0.13749 0.14644 0.15559 0.16605 0.17917 0.19663 0.21986 0.24709 0.26502 0.25879 0.27959 0.42448 1.9096 239.95 242.62 251.06 258.49 265.30 271.89 278.43 284.90 291.19 297.15 302.63 307.47 311.48 314.48 316.20 316.34 314.53 310.36 303.71 295.26 285.25 267.83 247.46 212.65 0 −0.40884 −0.40373 −0.39791 −0.39361 −0.38674 −0.37793 −0.36733 −0.35457 −0.33915 −0.32073 −0.29904 −0.27385 −0.24479 −0.21121 −0.17199 −0.12529 −0.068163 0.0042669 0.10021 0.23444 0.43762 0.79465 1.6506 4.6061 6.7425 1187400. 857090. 293110. 105090. 39363. 15552. 6557.5 2971.8 1449.9 759.96 426.34 254.84 161.53 108.02 75.802 55.467 42.002 32.587 25.532 19.860 15.568 13.904 12.099 9.5115 6.7425 Single-Phase Properties 200.00 300.00 337.30 0.10000 0.10000 0.10000 337.30 400.00 500.00 600.00 0.10000 0.10000 0.10000 0.10000 200.00 300.00 400.00 409.75 1.0000 1.0000 1.0000 1.0000 409.75 500.00 600.00 1.0000 1.0000 1.0000 200.00 300.00 400.00 484.95 5.0000 5.0000 5.0000 5.0000 484.95 500.00 600.00 5.0000 5.0000 5.0000 200.00 300.00 400.00 500.00 600.00 10.000 10.000 10.000 10.000 10.000 27.474 24.486 23.366 0.037626 0.030452 0.024157 0.020089 0.036398 0.040839 0.042798 −10.709 −3.2300 −0.030266 −0.040317 −0.010133 −0.000089518 0.056702 0.067862 0.075163 0.070943 0.081580 0.090451 1471.5 1094.1 977.93 −0.39677 −0.32081 −0.26023 32.613 36.075 40.921 46.476 35.271 39.359 45.060 51.454 0.10457 0.11581 0.12851 0.14014 0.11100 0.044972 0.051823 0.059065 0.14187 0.054208 0.060380 0.067441 309.54 349.19 387.15 420.71 −10.720 −3.2472 6.2298 7.3401 −10.684 −3.2064 6.2770 7.3883 −0.040354 −0.010176 0.016901 0.019645 0.056724 0.067848 0.088257 0.090347 0.070932 0.081541 0.11177 0.11623 1475.1 1100.0 775.46 736.51 33.758 40.335 46.300 36.586 44.303 51.178 0.090904 0.10818 0.12070 0.13203 0.056676 0.061344 0.20333 0.068069 0.070369 313.48 376.08 413.09 38.678 13.330 4.5635 0.036283 0.040592 0.046640 0.062203 −10.752 −3.3039 6.0896 17.655 −10.571 −3.1010 6.3228 17.966 −0.040517 −0.010367 0.016546 0.042725 0.056820 0.067795 0.087676 0.10826 0.070883 0.081377 0.11029 0.19836 1490.9 1125.5 818.58 381.15 −0.39825 −0.32568 −0.11504 0.98684 2.1711 1.7679 1.1389 0.46060 0.56566 0.87808 33.047 35.907 45.247 35.350 38.735 49.638 0.078574 0.085457 0.10553 0.12499 0.098975 0.072927 0.32263 0.17315 0.087489 260.06 301.43 379.21 13.826 12.155 5.1009 27.648 24.779 21.717 15.932 2.6640 0.036169 0.040357 0.046048 0.062765 0.37537 −10.791 −3.3713 5.9321 19.374 43.262 −10.430 −2.9677 6.3925 20.002 47.015 −0.040716 −0.010598 0.016141 0.046226 0.096406 0.056935 0.067746 0.087087 0.10760 0.088868 0.070820 0.081196 0.10880 0.18959 0.12122 1509.9 1155.3 865.91 424.68 343.60 −0.39966 −0.32990 −0.13884 0.83939 5.0965 −7.8460 −0.44914 8.4277 19.458 32.525 −0.043691 −0.013840 0.011565 0.036085 0.059862 0.057827 0.067889 0.082823 0.095694 0.10406 0.068992 0.079818 0.098951 0.12152 0.13787 1772.1 1515.8 1334.7 1164.1 977.50 −0.41976 −0.35799 −0.26099 −0.14407 −0.023905 10.949 19.430 29.089 40.322 −0.022106 0.0022308 0.023726 0.044161 0.070293 0.077541 0.084883 0.092281 0.080627 0.089761 0.10419 0.12017 2316.0 2194.8 2123.2 2074.1 −0.34762 −0.30897 −0.24751 −0.19279 27.491 24.514 21.193 20.772 0.35352 0.25202 0.20501 27.561 24.635 21.441 16.076 26.577 32.839 41.396 49.779 −10.713 −3.2341 −0.034546 0.036376 0.040793 0.047185 0.048143 2.8287 3.9680 4.8778 200.00 300.00 400.00 500.00 600.00 100.00 100.00 100.00 100.00 100.00 28.911 26.630 24.493 22.020 19.139 0.034588 0.037552 0.040827 0.045413 0.052250 −11.305 −4.2043 4.3449 14.917 27.300 300.00 400.00 500.00 600.00 500.00 500.00 500.00 500.00 30.547 29.154 27.670 26.003 0.032736 0.034300 0.036140 0.038457 −5.4195 2.2795 11.020 21.094 202.71 40.941 12.933 4.3382 −0.39705 −0.32177 −0.090229 −0.047179 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is de Reuck, K. M., and Craven, R. J. B., “Methanol, International Thermodynamic Tables of the Fluid State—12,” IUPAC, Blackwell Scientific Publications, London, 1993. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are generally 0.1% in density and 2% in the speed of sound, except in the critical region and high pressures. 2-219 2-220 TABLE 2-121 Thermodynamic Properties of nitrogen Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) −4.2230 −4.1194 −4.0071 −3.8946 −3.7819 −3.6689 −3.5556 −3.4419 −3.3278 −3.2132 −3.0980 −2.9822 −2.8657 −2.7483 −2.6301 −2.5107 −2.3902 −2.2683 −2.1449 −2.0196 −1.8923 −1.7625 −1.6298 −1.4938 −1.3537 −1.2086 −1.0571 −0.89741 −0.72635 −0.53833 −0.32093 −0.031475 0.51527 −4.2226 −4.1188 −4.0063 −3.8935 −3.7804 −3.6669 −3.5530 −3.4385 −3.3235 −3.2078 −3.0913 −2.9739 −2.8555 −2.7360 −2.6152 −2.4930 −2.3691 −2.2434 −2.1156 −1.9854 −1.8525 −1.7163 −1.5765 −1.4323 −1.2828 −1.1271 −0.96336 −0.78944 −0.60161 −0.39322 −0.14962 0.17937 0.81891 0.067951 0.069569 0.071270 0.072924 0.074535 0.076105 0.077637 0.079133 0.080597 0.082030 0.083436 0.084815 0.086172 0.087507 0.088823 0.090123 0.091408 0.092682 0.093946 0.095204 0.096459 0.097715 0.098977 0.10025 0.10154 0.10285 0.10420 0.10561 0.10710 0.10873 0.11059 0.11310 0.11807 1.2945 1.3299 1.3675 1.4042 1.4400 1.4747 1.5082 1.5404 1.5713 1.6007 1.6284 1.6544 1.6784 1.7005 1.7203 1.7377 1.7525 1.7645 1.7733 1.7788 1.7804 1.7778 1.7703 1.8147 1.8639 1.9160 1.9668 2.0162 2.0639 2.1099 2.1539 2.1957 2.2353 2.2725 2.3070 2.3386 2.3672 2.3925 2.4143 2.4324 2.4463 2.4557 2.4603 2.4595 2.4528 2.4394 0.16355 0.16161 0.15966 0.15786 0.15618 0.15461 0.15314 0.15176 0.15046 0.14923 0.14806 0.14694 0.14587 0.14485 0.14385 0.14289 0.14195 0.14103 0.14012 0.13922 0.13832 0.13742 0.13651 Cp kJ/(mol⋅K) Sound speed m/s 0.032951 0.032591 0.032207 0.031831 0.031463 0.031106 0.030760 0.030427 0.030105 0.029795 0.029499 0.029215 0.028944 0.028687 0.028444 0.028215 0.028001 0.027804 0.027624 0.027464 0.027327 0.027214 0.027133 0.027088 0.027089 0.027149 0.027290 0.027545 0.027981 0.028755 0.030317 0.034680 0.056033 0.056121 0.056231 0.056360 0.056512 0.056690 0.056899 0.057142 0.057425 0.057752 0.058130 0.058566 0.059068 0.059647 0.060315 0.061088 0.061983 0.063026 0.064246 0.065684 0.067392 0.069443 0.071937 0.075021 0.078914 0.083966 0.090771 0.10044 0.11531 0.14140 0.20028 0.46831 995.28 976.36 956.04 935.83 915.66 895.49 875.28 855.00 834.61 814.07 793.36 772.44 751.28 729.84 708.09 685.99 663.50 640.57 617.14 593.17 568.58 543.30 517.24 490.29 462.32 433.19 402.67 370.43 335.85 297.68 253.32 195.48 0 −0.40419 −0.39833 −0.39135 −0.38364 −0.37508 −0.36560 −0.35506 −0.34334 −0.33029 −0.31574 −0.29951 −0.28135 −0.26099 −0.23813 −0.21237 −0.18326 −0.15025 −0.11264 −0.069613 −0.020100 0.037239 0.10414 0.18288 0.27654 0.38936 0.52741 0.69974 0.92076 1.2154 1.6317 2.2811 3.5308 6.0831 0.021007 0.021059 0.021123 0.021196 0.021278 0.021370 0.021472 0.021585 0.021709 0.021845 0.021994 0.022157 0.022334 0.022528 0.022738 0.022967 0.023217 0.023489 0.023787 0.024113 0.024471 0.024860 0.025284 0.029647 0.029788 0.029969 0.030180 0.030427 0.030712 0.031039 0.031413 0.031839 0.032323 0.032873 0.033496 0.034204 0.035008 0.035925 0.036973 0.038177 0.039568 0.041185 0.043081 0.045326 0.048012 0.051276 161.11 163.20 165.37 167.43 169.39 171.23 172.95 174.55 176.03 177.38 178.60 179.68 180.63 181.43 182.10 182.62 182.99 183.21 183.28 183.18 182.93 182.51 181.93 40.718 38.268 35.907 33.803 31.922 30.231 28.707 27.328 26.074 24.931 23.884 22.923 22.035 21.212 20.446 19.730 19.057 18.421 17.815 17.236 16.676 16.132 15.600 Cv kJ/(mol⋅K) Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 173.24 169.51 165.49 161.47 157.47 153.46 149.47 145.48 141.50 137.55 133.61 129.66 125.72 121.77 117.83 113.89 109.95 106.02 102.08 98.144 94.208 90.272 86.337 82.404 78.472 74.544 70.626 66.728 62.883 59.196 56.121 56.435 311.59 282.07 254.55 230.85 210.32 192.43 176.75 162.94 150.71 139.82 130.07 121.31 113.38 106.18 99.602 93.568 88.004 82.847 78.042 73.543 69.306 65.292 61.464 57.786 54.224 50.740 47.290 43.824 40.270 36.509 32.310 26.935 Saturated Properties 63.151 65.000 67.000 69.000 71.000 73.000 75.000 77.000 79.000 81.000 83.000 85.000 87.000 89.000 91.000 93.000 95.000 97.000 99.000 101.00 103.00 105.00 107.00 109.00 111.00 113.00 115.00 117.00 119.00 121.00 123.00 125.00 126.19 0.012520 0.017404 0.024300 0.033213 0.044527 0.058656 0.076043 0.097152 0.12247 0.15251 0.18780 0.22886 0.27626 0.33055 0.39230 0.46210 0.54052 0.62817 0.72566 0.83358 0.95259 1.0833 1.2264 1.3826 1.5526 1.7371 1.9370 2.1533 2.3869 2.6391 2.9116 3.2069 3.3958 63.151 65.000 67.000 69.000 71.000 73.000 75.000 77.000 79.000 81.000 83.000 85.000 87.000 89.000 91.000 93.000 95.000 97.000 99.000 101.00 103.00 105.00 107.00 0.012520 0.017404 0.024300 0.033213 0.044527 0.058656 0.076043 0.097152 0.12247 0.15251 0.18780 0.22886 0.27626 0.33055 0.39230 0.46210 0.54052 0.62817 0.72566 0.83358 0.95259 1.0833 1.2264 30.957 30.685 30.387 30.085 29.779 29.468 29.153 28.832 28.506 28.175 27.837 27.492 27.139 26.779 26.409 26.030 25.640 25.238 24.822 24.390 23.941 23.471 22.978 22.457 21.902 21.306 20.658 19.943 19.134 18.187 16.997 15.210 11.184 0.024070 0.032594 0.044300 0.059031 0.077273 0.099542 0.12638 0.15838 0.19613 0.24030 0.29157 0.35069 0.41846 0.49576 0.58355 0.68291 0.79504 0.92134 1.0634 1.2231 1.4027 1.6049 1.8331 0.032303 0.032589 0.032909 0.033239 0.033581 0.033935 0.034302 0.034683 0.035080 0.035493 0.035924 0.036375 0.036847 0.037343 0.037865 0.038417 0.039002 0.039623 0.040288 0.041000 0.041769 0.042605 0.043520 0.044530 0.045658 0.046935 0.048407 0.050144 0.052262 0.054985 0.058834 0.065747 0.089414 41.546 30.680 22.573 16.940 12.941 10.046 7.9124 6.3140 5.0986 4.1614 3.4297 2.8515 2.3897 2.0171 1.7137 1.4643 1.2578 1.0854 0.94038 0.81759 0.71291 0.62309 0.54553 5.6209 5.8164 6.0298 6.2457 6.4645 6.6870 6.9138 7.1458 7.3839 7.6295 7.8837 8.1483 8.4251 8.7163 9.0247 9.3533 9.7060 10.087 10.503 10.960 11.467 12.035 12.679 4.3763 4.5123 4.6601 4.8088 4.9585 5.1096 5.2621 5.4164 5.5727 5.7313 5.8924 6.0565 6.2238 6.3948 6.5700 6.7499 6.9353 7.1270 7.3260 7.5334 7.7509 7.9804 8.2245 109.00 111.00 113.00 115.00 117.00 119.00 121.00 123.00 125.00 126.19 1.3826 1.5526 1.7371 1.9370 2.1533 2.3869 2.6391 2.9116 3.2069 3.3958 100.00 600.00 1100.0 1600.0 0.10000 0.10000 0.10000 0.10000 100.00 103.75 1.0000 1.0000 103.75 600.00 1100.0 1600.0 1.0000 1.0000 1.0000 1.0000 100.00 600.00 1100.0 1600.0 5.0000 5.0000 5.0000 5.0000 2.0916 2.3860 2.7240 3.1162 3.5786 4.1370 4.8380 5.7846 7.3244 11.184 0.47811 0.41911 0.36711 0.32091 0.27944 0.24172 0.20670 0.17287 0.13653 0.089414 1.7573 1.7377 1.7102 1.6730 1.6234 1.5572 1.4665 1.3343 1.1039 0.51527 2.4183 2.3884 2.3479 2.2946 2.2251 2.1341 2.0119 1.8376 1.5417 0.81891 0.13557 0.13461 0.13360 0.13253 0.13138 0.13009 0.12860 0.12675 0.12400 0.11807 0.025750 0.026284 0.026924 0.027721 0.028723 0.029997 0.031683 0.034185 0.039278 0.055332 0.060528 0.067435 0.077010 0.091003 0.11312 0.15295 0.24490 0.66512 181.19 180.28 179.15 177.75 176.01 173.87 171.17 167.43 160.26 0 15.075 14.546 13.996 13.409 12.767 12.045 11.203 10.148 8.6030 6.0831 13.419 14.284 15.315 16.580 18.186 20.329 23.424 28.604 41.535 8.4867 8.7716 9.0860 9.4395 9.8474 10.336 10.953 11.813 13.326 9.3806 44.840 70.075 92.344 6.9581 29.577 44.199 56.398 Single-Phase Properties 100.00 600.00 1100.0 1600.0 600.00 1100.0 1600.0 600.00 1100.0 1600.0 10.000 10.000 10.000 10.000 500.00 500.00 500.00 1000.0 1000.0 1000.0 0.12268 0.020037 0.010930 0.0075152 24.658 23.768 1.4754 0.19960 0.10899 0.074993 8.1514 49.908 91.489 133.06 0.040554 0.042073 0.67778 5.0099 9.1755 13.335 2.0396 12.573 24.284 37.272 2.8547 17.564 33.433 50.579 0.15950 0.21217 0.23131 0.24414 0.021049 0.021796 0.024932 0.026815 0.030012 0.030118 0.033248 0.035130 201.64 496.27 660.05 788.94 16.082 0.021483 −0.65654 −0.81543 −2.0907 −1.8441 −2.0501 −1.8020 0.094493 0.096928 0.027546 0.027281 0.064564 0.068113 609.42 559.22 −0.054514 0.060996 100.58 92.738 76.255 67.783 1.7800 12.554 24.277 37.270 2.4577 17.564 33.452 50.605 0.13799 0.19300 0.21216 0.22499 0.024612 0.021812 0.024938 0.026820 0.046272 0.030198 0.033267 0.035138 182.79 498.66 662.07 790.64 16.471 0.0061465 −0.65940 −0.81612 11.671 44.992 70.155 92.399 7.8351 29.626 44.221 56.411 25.436 0.98084 0.53797 0.37146 0.039314 1.0195 1.8588 2.6921 −2.2176 12.469 24.247 37.259 −2.0210 17.567 33.541 50.720 0.093188 0.17948 0.19875 0.21161 0.027713 0.021881 0.024969 0.026839 0.059868 0.030539 0.033350 0.035170 673.24 509.60 671.08 798.18 −0.17096 −0.057679 −0.67112 −0.81886 108.13 45.797 70.555 92.663 84.510 29.882 44.330 56.476 26.188 1.9183 1.0590 0.73435 0.038186 0.52130 0.94433 1.3618 −2.3398 12.368 24.211 37.246 −1.9580 17.581 33.654 50.864 0.091882 0.17355 0.19296 0.20583 0.028004 0.021965 0.025006 0.026863 0.056646 0.030926 0.033447 0.035209 734.22 523.87 682.37 807.57 −0.25658 −0.12928 −0.68394 −0.82170 115.90 46.995 71.130 93.033 93.648 30.284 44.493 56.570 27.434 21.868 18.335 0.036451 0.045729 0.054541 10.778 23.840 37.584 29.003 46.705 64.855 0.13791 0.15935 0.17295 0.026493 0.027586 0.028647 0.035336 0.035848 0.036665 1574.4 1501.4 1506.6 −0.70223 −0.72394 −0.73166 177.40 149.37 147.47 103.10 79.801 79.226 34.270 29.362 25.920 0.029180 0.034057 0.038580 11.714 25.065 38.999 40.894 59.122 77.579 0.13093 0.15303 0.16685 0.029169 0.029373 0.029977 0.036905 0.036577 0.037212 2107.2 1985.1 1942.0 −0.61888 −0.65271 −0.65439 278.97 232.49 214.36 208.00 129.86 110.35 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Span, R., Lemmon, E. W., Jacobsen, R. T., Wagner, W., and Yokozeki, A., “A Reference Quality Thermodynamic Property Formulation for Nitrogen,” J. Phys. Chem. Ref. Data 29(6):1361–1433, 2000. See also Int. J. Thermophys. 14(4):1121–1132, 1998. The source for viscosity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. The source for thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density of the equation of state is 0.02% from the triple point up to temperatures of 523 K and pressures up to 12 MPa and from temperatures of 240 to 523 K at pressures less than 30 MPa. In the range from 270 to 350 K at pressures less than 12 MPa, the uncertainty in density is 0.01%. The uncertainty at very high pressures (>1 GPa) is 0.6% in density. The uncertainty in pressure in the critical region is estimated to be 0.02%. In the gaseous and supercritical region, the speed of sound can be calculated with a typical uncertainty of 0.005% to 0.1%. At liquid states and at high pressures, the uncertainty increases to 0.5% to 1.5%. For pressures up to 30 MPa, the estimated uncertainty for heat capacities ranges from 0.3% at gaseous and gaslike supercritical states up to 0.8% at liquid states and at certain gaseous and supercritical states at low temperatures. The uncertainty is 2% for pressures up to 200 MPa and larger at higher pressures. The estimated uncertainties of vapor pressure, saturated-liquid density, and saturated-vapor density are in general 0.02% for each property. The formulation yields a reasonable extrapolation behavior up to the limits of chemical stability of nitrogen. For viscosity, the uncertainty is 0.5% in dilute gas. Away from the dilute gas (pressures greater than 1 MPa and in the liquid), the uncertainties are as low as 1% between 270 and 300 K at pressures less than 100 MPa, and increase outside that range. The uncertainties are around 2% at temperatures of 180 K and higher. Below this and away from the critical region, the uncertainties steadily increase to around 5% at the triple points of the fluids. The uncertainties in the critical region are higher. For thermal conductivity, the uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For the nondilute gas, the uncertainty is 2% for temperatures greater than 150 K. The uncertainty is 3% at temperatures less than the critical point and 5% in the critical region, except for states very near the critical point. 2-221 2-222 FIG. 2-7 Pressure-enthalpy diagram for nitrogen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Span, R., E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki, “A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa.,” J. Phys. Chem. Ref. Data 29:1361–1433, 2000. TABLE 2-122 Thermodynamic Properties of Oxygen Temperature K Pressure MPa Density mol/dm3 54.361 55.000 60.000 65.000 70.000 75.000 80.000 85.000 90.000 95.000 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 154.58 0.00014628 0.00017857 0.00072582 0.0023349 0.0062623 0.014547 0.030123 0.056831 0.099350 0.16308 0.25400 0.37853 0.54340 0.75559 1.0223 1.3509 1.7491 2.2250 2.7878 3.4477 4.2186 5.0428 40.816 40.734 40.064 39.367 38.656 37.936 37.203 36.457 35.692 34.905 34.092 33.245 32.360 31.426 30.434 29.367 28.203 26.907 25.415 23.599 21.110 13.630 54.361 55.000 60.000 65.000 70.000 75.000 80.000 85.000 90.000 95.000 100.00 105.00 110.00 115.00 120.00 125.00 130.00 135.00 140.00 145.00 150.00 154.58 0.00014628 0.00017857 0.00072582 0.0023349 0.0062623 0.014547 0.030123 0.056831 0.099350 0.16308 0.25400 0.37853 0.54340 0.75559 1.0223 1.3509 1.7491 2.2250 2.7878 3.4477 4.2186 5.0428 0.00032370 0.00039060 0.0014561 0.0043291 0.010804 0.023509 0.045891 0.082138 0.13710 0.21627 0.32579 0.47267 0.66506 0.91283 1.2284 1.6285 2.1366 2.7893 3.6487 4.8412 6.7170 13.630 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 0.024500 0.024549 0.024960 0.025402 0.025869 0.026360 0.026879 0.027430 0.028017 0.028649 0.029333 0.030079 0.030903 0.031820 0.032858 0.034051 0.035457 0.037165 0.039347 0.042375 0.047372 0.073368 −6.1954 −6.1613 −5.8938 −5.6258 −5.3573 −5.0889 −4.8202 −4.5510 −4.2806 −4.0084 −3.7337 −3.4556 −3.1732 −2.8853 −2.5904 −2.2867 −1.9711 −1.6394 −1.2839 −0.88908 −0.41330 0.66752 −6.1954 −6.1612 −5.8938 −5.6257 −5.3572 −5.0885 −4.8194 −4.5495 −4.2778 −4.0038 −3.7263 −3.4442 −3.1564 −2.8612 −2.5568 −2.2407 −1.9091 −1.5567 −1.1742 −0.74298 −0.21346 1.0375 0.066946 0.067571 0.072225 0.076516 0.080495 0.084199 0.087667 0.090931 0.094023 0.096967 0.099787 0.10250 0.10513 0.10770 0.11022 0.11271 0.11520 0.11773 0.12035 0.12319 0.12654 0.13442 3089.2 2560.2 686.75 230.99 92.556 42.536 21.791 12.175 7.2938 4.6239 3.0695 2.1156 1.5036 1.0955 0.81405 0.61407 0.46803 0.35852 0.27407 0.20656 0.14888 0.073368 1.1195 1.1327 1.2355 1.3377 1.4393 1.5397 1.6377 1.7320 1.8209 1.9031 1.9772 2.0421 2.0966 2.1391 2.1678 2.1801 2.1722 2.1380 2.0670 1.9383 1.6938 0.66752 1.5714 1.5898 1.7339 1.8770 2.0189 2.1584 2.2941 2.4239 2.5455 2.6571 2.7569 2.8430 2.9136 2.9668 3.0000 3.0097 2.9908 2.9357 2.8311 2.6505 2.3219 1.0375 0.20982 0.20850 0.19935 0.19194 0.18587 0.18083 0.17659 0.17297 0.16984 0.16708 0.16462 0.16238 0.16032 0.15838 0.15652 0.15471 0.15289 0.15100 0.14896 0.14659 0.14345 0.13442 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.038252 0.037651 0.034835 0.033469 0.032532 0.031745 0.031030 0.030365 0.029745 0.029169 0.028636 0.028146 0.027703 0.027311 0.026976 0.026712 0.026536 0.026485 0.026634 0.027189 0.028982 0.053541 0.053489 0.053548 0.053668 0.053697 0.053719 0.053808 0.054012 0.054361 0.054880 0.055599 0.056557 0.057816 0.059469 0.061666 0.064659 0.068905 0.075327 0.086099 0.10778 0.17484 1123.4 1126.9 1127.4 1101.7 1066.3 1027.5 987.43 946.87 905.90 864.40 822.19 779.06 734.77 689.03 641.52 591.86 539.50 483.69 423.10 355.20 273.80 0 −0.37992 −0.37886 −0.37011 −0.36312 −0.35686 −0.34972 −0.34056 −0.32856 −0.31302 −0.29316 −0.26804 −0.23637 −0.19639 −0.14551 −0.079899 0.0063780 0.12309 0.28750 0.53357 0.93865 1.7389 5.0628 201.92 201.02 193.94 186.82 179.70 172.58 165.44 158.27 151.05 143.81 136.55 129.25 121.92 114.57 107.23 99.912 92.634 85.404 78.217 71.056 64.190 773.62 747.53 578.07 457.94 371.79 308.66 261.22 224.62 195.64 172.12 152.56 135.93 121.52 108.81 97.426 87.086 77.571 68.687 60.223 51.869 42.900 0.021241 0.021297 0.021815 0.022310 0.022565 0.022513 0.022239 0.021896 0.021624 0.021515 0.021605 0.021894 0.022361 0.022978 0.023726 0.024597 0.025604 0.026794 0.028269 0.030276 0.033574 0.029631 0.029698 0.030320 0.030934 0.031294 0.031336 0.031177 0.031019 0.031053 0.031420 0.032204 0.033461 0.035245 0.037647 0.040839 0.045146 0.051204 0.060349 0.075824 0.10781 0.21201 140.32 141.11 147.03 152.65 158.07 163.33 168.36 173.06 177.30 180.99 184.06 186.44 188.14 189.13 189.41 188.96 187.75 185.74 182.82 178.78 172.82 0 Cv kJ/(mol⋅K) Saturated Properties 507.90 480.26 284.62 156.71 87.254 52.570 35.817 27.728 23.649 21.338 19.753 18.446 17.250 16.118 15.045 14.029 13.062 12.120 11.155 10.071 8.6358 5.0628 4.4204 4.4842 4.9840 5.4863 5.9925 6.5051 7.0277 7.5654 8.1241 8.7113 9.3362 10.010 10.748 11.571 12.509 13.607 14.940 16.641 18.977 22.582 29.666 4.0962 4.1481 4.5528 4.9555 5.3557 5.7533 6.1486 6.5423 6.9355 7.3301 7.7281 8.1324 8.5467 8.9760 9.4273 9.9112 10.445 11.061 11.823 12.881 14.721 (Continued) 2-223 2-224 TABLE 2-122 Thermodynamic Properties of Oxygen (Continued ) Temperature K Pressure MPa Cp kJ/(mol⋅K) Sound speed m/s 0.020885 0.021078 0.022781 0.024672 0.026045 0.029925 0.029435 0.031108 0.032992 0.034363 188.37 329.72 421.27 493.31 555.60 18.479 2.6530 0.75388 0.10517 −0.18735 0.099680 0.11003 0.028683 0.027000 0.055399 0.061476 826.85 645.19 −0.27181 −0.085501 2.9983 8.6563 14.741 21.176 27.929 0.15666 0.18598 0.20149 0.21230 0.22078 0.023665 0.021148 0.022802 0.024682 0.026051 0.040564 0.029887 0.031240 0.033052 0.034395 189.41 329.90 422.68 494.87 557.14 15.124 2.6066 0.73726 0.098376 −0.19062 12.433 26.894 41.288 54.139 66.001 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 0.12316 0.040116 0.024050 0.017177 0.013360 8.1192 24.928 41.579 58.216 74.849 2.0355 6.2338 10.604 15.357 20.438 2.8474 8.7265 14.762 21.179 27.923 0.17297 0.20531 0.22069 0.23147 0.23994 0.029276 0.032774 −3.7444 −2.6131 −3.7151 −2.5803 0.83209 2.4791 4.1649 5.8360 7.5029 2.1662 6.1772 10.576 15.340 20.426 Cv kJ/(mol⋅K) Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity mPa⋅s 9.0852 26.485 41.046 53.966 65.867 7.7121 20.652 30.486 38.653 45.806 Single-Phase Properties 100.00 300.00 500.00 700.00 900.00 0.10000 0.10000 0.10000 0.10000 0.10000 100.00 119.62 1.0000 1.0000 119.62 300.00 500.00 700.00 900.00 1.0000 1.0000 1.0000 1.0000 1.0000 100.00 154.36 5.0000 5.0000 34.497 16.011 0.028988 0.062457 −3.7983 0.35374 −3.6533 0.66602 0.099132 0.13204 0.028935 0.038878 0.054458 3.5718 850.39 163.89 −0.28978 4.2044 140.71 75.954 160.92 29.668 154.36 300.00 500.00 700.00 900.00 5.0000 5.0000 5.0000 5.0000 5.0000 11.160 2.0616 1.1908 0.84728 0.65931 0.089610 0.48505 0.83975 1.1802 1.5167 1.0294 5.9227 10.454 15.264 20.373 1.4774 8.3480 14.653 21.165 27.956 0.13729 0.17177 0.18787 0.19881 0.20734 0.041906 0.021448 0.022894 0.024726 0.026076 4.2513 0.032003 0.031815 0.033309 0.034537 158.85 332.25 429.36 501.98 564.07 6.0016 2.3730 0.66261 0.068114 −0.20519 72.313 28.797 42.362 54.901 66.593 20.574 21.766 31.267 39.261 46.305 34.158 30.512 1.2018 0.40337 0.24010 0.17135 0.13328 137.23 107.79 153.89 98.249 9.3921 20.846 30.630 38.766 45.899 100.00 300.00 500.00 700.00 900.00 10.000 10.000 10.000 10.000 10.000 34.885 4.2056 2.3538 1.6705 1.3010 0.028665 0.23778 0.42484 0.59861 0.76866 −3.8593 5.6024 10.306 15.171 20.307 −3.5726 7.9802 14.554 21.157 27.993 0.098498 0.16499 0.18182 0.19292 0.20150 0.029235 0.021790 0.022999 0.024776 0.026104 0.053516 0.034749 0.032491 0.033613 0.034706 877.07 339.35 438.67 511.24 572.92 −0.30803 2.0332 0.56900 0.030534 −0.22339 144.82 31.466 43.708 55.839 67.321 169.49 23.153 32.074 39.873 46.804 100.00 300.00 500.00 700.00 900.00 25.000 25.000 25.000 25.000 25.000 35.884 10.393 5.6243 3.9923 3.1222 0.027867 0.096215 0.17780 0.25048 0.32028 −4.0109 4.7194 9.8920 14.907 20.117 −3.3142 7.1247 14.337 21.169 28.124 0.096845 0.15490 0.17346 0.18495 0.19369 0.030037 0.022521 0.023256 0.024901 0.026174 0.051627 0.040917 0.034167 0.034397 0.035155 945.24 390.80 472.62 541.32 600.66 −0.34532 1.0167 0.30658 −0.076019 −0.27597 155.97 41.851 47.943 58.651 69.464 194.38 29.605 34.705 41.714 48.271 100.00 300.00 500.00 700.00 900.00 75.000 75.000 75.000 75.000 75.000 38.263 21.603 13.760 10.201 8.1749 0.026135 0.046289 0.072675 0.098029 0.12233 −4.3340 3.1884 8.8798 14.192 19.571 −2.3739 6.6601 14.330 21.544 28.745 0.092788 0.14315 0.16284 0.17498 0.18403 0.031906 0.023601 0.023725 0.025126 0.026293 0.049123 0.041272 0.036534 0.035903 0.036153 1115.1 645.54 619.75 657.04 701.72 −0.39472 −0.18640 −0.20732 −0.31840 −0.40609 184.96 75.261 64.149 68.835 76.863 274.96 53.378 45.084 48.269 53.163 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Schmidt, R., and Wagner, W., “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria, 19:175–200, 1985. The source for viscosity and thermal conductivity is Lemmon, E. W., and Jacobsen, R. T., “Viscosity and Thermal Conductivity Equations for Nitrogen, Oxygen, Argon, and Air,” Int. J. Thermophys. 25:21–69, 2004. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.1% in density, 2% in heat capacity, and 1% in the speed of sound, except in the critical region. For viscosity, the uncertainty is 1% in the dilute gas at temperatures above 200 K, and 5% in the dilute gas at lower temperatures. The uncertainty is around 2% between 270 and 300 K, and increases to 5% outside of this region. The uncertainty may be higher in the liquid near the triple point. The uncertainty for the dilute gas is 2% with increasing uncertainties near the triple point. For thermal conductivity, the uncertainties range from 3% between 270 and 300 K to 5% elsewhere. The uncertainties above 100 MPa are not known due to a lack of experimental data. FIG. 2-8 Pressure-enthalpy diagram for oxygen. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Schmidt, R., and W. Wagner, “A New Form of the Equation of State for Pure Substances and Its Application to Oxygen,” Fluid Phase Equilibria 19: 175–200, 1985. 2-225 FIG. 2-9 Enthalpy-concentration diagram for oxygen-nitrogen mixture at 1 atm. Reference states: Enthalpies of liquid oxygen and liquid nitrogen at the normal boiling point of nitrogen are zero. (Dodge, B.F. Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1944.) Wilson, G.M., P.M. Silverberg, and M.G. Zellner, AFAPL TDR 64-64 (AD 603151), 1964, p. 314, present extensive vapor-liquid equilibrium data for the three-component system argon-nitrogen-oxygen as well as for binary systems including oxygen-nitrogen. Calculations for this mixture are also available with the NIST REFPROP software. 6 20 10 1.5 9 .2 .05 1.0 .6 .9 .8 .1 .5 .4 4 Ethylene 2 Methane 1.5 .3 .04 .005 .02 .004 .005 .004 .03 .07 .015 .06 .07 .05 .06 Ethane .4 3 .1 .09 .08 .09 .08 .7 .6 .006 .006 .7 5000 6000 .01 .009 .03 .008 .007 .15 .8 6 .01 .009 .008 .007 .01 .009 .02 .04 .05 .008 .045 .015 –10 –20 09 .00 .003 .04 .06 .9 5 .001 .004 .05.015 .07 .001 .002 .005 .02 .08 .2 .5 4000 .09 1.0 5 3000 .3 .3 2 7 2000 .1 .4 1.5 00.5 .003 .01 .009 .008 .007 .006 .03 .04 .4 .5 .04 .1 .09.03 .08 .07 .02 .06 .5 3 15 8 1500 .2 .6 .004 .015 .15.05 .7 .6 2 Pressure, kPa 900 1000 4 .3 Propane 500 1 .9 .8 .7 3 5 .9 .8 Temperature, °C 30 4 .02 .05 n-Nonane 1 7 400 .3 .1 .09 .08 .07 .2 .06 .4 0 ne 8 .5 1.5 .03 .1 .09 .08 .07 .06 .005 1 .001 .004 .01 8 0 0 .0 .009 .003 .008 6 .000 .007 .006 .002 5 0 .0 .04 cta n-O 300 5 .015 10 n-Heptane 6 10 9 40 1.5 .15 .5 .15 .4 .6 2 .02 .05 .6 .2 .7 7 250 700 800 2 8 50 600 10 .9 .8 3 .2 n-Hexane 10 9 15 60 3 20 .004 .005 .01 .009 .008 .006 .007 .006 .03 .1 .09 .08 .07 .06 .3 .003 .015 .04 .4 .4 1 .9.3 .8 .7 4 4 20 70 200 5 .15 n-Pentane 6 15 80 5 20 .05 .5 .6 1.5.5 6 .06 .2 .6 Isopentane 30 .8 2 .7 –30 –40 –50 .007 .01 n-Butane 20 100 90 150 8 30 7 9 8 7 Isobutane 25 40 150 Propylene A 101.3 110 –60 –70 FIG. 2-10 K values (K = y/x) in light-hydrocarbon systems. (a) Low-temperature range. (b) High-temperature range. [C.L. DePriester, Chem. Eng. Prog. Symp., Ser. 7, 49: 1 (1953); converted to SI units by D.B. Dadyburjor, Chem. Eng. Prog. 74: 4 (1978).] 2-226 THERMODYnAMIC PROPERTIES 0 25 150 200 250 300 20 FIG. 2-10 n-Nonane n-Decane 20 30 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 .001 n-Octane .005 n-Heptane Methane 5000 40 n-Hexane 3000 3500 4000 50 Isopentane n-Pentane 2500 60 Isobutane n-Butane 2000 70 90 60 80 Propylene Propane 1500 0 10 Ethane 600 700 800 900 1000 0 Ethylene 500 Pressure, kPa 400 11 0 2 3 5 8 4 1.5 10 76 2 9 15 3 1 30 8 5 0 0 1.5 0 0 4 5 0 1 15 .8 7 70 20 4 90 2 .6 6 10 80 1 20 60 40 3 .5 20 9 5 30 1.5 70 0 8 10 .4 15 50 0 4 7 15 8 3 2 .3 15 60 1 .5 6 7 3 1.5 .9 .4 20 40 .8 .2 5 0 6 5 10 .7 9 5 .6 .3 20 4 2 100 10 1 8 15 9 .9 .5 4 30 .1 .2 90 7 3 40 8 1.5 .8 .4 15 .08 .7 6 .15 80 7 3 .6 .06 .3 5 10 6 70 .5 1. .05 2 .1 30 .9 9 5 20 10 .04 5 .4 2 .8 .2 .08 60 9 8 1.5 .7 .03 4 .3 .06 8 3 .15 7 .6 50 15 1.5 .05 7 .5 .02 6 20 .1 3 .04 .2 .1 .9 6 .09 .015 .4 5 40 2 1 .08 .03 .8 9 .15 .07 10 5 .7 .01 15 .3 4 2 .06 1.5 9 .6 .008 7 4 30 .1 .05 .02 8 .5 6 .006 9 .04 .0 .2 1.0 3 .015 .005 7 .08 1 5 .4 10 3 .07 .004 .9 .03 .15 6 9 6 .0 .8 4 .01 .3 8 .009 .003 .05 1 2 .7 20 5 .02 .008 .9 3 7 .1 2 .007 .04 .6 .8 .09 02 .006 .0 6 .2 8 1.5 .7 .0 .015 4 .5 3 .005 .0015 .07 .0 1.5 15 2 .6 5 .4 .15 .06 4 .01 .00 3 .5 .05 1 .02 .009 1.5 4 3 .001 8 .00 .00 .3 .9 1 .1 .04 .9 .8 .4 15 .007 10 .0 9 .0 .25 .006 .8 9 .08 .7 3 .1 2 .002 .03 .3 .7 .07 .09 .005 8 .6 .01 8 .0 .06 .6 7 .009 .004 1.5 .5 .02 .008 .15 .05 2 .5 6 .06 .007 .2 .4 .003 01 .0 .04 .015 .006 .05 5 .4 1.5 .005 1 .1 .15 .3 3 .0 .9 .09 4 .004 .002 .01 .3 .25 .08 .8 .009 .03 .008 .02 .003 .015 .1 .06 .007 3 06 .0 .015 .02 15 Temperature, °C B 101.3 110 0 –5 (Continued) TABLE 2-123 Composition of Selected Refrigerant Mixtures* Composition, mass% Mixed Product Name R-32 R-125 R-134a R-143a R-404A R-407C R-410A Property Table/Figure 2-126, Fig. 2-12 2-127, Fig. 2-13 2-128, Fig. 2-14 2-129 2-130 2-131, Fig. 2-15 2-132 R-32 R-125 R-134a R-143a 100 100 100 23 50 44 25 50 4 52 100 52 Ozone Depletion Potential (ODP)† Global Warming Potential (GWP)‡ (100 year) 0 0 0 0 0 0 0 650 3400 1300 4300 3300 1600 2088 *All products listed here are HFCs (hydrofluorocarbons), the primary replacement for hydrochlorofluorocarbons (HCFCs) like R-22. † The ODP of the old CFC refrigerants R-11 and R-12 is 1. ‡ CO2 is the GWP reference: GWP of CO2 = 1. 2-227 2-228 TABLE 2-124 Thermodynamic Properties of R-22, Chlorodifluoromethane Temperature K Pressure MPa 115.73 120.00 135.00 150.00 165.00 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 369.30 3.7947E-07 9.9588E-07 1.7187E-05 0.00015627 0.00089946 0.0037009 0.011835 0.031218 0.070909 0.14319 0.26329 0.44888 0.71966 1.0970 1.6039 2.2661 3.1130 4.1837 4.9900 115.73 120.00 135.00 150.00 165.00 180.00 195.00 210.00 225.00 240.00 255.00 270.00 285.00 300.00 315.00 330.00 345.00 360.00 369.30 3.7947E-07 9.9588E-07 1.7187E-05 0.00015627 0.00089946 0.0037009 0.011835 0.031218 0.070909 0.14319 0.26329 0.44888 0.71966 1.0970 1.6039 2.2661 3.1130 4.1837 4.9900 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Saturated Properties 19.907 19.777 19.325 18.873 18.420 17.963 17.500 17.028 16.542 16.036 15.506 14.944 14.341 13.686 12.956 12.114 11.069 9.5229 6.0582 3.9436E-07 9.9813E-07 1.5313E-05 0.00012533 0.00065634 0.0024808 0.0073561 0.018161 0.038991 0.075182 0.13342 0.22208 0.35201 0.53822 0.80363 1.1882 1.7777 2.8529 6.0582 0.050235 0.050564 0.051747 0.052985 0.054289 0.055670 0.057141 0.058726 0.060453 0.062359 0.064493 0.066919 0.069730 0.073070 0.077181 0.082547 0.090340 0.10501 0.16506 2,535,700. 1,001,900. 65,305. 7,979.0 1,523.6 403.09 135.94 55.062 25.647 13.301 7.4950 4.5029 2.8409 1.8580 1.2443 0.84159 0.56253 0.35052 0.16506 2.5595 2.9559 4.3400 5.7179 7.0951 8.4715 9.8483 11.230 12.622 14.034 15.472 16.945 18.462 20.034 21.676 23.418 25.325 27.613 30.901 2.5595 2.9559 4.3400 5.7179 7.0951 8.4717 9.8490 11.232 12.627 14.043 15.489 16.975 18.513 20.114 21.800 23.605 25.606 28.053 31.725 0.0065813 0.0099451 0.020814 0.030493 0.039243 0.047227 0.054574 0.061399 0.067804 0.073877 0.079692 0.085308 0.090782 0.096166 0.10152 0.10696 0.11267 0.11931 0.12907 0.061918 0.061567 0.060123 0.059099 0.058356 0.057679 0.057097 0.056707 0.056579 0.056737 0.057171 0.057856 0.058767 0.059887 0.061218 0.062814 0.064858 0.068488 0.092976 0.092700 0.091960 0.091824 0.091789 0.091751 0.091898 0.092431 0.093482 0.095120 0.097391 0.10037 0.10424 0.10941 0.11688 0.12929 0.15550 0.25950 1410.9 1388.4 1312.3 1239.0 1166.5 1095.0 1024.5 954.55 884.79 814.96 744.97 674.69 603.91 532.11 458.37 381.15 298.16 201.90 0 27.807 27.929 28.373 28.840 29.329 29.836 30.357 30.885 31.411 31.928 32.428 32.900 33.335 33.717 34.021 34.207 34.184 33.661 30.901 28.769 28.927 29.495 30.087 30.699 31.328 31.966 32.603 33.229 33.833 34.401 34.922 35.380 35.755 36.017 36.114 35.935 35.127 31.725 0.23305 0.22637 0.20715 0.19295 0.18230 0.17421 0.16800 0.16317 0.15937 0.15634 0.15386 0.15178 0.14996 0.14830 0.14666 0.14486 0.14261 0.13896 0.12907 0.028465 0.028872 0.030386 0.031990 0.033655 0.035388 0.037218 0.039177 0.041300 0.043615 0.046138 0.048881 0.051851 0.055064 0.058574 0.062516 0.067254 0.074178 0.036779 0.037186 0.038703 0.040316 0.042018 0.043849 0.045881 0.048204 0.050920 0.054144 0.058023 0.062763 0.068713 0.076534 0.087659 0.10579 0.14389 0.29995 119.91 121.91 128.58 134.79 140.59 145.98 150.87 155.15 158.70 161.35 162.96 163.38 162.45 159.98 155.73 149.36 140.39 127.92 0 −0.44463 −0.44526 −0.44448 −0.43872 −0.43084 −0.42063 −0.40608 −0.38505 −0.35555 −0.31561 −0.26263 −0.19248 −0.097827 0.035333 0.23608 0.57205 1.2334 3.0745 10.366 398.80 367.18 269.83 197.57 146.30 110.28 84.902 66.865 53.872 44.348 37.240 31.852 27.725 24.549 22.102 20.201 18.613 16.641 10.366 Single-Phase Properties 150.00 232.06 0.10000 0.10000 232.06 250.00 350.00 450.00 550.00 0.10000 0.10000 0.10000 0.10000 0.10000 150.00 250.00 296.57 1.0000 1.0000 1.0000 296.57 350.00 450.00 550.00 1.0000 1.0000 1.0000 1.0000 150.00 250.00 350.00 450.00 550.00 5.0000 5.0000 5.0000 5.0000 5.0000 5.7167 13.284 5.7220 13.290 0.030484 0.070699 0.059102 0.056618 0.091820 0.094177 1239.3 851.94 −0.43876 −0.33819 31.656 32.442 37.325 43.093 49.620 33.517 34.465 40.211 46.822 54.186 0.15786 0.16180 0.18105 0.19762 0.21238 0.042364 0.043860 0.053191 0.061672 0.068475 0.052366 0.053391 0.061845 0.070141 0.076877 160.06 166.39 196.16 221.08 243.30 49.032 38.154 13.439 6.7638 4.0604 0.052952 0.063648 0.072248 5.7053 14.961 19.669 5.7582 15.024 19.741 0.030408 0.077665 0.094938 0.059134 0.057020 0.059612 0.091780 0.096318 0.10807 1241.8 773.25 548.68 2.0425 2.6523 3.6110 4.5027 33.635 36.754 42.774 49.400 35.677 39.407 46.385 53.903 0.14867 0.16025 0.17776 0.19283 0.054305 0.055369 0.062289 0.068737 0.074523 0.068138 0.072300 0.077971 160.70 184.85 216.22 241.16 25.205 14.183 6.8582 4.0624 18.931 15.837 11.141 1.6422 1.1832 0.052823 0.063142 0.089759 0.60893 0.84520 5.6555 14.822 25.585 41.131 48.377 5.9197 15.138 26.034 44.175 52.603 0.030074 0.077105 0.11341 0.16067 0.17760 0.059277 0.057135 0.064765 0.065284 0.069855 0.091614 0.095206 0.14356 0.087278 0.083655 1253.0 797.37 317.33 194.56 232.93 −0.44109 −0.30700 1.0314 7.0507 3.9600 18.874 16.306 0.053734 0.049441 0.034652 0.026819 0.021901 18.885 15.711 13.841 0.48960 0.37703 0.27693 0.22209 0.052982 0.061325 18.610 20.226 28.859 37.287 45.660 −0.43921 −0.28642 0.00029448 150.00 250.00 350.00 450.00 550.00 10.000 10.000 10.000 10.000 10.000 18.987 15.982 12.008 4.2433 2.5432 0.052667 0.062569 0.083275 0.23566 0.39321 5.5953 14.663 24.782 38.423 47.019 6.1220 15.289 25.615 40.780 50.951 0.029665 0.076450 0.11098 0.14893 0.16944 0.059460 0.057274 0.063647 0.068870 0.071068 0.091420 0.094054 0.11843 0.12461 0.092204 1266.7 825.41 412.24 184.82 229.21 −0.44331 −0.32844 0.39255 5.5220 3.5059 150.00 250.00 350.00 450.00 550.00 30.000 30.000 30.000 30.000 30.000 19.198 16.469 13.518 10.241 7.3810 0.052089 0.060719 0.073976 0.097648 0.13548 5.3741 14.132 23.279 33.086 42.738 6.9367 15.953 25.499 36.016 46.802 0.028113 0.074181 0.10621 0.13259 0.15425 0.060251 0.057799 0.063170 0.069234 0.073417 0.090769 0.091018 0.10053 0.10864 0.10533 1318.0 921.00 603.47 392.35 317.51 −0.45090 −0.38542 −0.13764 0.40072 0.89994 150.00 250.00 350.00 450.00 550.00 60.000 60.000 60.000 60.000 60.000 19.480 17.029 14.650 12.381 10.405 0.051336 0.058724 0.068258 0.080770 0.096108 5.0916 13.533 22.111 31.083 40.152 8.1717 17.056 26.206 35.929 45.919 0.026007 0.071434 0.10216 0.12657 0.14662 0.061560 0.058519 0.063912 0.070220 0.075020 0.089983 0.088686 0.094730 0.099099 0.10030 1384.9 1034.6 764.59 589.21 492.11 −0.45992 −0.42947 −0.31532 −0.17799 −0.055349 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Kamei, A., Beyerlein, S. W., and Jacobsen, R. T., “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophys. 16:1155–1164, 1995. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainties of the equation of state are 0.1% in density, 1% in heat capacity, and 0.3% in the speed of sound, except in the critical region. The uncertainty in vapor pressure is 0.2%. 2-229 2-230 FIG. 2-11 Pressure-enthalpy diagram for Refrigerant 22. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Kamei, A., S. W. Beyerlein, and R. T. Jacobsen, “Application of Nonlinear Regression in the Development of a Wide Range Formulation for HCFC-22,” Int. J. Thermophysics 16:1155–1164, 1995. TABLE 2-125 Thermodynamic Properties of R-32, Difluoromethane Temperature K Pressure MPa 136.34 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 351.26 4.8000E-05 8.3535E-05 0.00032474 0.0010410 0.0028536 0.0068782 0.014904 0.029545 0.054344 0.093819 0.15345 0.23965 0.35967 0.52157 0.73415 1.0069 1.3501 1.7749 2.2934 2.9194 3.6686 4.5614 5.6311 5.7826 136.34 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 351.26 4.8000E-05 8.3535E-05 0.00032474 0.0010410 0.0028536 0.0068782 0.014904 0.029545 0.054344 0.093819 0.15345 0.23965 0.35967 0.52157 0.73415 1.0069 1.3501 1.7749 2.2934 2.9194 3.6686 4.5614 5.6311 5.7826 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol −0.99220 −0.68946 0.13324 0.95053 1.7640 2.5753 3.3862 4.1983 5.0135 5.8337 6.6608 7.4969 8.3443 9.2056 10.084 10.983 11.908 12.866 13.867 14.930 16.088 17.428 19.453 20.836 −0.99220 −0.68946 0.13325 0.95057 1.7641 2.5756 3.3868 4.1995 5.0158 5.8377 6.6675 7.5077 8.3609 9.2303 10.120 11.034 11.979 12.963 13.998 15.107 16.328 17.760 19.977 21.546 21.981 22.076 22.335 22.593 22.850 23.103 23.350 23.588 23.816 24.032 24.234 24.421 24.590 24.738 24.860 24.952 25.006 25.011 24.950 24.797 24.503 23.943 22.380 20.836 23.115 23.239 23.581 23.921 24.258 24.589 24.910 25.219 25.513 25.788 26.042 26.272 26.474 26.643 26.775 26.862 26.894 26.858 26.735 26.491 26.068 25.316 23.365 21.546 Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) −0.0054608 −0.0032696 0.0024067 0.0076815 0.012613 0.017251 0.021635 0.025800 0.029778 0.033594 0.037271 0.040830 0.044291 0.047671 0.050989 0.054264 0.057517 0.060775 0.064076 0.067477 0.071088 0.075179 0.081343 0.085769 0.055447 0.054980 0.053793 0.052740 0.051818 0.051021 0.050345 0.049783 0.049333 0.048988 0.048747 0.048604 0.048559 0.048610 0.048761 0.049019 0.049399 0.049934 0.050685 0.051776 0.053487 0.056594 0.066340 0.082847 0.082588 0.081975 0.081513 0.081215 0.081087 0.081137 0.081373 0.081803 0.082443 0.083313 0.084442 0.085874 0.087676 0.089947 0.092852 0.096659 0.10185 0.10938 0.12140 0.14404 0.20457 1.2085 1414.4 1395.1 1342.3 1289.9 1237.6 1185.7 1133.8 1082.1 1030.4 978.59 926.62 874.35 821.65 768.33 714.18 658.88 602.05 543.11 481.27 415.41 343.84 263.77 163.70 0 −0.33760 −0.33728 −0.33542 −0.33191 −0.32650 −0.31891 −0.30886 −0.29600 −0.27988 −0.25996 −0.23550 −0.20551 −0.16864 −0.12292 −0.065518 0.0079177 0.10428 0.23517 0.42163 0.70602 1.1876 2.1660 5.4955 8.0731 242.91 241.74 237.64 232.45 226.39 219.64 212.37 204.70 196.75 188.62 180.39 172.14 163.92 155.78 147.75 139.86 132.11 124.48 116.94 109.42 101.80 94.166 97.067 0.17135 0.16765 0.15872 0.15125 0.14493 0.13955 0.13492 0.13090 0.12738 0.12428 0.12151 0.11901 0.11674 0.11464 0.11268 0.11079 0.10895 0.10709 0.10516 0.10305 0.10060 0.097403 0.091024 0.085769 0.025987 0.026110 0.026507 0.027014 0.027667 0.028505 0.029560 0.030843 0.032341 0.034016 0.035821 0.037709 0.039648 0.041621 0.043631 0.045693 0.047840 0.050119 0.052598 0.055390 0.058707 0.063103 0.071998 0.034319 0.034451 0.034889 0.035477 0.036272 0.037336 0.038728 0.040483 0.042613 0.045105 0.047943 0.051127 0.054696 0.058741 0.063434 0.069063 0.076110 0.085424 0.098649 0.11948 0.15836 0.26199 1.9028 169.60 171.76 177.47 182.88 187.97 192.69 197.00 200.85 204.20 206.99 209.19 210.73 211.57 211.65 210.90 209.26 206.64 202.95 198.02 191.66 183.49 172.68 154.59 0 Entropy kJ/(mol⋅K) Saturated Properties 27.473 27.302 26.835 26.364 25.889 25.409 24.921 24.424 23.916 23.394 22.858 22.303 21.726 21.124 20.491 19.820 19.102 18.323 17.460 16.477 15.299 13.740 10.732 8.1501 4.2353E-05 7.1788E-05 0.00026061 0.00078411 0.0020270 0.0046295 0.0095503 0.018112 0.032028 0.053428 0.084890 0.12949 0.19093 0.27370 0.38340 0.52726 0.71503 0.96054 1.2848 1.7233 2.3442 3.3211 5.7166 8.1501 0.036399 0.036627 0.037265 0.037930 0.038626 0.039357 0.040127 0.040944 0.041814 0.042745 0.043749 0.044838 0.046028 0.047340 0.048802 0.050454 0.052350 0.054577 0.057273 0.060691 0.065364 0.072779 0.093180 0.12270 23,611. 13,930. 3,837.2 1,275.3 493.35 216.01 104.71 55.213 31.223 18.717 11.780 7.7224 5.2375 3.6537 2.6083 1.8966 1.3985 1.0411 0.77830 0.58029 0.42658 0.30111 0.17493 0.12270 881.12 769.01 541.12 391.73 291.02 221.02 170.81 133.79 106.00 84.924 68.870 56.605 47.194 39.922 34.246 29.758 26.148 23.187 20.693 18.510 16.477 14.312 10.637 8.0731 6.9492 6.9554 7.0006 7.0875 7.2166 7.3887 7.6049 7.8668 8.1765 8.5374 8.9546 9.4365 9.9965 10.656 11.449 12.431 13.691 15.376 17.748 21.309 27.173 38.601 87.141 (Continued) 2-231 2-232 TABLE 2-125 Temperature K Thermodynamic Properties of R-32, Difluoromethane (Continued ) Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Single-Phase Properties 0.037263 0.042866 0.13226 5.9359 0.13599 5.9402 0.0024002 0.034057 0.053795 0.048953 0.081971 0.082538 1342.7 972.15 −0.33547 −0.25719 237.67 187.60 0.056727 0.055592 0.040576 0.032244 26.851 23.159 19.836 17.628 17.988 24.645 31.013 0.037243 0.043179 0.050414 24.058 24.191 26.760 29.631 0.12350 6.2265 10.962 25.821 25.989 29.224 32.733 0.16075 6.2697 11.013 0.12392 0.12467 0.13708 0.14749 0.0023417 0.035360 0.054190 0.034234 0.033681 0.035327 0.041082 0.053807 0.048867 0.049012 0.045439 0.044513 0.044188 0.049630 0.081935 0.082690 0.092777 207.30 209.39 241.95 267.64 1345.7 957.47 660.15 82.688 76.114 25.024 12.117 −0.33584 −0.25084 0.0060372 8.5859 8.7199 12.643 18.907 237.89 185.10 140.04 0.52357 0.46100 0.33917 1.9100 2.1692 2.9484 24.951 25.950 29.227 26.861 28.120 32.175 0.11084 0.11518 0.12727 0.045646 0.041298 0.042549 0.068922 0.057916 0.053538 209.31 223.83 259.50 0.037154 0.042923 0.053448 0.078078 0.085198 6.1394 12.637 18.130 0.27097 6.3541 12.905 18.520 0.0020846 0.034970 0.060001 0.077304 0.053863 0.048922 0.049679 0.059015 0.081784 0.082027 0.096911 0.28240 1358.9 978.81 586.17 224.84 0.25071 0.43051 23.524 26.928 24.777 29.080 0.095475 0.10755 0.065786 0.050835 0.39574 0.090625 166.61 218.44 150.00 221.24 0.10000 0.10000 26.836 23.329 221.24 225.00 300.00 375.00 150.00 225.00 279.77 0.10000 0.10000 0.10000 0.10000 1.0000 1.0000 1.0000 279.77 300.00 375.00 1.0000 1.0000 1.0000 150.00 225.00 300.00 344.33 5.0000 5.0000 5.0000 5.0000 344.33 375.00 5.0000 5.0000 26.915 23.298 18.710 12.808 3.9887 2.3228 29.848 23.889 11.929 −0.33741 −0.26135 0.13431 2.9944 13.148 10.800 12.406 13.334 19.059 238.83 187.71 128.72 91.412 48.235 26.239 150.00 225.00 300.00 375.00 10.000 10.000 10.000 10.000 26.993 23.461 19.196 10.448 0.037047 0.042625 0.052094 0.095714 0.038702 6.0369 12.346 21.112 0.40917 6.4632 12.867 22.069 0.0017692 0.034504 0.058997 0.085980 0.053932 0.048996 0.049538 0.057265 0.081608 0.081303 0.092105 0.21222 1375.0 1004.1 639.69 231.14 −0.33924 −0.27287 0.031716 3.5190 239.97 190.81 134.49 77.284 150.00 225.00 300.00 375.00 30.000 30.000 30.000 30.000 27.285 24.030 20.517 16.472 0.036650 0.041614 0.048739 0.060708 −0.13357 5.6813 11.542 17.786 0.96593 6.9297 13.004 19.607 0.00056834 0.032836 0.056105 0.075712 0.054209 0.049307 0.049670 0.052941 0.081027 0.079197 0.083697 0.093069 1436.1 1094.1 789.57 536.98 −0.34524 −0.30661 −0.15824 0.21392 244.02 201.89 152.78 112.94 225.00 300.00 375.00 70.000 70.000 70.000 24.916 22.090 19.309 0.040135 0.045270 0.051788 5.1400 10.583 16.127 7.9495 13.752 19.752 0.030109 0.052355 0.070195 0.049916 0.050281 0.053544 0.076915 0.078370 0.081767 1240.7 986.17 788.81 −0.34341 −0.28333 −0.18583 219.54 179.29 147.00 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., and Yokozeki, A., “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 26(6):1273–1328, 1997. Validated equations for the viscosity are not currently available for this fluid. The source for thermal conductivity is unpublished; however, the fit uses the functional form found in Marsh, K., Perkins, R., and Ramires, M. L. V., “Measurement and Correlation of the Thermal Conductivity of Propane from 86 to 600 K at Pressures to 70 MPa,” J. Chem. Eng. Data 47(4):932–940, 2002. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. For the equation of state, typical uncertainties are 0.05% for density, 0.02% for the vapor pressure, and 0.5% to 1% for the heat capacity and speed of sound in the liquid phase. In the vapor phase, the uncertainty in the speed of sound is 0.02%. For thermal conductivity, the estimated uncertainty of the correlation is 5%, except for the dilute gas and points approaching critical where the uncertainty rises to 10%. FIG. 2-12 Pressure-enthalpy diagram for Refrigerant 32. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Tillner-Roth, R., and A. Yokozeki, “An International Standard Equation of State for Difluoromethane (R-32) for Temperatures from the Triple Point at 136.34 K to 435 K and Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 26(6): 1273–1328, 1997. 2-233 2-234 TABLE 2-126 Thermodynamic Properties of R-125, Pentafluoroethane Temperature K Pressure MPa 172.52 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 339.17 0.0029140 0.0056285 0.012328 0.024602 0.045417 0.078505 0.12833 0.20004 0.29934 0.43250 0.60624 0.82782 1.1050 1.4463 1.8610 2.3600 2.9579 3.6179 172.52 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 339.17 0.0029140 0.0056285 0.012328 0.024602 0.045417 0.078505 0.12833 0.20004 0.29934 0.43250 0.60624 0.82782 1.1050 1.4463 1.8610 2.3600 2.9579 3.6179 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 10.457 11.389 12.646 13.919 15.210 16.523 17.858 19.219 20.607 22.025 23.478 24.971 26.511 28.112 29.793 31.595 33.632 37.417 10.457 11.389 12.647 13.921 15.214 16.529 17.869 19.235 20.632 22.063 23.532 25.048 26.619 28.259 29.994 31.869 34.017 38.174 0.058837 0.064124 0.070919 0.077448 0.083750 0.089856 0.095792 0.10158 0.10725 0.11282 0.11830 0.12374 0.12916 0.13461 0.14015 0.14593 0.15231 0.16438 0.081329 0.082012 0.083102 0.084327 0.085644 0.087029 0.088472 0.089971 0.091529 0.093153 0.094843 0.096594 0.098430 0.10043 0.10274 0.10571 0.11043 0.12417 0.12500 0.12647 0.12825 0.13028 0.13254 0.13505 0.13785 0.14102 0.14468 0.14903 0.15440 0.16135 0.17099 0.18593 0.21395 0.29625 932.57 893.63 843.11 793.91 745.67 698.07 650.89 603.92 556.99 510.02 462.91 415.46 367.36 318.17 267.31 213.55 153.34 0 −0.38374 −0.37406 −0.35818 −0.33901 −0.31627 −0.28935 −0.25723 −0.21839 −0.17062 −0.11056 −0.032921 0.070972 0.21606 0.43036 0.77370 1.4029 2.9184 12.361 31.863 32.307 32.913 33.530 34.157 34.788 35.421 36.052 36.678 37.292 37.890 38.460 38.988 39.453 39.828 40.054 39.964 37.417 33.293 33.795 34.477 35.167 35.860 36.552 37.237 37.911 38.568 39.202 39.805 40.363 40.858 41.267 41.554 41.651 41.355 38.174 0.19120 0.18860 0.18582 0.18368 0.18207 0.18087 0.18000 0.17940 0.17900 0.17874 0.17857 0.17844 0.17826 0.17797 0.17744 0.17649 0.17454 0.16438 0.059815 0.061648 0.064126 0.066646 0.069223 0.071864 0.074575 0.077362 0.080230 0.083141 0.086003 0.088869 0.092050 0.095933 0.10077 0.10679 0.11481 0.068285 0.070217 0.072893 0.075712 0.078713 0.081939 0.085437 0.089271 0.093526 0.098283 0.10368 0.11025 0.11918 0.13255 0.15449 0.19725 0.32843 116.43 118.54 121.15 123.47 125.44 127.01 128.11 128.68 128.64 127.93 126.44 124.10 120.81 116.42 110.71 103.29 93.550 0 90.257 77.516 64.018 53.589 45.456 39.066 34.014 29.998 26.787 24.232 22.293 20.938 20.043 19.438 19.016 18.738 18.404 12.361 Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 116.02 112.52 107.79 103.06 98.331 93.653 89.019 84.443 79.940 75.520 71.187 66.940 62.772 58.667 54.597 50.534 46.661 1152.4 957.54 768.40 631.00 527.00 445.76 380.67 327.41 283.01 245.39 213.02 184.73 159.60 136.86 115.81 95.602 74.602 Saturated Properties 14.086 13.885 13.613 13.336 13.052 12.762 12.461 12.150 11.824 11.481 11.117 10.724 10.295 9.8162 9.2637 8.5923 7.6744 4.7790 0.0020381 0.0037809 0.0078784 0.015031 0.026661 0.044514 0.070679 0.10763 0.15835 0.22645 0.31661 0.43510 0.59084 0.79742 1.0777 1.4778 2.1269 4.7790 0.070990 0.072020 0.073461 0.074988 0.076615 0.078360 0.080247 0.082305 0.084572 0.087098 0.089954 0.093245 0.097130 0.10187 0.10795 0.11638 0.13030 0.20925 490.65 264.49 126.93 66.529 37.508 22.465 14.148 9.2907 6.3153 4.4159 3.1585 2.2983 1.6925 1.2540 0.92787 0.67670 0.47016 0.20925 5.2349 5.7185 6.3724 7.0353 7.7081 8.3929 9.0929 9.8136 10.563 11.356 12.213 13.169 14.286 15.680 17.586 20.574 26.607 7.4339 7.7624 8.1999 8.6344 9.0657 9.4944 9.9221 10.353 10.791 11.246 11.732 12.266 12.884 13.638 14.635 16.104 18.766 Single-Phase Properties 200.00 224.79 0.10000 0.10000 224.79 300.00 400.00 500.00 0.10000 0.10000 0.10000 0.10000 200.00 286.46 1.0000 1.0000 286.46 300.00 400.00 500.00 1.0000 1.0000 1.0000 1.0000 200.00 300.00 400.00 500.00 5.0000 5.0000 5.0000 5.0000 13.916 17.160 13.924 17.168 0.077436 0.092721 0.084327 0.087714 0.12823 0.13371 794.34 675.42 −0.33920 −0.27468 35.092 41.155 50.746 61.864 36.881 43.613 54.054 66.012 0.18042 0.20616 0.23608 0.26271 0.073155 0.086960 0.10398 0.11764 0.083578 0.095910 0.11252 0.12607 127.60 149.16 172.25 192.24 36.498 13.603 5.6807 3.1093 0.074878 0.095673 13.888 25.960 13.963 26.055 0.077295 0.12724 0.084329 0.097767 0.12805 0.15865 799.42 384.49 −0.34145 0.15862 103.50 64.240 1.8842 2.0720 3.1466 4.0661 38.807 40.159 50.310 61.591 40.691 42.231 53.456 65.657 0.17833 0.18359 0.21585 0.24302 0.090862 0.092286 0.10520 0.11806 0.11564 0.11224 0.11626 0.12764 122.09 129.90 165.47 189.33 20.318 16.539 5.9354 3.1109 13.866 14.732 22.513 31.336 12.653 13.270 17.404 21.014 13.432 10.214 2.1222 1.3333 0.074450 0.097901 0.47120 0.75004 13.768 27.606 47.739 60.288 14.140 28.095 50.095 64.038 0.076686 0.13288 0.19593 0.22710 0.084364 0.099404 0.11164 0.12001 0.12732 0.15790 0.15240 0.13643 820.94 379.39 136.55 180.53 −0.35061 0.16755 6.6581 2.9952 105.29 62.727 27.340 33.551 671.00 155.81 22.244 23.530 13.337 12.619 0.055877 0.040689 0.030228 0.024108 13.355 10.452 0.53072 0.48261 0.31780 0.24593 0.074979 0.079245 17.897 24.576 33.082 41.479 103.09 91.425 8.7263 14.156 22.115 30.917 631.60 412.85 9.6994 13.041 17.070 20.691 638.78 168.19 200.00 300.00 400.00 500.00 10.000 10.000 10.000 10.000 13.522 10.597 5.5436 2.8438 0.073953 0.094369 0.18039 0.35165 13.626 27.096 43.724 58.555 14.366 28.039 45.528 62.072 0.075959 0.13109 0.18103 0.21813 0.084459 0.098728 0.11417 0.12198 0.12655 0.14971 0.19389 0.14925 845.71 441.85 165.42 183.47 −0.36040 −0.0032571 2.8474 2.4316 107.42 67.164 40.583 37.529 712.07 177.37 46.568 29.745 200.00 300.00 400.00 500.00 30.000 30.000 30.000 30.000 13.835 11.489 9.0272 6.8239 0.072281 0.087039 0.11078 0.14654 13.138 25.838 39.705 54.141 15.306 28.449 43.028 58.538 0.073355 0.12645 0.16830 0.20288 0.085197 0.098551 0.11217 0.12339 0.12439 0.13883 0.15193 0.15662 927.73 597.35 391.05 307.14 −0.38765 −0.23171 0.060756 0.34144 115.19 79.855 59.824 53.649 889.29 245.90 112.78 67.694 300.00 400.00 500.00 60.000 60.000 60.000 12.259 10.465 8.9121 0.081575 0.095559 0.11221 24.732 37.854 51.703 29.626 43.587 58.436 0.12196 0.16206 0.19516 0.10001 0.11339 0.12470 0.13426 0.14453 0.15193 735.32 563.68 471.23 −0.32748 −0.23451 −0.15582 93.938 75.022 67.810 338.04 173.26 113.08 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Jacobsen, R. T., “A New Functional Form and New Fitting Techniques for Equations of State with Application to Pentafluoroethane (HFC-125),” J. Phys. Chem. Ref. Data 34(1):69–108, 2005. The source for viscosity is Huber, M. L., and Laesecke, A., “Correlation for the Viscosity of Pentafluoroethane (R125) from the Triple Point to 500 K at Pressures up to 60 MPa,” Ind. Eng. Chem. Res., 45(12):4447–4453, 2006. The source for thermal conductivity is Perkins, R., and Huber, M. L., “Measurement and Correlation of the Thermal Conductivity of Pentafluoroethane (R125) from 190 K to 512 K at Pressures to 70 MPa,” J. Chem. Eng. Data 51(3):898–904, 2006. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density is 0.1% at temperatures from the triple point to 400 K at pressures up to 60 MPa, except in the critical region, where an uncertainty of 0.2% in pressure is generally attained. In the limited region between 340 and 400 K and at pressures from 4 to 10 MPa, as well as for all states above 400 K, the uncertainty in density increases to 0.5%. At temperatures below 330 K and pressures below 30 MPa, the uncertainty in density in the liquid phase may be as low as 0.04%. In the vapor and supercritical region, speed of sound data are represented within 0.05% at pressures below 1 MPa. The estimated uncertainty for heat capacities is 0.5%, and the estimated uncertainty for the speed of sound in the liquid phase is 0.5% for T > 250 K. The estimated uncertainties of vapor pressures and saturated liquid densities calculated using the Maxwell criterion are 0.1% for each property, and the estimated uncertainty for saturated vapor densities is 0.2%. The uncertainty in density increases as the critical point is approached, while the accompanying uncertainty in calculated pressures is 0.2%. The viscosity correlation has an estimated uncertainty of 3.0% along the saturation boundary in the liquid phase, and 0.8% in the vapor. For thermal conductivity, the estimated uncertainty of the correlation is 3%, except for the dilute gas and points approaching critical, where the uncertainty rises to 5%. 2-235 2-236 FIG. 2-13 Pressure-enthalpy diagram for Refrigerant 125. TABLE 2-127 Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane Temperature K Pressure MPa 169.85 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 374.21 0.00038956 0.00039617 0.0011275 0.0028170 0.0063130 0.012910 0.024433 0.043287 0.072481 0.11561 0.17684 0.26082 0.37271 0.51805 0.70282 0.93340 1.2166 1.5599 1.9715 2.4611 3.0405 3.7278 4.0591 169.85 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00 370.00 374.21 0.00038956 0.00039617 0.0011275 0.0028170 0.0063130 0.012910 0.024433 0.043287 0.072481 0.11561 0.17684 0.26082 0.37271 0.51805 0.70282 0.93340 1.2166 1.5599 1.9715 2.4611 3.0405 3.7278 4.0591 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 7.2907 7.3088 8.5179 9.7328 10.957 12.194 13.444 14.710 15.992 17.293 18.613 19.956 21.322 22.716 24.141 25.603 27.108 28.667 30.297 32.029 33.932 36.283 38.947 7.2907 7.3088 8.5179 9.7330 10.958 12.195 13.446 14.713 15.997 17.301 18.627 19.976 21.352 22.759 24.201 25.685 27.219 28.816 30.495 32.293 34.289 36.797 39.756 0.042100 0.042207 0.049117 0.055686 0.061966 0.067999 0.073815 0.079441 0.084899 0.090209 0.095389 0.10046 0.10543 0.11032 0.11516 0.11996 0.12475 0.12956 0.13446 0.13952 0.14496 0.15159 0.15938 0.080831 0.080824 0.080732 0.081114 0.081784 0.082633 0.083595 0.084636 0.085734 0.086879 0.088067 0.089298 0.090576 0.091908 0.093303 0.094777 0.096352 0.098067 0.10001 0.10241 0.10601 0.11372 0.12079 0.12079 0.12112 0.12193 0.12303 0.12434 0.12582 0.12746 0.12927 0.13126 0.13348 0.13597 0.13883 0.14216 0.14615 0.15108 0.15740 0.16598 0.17863 0.20012 0.24863 0.52085 32.764 32.772 33.287 33.821 34.371 34.934 35.508 36.090 36.675 37.261 37.844 38.420 38.986 39.538 40.069 40.573 41.038 41.451 41.785 41.994 41.973 41.323 38.947 34.175 34.184 34.781 35.395 36.023 36.662 37.308 37.956 38.602 39.242 39.870 40.482 41.073 41.636 42.166 42.653 43.083 43.438 43.687 43.775 43.576 42.617 39.756 0.20038 0.20029 0.19502 0.19075 0.18729 0.18451 0.18228 0.18050 0.17909 0.17797 0.17709 0.17640 0.17586 0.17542 0.17504 0.17469 0.17432 0.17387 0.17326 0.17232 0.17075 0.16731 0.15938 0.051318 0.051354 0.053742 0.056118 0.058489 0.060874 0.063296 0.065783 0.068357 0.071031 0.073812 0.076698 0.079686 0.082776 0.085974 0.089297 0.092780 0.096484 0.10052 0.10510 0.11074 0.11928 0.059719 0.059756 0.062208 0.064682 0.067201 0.069802 0.072534 0.075455 0.078618 0.082078 0.085888 0.090115 0.094850 0.10023 0.10650 0.11404 0.12355 0.13638 0.15548 0.18870 0.26594 0.70016 Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 1120.0 1119.2 1068.3 1017.7 967.61 918.33 869.85 822.11 775.00 728.39 682.14 636.12 590.17 544.15 497.89 451.23 404.00 355.90 306.37 254.06 196.05 127.23 0 −0.38145 −0.38136 −0.37370 −0.36352 −0.35119 −0.33678 −0.32011 −0.30082 −0.27839 −0.25204 −0.22073 −0.18299 −0.13675 −0.079015 −0.0052732 0.091533 0.22306 0.41006 0.69376 1.1714 2.1419 5.1434 11.931 145.24 145.15 139.12 133.32 127.74 122.36 117.17 112.14 107.27 102.53 97.922 93.414 88.995 84.644 80.341 76.063 71.781 67.464 63.075 58.581 54.062 51.767 2153.6 2139.7 1479.1 1106.2 867.31 702.27 582.15 491.22 420.20 363.25 316.57 277.54 244.34 215.64 190.46 168.04 147.78 129.20 111.81 95.095 78.146 57.956 Saturated Properties 15.594 15.590 15.331 15.069 14.804 14.535 14.262 13.984 13.699 13.406 13.104 12.791 12.465 12.121 11.758 11.368 10.945 10.478 9.9483 9.3237 8.5279 7.2558 5.0171 0.00027611 0.00028055 0.00075481 0.0017896 0.0038201 0.0074704 0.013574 0.023188 0.037603 0.058360 0.087278 0.12651 0.17865 0.24685 0.33512 0.44874 0.59505 0.78498 1.0363 1.3818 1.8973 2.8805 5.0171 0.064126 0.064142 0.065228 0.066362 0.067550 0.068798 0.070116 0.071512 0.072999 0.074593 0.076311 0.078179 0.080227 0.082499 0.085050 0.087965 0.091364 0.095439 0.10052 0.10725 0.11726 0.13782 0.19932 3621.7 3564.4 1324.8 558.79 261.77 133.86 73.669 43.125 26.593 17.135 11.458 7.9043 5.5976 4.0511 2.9840 2.2285 1.6805 1.2739 0.96498 0.72368 0.52707 0.34717 0.19932 126.79 126.84 130.05 133.11 135.98 138.63 141.01 143.06 144.73 145.98 146.75 146.99 146.63 145.61 143.88 141.33 137.86 133.33 127.57 120.33 111.25 99.370 0 373.57 370.78 234.43 160.10 116.94 90.215 72.584 60.236 51.130 44.137 38.613 34.169 30.561 27.621 25.230 23.301 21.768 20.578 19.687 19.033 18.448 17.050 11.931 3.0801 3.0921 3.8934 4.6952 5.4978 6.3018 7.1080 7.9176 8.7324 9.5551 10.389 11.241 12.118 13.035 14.011 15.081 16.303 17.780 19.711 22.525 27.365 40.137 6.8294 6.8353 7.2319 7.6253 8.0147 8.3993 8.7786 9.1524 9.5209 9.8853 10.247 10.611 10.980 11.363 11.771 12.219 12.735 13.358 14.164 15.300 17.140 21.336 (Continued) 2-237 2-238 TABLE 2-127 Temperature K Thermodynamic Properties of R-134a, 1,1,1,2-Tetrafluoroethane (Continued ) Pressure MPa Density mol/dm3 Volume dm3/mol Entropy kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity mPa⋅s Int. energy kJ/mol Enthalpy kJ/mol 10.955 16.873 10.962 16.880 0.061955 0.088519 0.081787 0.086506 0.12301 0.13060 968.03 743.31 −0.35132 −0.26099 37.073 39.124 45.154 52.096 39.037 41.348 48.032 55.610 0.17830 0.18716 0.20860 0.22818 0.070161 0.073781 0.086248 0.098386 0.080931 0.083445 0.095065 0.10695 145.63 154.76 175.31 192.97 46.198 29.047 12.552 6.7852 0.067479 0.079009 0.088775 10.933 20.597 25.980 11.001 20.676 26.069 0.061846 0.10281 0.12117 0.081812 0.089915 0.095165 0.12291 0.13695 0.15252 972.08 619.10 439.31 −0.35256 −0.16746 0.12101 128.11 91.627 74.978 2.0729 2.5555 3.3352 40.695 44.290 51.597 42.768 46.846 54.933 0.17460 0.18694 0.20785 0.090164 0.090315 0.099891 0.11623 0.10603 0.11116 140.54 159.63 185.14 22.877 13.885 7.0297 15.374 17.989 23.806 12.343 13.936 16.917 14.880 12.804 9.8674 2.0736 0.067202 0.078103 0.10134 0.48225 10.839 20.385 31.397 48.647 11.175 20.776 31.904 51.058 0.061371 0.10203 0.13765 0.18734 0.081929 0.089864 0.10066 0.10791 0.12246 0.13495 0.17178 0.15381 989.55 651.41 320.01 148.25 −0.35768 −0.19924 0.59952 7.9048 129.56 94.015 63.012 28.574 915.11 277.35 109.32 20.974 966.05 295.02 128.79 46.711 Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Single-Phase Properties 200.00 246.79 0.10000 0.10000 246.79 275.00 350.00 425.00 0.10000 0.10000 0.10000 0.10000 200.00 275.00 312.54 1.0000 1.0000 1.0000 312.54 350.00 425.00 1.0000 1.0000 1.0000 200.00 275.00 350.00 425.00 5.0000 5.0000 5.0000 5.0000 14.805 13.501 0.050898 0.044972 0.034753 0.028455 14.819 12.657 11.264 0.48242 0.39132 0.29983 0.067543 0.074068 19.647 22.236 28.775 35.143 127.78 104.04 9.2899 11.540 17.537 23.539 868.18 380.27 9.7687 10.906 13.823 16.650 876.60 262.84 162.71 200.00 275.00 350.00 425.00 10.000 10.000 10.000 10.000 14.954 12.967 10.478 6.1370 0.066874 0.077121 0.095440 0.16295 10.727 20.149 30.642 43.563 11.395 20.920 31.597 45.193 0.060796 0.10115 0.13537 0.17038 0.082085 0.089868 0.099573 0.11141 0.12196 0.13304 0.15486 0.20870 1010.3 687.36 400.60 177.89 −0.36339 −0.22964 0.21924 3.0434 131.31 96.744 68.919 44.888 200.00 275.00 350.00 425.00 30.000 30.000 30.000 30.000 15.216 13.479 11.662 9.7202 0.065720 0.074190 0.085750 0.10288 10.326 19.398 29.071 39.385 12.298 21.624 31.644 42.471 0.058683 0.098210 0.13038 0.15838 0.082769 0.090220 0.098885 0.10808 0.12047 0.12865 0.13885 0.14967 1084.1 801.47 582.52 425.63 −0.38053 −0.30014 −0.15240 0.10364 137.79 105.87 82.955 67.154 1211.0 364.87 183.26 107.03 275.00 350.00 425.00 70.000 70.000 70.000 14.181 12.797 11.494 0.070517 0.078141 0.087004 18.373 27.492 37.066 23.310 32.961 43.157 0.093839 0.12484 0.15121 0.091314 0.099542 0.10829 0.12519 0.13226 0.13963 962.41 787.10 661.39 −0.35619 −0.30093 −0.23655 119.84 99.868 86.640 521.91 277.09 181.77 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Tillner-Roth, R., and Baehr, H. D., “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) for Temperatures from 170 K to 455 K at Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 23:657–729, 1994. The source for viscosity is Huber, M. L., Laesecke, A., and Perkins, R. A., “Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a,” Ind. Eng. Chem. Res. 42:3163–3178, 2003. The source for thermal conductivity is Perkins, R. A., Laesecke, A., Howley, J., Ramires, M. L. V., Gurova, A. N., and Cusco, L., “Experimental Thermal Conductivity Values for the IUPAC Round-Robin Sample of 1,1,1,2-Tetrafluoroethane (R134a),” NISTIR, 2000. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. Typical uncertainties are 0.05% for density, 0.02% for vapor pressure, 0.5% to 1% for heat capacity, 0.05% for vapor speed of sound, and 1% for liquid speed of sound, except in the critical region. The uncertainty in viscosity is 1.5% along the saturated-liquid line, 3% in the liquid phase, 0.5% in the dilute gas, 3% to 5% in the vapor phase, and 5% in the supercritical region, rising to 8% at pressures above 40 MPa. Below 200 K, the uncertainty is 8%. The uncertainty in thermal conductivity is 5%. FIG. 2-14 Pressure-enthalpy diagram for Refrigerant 134a. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the equation of state of Tillner-Roth, R., and H. D. Baehr, “An International Standard Formulation of the Thermodynamic Properties of 1,1,1,2-Tetrafluoroethane (HFC-134a) Covering Temperatures from 170 K to 455 K at Pressures up to 70 MPa,” J. Phys. Chem. Ref. Data 23(5): 657–729, 1994. 2-239 2-240 TABLE 2-128 Temperature K Thermodynamic Properties of R-143a, 1,1,1-Trifluoroethane Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa −0.43936 −0.42914 −0.41402 −0.39585 −0.37472 −0.35034 −0.32211 −0.28906 −0.24979 −0.20231 −0.14368 −0.069548 0.026895 0.15683 0.34002 0.61491 1.0681 1.9469 4.3897 12.397 Saturated Properties 161.34 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 345.86 0.0010749 0.0025084 0.0059324 0.012629 0.024624 0.044602 0.075908 0.12252 0.18902 0.28049 0.40251 0.56112 0.76276 1.0144 1.3234 1.6983 2.1483 2.6850 3.3250 3.7618 161.34 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 345.86 0.0010749 0.0025084 0.0059324 0.012629 0.024624 0.044602 0.075908 0.12252 0.18902 0.28049 0.40251 0.56112 0.76276 1.0144 1.3234 1.6983 2.1483 2.6850 3.3250 3.7618 15.832 15.583 15.291 14.994 14.692 14.384 14.069 13.745 13.410 13.062 12.698 12.314 11.904 11.461 10.975 10.426 9.7846 8.9829 7.7913 5.1285 0.00080362 0.0017832 0.0039967 0.0081006 0.015110 0.026311 0.043269 0.067850 0.10227 0.14916 0.21175 0.29409 0.40144 0.54109 0.72367 0.96617 1.2991 1.7898 2.6696 5.1285 0.063163 0.064174 0.065399 0.066693 0.068062 0.069519 0.071077 0.072753 0.074570 0.076556 0.078751 0.081208 0.084004 0.087249 0.091119 0.095914 0.10220 0.11132 0.12835 0.19499 1244.4 560.78 250.20 123.45 66.180 38.007 23.111 14.738 9.7783 6.7041 4.7225 3.4004 2.4910 1.8481 1.3818 1.0350 0.76974 0.55871 0.37458 0.19499 4.4138 5.2969 6.3240 7.3629 8.4164 9.4869 10.576 11.685 12.817 13.973 15.156 16.368 17.615 18.903 20.239 21.638 23.125 24.750 26.688 29.429 4.4138 5.2971 6.3244 7.3637 8.4181 9.4900 10.581 11.694 12.831 13.995 15.188 16.414 17.680 18.991 20.360 21.801 23.344 25.048 27.114 30.163 0.026403 0.031735 0.037606 0.043223 0.048626 0.053849 0.058915 0.063848 0.068665 0.073385 0.078027 0.082607 0.087149 0.091675 0.096221 0.10083 0.10559 0.11065 0.11659 0.12527 0.068393 0.068179 0.068405 0.068990 0.069825 0.070836 0.071969 0.073190 0.074475 0.075809 0.077186 0.078605 0.080078 0.081625 0.083293 0.085172 0.087455 0.090641 0.096654 0.10179 0.10225 0.10325 0.10460 0.10621 0.10803 0.11005 0.11227 0.11474 0.11750 0.12066 0.12435 0.12879 0.13438 0.14180 0.15244 0.16980 0.20591 0.35704 1058.1 1016.7 969.14 921.61 874.04 826.46 778.88 731.28 683.65 635.90 587.94 539.61 490.70 440.95 389.93 337.04 281.21 220.39 149.32 0 25.521 25.895 26.340 26.796 27.262 27.736 28.213 28.693 29.170 29.641 30.102 30.548 30.972 31.366 31.715 32.000 32.183 32.184 31.732 29.429 26.859 27.302 27.824 28.355 28.892 29.431 29.968 30.498 31.018 31.521 32.003 32.456 32.872 33.240 33.544 33.758 33.837 33.684 32.977 30.163 0.16552 0.16118 0.15705 0.15370 0.15100 0.14881 0.14704 0.14560 0.14444 0.14349 0.14270 0.14202 0.14141 0.14081 0.14017 0.13940 0.13838 0.13682 0.13384 0.12527 0.044397 0.046371 0.048691 0.051040 0.053424 0.055867 0.058395 0.061026 0.063766 0.066612 0.069560 0.072606 0.075756 0.079035 0.082489 0.086214 0.090400 0.095488 0.10298 0.052938 0.055037 0.057550 0.060156 0.062886 0.065796 0.068954 0.072428 0.076287 0.080611 0.085515 0.091184 0.097932 0.10632 0.11743 0.13359 0.16076 0.22018 0.47999 137.57 140.62 143.91 146.92 149.60 151.89 153.71 155.02 155.74 155.81 155.15 153.70 151.36 148.04 143.59 137.85 130.56 121.34 109.29 0 385.09 262.77 176.43 124.70 92.835 72.442 58.764 49.133 42.049 36.657 32.456 29.136 26.498 24.406 22.765 21.499 20.526 19.682 18.259 12.397 Single-Phase Properties 200.00 225.63 0.10000 0.10000 225.63 300.00 400.00 500.00 600.00 0.10000 0.10000 0.10000 0.10000 0.10000 200.00 289.48 1.0000 1.0000 289.48 300.00 400.00 500.00 600.00 1.0000 1.0000 1.0000 1.0000 1.0000 200.00 300.00 400.00 500.00 600.00 5.0000 5.0000 5.0000 5.0000 5.0000 8.4143 11.198 8.4211 11.205 0.048616 0.061709 0.069829 0.072648 0.10620 0.11128 874.45 752.07 −0.37493 −0.30416 28.483 33.380 41.260 50.551 61.004 30.268 35.833 44.566 54.698 65.987 0.14619 0.16745 0.19247 0.21503 0.23558 0.059863 0.070758 0.086121 0.099065 0.10950 0.070868 0.079793 0.094695 0.10751 0.11790 154.52 179.93 207.36 231.13 252.55 52.958 18.414 7.5341 4.1010 2.5191 0.067956 0.087067 8.3891 18.835 8.4570 18.922 0.048489 0.091441 0.069866 0.081543 0.10604 0.13406 879.27 443.55 −0.37736 0.14902 1.8765 2.0285 3.1249 4.0544 4.9391 31.346 32.269 40.778 50.244 60.781 33.223 34.298 43.903 54.298 65.720 0.14084 0.14449 0.17212 0.19527 0.21607 0.078861 0.077834 0.087343 0.099519 0.10975 0.10583 0.099455 0.098681 0.10927 0.11891 148.24 155.53 198.53 227.30 251.11 24.503 20.787 7.7199 4.0976 2.4913 14.806 11.380 2.2504 1.3639 1.0491 0.067539 0.087876 0.44436 0.73318 0.95318 8.2811 19.812 38.004 48.802 59.789 8.6188 20.251 40.225 52.468 64.554 0.047943 0.094764 0.15165 0.17903 0.20106 0.070021 0.082741 0.093496 0.10135 0.11075 0.10541 0.13222 0.13815 0.11872 0.12364 900.01 452.11 159.25 213.49 246.86 −0.38724 0.11636 8.1026 3.8903 2.2996 14.694 13.888 0.056043 0.040759 0.030247 0.024114 0.020066 14.715 11.485 0.53292 0.49298 0.32001 0.24665 0.20246 0.068054 0.072006 17.843 24.534 33.061 41.469 49.836 200.00 300.00 400.00 500.00 600.00 10.000 10.000 10.000 10.000 10.000 14.913 11.776 6.3531 3.0122 2.1596 0.067054 0.084916 0.15740 0.33199 0.46305 8.1545 19.382 33.679 46.933 58.580 8.8250 20.231 35.253 50.252 63.211 0.047292 0.093258 0.13608 0.16976 0.19339 0.070195 0.082583 0.095653 0.10303 0.11178 0.10473 0.12585 0.17697 0.13206 0.12945 924.61 514.06 196.98 211.16 248.28 −0.39776 −0.037998 2.9315 3.0876 1.9304 200.00 300.00 400.00 500.00 600.00 50.000 50.000 50.000 50.000 50.000 15.598 13.358 11.268 9.4018 7.8978 0.064113 0.074862 0.088747 0.10636 0.12662 7.3673 17.612 28.859 40.839 53.306 10.573 21.355 33.296 46.157 59.637 0.042937 0.086486 0.12077 0.14943 0.17399 0.070934 0.083360 0.096003 0.10668 0.11548 0.10170 0.11389 0.12454 0.13213 0.13720 1089.7 794.12 590.09 478.93 431.69 −0.44295 −0.33796 −0.20571 −0.077157 −0.0052131 14.343 12.767 11.435 10.314 0.069721 0.078330 0.087453 0.096952 16.500 27.298 38.923 51.227 23.472 35.131 47.668 60.923 0.081539 0.11502 0.14296 0.16711 0.084059 0.097186 0.10821 0.11716 0.11166 0.12126 0.12921 0.13566 1008.9 833.69 723.22 656.57 −0.40055 −0.35302 −0.31534 −0.28902 300.00 400.00 500.00 600.00 100.00 100.00 100.00 100.00 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., and Jacobsen, R. T., “An International Standard Formulation for the Thermodynamic Properties of 1,1,1-Trifluoroethane (HFC-143a) for Temperatures from 161 to 450 K and Pressures to 50 MPa,” J. Phys. Chem. Ref. Data 29(4):521–552, 2000. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainties of properties calculated using the equation of state are 0.1% in density, 0.5% in heat capacities, 0.02% in the speed of sound for the vapor at pressures less than 1 MPa, 0.5% in speed of sound elsewhere, and 0.1% in vapor pressure, except in the critical region. 2-241 2-242 TABLE 2-129 Thermodynamic Properties of R-404A Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 345.27 0.022649 0.030989 0.041658 0.055101 0.071804 0.092293 0.11713 0.14693 0.18232 0.22397 0.27258 0.32888 0.39363 0.46763 0.55168 0.64664 0.75338 0.87280 1.0059 1.1536 1.3169 1.4970 1.6950 1.9122 2.1499 2.4096 2.6932 3.0027 3.3414 3.7150 3.7348 14.209 14.059 13.907 13.755 13.600 13.444 13.286 13.126 12.963 12.796 12.627 12.453 12.275 12.092 11.904 11.709 11.508 11.298 11.078 10.848 10.605 10.346 10.069 9.7686 9.4384 9.0688 8.6431 8.1285 7.4362 5.7429 4.9400 0.070377 0.071131 0.071905 0.072703 0.073527 0.074380 0.075265 0.076185 0.077145 0.078147 0.079197 0.080301 0.081465 0.082697 0.084006 0.085402 0.086899 0.088513 0.090266 0.092182 0.094295 0.096652 0.099314 0.10237 0.10595 0.11027 0.11570 0.12302 0.13448 0.17413 0.20243 10.353 10.948 11.544 12.144 12.746 13.353 13.963 14.578 15.199 15.824 16.456 17.094 17.738 18.390 19.049 19.717 20.394 21.081 21.780 22.490 23.215 23.956 24.717 25.500 26.310 27.157 28.054 29.026 30.147 32.108 32.875 200.00 205.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 0.021264 0.029285 0.039592 0.052629 0.068883 0.088879 0.11318 0.14240 0.17718 0.21817 0.26610 0.32169 0.38571 0.45896 0.54225 0.63645 0.74245 0.86115 0.99353 1.1406 1.3034 1.4830 29.920 30.185 30.451 30.718 30.987 31.256 31.525 31.795 32.063 32.330 32.596 32.859 33.119 33.375 33.626 33.872 34.111 34.342 34.563 34.773 34.968 35.147 Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) 10.355 10.950 11.547 12.148 12.751 13.359 13.972 14.590 15.213 15.842 16.478 17.120 17.770 18.429 19.096 19.772 20.460 21.159 21.870 22.597 23.339 24.101 24.885 25.695 26.538 27.423 28.365 29.396 30.597 32.755 33.631 0.058867 0.061803 0.064678 0.067498 0.070269 0.072995 0.075679 0.078326 0.080939 0.083520 0.086073 0.088600 0.091104 0.093589 0.096056 0.098510 0.10095 0.10339 0.10583 0.10826 0.11071 0.11317 0.11566 0.11818 0.12075 0.12341 0.12619 0.12918 0.13261 0.13874 0.14126 0.076939 0.077522 0.078116 0.078719 0.079326 0.079940 0.080558 0.081183 0.081815 0.082456 0.083107 0.083770 0.084446 0.085137 0.085846 0.086574 0.087326 0.088104 0.088914 0.089761 0.090653 0.091603 0.092625 0.093744 0.094998 0.096455 0.098241 0.10064 0.10445 0.11650 31.555 31.853 32.152 32.451 32.749 33.046 33.340 33.633 33.922 34.208 34.489 34.765 35.034 35.296 35.550 35.794 36.028 36.249 36.455 36.645 36.814 36.960 0.16521 0.16408 0.16307 0.16217 0.16138 0.16068 0.16006 0.15952 0.15903 0.15861 0.15823 0.15789 0.15759 0.15732 0.15707 0.15684 0.15661 0.15639 0.15616 0.15592 0.15566 0.15536 0.058696 0.059968 0.061245 0.062526 0.063815 0.065113 0.066424 0.067750 0.069095 0.070463 0.071855 0.073276 0.074728 0.076214 0.077737 0.079300 0.080909 0.082567 0.084282 0.086062 0.087917 0.089863 Sound speed m/s Joule-Thomson K/MPa 0.11881 0.11915 0.11965 0.12028 0.12103 0.12188 0.12282 0.12386 0.12499 0.12621 0.12754 0.12899 0.13057 0.13229 0.13419 0.13630 0.13866 0.14133 0.14438 0.14793 0.15211 0.15715 0.16339 0.17139 0.18212 0.19751 0.22197 0.26871 0.40392 8.2559 859.89 831.56 804.42 778.20 752.69 727.72 703.16 678.91 654.88 631.01 607.23 583.50 559.77 535.99 512.13 488.15 464.02 439.69 415.13 390.28 365.11 339.56 313.56 287.00 259.73 231.53 201.95 170.20 134.59 89.976 0 −0.34161 −0.33384 −0.32460 −0.31394 −0.30185 −0.28830 −0.27318 −0.25636 −0.23766 −0.21683 −0.19356 −0.16749 −0.13814 −0.10493 −0.067104 −0.023728 0.026418 0.084928 0.15392 0.23626 0.33594 0.45865 0.61280 0.81141 1.0757 1.4433 1.9881 2.8807 4.6353 10.564 12.409 0.068032 0.069509 0.071021 0.072573 0.074172 0.075826 0.077546 0.079344 0.081232 0.083226 0.085343 0.087604 0.090033 0.092660 0.095524 0.098671 0.10217 0.10609 0.11056 0.11574 0.12186 0.12929 138.13 139.28 140.34 141.29 142.12 142.84 143.43 143.88 144.18 144.33 144.32 144.14 143.77 143.22 142.46 141.49 140.29 138.85 137.16 135.19 132.92 130.34 88.073 77.215 68.305 60.948 54.835 49.721 45.413 41.761 38.642 35.962 33.645 31.630 29.871 28.327 26.970 25.773 24.718 23.789 22.972 22.256 21.633 21.094 Cp kJ/(mol⋅K) Saturated Properties 0.013010 0.017550 0.023271 0.030378 0.039095 0.049667 0.062359 0.077463 0.095292 0.11619 0.14055 0.16879 0.20137 0.23885 0.28183 0.33102 0.38725 0.45152 0.52501 0.60922 0.70599 0.81772 76.866 56.979 42.971 32.919 25.579 20.134 16.036 12.909 10.494 8.6063 7.1149 5.9247 4.9659 4.1867 3.5483 3.0210 2.5823 2.2148 1.9047 1.6414 1.4165 1.2229 310.00 315.00 320.00 325.00 330.00 335.00 340.00 345.00 345.27 1.6806 1.8975 2.1351 2.3950 2.6789 2.9893 3.3299 3.7109 3.7348 226.65 0.10000 227.41 300.00 400.00 500.00 0.10000 0.10000 0.10000 0.10000 289.79 1.0000 290.23 300.00 400.00 500.00 1.0000 1.0000 1.0000 1.0000 300.00 400.00 500.00 5.0000 5.0000 5.0000 0.94761 1.1001 1.2815 1.5019 1.7781 2.1438 2.6882 4.2113 4.9400 1.0553 0.90903 0.78032 0.66583 0.56239 0.46645 0.37199 0.23746 0.20243 35.304 35.435 35.530 35.578 35.558 35.429 35.084 33.615 32.875 37.078 37.159 37.196 37.173 37.065 36.824 36.323 34.496 33.631 0.074669 13.554 13.561 31.386 36.596 45.121 55.103 0.090189 0.15501 0.15459 0.15408 0.15343 0.15257 0.15136 0.14946 0.14379 0.14126 0.091922 0.094123 0.096513 0.099162 0.10220 0.10585 0.11074 0.12022 0.13856 0.15062 0.16713 0.19141 0.23111 0.30867 0.53035 8.6291 127.41 124.10 120.38 116.21 111.51 106.19 100.03 90.307 0 20.630 20.234 19.889 19.571 19.233 18.763 17.851 14.130 12.409 0.073887 0.080143 0.12218 719.55 −0.28348 33.188 39.050 48.428 59.250 0.16038 0.18269 0.20956 0.23365 0.065742 0.076875 0.092844 0.10612 0.076645 0.085907 0.10141 0.11456 143.14 166.24 191.81 213.92 47.558 16.998 6.9229 3.7455 21.750 21.840 0.10572 0.088879 0.14425 416.16 1.8916 2.0323 3.1292 4.0571 34.573 35.486 44.644 54.804 36.464 37.518 47.773 58.861 0.15615 0.15972 0.18922 0.21391 0.084363 0.083854 0.094142 0.10659 0.11078 0.10554 0.10545 0.11631 137.07 143.42 183.69 210.41 10.994 2.2256 1.3561 0.090955 0.44932 0.73741 22.770 41.867 53.389 23.225 44.113 57.076 0.10919 0.16875 0.19774 0.089725 0.10069 0.10859 0.14193 0.14547 0.12579 427.56 148.00 198.35 0.11428 7.6582 3.5826 Single-Phase Properties 13.392 0.055492 0.040750 0.030243 0.024113 11.088 0.52866 0.49205 0.31957 0.24648 18.021 24.540 33.066 41.471 0.15078 22.936 19.634 7.1401 3.7496 300.00 400.00 500.00 10.000 10.000 10.000 11.371 6.1241 2.9622 0.087944 0.16329 0.33758 22.323 37.557 51.539 23.203 39.190 54.915 0.10763 0.15323 0.18852 0.089307 0.10301 0.11046 0.13525 0.18569 0.13925 489.01 184.17 198.11 −0.035312 2.8522 2.8527 300.00 400.00 500.00 25.000 25.000 25.000 12.107 9.2730 6.6326 0.082594 0.10784 0.15077 21.419 34.286 47.758 23.484 36.982 51.527 0.10432 0.14304 0.17548 0.089393 0.10166 0.11215 0.12713 0.14227 0.14633 614.12 381.56 292.53 −0.22002 0.20064 0.65319 300.00 400.00 500.00 50.000 50.000 50.000 12.867 10.834 9.0225 0.077719 0.092300 0.11083 20.472 32.538 45.317 24.358 37.153 50.859 0.10057 0.13731 0.16786 0.090168 0.10251 0.11339 0.12262 0.13302 0.14051 753.19 559.24 455.37 −0.32391 −0.19415 −0.070101 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%. 2-243 2-244 TABLE 2-130 Thermodynamic Properties of R-407C Temperature K Pressure MPa 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 359.35 0.019158 0.035795 0.062640 0.10366 0.16353 0.24755 0.36157 0.51193 0.70540 0.94916 1.2507 1.6182 2.0599 2.5851 3.2038 3.9255 4.6317 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 359.35 0.011312 0.022624 0.041929 0.072846 0.11979 0.18793 0.28317 0.41203 0.58173 0.80008 1.0757 1.4179 1.8375 2.3470 2.9627 3.7100 4.6317 Density mol/dm3 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa −0.31996 −0.30662 −0.28934 −0.26790 −0.24161 −0.20937 −0.16951 −0.11964 −0.056172 0.026372 0.13683 0.29038 0.51547 0.87274 1.5203 3.0499 10.947 Saturated Properties 17.036 16.697 16.352 15.999 15.637 15.264 14.877 14.472 14.045 13.591 13.102 12.567 11.969 11.278 10.435 9.2661 5.2600 0.0068643 0.013151 0.023450 0.039384 0.062913 0.096374 0.14256 0.20484 0.28739 0.39560 0.53670 0.72101 0.96439 1.2939 1.7642 2.5260 5.2600 0.058698 0.059892 0.061156 0.062503 0.063949 0.065512 0.067218 0.069099 0.071198 0.073576 0.076322 0.079573 0.083552 0.088671 0.095832 0.10792 0.19011 145.68 76.041 42.644 25.391 15.895 10.376 7.0147 4.8820 3.4796 2.5278 1.8632 1.3869 1.0369 0.77283 0.56682 0.39588 0.19011 8.8272 9.9359 11.051 12.175 13.312 14.464 15.632 16.822 18.035 19.278 20.555 21.877 23.255 24.711 26.287 28.110 32.145 8.8283 9.9380 11.055 12.182 13.323 14.480 15.657 16.857 18.085 19.348 20.651 22.006 23.427 24.940 26.594 28.534 33.025 0.050593 0.056002 0.061189 0.066188 0.071026 0.075728 0.080314 0.084805 0.089223 0.093590 0.097931 0.10228 0.10668 0.11119 0.11596 0.12137 0.13372 0.070988 0.071320 0.071817 0.072410 0.073074 0.073803 0.074597 0.075463 0.076412 0.077458 0.078624 0.079950 0.081509 0.083453 0.086157 0.090943 0.11073 0.11118 0.11203 0.11319 0.11465 0.11641 0.11853 0.12111 0.12427 0.12822 0.13331 0.14013 0.14989 0.16541 0.19551 0.28993 956.60 903.06 851.40 801.12 751.77 703.01 654.53 606.09 557.44 508.32 458.46 407.51 354.98 300.07 241.20 174.57 0 30.051 30.504 30.957 31.409 31.857 32.298 32.728 33.145 33.544 33.918 34.259 34.556 34.790 34.931 34.916 34.578 32.145 31.699 32.224 32.745 33.259 33.761 34.248 34.715 35.157 35.568 35.940 36.263 36.523 36.696 36.745 36.595 36.047 33.025 0.16726 0.16412 0.16151 0.15933 0.15749 0.15593 0.15460 0.15343 0.15240 0.15144 0.15051 0.14956 0.14852 0.14727 0.14560 0.14299 0.13372 0.048920 0.050967 0.053143 0.055439 0.057839 0.060328 0.062897 0.065542 0.068266 0.071085 0.074027 0.077140 0.080507 0.084283 0.088801 0.095065 0.057805 0.060200 0.062854 0.065784 0.069010 0.072563 0.076500 0.080917 0.085971 0.091920 0.099203 0.10861 0.12170 0.14208 0.18030 0.28700 149.59 152.36 154.78 156.79 158.33 159.36 159.80 159.60 158.69 156.99 154.41 150.83 146.11 140.03 132.24 122.09 0 109.12 88.122 72.006 59.560 49.904 42.378 36.483 31.840 28.163 25.236 22.898 21.024 19.516 18.284 17.206 15.951 10.947 Single-Phase Properties 200.00 229.25 0.10000 0.10000 236.25 300.00 400.00 500.00 0.10000 0.10000 0.10000 0.10000 291.84 1.0000 297.47 300.00 400.00 500.00 1.0000 1.0000 1.0000 1.0000 300.00 400.00 500.00 5.0000 5.0000 5.0000 8.8253 12.091 8.8312 12.097 0.050583 0.065819 0.070990 0.072363 0.11072 0.11310 956.99 804.85 −0.32010 −0.26966 31.690 35.535 42.554 50.849 33.574 37.991 45.862 54.997 0.15814 0.17467 0.19722 0.21756 0.056928 0.063341 0.076588 0.088895 0.067764 0.072378 0.085147 0.097330 157.81 179.00 205.99 229.27 53.242 20.041 7.7925 4.0471 0.074050 19.510 19.584 0.094388 0.077662 0.12906 499.23 2.0105 2.0465 3.1425 4.0637 34.177 34.384 42.101 50.576 36.187 36.431 45.244 54.639 0.15075 0.15156 0.17694 0.19786 0.073268 0.072744 0.078067 0.089416 0.097199 0.095419 0.089213 0.099001 155.15 156.77 198.26 225.88 13.412 2.1880 1.3504 0.074559 0.45703 0.74050 20.240 39.458 49.289 20.613 41.743 52.992 0.096862 0.15675 0.18193 0.078093 0.086188 0.091753 0.12762 0.12964 0.10811 507.10 161.10 213.00 0.027202 8.5257 3.9036 17.038 16.026 0.053062 0.040722 0.030231 0.024109 13.504 0.49738 0.48865 0.31821 0.24608 0.058692 0.062399 18.846 24.557 33.079 41.479 0.044233 23.442 22.566 7.9701 4.0390 300.00 400.00 500.00 10.000 10.000 10.000 13.740 7.1029 2.9957 0.072780 0.14079 0.33381 19.898 34.426 47.547 20.626 35.834 50.885 0.095679 0.13888 0.17282 0.077756 0.090433 0.094263 0.12301 0.20031 0.12254 558.94 184.71 207.67 −0.063246 3.3408 3.3327 300.00 400.00 500.00 25.000 25.000 25.000 14.443 10.899 7.3363 0.069238 0.091752 0.13631 19.146 30.990 43.479 20.877 33.284 46.886 0.092972 0.12855 0.15889 0.077634 0.087056 0.096319 0.11624 0.13223 0.13592 672.43 399.92 289.22 −0.19834 0.28513 0.97116 300.00 400.00 500.00 50.000 50.000 50.000 15.220 12.648 10.260 0.065703 0.079064 0.097468 18.302 29.255 40.787 21.587 33.209 45.660 0.089730 0.12310 0.15086 0.078160 0.087179 0.096753 0.11176 0.12077 0.12761 802.78 579.57 457.54 −0.28843 −0.12975 0.047330 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%. 2-245 2-246 FIG. 2-15 Pressure-enthalpy diagram for Refrigerant 407C. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M. O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology), based on the mixture model of Lemmon, E. W., and R. T. Jacobsen, “Equations of State for Mixtures of R-32, R-125, R-134a, R-143a, and R-152a,” J. Phys. Chem. Ref. Data 33: 593–620, 2004. TABLE 2-131 Thermodynamic Properties of R-410A Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol 200.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00 325.00 330.00 335.00 340.00 344.49 0.029160 0.053727 0.071143 0.092819 0.11946 0.15182 0.19070 0.23697 0.29152 0.35531 0.42933 0.51461 0.61223 0.72330 0.84899 0.99048 1.1490 1.3260 1.5226 1.7404 1.9809 2.2456 2.5364 2.8550 3.2037 3.5848 4.0009 4.4556 4.9012 19.510 19.093 18.881 18.667 18.449 18.229 18.005 17.776 17.543 17.305 17.062 16.812 16.555 16.290 16.016 15.732 15.436 15.127 14.802 14.459 14.095 13.704 13.282 12.816 12.294 11.685 10.930 9.8413 6.3240 0.051256 0.052375 0.052962 0.053571 0.054202 0.054858 0.055542 0.056255 0.057002 0.057786 0.058611 0.059482 0.060406 0.061388 0.062439 0.063567 0.064785 0.066109 0.067559 0.069160 0.070948 0.072969 0.075293 0.078025 0.081343 0.085578 0.091491 0.10161 0.15813 7.0380 8.0188 8.5112 9.0052 9.5012 9.9997 10.501 11.006 11.514 12.026 12.543 13.065 13.593 14.127 14.669 15.218 15.776 16.344 16.924 17.516 18.123 18.747 19.392 20.064 20.772 21.531 22.376 23.414 25.988 200.00 210.00 215.00 220.00 225.00 230.00 235.00 240.00 245.00 250.00 255.00 260.00 265.00 270.00 275.00 280.00 285.00 290.00 295.00 300.00 305.00 310.00 315.00 320.00 0.029010 0.053489 0.070844 0.092447 0.11900 0.15125 0.19000 0.23611 0.29049 0.35407 0.42786 0.51287 0.61019 0.72092 0.84622 0.98729 1.1454 1.3218 1.5179 1.7351 1.9749 2.2390 2.5291 2.8472 26.495 26.835 27.002 27.167 27.329 27.488 27.645 27.798 27.947 28.092 28.232 28.367 28.496 28.619 28.733 28.839 28.935 29.019 29.090 29.144 29.178 29.189 29.170 29.112 Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa 7.0395 8.0217 8.5149 9.0101 9.5077 10.008 10.512 11.019 11.530 12.047 12.568 13.096 13.630 14.172 14.722 15.281 15.851 16.432 17.026 17.636 18.263 18.911 19.583 20.287 21.032 21.837 22.742 23.867 26.763 0.040995 0.045781 0.048098 0.050370 0.052600 0.054791 0.056948 0.059073 0.061169 0.063240 0.065289 0.067318 0.069331 0.071331 0.073321 0.075304 0.077284 0.079266 0.081254 0.083253 0.085270 0.087314 0.089398 0.091537 0.093762 0.096123 0.098732 0.10194 0.11022 0.062260 0.062050 0.062014 0.062020 0.062066 0.062151 0.062271 0.062426 0.062615 0.062837 0.063092 0.063380 0.063701 0.064057 0.064451 0.064884 0.065363 0.065893 0.066483 0.067147 0.067901 0.068773 0.069800 0.071046 0.072616 0.074717 0.077843 0.083650 0.097942 0.098396 0.098729 0.099138 0.099628 0.10020 0.10088 0.10165 0.10253 0.10353 0.10466 0.10594 0.10738 0.10902 0.11088 0.11300 0.11543 0.11825 0.12156 0.12550 0.13029 0.13630 0.14413 0.15493 0.17109 0.19853 0.25685 0.46832 929.01 879.84 855.20 830.52 805.81 781.06 756.26 731.41 706.48 681.45 656.31 631.02 605.55 579.88 553.95 527.72 501.14 474.14 446.66 418.60 389.87 360.33 329.82 298.10 264.83 229.46 190.98 147.49 0 −0.30179 −0.28524 −0.27544 −0.26446 −0.25217 −0.23841 −0.22300 −0.20574 −0.18637 −0.16459 −0.14006 −0.11232 −0.080861 −0.045000 −0.0039006 0.043515 0.098651 0.16337 0.24022 0.33275 0.44607 0.58788 0.77028 1.0135 1.3544 1.8665 2.7232 4.4554 9.7623 28.125 28.530 28.726 28.919 29.107 29.290 29.468 29.640 29.806 29.965 30.116 30.258 30.392 30.515 30.626 30.725 30.809 30.876 30.925 30.951 30.951 30.920 30.850 30.732 0.14644 0.14345 0.14212 0.14087 0.13972 0.13864 0.13762 0.13667 0.13577 0.13492 0.13411 0.13333 0.13259 0.13187 0.13116 0.13047 0.12978 0.12908 0.12837 0.12764 0.12688 0.12606 0.12517 0.12418 0.042482 0.044604 0.045719 0.046862 0.048026 0.049206 0.050400 0.051603 0.052814 0.054033 0.055260 0.056497 0.057747 0.059014 0.060302 0.061618 0.062969 0.064364 0.065814 0.067335 0.068945 0.070671 0.072551 0.074643 0.052236 0.055055 0.056590 0.058205 0.059899 0.061674 0.063533 0.065483 0.067535 0.069705 0.072011 0.074481 0.077148 0.080057 0.083265 0.086846 0.090901 0.095568 0.10104 0.10760 0.11566 0.12589 0.13943 0.15831 164.41 167.03 168.16 169.16 170.03 170.75 171.32 171.73 171.97 172.04 171.93 171.62 171.11 170.39 169.45 168.27 166.84 165.16 163.20 160.94 158.36 155.44 152.13 148.40 Saturated Properties 0.017797 0.031567 0.041089 0.052763 0.066925 0.083936 0.10420 0.12814 0.15625 0.18905 0.22714 0.27117 0.32190 0.38018 0.44702 0.52357 0.61123 0.71170 0.82707 0.95997 1.1138 1.2933 1.5048 1.7576 56.190 31.678 24.338 18.953 14.942 11.914 9.5972 7.8039 6.4000 5.2895 4.4026 3.6877 3.1066 2.6303 2.2371 1.9100 1.6360 1.4051 1.2091 1.0417 0.89779 0.77322 0.66456 0.56894 113.67 90.100 80.508 72.155 64.889 58.571 53.077 48.299 44.137 40.508 37.336 34.560 32.123 29.979 28.087 26.412 24.924 23.598 22.410 21.338 20.365 19.470 18.632 17.826 2-247 (Continued) 2-248 TABLE 2-131 Thermodynamic Properties of R-410A (Continued ) Temperature K Pressure MPa Density mol/dm3 Volume dm3/mol Int. energy kJ/mol 325.00 330.00 335.00 340.00 344.49 3.1955 3.5766 3.9935 4.4504 4.9012 2.0668 2.4582 2.9848 3.7974 6.3240 0.48384 0.40681 0.33503 0.26334 0.15813 29.002 28.817 28.510 27.951 25.988 221.45 0.10000 221.53 300.00 400.00 500.00 0.10000 0.10000 0.10000 0.10000 280.32 1.0000 280.42 300.00 400.00 500.00 1.0000 1.0000 1.0000 1.0000 300.00 400.00 500.00 5.0000 5.0000 5.0000 Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Saturated Properties (Continued) 30.548 30.272 29.848 29.123 26.763 0.12305 0.12169 0.11995 0.11740 0.11022 0.077041 0.079915 0.083629 0.089197 0.18670 0.23464 0.33370 0.65947 144.16 139.30 133.59 126.39 0 17.018 16.153 15.123 13.641 9.7623 0.051020 0.062030 0.099271 823.36 −0.26104 69.827 19.643 7.7467 4.0758 Single-Phase Properties 18.604 0.056810 0.040605 0.030202 0.024099 0.053751 9.1541 27.217 31.028 36.670 43.331 28.977 33.491 39.981 47.480 0.14051 0.15794 0.17654 0.19323 0.047215 0.050980 0.061554 0.071249 0.058714 0.059877 0.070067 0.079663 169.44 198.35 227.37 252.59 0.063641 15.253 15.317 0.075429 0.064913 0.11314 526.05 1.8849 2.1460 3.1769 4.0808 28.848 30.151 36.304 43.106 30.733 32.297 39.481 47.187 0.13041 0.13580 0.15648 0.17364 0.061731 0.057548 0.062713 0.071665 0.087169 0.075210 0.073258 0.081012 168.16 180.65 220.92 249.79 14.870 1.9755 1.3185 0.067248 0.50621 0.75845 17.202 34.349 42.072 17.539 36.880 45.864 0.082188 0.13813 0.15821 0.066139 0.068570 0.073521 0.11773 0.097588 0.087959 472.56 192.34 239.51 0.17344 7.6786 3.7957 0.036775 5.0121 3.3106 15.713 0.53054 0.46599 0.31478 0.24505 17.603 24.628 33.111 41.495 9.1488 0.046760 26.279 20.254 7.7768 4.0343 300.00 400.00 500.00 10.000 10.000 10.000 15.342 5.7949 2.8642 0.065180 0.17257 0.34914 16.830 30.845 40.710 17.482 32.570 44.202 0.080897 0.12363 0.14982 0.065435 0.074099 0.075667 0.11125 0.16518 0.098492 533.86 182.45 233.93 300.00 400.00 500.00 25.000 25.000 25.000 16.289 11.685 7.4115 0.061392 0.085582 0.13493 16.058 26.530 37.197 17.592 28.670 40.570 0.078110 0.10987 0.13644 0.065000 0.072157 0.078574 0.10273 0.11830 0.11515 658.09 379.59 291.31 −0.14678 0.50709 1.2724 300.00 400.00 500.00 50.000 50.000 50.000 17.287 14.049 11.128 0.057845 0.071182 0.089864 15.231 24.722 34.526 18.123 28.281 39.019 0.074923 0.10409 0.12804 0.065499 0.072480 0.079657 0.097459 0.10533 0.10880 792.80 566.13 449.76 −0.26163 −0.063564 0.13566 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Lemmon, E. W., “Pseudo Pure-Fluid Equations of State for the Refrigerant Blends R-410A, R-404A, R-507A, and R-407C,” Int. J. Thermophys. 24(4):991–1006, 2003. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. Properties at the critical point temperature are given in the last entry of the saturation tables. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperaturepressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The estimated uncertainty of density values calculated with the equation of state is 0.1%. The estimated uncertainty of calculated heat capacities and speed of sound values is 0.5%. Uncertainties of bubble and dew point pressures are 0.5%. TABLE 2-132 Opteon™ YF (R-1234yf) Saturation Properties—Temperature Table Temp [°C] −40 −39 −38 −37 −36 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 Pressure [kPa] 62.367 65.454 68.661 71.992 75.450 79.039 82.761 86.620 90.620 94.764 99.056 103.500 108.098 112.856 117.775 122.861 128.117 133.548 139.155 144.945 150.921 157.086 163.444 170.001 176.759 183.724 190.898 198.287 205.895 213.726 221.783 230.072 238.597 247.363 256.373 265.632 275.144 284.915 294.948 305.249 315.821 326.670 337.800 349.216 Volume [m3/kg] Liquid vf Vapor vg 0.000774 0.000776 0.000777 0.000779 0.000781 0.000782 0.000784 0.000786 0.000787 0.000789 0.000791 0.000793 0.000794 0.000796 0.000798 0.000800 0.000801 0.000803 0.000805 0.000807 0.000809 0.000811 0.000813 0.000815 0.000817 0.000818 0.000820 0.000822 0.000824 0.000826 0.000829 0.000831 0.000833 0.000835 0.000837 0.000839 0.000841 0.000843 0.000846 0.000848 0.000850 0.000852 0.000855 0.000857 0.2635 0.2519 0.2409 0.2304 0.2205 0.2111 0.2022 0.1937 0.1857 0.1780 0.1708 0.1639 0.1573 0.1511 0.1451 0.1394 0.1340 0.1289 0.1240 0.1193 0.1148 0.1105 0.1065 0.1026 0.0988 0.0953 0.0919 0.0886 0.0855 0.0825 0.0796 0.0769 0.0742 0.0717 0.0693 0.0670 0.0647 0.0626 0.0605 0.0586 0.0567 0.0548 0.0531 0.0514 Density [kg/m3] Liquid df 1291.9 1289.2 1286.5 1283.8 1281.0 1278.3 1275.6 1272.8 1270.1 1267.3 1264.5 1261.8 1259.0 1256.2 1253.4 1250.5 1247.7 1244.9 1242.0 1239.2 1236.3 1233.4 1230.5 1227.6 1224.7 1221.8 1218.8 1215.9 1212.9 1209.9 1207.0 1203.9 1200.9 1197.9 1194.9 1191.8 1188.7 1185.6 1182.5 1179.4 1176.3 1173.1 1170.0 1166.8 Enthalpy [kJ/kg] Vapor dg Liquid hf Latent hfg 3.795 3.970 4.152 4.340 4.535 4.737 4.946 5.162 5.386 5.617 5.855 6.102 6.357 6.620 6.891 7.171 7.460 7.758 8.066 8.383 8.709 9.046 9.392 9.750 10.117 10.496 10.885 11.286 11.699 12.123 12.559 13.008 13.469 13.943 14.431 14.931 15.446 15.974 16.517 17.074 17.647 18.234 18.837 19.457 151.1 152.2 153.4 154.6 155.7 156.9 158.1 159.3 160.4 161.6 162.8 164.0 165.2 166.4 167.6 168.8 170.0 171.2 172.4 173.7 174.9 176.1 177.3 178.6 179.8 181.0 182.3 183.5 184.8 186.0 187.3 188.5 189.8 191.0 192.3 193.6 194.9 196.1 197.4 198.7 200.0 201.3 202.6 203.9 185.5 185.0 184.5 184.0 183.5 183.0 182.5 182.0 181.5 181.0 180.5 180.0 179.5 178.9 178.4 177.9 177.4 176.8 176.3 175.7 175.2 174.6 174.1 173.5 172.9 172.4 171.8 171.2 170.6 170.0 169.5 168.9 168.3 167.7 167.0 166.4 165.8 165.2 164.6 163.9 163.3 162.6 162.0 161.3 Entropy [kJ/kg⋅K] Vapor hg Liquid sf 336.6 337.3 337.9 338.6 339.3 339.9 340.6 341.3 342.0 342.6 343.3 344.0 344.7 345.3 346.0 346.7 347.4 348.0 348.7 349.4 350.1 350.7 351.4 352.1 352.7 353.4 354.1 354.7 355.4 356.1 356.7 357.4 358.0 358.7 359.4 360.0 360.7 361.3 362.0 362.6 363.3 363.9 364.6 365.2 0.807 0.812 0.817 0.822 0.827 0.832 0.837 0.842 0.847 0.852 0.857 0.861 0.866 0.871 0.876 0.881 0.886 0.891 0.895 0.900 0.905 0.910 0.915 0.919 0.924 0.929 0.934 0.939 0.943 0.948 0.953 0.958 0.962 0.967 0.972 0.976 0.981 0.986 0.991 0.995 1.000 1.005 1.009 1.014 Vapor sg 1.603 1.603 1.602 1.602 1.601 1.601 1.600 1.600 1.600 1.599 1.599 1.599 1.598 1.598 1.598 1.598 1.598 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.597 1.598 1.598 1.598 1.598 1.598 1.598 Temp [°C] −40 −39 −38 −37 −36 −35 −34 −33 −32 −31 −30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 2-249 (Continued) 2-250 TABLE 2-132 Opteon™ YF (R-1234yf) (Continued ) Saturation Properties—Temperature Table Volume [m3/kg] Temp [°C] 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 Pressure [kPa] Liquid vf Vapor vg 360.923 372.925 385.227 397.833 410.750 423.981 437.532 451.408 465.613 480.152 495.031 510.255 525.828 541.756 558.044 574.697 591.721 609.120 626.901 645.068 663.626 682.582 701.940 721.707 741.887 762.487 783.511 804.966 826.857 849.190 871.971 895.206 918.900 943.060 967.691 992.800 1018.393 1044.476 1071.055 1098.137 1125.728 1153.834 1182.462 1211.618 0.000859 0.000862 0.000864 0.000867 0.000869 0.000872 0.000874 0.000877 0.000879 0.000882 0.000884 0.000887 0.000890 0.000893 0.000895 0.000898 0.000901 0.000904 0.000907 0.000910 0.000913 0.000916 0.000919 0.000922 0.000925 0.000928 0.000932 0.000935 0.000938 0.000942 0.000945 0.000949 0.000952 0.000956 0.000960 0.000963 0.000967 0.000971 0.000975 0.000979 0.000983 0.000988 0.000992 0.000996 0.0498 0.0482 0.0467 0.0452 0.0439 0.0425 0.0412 0.0400 0.0387 0.0376 0.0365 0.0354 0.0343 0.0333 0.0323 0.0314 0.0305 0.0296 0.0288 0.0279 0.0271 0.0264 0.0256 0.0249 0.0242 0.0235 0.0229 0.0222 0.0216 0.0210 0.0204 0.0199 0.0193 0.0188 0.0183 0.0178 0.0173 0.0168 0.0164 0.0159 0.0155 0.0151 0.0147 0.0143 Density [kg/m3] Liquid df 1163.6 1160.4 1157.2 1153.9 1150.6 1147.3 1144.0 1140.7 1137.4 1134.0 1130.6 1127.2 1123.8 1120.3 1116.9 1113.4 1109.9 1106.3 1102.8 1099.2 1095.5 1091.9 1088.2 1084.5 1080.8 1077.1 1073.3 1069.5 1065.7 1061.8 1057.9 1054.0 1050.0 1046.0 1042.0 1037.9 1033.8 1029.6 1025.5 1021.2 1017.0 1012.6 1008.3 1003.9 Enthalpy [kJ/kg] Vapor dg Liquid hf Latent hfg 20.092 20.744 21.413 22.100 22.804 23.526 24.267 25.027 25.807 26.606 27.425 28.266 29.127 30.011 30.916 31.845 32.796 33.772 34.772 35.797 36.848 37.925 39.029 40.161 41.321 42.510 43.729 44.979 46.260 47.573 48.920 50.301 51.717 53.169 54.658 56.186 57.753 59.360 61.010 62.702 64.440 66.223 68.053 69.933 205.2 206.5 207.8 209.1 210.5 211.8 213.1 214.4 215.8 217.1 218.5 219.8 221.2 222.5 223.9 225.2 226.6 228.0 229.3 230.7 232.1 233.5 234.9 236.3 237.7 239.1 240.5 241.9 243.4 244.8 246.2 247.6 249.1 250.5 252.0 253.4 254.9 256.4 257.8 259.3 260.8 262.3 263.8 265.3 160.7 160.0 159.3 158.7 158.0 157.3 156.6 155.9 155.2 154.5 153.8 153.0 152.3 151.6 150.8 150.1 149.3 148.5 147.7 147.0 146.2 145.4 144.6 143.7 142.9 142.1 141.2 140.4 139.5 138.7 137.8 136.9 136.0 135.1 134.1 133.2 132.3 131.3 130.3 129.4 128.4 127.4 126.3 125.3 Entropy [kJ/kg⋅K] Vapor hg Liquid sf 365.9 366.5 367.2 367.8 368.4 369.1 369.7 370.3 371.0 371.6 372.2 372.8 373.4 374.1 374.7 375.3 375.9 376.5 377.1 377.7 378.3 378.9 379.5 380.0 380.6 381.2 381.8 382.3 382.9 383.4 384.0 384.5 385.1 385.6 386.1 386.7 387.2 387.7 388.2 388.7 389.2 389.7 390.1 390.6 1.019 1.023 1.028 1.033 1.037 1.042 1.047 1.051 1.056 1.061 1.065 1.070 1.075 1.079 1.084 1.088 1.093 1.098 1.102 1.107 1.112 1.116 1.121 1.125 1.130 1.135 1.139 1.144 1.148 1.153 1.158 1.162 1.167 1.171 1.176 1.181 1.185 1.190 1.194 1.199 1.204 1.208 1.213 1.217 Vapor sg 1.599 1.599 1.599 1.599 1.599 1.600 1.600 1.600 1.600 1.601 1.601 1.601 1.601 1.602 1.602 1.602 1.602 1.603 1.603 1.603 1.603 1.604 1.604 1.604 1.605 1.605 1.605 1.605 1.606 1.606 1.606 1.606 1.607 1.607 1.607 1.607 1.608 1.608 1.608 1.608 1.608 1.608 1.609 1.609 Temp [°C] 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 1241.310 1271.543 1302.325 1333.663 1365.563 1398.032 1431.079 1464.709 1498.931 1533.751 1569.178 1605.219 1641.882 1679.174 1717.104 1755.680 1794.911 1834.805 1875.370 1916.617 1958.553 2001.189 2044.535 2088.600 2133.395 2178.931 2225.219 2272.271 2320.100 2368.717 2418.137 2468.375 2519.445 0.001001 0.001005 0.001010 0.001014 0.001019 0.001024 0.001029 0.001034 0.001040 0.001045 0.001051 0.001056 0.001062 0.001068 0.001075 0.001081 0.001088 0.001094 0.001101 0.001109 0.001116 0.001124 0.001132 0.001141 0.001149 0.001159 0.001168 0.001178 0.001189 0.001199 0.001211 0.001223 0.001236 0.0139 0.0135 0.0132 0.0128 0.0125 0.0121 0.0118 0.0115 0.0112 0.0109 0.0106 0.0103 0.0100 0.0098 0.0095 0.0092 0.0090 0.0087 0.0085 0.0082 0.0080 0.0078 0.0076 0.0073 0.0071 0.0069 0.0067 0.0065 0.0063 0.0061 0.0059 0.0057 0.0055 999.4 994.9 990.4 985.8 981.1 976.4 971.6 966.7 961.8 956.8 951.7 946.6 941.3 936.0 930.6 925.1 919.5 913.7 907.9 901.9 895.8 889.6 883.2 876.7 870.0 863.1 856.1 848.8 841.4 833.7 825.7 817.5 809.0 71.863 73.846 75.884 77.978 80.130 82.343 84.619 86.961 89.371 91.852 94.407 97.040 99.754 102.552 105.438 108.418 111.496 114.676 117.964 121.367 124.891 128.544 132.332 136.266 140.355 144.611 149.044 153.671 158.505 163.566 168.874 174.454 180.333 266.8 268.3 269.9 271.4 272.9 274.5 276.0 277.6 279.2 280.7 282.3 283.9 285.5 287.1 288.8 290.4 292.1 293.7 295.4 297.1 298.8 300.5 302.2 304.0 305.7 307.5 309.3 311.1 313.0 314.8 316.7 318.6 320.5 124.3 123.2 122.1 121.0 119.9 118.8 117.7 116.5 115.3 114.1 112.9 111.7 110.4 109.1 107.8 106.5 105.1 103.7 102.3 100.9 99.4 97.9 96.3 94.8 93.1 91.5 89.8 88.0 86.2 84.3 82.4 80.4 78.4 391.1 391.5 392.0 392.4 392.8 393.3 393.7 394.1 394.5 394.9 395.2 395.6 395.9 396.3 396.6 396.9 397.2 397.5 397.7 398.0 398.2 398.4 398.6 398.7 398.9 399.0 399.1 399.1 399.2 399.2 399.1 399.0 398.9 1.222 1.227 1.231 1.236 1.241 1.245 1.250 1.254 1.259 1.264 1.269 1.273 1.278 1.283 1.287 1.292 1.297 1.302 1.307 1.311 1.316 1.321 1.326 1.331 1.336 1.341 1.346 1.351 1.356 1.361 1.366 1.372 1.377 1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.610 1.610 1.610 1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.609 1.608 1.608 1.608 1.607 1.607 1.606 1.606 1.605 1.605 1.604 1.603 1.602 1.601 1.600 1.599 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 (Continued) 2-251 2-252 TABLE 2-132 Opteon™ YF (R-1234yf) (Continued ) Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg H = Enthalpy in kJ/kg S = Entropy in kJ/kg⋅K Saturation Properties in Light Gray Absolute Pressure, kPa V 90 100 101.325 110 −32.15°C −29.78°C −29.49°C −27.60°C S V S V H S V H Temp [°C] 0.1869 341.9 H 1.600 0.1693 343.5 H 1.599 0.1672 343.7 1.599 0.1548 344.9 1.598 S Temp [°C] −30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 0.1888 0.1933 0.1978 0.2022 0.2066 0.2110 0.2153 0.2197 0.2240 0.2283 0.2325 0.2368 0.2410 0.2453 0.2495 0.2537 0.2579 0.2621 0.2663 0.2705 0.2746 0.2788 0.2830 0.2871 0.2913 0.2954 0.2996 0.3037 0.3078 0.3120 343.6 347.7 351.8 355.9 360.1 364.3 368.6 372.9 377.3 381.7 386.1 390.6 395.2 399.8 404.4 409.1 413.8 418.5 423.3 428.2 433.0 438.0 442.9 447.9 453.0 458.1 463.2 468.4 473.6 478.8 1.607 1.623 1.640 1.656 1.672 1.688 1.704 1.719 1.735 1.750 1.766 1.781 1.796 1.811 1.826 1.841 1.855 1.870 1.884 1.899 1.913 1.927 1.942 1.956 1.970 1.984 1.997 2.011 2.025 2.038 0.1732 0.1773 0.1813 0.1853 0.1893 0.1932 0.1971 0.2010 0.2049 0.2088 0.2126 0.2165 0.2203 0.2241 0.2279 0.2317 0.2355 0.2393 0.2431 0.2468 0.2506 0.2544 0.2581 0.2619 0.2656 0.2693 0.2731 0.2768 0.2805 347.4 351.5 355.6 359.9 364.1 368.4 372.7 377.1 381.5 386.0 390.5 395.0 399.6 404.2 408.9 413.6 418.4 423.2 428.0 432.9 437.9 442.8 447.8 452.9 458.0 463.1 468.3 473.5 478.7 1.615 1.631 1.647 1.664 1.680 1.695 1.711 1.727 1.742 1.758 1.773 1.788 1.803 1.818 1.833 1.847 1.862 1.877 1.891 1.905 1.920 1.934 1.948 1.962 1.976 1.990 2.003 2.017 2.031 0.1708 0.1748 0.1788 0.1828 0.1867 0.1906 0.1945 0.1983 0.2022 0.2060 0.2098 0.2136 0.2174 0.2211 0.2249 0.2286 0.2324 0.2361 0.2399 0.2436 0.2473 0.2510 0.2547 0.2584 0.2621 0.2658 0.2695 0.2731 0.2768 347.3 351.5 355.6 359.8 364.1 368.4 372.7 377.1 381.5 385.9 390.4 395.0 399.6 404.2 408.9 413.6 418.4 423.2 428.0 432.9 437.8 442.8 447.8 452.9 458.0 463.1 468.3 473.5 478.7 1.614 1.630 1.646 1.663 1.679 1.694 1.710 1.726 1.741 1.757 1.772 1.787 1.802 1.817 1.832 1.846 1.861 1.876 1.890 1.904 1.919 1.933 1.947 1.961 1.975 1.989 2.002 2.016 2.030 0.1567 0.1604 0.1642 0.1678 0.1715 0.1751 0.1787 0.1822 0.1858 0.1893 0.1929 0.1964 0.1999 0.2034 0.2068 0.2103 0.2138 0.2172 0.2207 0.2241 0.2275 0.2310 0.2344 0.2378 0.2412 0.2446 0.2480 0.2514 0.2548 347.1 351.2 355.4 359.6 363.9 368.2 372.5 376.9 381.3 385.8 390.3 394.9 399.5 404.1 408.8 413.5 418.3 423.1 427.9 432.8 437.8 442.7 447.7 452.8 457.9 463.0 468.2 473.4 478.7 1.607 1.623 1.640 1.656 1.672 1.688 1.704 1.719 1.735 1.750 1.765 1.781 1.796 1.811 1.825 1.840 1.855 1.869 1.884 1.898 1.912 1.927 1.941 1.955 1.969 1.982 1.996 2.010 2.024 −30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 Absolute Pressure, kPa V 120 130 140 150 −25.56°C −23.65°C −21.85°C −20.15°C S V V H S V H Temp [°C] 0.1426 346.3 H 1.598 0.1322 347.6 H 1.598 S 0.1233 348.8 1.597 0.1155 349.9 1.597 S Temp [°C] −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 0.1430 0.1464 0.1499 0.1533 0.1566 0.1600 0.1633 0.1666 0.1699 0.1731 0.1764 0.1796 0.1828 0.1861 0.1893 0.1925 0.1956 0.1988 0.2020 0.2051 0.2083 0.2114 0.2146 0.2177 0.2209 0.2240 0.2271 0.2302 0.2334 0.2365 346.8 350.9 355.1 359.4 363.6 367.9 372.3 376.7 381.1 385.6 390.1 394.7 399.3 403.9 408.6 413.4 418.1 422.9 427.8 432.7 437.6 442.6 447.6 452.7 457.8 462.9 468.1 473.3 478.6 483.9 1.600 1.616 1.633 1.649 1.665 1.681 1.697 1.712 1.728 1.743 1.759 1.774 1.789 1.804 1.819 1.833 1.848 1.863 1.877 1.892 1.906 1.920 1.934 1.948 1.962 1.976 1.990 2.003 2.017 2.031 0.1346 0.1378 0.1409 0.1441 0.1472 0.1503 0.1533 0.1564 0.1594 0.1624 0.1655 0.1684 0.1714 0.1744 0.1773 0.1803 0.1832 0.1862 0.1891 0.1920 0.1949 0.1978 0.2007 0.2037 0.2065 0.2094 0.2123 0.2152 0.2181 350.7 354.9 359.1 363.4 367.7 372.1 376.5 380.9 385.4 390.0 394.5 399.1 403.8 408.5 413.2 418.0 422.8 427.7 432.6 437.5 442.5 447.5 452.6 457.7 462.8 468.0 473.2 478.5 483.8 1.610 1.626 1.642 1.659 1.675 1.690 1.706 1.722 1.737 1.752 1.768 1.783 1.798 1.813 1.827 1.842 1.857 1.871 1.885 1.900 1.914 1.928 1.942 1.956 1.970 1.984 1.997 2.011 2.025 0.1244 0.1274 0.1304 0.1333 0.1362 0.1391 0.1420 0.1448 0.1477 0.1505 0.1533 0.1561 0.1589 0.1616 0.1644 0.1671 0.1699 0.1726 0.1753 0.1781 0.1808 0.1835 0.1862 0.1889 0.1916 0.1943 0.1970 0.1997 0.2023 350.4 354.6 358.9 363.2 367.5 371.9 376.3 380.8 385.3 389.8 394.4 399.0 403.6 408.3 413.1 417.9 422.7 427.6 432.5 437.4 442.4 447.4 452.5 457.6 462.7 467.9 473.1 478.4 483.7 1.603 1.620 1.636 1.653 1.669 1.684 1.700 1.716 1.731 1.747 1.762 1.777 1.792 1.807 1.822 1.836 1.851 1.865 1.880 1.894 1.908 1.922 1.937 1.950 1.964 1.978 1.992 2.005 2.019 0.1156 0.1184 0.1212 0.1240 0.1267 0.1294 0.1321 0.1348 0.1375 0.1401 0.1428 0.1454 0.1480 0.1506 0.1532 0.1557 0.1583 0.1609 0.1634 0.1660 0.1685 0.1711 0.1736 0.1761 0.1786 0.1812 0.1837 0.1862 0.1887 350.1 354.3 358.6 362.9 367.3 371.7 376.1 380.6 385.1 389.6 394.2 398.8 403.5 408.2 413.0 417.7 422.6 427.4 432.4 437.3 442.3 447.3 452.4 457.5 462.6 467.8 473.1 478.3 483.6 1.598 1.614 1.631 1.647 1.663 1.679 1.695 1.710 1.726 1.741 1.756 1.772 1.787 1.801 1.816 1.831 1.846 1.860 1.875 1.889 1.903 1.917 1.931 1.945 1.959 1.973 1.987 2.000 2.014 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 (Continued) 2-253 2-254 TABLE 2-132 Opteon™ YF (R-1234yf) (Continued ) Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg H = Enthalpy in kJ/kg S = Entropy in kJ/kg⋅K Saturation Properties in Light Gray Absolute Pressure, kPa V 160 170 180 190 −18.54°C −17.00°C −15.53°C −14.12°C H S V H S V H S V H S Temp [°C] 0.1086 351.0 1.597 0.1026 352.1 1.597 0.0972 353.0 1.597 0.0923 354.0 1.597 Temp [°C] −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 0.1105 0.1132 0.1158 0.1184 0.1210 0.1235 0.1261 0.1286 0.1311 0.1335 0.1360 0.1385 0.1409 0.1433 0.1458 0.1482 0.1506 0.1530 0.1554 0.1578 0.1602 0.1626 0.1649 0.1673 0.1697 0.1720 0.1744 0.1767 0.1791 0.1815 354.1 358.4 362.7 367.1 371.5 375.9 380.4 384.9 389.4 394.0 398.7 403.3 408.1 412.8 417.6 422.4 427.3 432.2 437.2 442.2 447.2 452.3 457.4 462.6 467.7 473.0 478.2 483.5 488.9 494.2 1.609 1.625 1.641 1.658 1.674 1.689 1.705 1.721 1.736 1.751 1.766 1.782 1.796 1.811 1.826 1.841 1.855 1.870 1.884 1.898 1.912 1.926 1.940 1.954 1.968 1.982 1.995 2.009 2.023 2.036 0.1036 0.1061 0.1086 0.1111 0.1135 0.1159 0.1183 0.1207 0.1231 0.1254 0.1277 0.1301 0.1324 0.1347 0.1370 0.1393 0.1415 0.1438 0.1461 0.1483 0.1506 0.1528 0.1551 0.1573 0.1595 0.1618 0.1640 0.1662 0.1684 0.1706 353.8 358.1 362.4 366.8 371.2 375.7 380.2 384.7 389.3 393.9 398.5 403.2 407.9 412.7 417.5 422.3 427.2 432.1 437.1 442.1 447.1 452.2 457.3 462.5 467.6 472.9 478.1 483.4 488.8 494.2 1.603 1.620 1.636 1.653 1.669 1.684 1.700 1.716 1.731 1.747 1.762 1.777 1.792 1.807 1.821 1.836 1.850 1.865 1.879 1.894 1.908 1.922 1.936 1.950 1.963 1.977 1.991 2.004 2.018 2.031 0.0974 0.0998 0.1022 0.1045 0.1069 0.1092 0.1114 0.1137 0.1160 0.1182 0.1204 0.1226 0.1248 0.1270 0.1292 0.1313 0.1335 0.1356 0.1378 0.1399 0.1420 0.1442 0.1463 0.1484 0.1505 0.1526 0.1547 0.1568 0.1589 0.1610 353.5 357.8 362.2 366.6 371.0 375.5 380.0 384.5 389.1 393.7 398.4 403.0 407.8 412.5 417.3 422.2 427.1 432.0 437.0 442.0 447.0 452.1 457.2 462.4 467.6 472.8 478.1 483.4 488.7 494.1 1.598 1.615 1.632 1.648 1.664 1.680 1.696 1.711 1.727 1.742 1.757 1.772 1.787 1.802 1.817 1.832 1.846 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.959 1.973 1.987 2.000 2.014 2.027 0.0942 0.0965 0.0987 0.1009 0.1031 0.1053 0.1074 0.1096 0.1117 0.1138 0.1159 0.1180 0.1201 0.1222 0.1242 0.1263 0.1283 0.1303 0.1324 0.1344 0.1364 0.1384 0.1405 0.1425 0.1445 0.1465 0.1485 0.1505 0.1524 357.6 362.0 366.4 370.8 375.3 379.8 384.3 388.9 393.5 398.2 402.9 407.6 412.4 417.2 422.1 427.0 431.9 436.9 441.9 446.9 452.0 457.1 462.3 467.5 472.7 478.0 483.3 488.6 494.0 1.610 1.627 1.643 1.659 1.675 1.691 1.707 1.722 1.738 1.753 1.768 1.783 1.798 1.813 1.827 1.842 1.856 1.871 1.885 1.899 1.913 1.927 1.941 1.955 1.969 1.982 1.996 2.010 2.023 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Absolute Pressure, kPa 200 210 −12.77°C V H 220 −11.47°C S V H 230 −10.22°C −9.01°C S V H S V H S Temp [°C] 0.0879 354.9 1.597 0.0839 355.7 1.597 0.0802 356.6 1.597 0.0769 357.4 1.597 Temp [°C] −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 0.0891 0.0913 0.0934 0.0956 0.0977 0.0997 0.1018 0.1039 0.1059 0.1079 0.1099 0.1119 0.1139 0.1159 0.1178 0.1198 0.1217 0.1237 0.1256 0.1275 0.1295 0.1314 0.1333 0.1352 0.1371 0.1390 0.1409 0.1428 0.1447 0.1466 357.3 361.7 366.1 370.6 375.1 379.6 384.2 388.7 393.4 398.0 402.7 407.5 412.3 417.1 421.9 426.8 431.8 436.7 441.7 446.8 451.9 457.0 462.2 467.4 472.6 477.9 483.2 488.5 493.9 499.3 1.606 1.623 1.639 1.655 1.671 1.687 1.703 1.718 1.733 1.749 1.764 1.779 1.794 1.809 1.823 1.838 1.852 1.867 1.881 1.895 1.909 1.923 1.937 1.951 1.965 1.979 1.992 2.006 2.019 2.032 0.0845 0.0866 0.0887 0.0907 0.0927 0.0947 0.0967 0.0987 0.1006 0.1025 0.1045 0.1064 0.1083 0.1101 0.1120 0.1139 0.1158 0.1176 0.1195 0.1213 0.1231 0.1250 0.1268 0.1286 0.1305 0.1323 0.1341 0.1359 0.1377 0.1395 357.0 361.5 365.9 370.4 374.9 379.4 384.0 388.6 393.2 397.9 402.6 407.3 412.1 417.0 421.8 426.7 431.6 436.6 441.6 446.7 451.8 456.9 462.1 467.3 472.5 477.8 483.1 488.5 493.8 499.3 1.602 1.618 1.635 1.651 1.667 1.683 1.699 1.714 1.730 1.745 1.760 1.775 1.790 1.805 1.819 1.834 1.849 1.863 1.877 1.891 1.906 1.920 1.934 1.947 1.961 1.975 1.988 2.002 2.015 2.029 0.0803 0.0824 0.0843 0.0863 0.0883 0.0902 0.0921 0.0940 0.0958 0.0977 0.0995 0.1013 0.1032 0.1050 0.1068 0.1086 0.1103 0.1121 0.1139 0.1157 0.1174 0.1192 0.1209 0.1227 0.1244 0.1261 0.1279 0.1296 0.1313 0.1331 356.8 361.2 365.7 370.1 374.7 379.2 383.8 388.4 393.0 397.7 402.4 407.2 412.0 416.8 421.7 426.6 431.5 436.5 441.5 446.6 451.7 456.8 462.0 467.2 472.4 477.7 483.0 488.4 493.8 499.2 1.597 1.614 1.631 1.647 1.663 1.679 1.695 1.710 1.726 1.741 1.756 1.771 1.786 1.801 1.816 1.830 1.845 1.859 1.874 1.888 1.902 1.916 1.930 1.944 1.958 1.971 1.985 1.998 2.012 2.025 0.0785 0.0804 0.0823 0.0842 0.0860 0.0878 0.0896 0.0914 0.0932 0.0950 0.0967 0.0985 0.1002 0.1020 0.1037 0.1054 0.1071 0.1088 0.1105 0.1122 0.1139 0.1155 0.1172 0.1189 0.1206 0.1222 0.1239 0.1255 0.1272 360.9 365.4 369.9 374.4 379.0 383.6 388.2 392.9 397.6 402.3 407.0 411.8 416.7 421.6 426.5 431.4 436.4 441.4 446.5 451.6 456.7 461.9 467.1 472.3 477.6 482.9 488.3 493.7 499.1 1.610 1.627 1.643 1.659 1.675 1.691 1.707 1.722 1.737 1.753 1.768 1.783 1.798 1.812 1.827 1.841 1.856 1.870 1.884 1.899 1.913 1.927 1.940 1.954 1.968 1.981 1.995 2.008 2.022 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 (Continued) 2-255 2-256 TABLE 2-132 Opteon™ YF (R-1234yf) (Continued ) Superheated Vapor—Constant Pressure Tables V = Volume in m3/kg H = Enthalpy in kJ/kg S = Entropy in kJ/kg⋅K Saturation Properties in Light Gray Absolute Pressure, kPa V 240 250 260 270 −7.84°C −6.70°C −5.60°C −4.54°C S V H S H S Temp [°C] 0.0738 358.2 H 1.597 S 0.0710 V 358.9 H 1.597 0.0684 359.6 1.597 0.0659 V 360.3 1.597 Temp [°C] −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 0.0749 0.0768 0.0786 0.0804 0.0822 0.0840 0.0857 0.0874 0.0891 0.0908 0.0925 0.0942 0.0959 0.0976 0.0992 0.1009 0.1025 0.1041 0.1058 0.1074 0.1090 0.1106 0.1122 0.1138 0.1154 0.1170 0.1186 0.1202 0.1218 0.1234 360.7 365.2 369.7 374.2 378.8 383.4 388.0 392.7 397.4 402.1 406.9 411.7 416.5 421.4 426.3 431.3 436.3 441.3 446.4 451.5 456.6 461.8 467.0 472.3 477.5 482.9 488.2 493.6 499.0 504.5 1.606 1.623 1.639 1.656 1.672 1.687 1.703 1.719 1.734 1.749 1.764 1.779 1.794 1.809 1.824 1.838 1.852 1.867 1.881 1.895 1.909 1.923 1.937 1.951 1.965 1.978 1.992 2.005 2.019 2.032 0.0716 0.0734 0.0752 0.0769 0.0787 0.0804 0.0821 0.0837 0.0854 0.0870 0.0887 0.0903 0.0919 0.0935 0.0951 0.0967 0.0983 0.0998 0.1014 0.1030 0.1045 0.1061 0.1076 0.1092 0.1107 0.1122 0.1138 0.1153 0.1168 0.1184 360.4 364.9 369.5 374.0 378.6 383.2 387.9 392.5 397.2 402.0 406.8 411.6 416.4 421.3 426.2 431.2 436.2 441.2 446.3 451.4 456.5 461.7 466.9 472.2 477.4 482.8 488.1 493.5 499.0 504.4 1.603 1.619 1.636 1.652 1.668 1.684 1.700 1.715 1.731 1.746 1.761 1.776 1.791 1.806 1.820 1.835 1.849 1.864 1.878 1.892 1.906 1.920 1.934 1.948 1.961 1.975 1.989 2.002 2.015 2.029 0.0686 0.0703 0.0721 0.0738 0.0754 0.0771 0.0787 0.0803 0.0819 0.0835 0.0851 0.0867 0.0882 0.0898 0.0913 0.0928 0.0944 0.0959 0.0974 0.0989 0.1004 0.1019 0.1034 0.1049 0.1064 0.1078 0.1093 0.1108 0.1123 0.1137 360.2 364.7 369.2 373.8 378.4 383.0 387.7 392.4 397.1 401.8 406.6 411.4 416.3 421.2 426.1 431.1 436.1 441.1 446.2 451.3 456.4 461.6 466.8 472.1 477.4 482.7 488.0 493.4 498.9 504.3 1.599 1.616 1.632 1.649 1.665 1.681 1.696 1.712 1.727 1.743 1.758 1.773 1.788 1.802 1.817 1.832 1.846 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.958 1.972 1.986 1.999 2.012 2.026 0.0675 0.0691 0.0708 0.0724 0.0740 0.0756 0.0772 0.0787 0.0803 0.0818 0.0833 0.0848 0.0863 0.0878 0.0893 0.0907 0.0922 0.0937 0.0951 0.0966 0.0980 0.0995 0.1009 0.1023 0.1038 0.1052 0.1066 0.1080 0.1094 364.4 369.0 373.6 378.2 382.8 387.5 392.2 396.9 401.7 406.5 411.3 416.1 421.0 426.0 430.9 435.9 441.0 446.1 451.2 456.3 461.5 466.7 472.0 477.3 482.6 488.0 493.4 498.8 504.3 1.612 1.629 1.645 1.661 1.677 1.693 1.709 1.724 1.739 1.755 1.770 1.785 1.799 1.814 1.829 1.843 1.858 1.872 1.886 1.900 1.914 1.928 1.942 1.956 1.969 1.983 1.996 2.010 2.023 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 Absolute Pressure, kPa V 280 290 300 310 −3.50°C −2.49°C −1.51°C −0.55°C S V H S H S Temp [°C] 0.0637 361.0 H 1.597 S 0.0615 V 361.7 H 1.597 0.0596 362.3 1.598 0.0577 V 362.9 1.598 Temp [°C] 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 0.0648 0.0664 0.0680 0.0696 0.0712 0.0727 0.0742 0.0757 0.0772 0.0787 0.0802 0.0816 0.0831 0.0845 0.0860 0.0874 0.0888 0.0902 0.0916 0.0930 0.0944 0.0958 0.0972 0.0986 0.1000 0.1013 0.1027 0.1041 0.1055 0.1068 364.2 368.8 373.4 378.0 382.6 387.3 392.0 396.7 401.5 406.3 411.1 416.0 420.9 425.8 430.8 435.8 440.9 445.9 451.1 456.2 461.4 466.6 471.9 477.2 482.5 487.9 493.3 498.7 504.2 509.7 1.609 1.626 1.642 1.658 1.674 1.690 1.706 1.721 1.736 1.752 1.767 1.782 1.797 1.811 1.826 1.840 1.855 1.869 1.883 1.897 1.911 1.925 1.939 1.953 1.966 1.980 1.993 2.007 2.020 2.033 0.0623 0.0639 0.0655 0.0670 0.0685 0.0700 0.0715 0.0730 0.0744 0.0758 0.0773 0.0787 0.0801 0.0815 0.0829 0.0842 0.0856 0.0870 0.0884 0.0897 0.0911 0.0924 0.0938 0.0951 0.0964 0.0978 0.0991 0.1004 0.1017 0.1031 363.9 368.5 373.2 377.8 382.4 387.1 391.8 396.6 401.4 406.2 411.0 415.9 420.8 425.7 430.7 435.7 440.8 445.8 451.0 456.1 461.3 466.5 471.8 477.1 482.4 487.8 493.2 498.6 504.1 509.6 1.606 1.622 1.639 1.655 1.671 1.687 1.703 1.718 1.734 1.749 1.764 1.779 1.794 1.808 1.823 1.838 1.852 1.866 1.880 1.894 1.909 1.922 1.936 1.950 1.964 1.977 1.991 2.004 2.017 2.031 0.0600 0.0616 0.0631 0.0646 0.0661 0.0675 0.0690 0.0704 0.0718 0.0732 0.0746 0.0759 0.0773 0.0786 0.0800 0.0813 0.0827 0.0840 0.0853 0.0866 0.0879 0.0892 0.0905 0.0918 0.0931 0.0944 0.0957 0.0970 0.0983 0.0996 363.7 368.3 372.9 377.6 382.2 386.9 391.7 396.4 401.2 406.0 410.9 415.7 420.6 425.6 430.6 435.6 440.6 445.7 450.9 456.0 461.2 466.4 471.7 477.0 482.3 487.7 493.1 498.6 504.0 509.6 1.603 1.619 1.636 1.652 1.668 1.684 1.700 1.715 1.731 1.746 1.761 1.776 1.791 1.806 1.820 1.835 1.849 1.864 1.878 1.892 1.906 1.920 1.934 1.947 1.961 1.975 1.988 2.002 2.015 2.028 0.0579 0.0594 0.0609 0.0623 0.0638 0.0652 0.0666 0.0680 0.0693 0.0707 0.0720 0.0733 0.0747 0.0760 0.0773 0.0786 0.0799 0.0812 0.0825 0.0837 0.0850 0.0863 0.0875 0.0888 0.0901 0.0913 0.0926 0.0938 0.0950 0.0963 363.4 368.1 372.7 377.4 382.0 386.8 391.5 396.2 401.0 405.9 410.7 415.6 420.5 425.5 430.5 435.5 440.5 445.6 450.7 455.9 461.1 466.3 471.6 476.9 482.3 487.6 493.0 498.5 504.0 509.5 1.600 1.616 1.633 1.649 1.665 1.681 1.697 1.713 1.728 1.743 1.758 1.773 1.788 1.803 1.818 1.832 1.847 1.861 1.875 1.889 1.903 1.917 1.931 1.945 1.958 1.972 1.986 1.999 2.012 2.026 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 2-257 2-258 PHYSICAL AnD CHEMICAL DATA FIG. 2-16 Pressure-enthalpy diagram for Refrigerant 1234yf. Properties computed with the NIST REFPROP Database, Version 7.0 (Lemmon, E. W., M.O. McLinden, and M. L. Huber, 2002, NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, Standard Reference Data Program, National Institute of Standards and Technology). Provided by Chemours. THERMODYnAMIC PROPERTIES TABLE 2-133 Thermophysical Properties of Saturated Seawater Temp., °C Pressure, bar v, (m3/kg)103 cp, kJ/(kg⋅K) µ, Ns/m2 k, W/(m⋅K) NPr 105κ, 1/bar 0 1 2 3 4 0.005993 0.006438 0.006916 0.007427 0.007970 1.000158 1.000099 1.000057 1.000033 1.000025 4.000 4.000 4.000 4.000 4.001 0.001884 0.001827 0.001772 0.001720 0.001669 0.560 0.563 0.565 0.567 0.569 13.46 12.98 12.55 12.13 11.74 5.06 5.02 4.98 4.95 4.92 5 6 7 8 9 0.008548 0.009163 0.009816 0.010511 0.011248 1.000033 1.000057 1.000096 1.000149 1.000261 4.001 4.001 4.002 4.002 4.002 0.001620 0.001574 0.001529 0.001486 0.001445 0.571 0.574 0.576 0.578 0.580 11.35 10.97 10.62 10.29 9.97 4.89 4.86 4.83 4.80 4.78 10 11 12 13 14 0.01203 0.01286 0.01374 0.01467 0.01566 1.000298 1.000392 1.000500 1.000620 1.000727 4.003 4.003 4.003 4.004 4.004 0.001405 0.001367 0.001330 0.001294 0.001259 0.582 0.584 0.586 0.588 0.590 9.70 9.37 9.09 8.81 8.54 4.76 4.74 4.72 4.70 4.68 15 16 17 18 19 0.01671 0.01781 0.01898 0.02022 0.02153 1.000899 1.001055 1.001224 1.001404 1.001595 4.005 4.005 4.006 4.006 4.007 0.001226 0.001195 0.001165 0.001136 0.001107 0.592 0.594 0.595 0.597 0.599 8.29 8.06 7.82 7.62 7.41 4.66 4.65 4.63 4.62 4.60 20 21 22 23 24 0.02291 0.02437 0.02591 0.02753 0.02924 1.001796 1.002009 1.002232 1.002465 1.002708 4.007 4.007 4.008 4.008 4.009 0.001080 0.001054 0.001029 0.001005 0.000981 0.600 0.602 0.604 0.605 0.607 7.21 7.02 6.82 6.66 6.48 4.59 4.57 4.56 4.55 4.54 25 26 27 28 29 0.03104 0.03294 0.03494 0.03705 0.03926 1.002961 1.003224 1.003496 1.003778 1.004069 4.009 4.009 4.010 4.010 4.011 0.000958 0.000936 0.000915 0.000895 0.000875 0.608 0.609 0.611 0.612 0.614 6.31 6.16 6.01 5.86 5.72 4.53 4.52 4.51 4.50 4.49 30 0.04159 1.004369 4.011 0.000855 0.615 5.58 4.48 κ = (−1/V)(∂v/∂p)T ⋅ 105. Thus, at 0°C, the compressibility is 5.06 × 10−5/bar. For further information see, for instance, Bromley, LeR. A., J. Chem. Eng. Data, 12, 2 (1967): 202–206; 13, 1 (1968): 60–62 and 13, 3: 399–402; 15, 2 (1970): 246–253; and A.I.Ch.E.J., 20, 2 (1974): 326–335. Thermal conductivity data sources include Castelli, V. J., E. M. Stanley, et al., Deep Sea Res., 211 (1974): 311–318; Levy, F. L., Int. J. Refrig., 5, 3 (1982): 155–159. For velocity of sound, see, for instance, U.S. Naval Oceanographic Office SP 58, 1962 (50 pp.). More recent information is contained in UNESCO technical papers. See Marine Science No. 38, 1981 (6 pp.) and No. 44, 1983 (53 pp.). For sea ice properties, see Fukusako, S., Int. J. Thermophys., 11, 2 (1990): 353–372. 2-259 FIG. 2-17 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states: enthalpy of liquid water at 32°F and vapor pressure is zero; partial molal enthalpy of infinitely dilute NaOH solution at 64°F and 1 atm is zero. [W.L. McCabe, Trans. Am. Inst. Chem. Eng., 31: 129 (1935).] FIG. 2-18 Enthalpy-concentration diagram for aqueous sulfuric acid at 1 atm. Reference states: enthalpies of pure-liquid components at 32°F and vapor pressures are zero. Note: It should be observed that the weight basis includes the vapor, which is particularly important in the two-phase region. The upper ends of the tie lines in this region are assumed to be pure water. (O.A. Hougen and K.M. Watson, Chemical Process Principles, part I, Wiley, New York, 1943.) 2-260 THERMODYnAMIC PROPERTIES TABLE 2-134 Temp., °F Saturated Solid/Vapor Water* Volume, ft3/lb Enthalpy, Btu/lb Entropy, Btu/(lb)(°F) Pressure, lb/in2 abs. Solid Vapor Solid Vapor Solid Vapor −160 −150 −140 −130 −120 4.949.−8 1.620.−7 4.928.−7 1.403.−6 3.757.−6 0.01722 0.01723 0.01724 0.01725 0.01726 3.607.+9 1.139.+9 3.864.+8 1.400.+8 5.386.+7 −222.05 −218.82 −215.49 −212.08 −208.58 990.38 994.80 999.21 1003.63 1008.05 −0.4907 −0.4801 −0.4695 −0.4590 −0.4485 3.5549 3.4387 3.3301 3.2284 3.1330 −110 −100 −90 −80 −70 9.517.−6 2.291.−5 5.260.−5 1.157.−4 2.443.−4 0.01728 0.01729 0.01730 0.01731 0.01732 2.189.+7 9.352.+6 4.186.+6 1.955.+6 9.501.+5 −204.98 −201.28 −197.49 −193.60 −189.61 1012.47 1016.89 1021.31 1025.73 1030.15 −0.4381 −0.4277 −0.4173 −0.4069 −0.3965 3.0434 2.9591 2.8796 2.8045 2.7336 −60 −50 −45 −40 −35 4.972.−4 9.776.−4 1.354.−3 1.861.−3 2.540.−3 0.01734 0.01735 0.01736 0.01737 0.01737 4.788.+5 2.496.+5 1.824.+5 1.343.+5 9.961.+4 −185.52 −181.34 −179.21 −177.06 −174.88 1034.58 1039.00 1041.21 1043.42 1045.63 −0.3862 −0.3758 −0.3707 −0.3655 −0.3604 2.6664 2.6028 2.5723 2.5425 2.5135 −30 −25 −20 −15 −10 3.440.−3 4.627.−3 6.181.−3 8.204.−3 1.082.−2 0.01738 0.01739 0.01739 0.01740 0.01741 7.441.+4 5.596.+4 4.237.+4 3.228.+4 2.475.+4 −172.68 −170.46 −168.21 −165.94 −163.65 1047.84 1050.05 1052.26 1054.47 1056.67 −0.3552 −0.3501 −0.3449 −0.3398 −0.3347 2.4853 2.4577 2.4308 2.4046 2.3791 −5 0 5 10 15 1.419.−2 1.849.−2 2.396.−2 3.087.−2 3.957.−2 0.01741 0.01742 0.01743 0.01744 0.01744 1.909.+4 1.481.+4 1.155.+4 9.060.+3 7.144.+3 −161.33 −158.98 −156.61 −154.22 −151.80 1058.88 1061.09 1063.29 1065.50 1067.70 −0.3295 −0.3244 −0.3193 −0.3142 −0.3090 2.3541 2.3297 2.3039 2.2827 2.2600 16 18 20 22 24 4.156.−2 4.581.−2 5.045.−2 5.552.−2 6.105.−2 0.01745 0.01745 0.01745 0.01746 0.01746 6.817.+3 6.210.+3 5.662.+3 5.166.+3 4.717.+3 −151.32 −150.34 −149.36 −148.38 −147.39 1068.14 1069.02 1069.90 1070.38 1071.66 −0.3080 −0.3060 −0.3039 −0.3019 −0.2998 2.2555 2.2466 2.2378 2.2291 2.2205 26 28 30 31 32 6.708.−2 7.365.−2 8.080.−2 8.461.−2 8.858.−2 0.01746 0.01746 0.01747 0.01747 0.01747 4.311.+3 3.943.+3 3.608.+3 3.453.+3 3.305.+3 −146.40 −145.40 −144.40 −143.90 −143.40 1072.53 1073.41 1074.29 1074.73 1075.16 −0.2978 −0.2957 −0.2937 −0.2927 −0.2916 2.2119 2.2034 2.1950 2.1908 2.1867 ∗Condensed from Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1967 and 1972. Reproduced by permission. The validity of many standard reference tables has been critically reviewed by Jancso, Pupezin, and van Hook, J. Phys. Chem., 74 (1970):2984. Current information on the properties of solid, vapor, and liquid water properties can be found at http://www.iapws.org. The notation 4.949.−8, 3.607.+9, etc., means 4.949 × 10−8, 3.607 × 109, etc. 2-261 2-262 TABLE 2-135 Thermodynamic Properties of Water Temperature K Pressure MPa Density mol/dm3 273.16 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 647.1 0.000612 0.000992 0.001920 0.003537 0.006231 0.010546 0.017213 0.027188 0.041682 0.062194 0.090535 0.12885 0.17964 0.24577 0.33045 0.43730 0.57026 0.73367 0.9322 1.1709 1.4551 1.7905 2.1831 2.6392 3.1655 3.7690 4.4569 5.2369 6.1172 7.1062 8.2132 9.448 10.821 12.345 14.033 15.901 17.969 20.265 22.064 55.497 55.501 55.440 55.315 55.139 54.919 54.662 54.371 54.049 53.698 53.321 52.918 52.490 52.038 51.563 51.064 50.541 49.994 49.421 48.824 48.199 47.545 46.861 46.145 45.393 44.603 43.770 42.889 41.954 40.956 39.885 38.725 37.456 36.048 34.451 32.577 30.210 26.729 17.874 273.16 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 0.000612 0.000992 0.001920 0.003537 0.006231 0.010546 0.017213 0.027188 0.041682 0.062194 0.090535 0.12885 0.17964 0.24577 0.33045 0.43730 0.57026 0.73367 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) 0 0.51875 1.2742 2.0278 2.7808 3.5339 4.2873 5.0414 5.7964 6.5526 7.3104 8.0701 8.8320 9.5966 10.364 11.136 11.911 12.692 13.477 14.269 15.068 15.875 16.690 17.515 18.352 19.200 20.064 20.943 21.841 22.762 23.709 24.688 25.707 26.777 27.917 29.160 30.585 32.422 36.314 1.1E-05 0.51877 1.2742 2.0279 2.7810 3.5340 4.2876 5.0419 5.7972 6.5538 7.3121 8.0725 8.8354 9.6013 10.371 11.144 11.923 12.706 13.496 14.293 15.098 15.913 16.737 17.573 18.421 19.285 20.165 21.065 21.987 22.935 23.915 24.932 25.996 27.119 28.324 29.648 31.180 33.180 37.548 0 0.001876 0.004527 0.007082 0.009551 0.011941 0.014260 0.016511 0.018700 0.020830 0.022906 0.024932 0.026911 0.028847 0.030743 0.032602 0.034427 0.036222 0.037988 0.039729 0.041448 0.043147 0.044830 0.046498 0.048156 0.049807 0.051454 0.053102 0.054756 0.056422 0.058106 0.059821 0.061577 0.063396 0.065309 0.067371 0.069715 0.072737 0.079393 42.785 42.954 43.201 43.446 43.690 43.931 44.169 44.404 44.634 44.860 45.079 45.291 45.496 45.691 45.876 46.050 46.211 46.359 45.055 45.280 45.609 45.936 46.261 46.582 46.900 47.212 47.519 47.819 48.111 48.393 48.665 48.924 49.170 49.400 49.613 49.807 0.16494 0.16174 0.15741 0.15344 0.14981 0.14647 0.14339 0.14054 0.13791 0.13546 0.13317 0.13104 0.12904 0.12715 0.12537 0.12369 0.12208 0.12054 Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s 0.075978 0.075669 0.075095 0.074412 0.073645 0.072811 0.071927 0.071008 0.070070 0.069124 0.068180 0.067247 0.066331 0.065438 0.064570 0.063731 0.062920 0.062140 0.061390 0.060671 0.059984 0.059327 0.058702 0.058109 0.057548 0.057023 0.056536 0.056089 0.055690 0.055347 0.055071 0.054881 0.054808 0.054902 0.055258 0.056100 0.058152 0.064521 0.076023 0.075688 0.075429 0.075320 0.075294 0.075317 0.075373 0.075456 0.075567 0.075708 0.075883 0.076098 0.076357 0.076664 0.077026 0.077447 0.077934 0.078495 0.079136 0.079869 0.080706 0.081662 0.082757 0.084013 0.085464 0.087149 0.089124 0.091464 0.094275 0.097713 0.10201 0.10754 0.11491 0.12526 0.14100 0.16852 0.23108 0.46736 1402.3 1434.1 1472.1 1501.4 1523.2 1538.7 1548.7 1553.9 1554.8 1552.0 1545.8 1536.5 1524.3 1509.5 1492.2 1472.5 1450.6 1426.5 1400.4 1372.2 1342.0 1309.8 1275.7 1239.6 1201.5 1161.3 1119.1 1074.6 1027.9 978.54 926.44 871.23 812.49 749.57 681.27 604.73 513.19 400.66 0 −0.24142 −0.23515 −0.22720 −0.22024 −0.21393 −0.20804 −0.20241 −0.19690 −0.19140 −0.18581 −0.18005 −0.17404 −0.16769 −0.16092 −0.15366 −0.14581 −0.13728 −0.12794 −0.11767 −0.10631 −0.09369 −0.07959 −0.06372 −0.04578 −0.02534 −0.00189 0.025264 0.057002 0.094527 0.13949 0.19425 0.26220 0.34857 0.46172 0.61660 0.84473 1.2251 1.9542 3.7410 561.04 574.04 592.73 610.28 626.05 639.71 651.18 660.55 668.00 673.76 678.02 681.00 682.83 683.64 683.52 682.53 680.70 678.05 674.59 670.28 665.12 659.07 652.06 644.05 634.95 624.68 613.15 600.26 585.95 570.21 553.08 534.74 515.43 495.46 475.03 454.10 432.51 414.93 1791.2 1433.7 1084.0 853.84 693.54 577.02 489.49 421.97 368.77 326.10 291.36 262.69 238.77 218.60 201.43 186.68 173.91 162.77 152.98 144.31 136.58 129.64 123.37 117.66 112.42 107.57 103.05 98.792 94.746 90.857 87.074 83.342 79.600 75.773 71.759 67.382 62.244 55.247 0.025553 0.025657 0.025816 0.025982 0.026158 0.026350 0.026568 0.026821 0.027118 0.027469 0.027883 0.028372 0.028944 0.029608 0.030369 0.031230 0.032187 0.033234 0.033947 0.034073 0.034270 0.034483 0.034716 0.034980 0.035287 0.035653 0.036091 0.036617 0.037249 0.038004 0.038903 0.039963 0.041203 0.042634 0.044269 0.046114 409.00 413.92 420.99 427.89 434.63 441.18 447.54 453.68 459.58 465.22 470.57 475.61 480.32 484.67 488.65 492.22 495.39 498.12 Cv kJ/(mol⋅K) Saturated Properties 0.000269 0.000426 0.000797 0.001420 0.002424 0.003978 0.006304 0.009681 0.014448 0.021014 0.029859 0.041537 0.056683 0.076014 0.10034 0.13055 0.16765 0.21276 0.018019 0.018018 0.018038 0.018078 0.018136 0.018209 0.018294 0.018392 0.018502 0.018623 0.018754 0.018897 0.019051 0.019217 0.019394 0.019583 0.019786 0.020003 0.020234 0.020482 0.020748 0.021033 0.021340 0.021671 0.022030 0.022420 0.022847 0.023316 0.023836 0.024417 0.025072 0.025823 0.026698 0.027741 0.029026 0.030697 0.033101 0.037413 0.055948 3711.0 2345.4 1254.3 704.01 412.60 251.39 158.62 103.30 69.213 47.586 33.491 24.075 17.642 13.156 9.9666 7.6601 5.9649 4.7002 592.65 477.26 351.65 264.35 203.74 161.25 130.92 108.77 92.178 79.440 69.427 61.373 54.749 49.181 44.405 40.237 36.550 33.259 17.071 17.442 18.031 18.673 19.369 20.117 20.922 21.784 22.707 23.695 24.750 25.875 27.074 28.347 29.699 31.128 32.638 34.230 9.2163 9.3815 9.6414 9.9195 10.213 10.518 10.833 11.157 11.487 11.823 12.162 12.504 12.848 13.192 13.538 13.883 14.228 14.573 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 647.1 0.93220 1.1709 1.4551 1.7905 2.1831 2.6392 3.1655 3.7690 4.4569 5.2369 6.1172 7.1062 8.2132 9.4480 10.821 12.345 14.033 15.901 17.969 20.265 22.064 0.26711 0.33209 0.40925 0.50035 0.60738 0.73265 0.87884 1.0491 1.2473 1.4780 1.7471 2.0620 2.4325 2.8720 3.3994 4.0434 4.8497 5.9009 7.3737 9.8331 17.874 3.7438 3.0113 2.4435 1.9986 1.6464 1.3649 1.1379 0.95318 0.80174 0.67659 0.57238 0.48497 0.41110 0.34819 0.29417 0.24732 0.20620 0.16946 0.13562 0.10170 0.055948 55.317 53.212 0.018078 0.018793 46.492 46.609 46.708 46.788 46.848 46.885 46.898 46.883 46.838 46.758 46.641 46.478 46.264 45.988 45.636 45.188 44.613 43.855 42.801 41.095 36.314 49.982 50.134 50.263 50.367 50.442 50.487 50.500 50.475 50.411 50.302 50.142 49.925 49.641 49.278 48.819 48.242 47.506 46.550 45.238 43.156 37.548 0.11907 0.11764 0.11627 0.11493 0.11362 0.11233 0.11105 0.10979 0.10852 0.10724 0.10595 0.10462 0.10324 0.10180 0.10026 0.098600 0.096755 0.094631 0.092029 0.088324 0.079393 0.034362 0.035561 0.036821 0.038137 0.039503 0.040920 0.042391 0.043920 0.045519 0.047197 0.048968 0.050848 0.052856 0.055017 0.057361 0.059939 0.062831 0.066197 0.070465 0.077576 0.048177 0.050469 0.053005 0.055809 0.058919 0.062388 0.066289 0.070723 0.075827 0.081789 0.088873 0.097461 0.10813 0.12178 0.13994 0.16540 0.20384 0.26923 0.40819 0.94736 500.41 502.24 503.60 504.45 504.78 504.55 503.71 502.23 500.05 497.10 493.31 488.58 482.79 475.80 467.41 457.33 445.11 429.99 410.21 379.64 0 30.307 27.653 25.265 23.118 21.187 19.450 17.886 16.475 15.197 14.035 12.973 11.997 11.093 10.248 9.4499 8.6837 7.9329 7.1743 6.3669 5.3854 3.7410 35.904 37.663 39.512 41.455 43.502 45.666 47.969 50.442 53.130 56.102 59.456 63.341 67.981 73.721 81.108 91.052 105.17 126.66 163.44 250.01 −0.22024 −0.17843 610.32 678.97 67.038 47.254 19.298 10.567 6.6444 4.5167 3.2280 2.3885 1.8122 1.4006 25.053 27.008 35.861 46.367 57.964 70.385 83.466 97.085 111.15 125.58 −0.22022 −0.16113 −0.11435 610.73 684.10 673.37 29.473 19.741 10.615 6.6387 4.5077 3.2212 2.3837 1.8089 1.3982 36.427 38.799 47.636 58.735 70.983 84.000 97.573 111.57 125.89 −0.22012 −0.16222 −0.04945 0.047232 612.54 686.54 646.52 604.15 14.917 15.261 15.606 15.952 16.300 16.653 17.011 17.377 17.755 18.149 18.563 19.007 19.489 20.024 20.634 21.350 22.229 23.374 25.018 27.938 Single-Phase Properties 300 372.76 0.1 0.1 372.76 400 500 600 700 800 900 1000 1100 1200 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.032769 0.030397 0.024154 0.020086 0.017201 0.015044 0.013369 0.012030 0.010936 0.010024 2.0295 7.5214 0.007081 0.02347 0.074406 0.067921 0.075315 0.075938 45.138 45.900 48.619 51.387 54.256 57.240 60.347 63.581 66.941 70.426 48.190 49.189 52.759 56.365 60.069 63.887 67.827 71.893 76.085 80.402 0.13257 0.13516 0.14313 0.14970 0.15541 0.16050 0.16514 0.16943 0.17342 0.17718 0.02801 0.02717 0.02717 0.028103 0.029225 0.030431 0.031687 0.032963 0.034228 0.035458 0.037444 0.036170 0.035693 0.036513 0.037592 0.038778 0.040024 0.041293 0.042554 0.043781 0.018070 0.019209 0.020307 2.0263 9.5914 13.717 2.0444 9.6106 13.737 0.007077 0.028834 0.038518 0.074353 0.065422 0.061169 0.075270 0.076628 0.079348 3.5015 3.9749 4.8861 5.7547 6.6074 7.4524 8.2932 9.1313 9.9677 46.529 48.111 51.123 54.087 57.121 60.258 63.511 66.885 70.380 50.030 52.086 56.009 59.842 63.729 67.710 71.804 76.016 80.347 0.11863 0.12295 0.13011 0.13602 0.14121 0.14590 0.15021 0.15422 0.15799 0.034718 0.030084 0.029002 0.029629 0.030651 0.031821 0.033051 0.034290 0.035504 0.048846 0.041065 0.038358 0.038495 0.039301 0.040358 0.041522 0.042719 0.043905 0.018038 0.019167 0.021614 0.023175 2.0204 9.5643 17.474 20.685 2.1106 9.6601 17.582 20.801 0.007057 0.028766 0.046415 0.052622 0.074119 0.065337 0.058082 0.056215 0.075070 0.076438 0.083643 0.090740 1501.5 1543.5 471.99 490.31 548.31 598.61 643.92 685.47 724.03 760.17 794.33 826.85 12.256 13.285 17.270 21.407 25.564 29.669 33.685 37.592 41.382 45.054 2-263 1 1 1 453.03 500 600 700 800 900 1000 1100 1200 1 1 1 1 1 1 1 1 1 300 400 500 537.09 5 5 5 5 537.09 600 700 5 5 5 1.4072 1.1320 0.91269 0.71063 0.88340 1.0957 46.785 49.734 53.286 50.338 54.151 58.765 0.10762 0.11436 0.12148 0.046699 0.034611 0.031678 0.079952 0.051045 0.043318 498.04 561.07 624.59 14.362 10.407 6.5536 55.203 54.653 62.680 18.032 21.062 25.547 5 5 5 5 5 0.77805 0.68224 0.60918 0.55109 0.50355 1.2853 1.4658 1.6416 1.8146 1.9859 56.576 59.855 63.197 66.632 70.172 63.002 67.183 71.405 75.705 80.101 0.12714 0.13207 0.13652 0.14061 0.14444 0.031683 0.032430 0.033447 0.034565 0.035704 0.041848 0.041922 0.042571 0.043465 0.044458 674.39 717.57 756.57 792.63 826.45 4.4532 3.1856 2.3599 1.7924 1.3865 73.950 86.626 99.971 113.64 127.51 29.806 33.891 37.821 41.606 45.257 0.28559 0.25158 0.20466 0.17377 0.15134 0.13418 0.12058 0.10951 0.10032 55.439 52.173 46.267 43.151 1503.0 1511.3 1392.0 853.83 282.91 300 400 453.03 800 900 1000 1100 1200 55.340 52.060 49.243 30.517 32.898 41.401 49.786 58.136 66.471 74.799 83.123 91.444 99.763 2.0277 7.5196 501.02 535.74 592.58 640.55 683.48 722.85 759.50 794.01 826.77 1509.8 1520.9 1250.0 1087.8 853.67 218.80 150.24 15.021 17.051 21.329 25.550 29.687 33.718 37.630 41.420 45.088 853.00 219.84 118.27 100.01 (Continued) 2-264 TABLE 2-135 Temperature K Thermodynamic Properties of Water (Continued ) Pressure MPa Density mol/dm3 300 400 500 584.15 10 10 10 10 55.561 52.312 46.517 38.213 584.15 600 700 800 900 1000 1100 1200 10 10 10 10 10 10 10 10 Volume dm3/mol Int. energy kJ/mol Enthalpy kJ/mol Entropy kJ/(mol⋅K) Cv kJ/(mol⋅K) Cp kJ/(mol⋅K) Sound speed m/s Joule-Thomson K/MPa Therm. cond. mW/(m⋅K) Viscosity µPa⋅s Single-Phase Properties (Continued ) 3.0787 2.7628 1.9625 1.6157 1.3945 1.2345 1.1111 1.0119 0.017998 0.019116 0.021497 0.026169 2.0131 9.5311 17.389 25.105 2.1931 9.7222 17.604 25.367 0.007031 0.028682 0.046244 0.060543 0.073834 0.065233 0.058028 0.054835 0.074829 0.076208 0.082910 0.11032 1518.2 1532.7 1271.3 847.33 −0.21999 −0.16351 −0.05669 0.29540 614.81 689.57 651.64 526.83 852.28 221.13 119.55 81.795 0.32482 0.36195 0.50956 0.61893 0.71709 0.81002 0.90002 0.98820 45.852 47.183 52.145 55.851 59.334 62.798 66.314 69.910 49.100 50.802 57.241 62.040 66.505 70.898 75.314 79.792 0.10117 0.10405 0.11405 0.12046 0.12572 0.13035 0.13456 0.13846 0.055964 0.047271 0.034838 0.033089 0.033219 0.033947 0.034908 0.035954 0.128640 0.092535 0.051779 0.045603 0.044062 0.043952 0.044427 0.045164 472.51 503.34 602.20 662.61 710.98 753.03 791.02 826.16 9.9124 9.4382 6.3228 4.3529 3.1289 2.3241 1.7683 1.3695 76.543 71.110 69.301 78.476 90.516 103.50 116.73 130.00 20.267 21.036 25.704 30.054 34.176 38.111 41.882 45.506 300 400 500 600 700 800 900 1000 1100 1200 100 100 100 100 100 100 100 100 100 100 57.573 54.500 49.914 43.935 36.179 26.768 19.073 14.734 12.246 10.631 0.017369 0.018349 0.020034 0.022761 0.027640 0.037359 0.052429 0.067868 0.081656 0.094062 1.8921 9.0423 16.289 23.820 31.916 40.700 48.805 55.188 60.470 65.222 3.6290 10.877 18.292 26.097 34.680 44.435 54.048 61.975 68.635 74.628 0.006516 0.027360 0.043895 0.058109 0.071320 0.084331 0.095669 0.10404 0.11039 0.11561 0.069812 0.063582 0.057324 0.052776 0.049610 0.047143 0.043932 0.041345 0.040131 0.039810 0.071696 0.073086 0.075607 0.081104 0.091576 0.10108 0.088057 0.071678 0.062539 0.057826 1667.9 1717.3 1555.7 1300.4 1020.0 813.97 765.30 792.50 832.67 872.28 −0.21618 −0.17905 −0.12564 −0.02079 0.21155 0.65939 1.0399 1.0944 0.98401 0.83544 654.50 741.80 730.42 645.83 510.14 351.46 257.03 232.07 223.70 219.07 856.88 243.50 138.92 101.51 79.363 62.042 53.250 51.518 52.497 54.415 300 400 500 600 700 800 900 1000 1100 1200 500 500 500 500 500 500 500 500 500 500 63.750 60.862 57.695 54.316 50.847 47.385 44.018 40.814 37.834 35.124 0.015686 0.016431 0.017332 0.018411 0.019667 0.021104 0.022718 0.024501 0.026432 0.028470 1.5247 7.9635 14.264 20.481 26.606 32.615 38.492 44.233 49.839 55.312 9.3678 16.179 22.930 29.687 36.439 43.167 49.851 56.484 63.055 69.547 0.003746 0.023347 0.038412 0.050731 0.061141 0.070124 0.077998 0.084987 0.091251 0.096900 0.063403 0.059634 0.055769 0.052734 0.050315 0.048442 0.047068 0.046126 0.045537 0.045218 0.068296 0.067603 0.067522 0.067584 0.067436 0.067080 0.066596 0.066041 0.065356 0.064451 2228.6 2258.7 2200.7 2093.8 1970.5 1850.1 1743.4 1655.7 1589.3 1543.9 −0.19915 −0.19486 −0.18339 −0.16883 −0.15188 −0.13256 −0.11124 −0.08910 −0.06907 −0.05511 763.82 929.09 1096.6 1097.9 935.15 738.72 572.49 445.17 350.97 282.78 1089.4 320.18 189.08 141.83 118.47 104.70 95.388 88.418 83.021 78.952 400 500 600 700 800 900 1000 1100 1200 1000 1000 1000 1000 1000 1000 1000 1000 1000 65.942 63.253 60.572 57.937 55.384 52.937 50.611 48.415 46.349 0.015165 0.015810 0.016509 0.017260 0.018056 0.018890 0.019759 0.020655 0.021575 7.4792 13.357 19.141 24.836 30.435 35.938 41.354 46.695 51.976 22.644 29.167 35.650 42.096 48.491 54.828 61.113 67.350 73.551 0.019833 0.034391 0.046212 0.056150 0.064689 0.072155 0.078776 0.084722 0.090117 0.057934 0.055063 0.053055 0.051393 0.050059 0.049062 0.048373 0.047942 0.047713 0.065743 0.064967 0.064676 0.064219 0.063663 0.063101 0.062594 0.062176 0.061861 2718.6 2677.2 2602.3 2513.7 2423.7 2338.7 2261.5 2193.2 2133.6 −0.19303 −0.19158 −0.18789 −0.18439 −0.18105 −0.17779 −0.17459 −0.17139 −0.16808 1172.7 2199.5 3250.5 3202.2 2408.7 1610.7 1052.9 703.41 487.61 329.93 190.55 137.73 108.98 91.430 80.198 72.716 67.520 63.774 The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Wagner, W., and Pruss, A., “The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,” J. Phys. Chem. Ref. Data 31(2):387–535, 2002. The source for viscosity is International Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance, IAPWS, 1997. The source for thermal conductivity is the International Association for the Properties of Water and Steam, Revised Release on the IAPS Formulation 1985 for the Thermal Conductivity of Ordinary Water Substance, IAPWS, 1998. Properties at the triple point temperature and the critical point temperature are given in the first and last entries of the saturation tables, respectively. In the single-phase table, when the temperature range for a given isobar includes a vapor-liquid phase boundary, the temperature of phase equilibrium is noted, and properties for both the saturated liquid and saturated vapor are given (with liquid properties given in the upper line). Lines are omitted from the temperature-pressure grid of the single-phase table, when the system would be in the solid phase or if there are potential problems with the source property surface. The uncertainty in density of the equation of state is 0.0001% at 1 atm in the liquid phase, and 0.001% at other liquid states at pressures up to 10 MPa and temperatures to 423 K. In the vapor phase, the uncertainty is 0.05% or less. The uncertainties rise at higher temperatures and/or pressures, but are generally less than 0.1% in density except at extreme conditions. The uncertainty in pressure in the critical region is 0.1%. The uncertainty of the speed of sound is 0.15% in the vapor and 0.1% or less in the liquid, and increases near the critical region and at high temperatures and pressures. The uncertainty in isobaric heat capacity is 0.2% in the vapor and 0.1% in the liquid, with increasing values in the critical region and at high pressures. The uncertainties of saturation conditions are 0.025% in vapor pressure, 0.0025% in saturated-liquid density, and 0.1% in saturatedvapor density. The uncertainties in the saturated densities increase substantially as the critical region is approached. For the uncertainties in the viscosity and thermal conductivity, see the IAPWS Release. THERMODYnAMIC PROPERTIES TABLE 2-136 Thermodynamic Properties of Water Substance along the Melting Line T, °C 103 v f , m3/kg h f , kJ/kg s f , kJ/kg⋅K cpf , kJ/kg⋅K cmelt , kJ/kg⋅K 106α f , K−1 106K f ,T bar−1 0.0100 0.0026 −0.3618 −0.7410 −1.1249 1.00021 1.00016 0.99770 0.99523 0.99278 0 0.0719 3.5140 6.9794 10.3964 0 −0.0001 −0.0054 −0.0110 −0.0167 4.219 4.218 4.196 4.174 4.152 3.969 3.970 3.997 4.023 4.047 −67.42 −67.17 −54.92 −42.52 −30.24 50.90 50.88 50.30 49.73 49.17 200 250 300 400 500 −1.5166 −1.9151 −2.3206 −3.1532 −4.0156 0.99037 0.98798 0.98562 0.98098 0.97643 13.7648 17.0843 20.3547 26.7472 32.9403 −0.0225 −0.0285 −0.0347 −0.0474 −0.0607 4.132 4.112 4.092 4.056 4.022 4.070 4.092 4.113 4.150 4.184 −18.05 −5.93 6.12 30.09 53.97 48.63 48.11 47.59 46.61 45.68 600 800 1000 −4.909 −6.790 −8.803 0.97196 0.96326 0.95493 38.932 50.300 60.836 −0.0747 −0.1046 −0.1371 3.992 3.937 3.893 4.215 4.270 4.320 77.87 126.18 175.98 44.80 43.19 41.74 P, bar 6.117 × 10 1.01325 50 100 150 –3t Condensed from U. Grigull, Private communication, January 18, 1995. Materials prepared at Technical University München, Germany by U. Grigull and S. Marek. For a table as a function of temperature, see Grigull, U. and S. Marek, Warme u. Stoff., 30 (1994): 1–8. t = the triple point (at 6.117 × 10−3 bar, 0.01°C); vf = 0.0010021 m3/kg: α f = −67.42 × 10−6/K. Other equations for properties are given by Jones, F. E. and G. L. Harris, J. Res. N.I.S.T., 97, 3 (1992): 335–340, and by Wagner, W. and A. Pruss, J. Phys. Chem. Ref. Data, 22, 3 (1993): 783–787. Steam tables include Walker, W. A., U.S. Naval Ordn. Lab. rept. NOLTR NOLTR-66-217 = AD 651105 (0–1000 bar, 0–150°C), 1967 (72 pp.); Grigull, U., J. Straub, et al., Steam Tables in S.I. Units (0.01–1000 bar, 0–1000°C), Springer-Verlag, Berlin, 1990 (133 pp.); Tseng, C. M., T. A. Hamp, et al., Atomic Energy of Canada rept. (30 props, sat liq & vap., 1–220 bar), AECL-5910 1977 (90 pp.). For dissociation, see e.g., Knonicek, V., Rozpr. Cesko Acad Ved., Rada techn ved (0.01–100 bar, 1000–5000 K). 77, 1 (1967). The proceedings of the 10th international conference on the properties of steam were edited by Sytchev, V. V. and A. A. Aleksandrov, Plenum, NY, 1984; and for the 11th conference by Pichal, M. and O. Sifner, Hemisphere, 1989 (550 pp.). Current information on the properties of solid, vapor, and liquid water properties can be found at http://www.iapws.org. For electrical conductivity, see e.g., Marshall, W. L., J. Chem. Eng. Data, 32 (1987): 221–226. 2-265 2-266 PHYSICAL AnD CHEMICAL DATA TRAnSPORT PROPERTIES Introduction The tables and nomographs in this subsection are organized roughly with mass transport properties first (surface tension, viscosity, diffusion coefficient) followed by thermal transport properties. Unit Conversions For this subsection, the following unit conversions are applicable: Diffusivity: to convert square centimeters per second to square feet per hour, multiply by 3.8750; to convert square meters per second to square feet per hour, multiply by 38,750. Pressure: to convert bars to pounds-force per square inch, multiply by 14.504. Temperature: °F = 9⁄5°C + 32; °R = 9⁄5 K. Thermal conductivity: to convert watts per meter-kelvin to British thermal unit–feet per hour–square foot–degree Fahrenheit, multiply by 0.57779; and to convert British thermal unit–feet per hour–square foot–degree Fahrenheit to watts per meter-kelvin, multiply by 1.7307. Viscosity: to convert pascal-seconds to centipoise, multiply by 1000. Additional References An extensive coverage of the general pressure and temperature variation of thermal conductivity is given in the monograph by Vargaftik, N. B., L. P. Filippov, A. A. Tarzimanov and E. E. Totskiy, Thermal Conductivity of Liquids and Gases (in Russian), Standards Press, Moscow, 1978, now published in English translation by CRC Press, Miami, Fla. For a similar work on viscosity, see Stephan and Lucas, Viscosity of Dense Fluids, Plenum, New York and London, 1979. Tables and polynomial fits for refrigerants in both the gaseous and the liquid states are contained in ASHRAE Handbook—Fundamentals, SI ed., ASHRAE, Atlanta, 2005. Other sources for viscosity include Fischer & Porter Co. catalog 10-A-94, “Fluid Densities and Viscosities,” 1953 (200 industrial fluids in 48 pp.) and TABLE 2-137 MASS TRAnSPORT PROPERTIES Surface Tension r (dyn/cm) of Various Liquids Compound Acetic acid Acetone Aniline Benzene Benzonitrile Bromobenzene n-Butane Carbon disulfide Carbon tetrachloride Chlorobenzene D. van Velzen, R. L. Cardozo et al., EURATOM Ispra, Italy rept. 4735 e, 1972 (160 pp.). Liquid viscosity, 314 cpds, is summarized in I&EC Fundtls., 11 (1972): 20–26. Five hundred forty-nine binary and ternary systems are discussed in Skubla, P., Coll. Czech. Chem. Commun., 46 (1981): 303–339. See also Duhne, C. R., Chem. Eng. (NY), 86: 15 (July 16, 1979): 83–91 (equations and 326 liquids); and Rao, K. V. K., Chem. Eng. (NY), 90, 11 (May 30, 1983): 90–91 (nomograph, 87 liquids). For rheology, non-Newtonian behavior, see, for instance, Barnes, H., The Chem. Engr. (UK), (June 24, 1993): 17–23; Hyman, W. A., I&EC Fundtls., 16 (1976): 215–218; and Ferguson, J., and Z. Kemblowski, Applied Fluid Rheology, Elsevier, 1991 (325 pp.). Other sources for thermal conductivity include Ho, C. Y., R. W. Powell et al., J. Phys. Chem. Ref. Data, 1 (1972) and 3, suppl. 1 (1974); Childs, Ericks et al., N.B.S. Monogr. 131, 1973; Jamieson, D. T., J. B. Irving et al., Liquid Thermal Conductivity, H.M.S.O., Edinburgh, Scotland, 1975 (220 pp.). Other references include B. Poling, J. Prausnitz, and J. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2000; N.B. Vargaftik, Y.K. Vinogradov, and V.S. Yargin, Handbook of Physical Properties of Liquids and Gases, Begell House, New York, 1996; Carl Yaws, Chemical Properties Handbook: Physical, Thermodynamics, Environmental Transport, Safety & Health Related Properties for Organic & Inorganic Chemicals, McGraw-Hill, New York, 1998; and M.R. Riazi, Characterization and Properties of Petroleum Fractions, ASTM, West Conshohocken, Pa., 2005. Free web resources include the NIST Webbook at http://webbook.nist.gov and the KDB (Korea thermophysical properties) database at http://www.cheric.org/ research/kdb/. T, K σ 293 333 298 308 318 293 313 333 353 293 313 333 353 293 323 363 293 323 373 203 233 293 293 313 288 308 328 348 368 293 323 373 27.59 23.62 24.02 22.34 21.22 42.67 40.5 38.33 36.15 28.88 26.25 23.67 21.2 39.37 35.89 31.26 35.82 32.34 26.54 23.31 19.69 12.46 32.32 29.35 27.65 25.21 22.76 20.31 17.86 33.59 30.01 24.06 Compound p-Cresol Cyclohexane Cyclopentane Diethyl ether 2,3-Dimethylbutane Ethyl acetate Ethyl benzoate Ethyl bromide Ethyl mercaptan Formamide n-Heptane T, K σ 313 373 293 313 333 293 313 288 303 293 313 293 313 333 353 373 293 313 333 283 303 288 303 298 338 373 293 313 333 353 34.88 29.32 25.24 22.87 20.49 22.61 19.68 17.56 16.2 17.38 15.38 23.97 21.65 19.32 17 14.68 35.04 32.92 30.81 25.36 23.04 23.87 22.68 57.02 53.66 50.71 20.14 18.18 16.22 14.26 Compound T, K σ Isobutyric acid 293 313 333 363 293 323 373 423 473 293 313 333 313 333 373 293 313 333 363 293 313 333 353 373 293 313 333 25.04 23.2 21.36 18.6 24.62 20.05 12.9 6.3 0.87 22.56 20.96 19.41 39.27 37.13 32.96 23.71 22.15 20.6 18.27 29.98 26.83 24.68 22.53 20.38 37.21 34.6 31.98 Methyl formate Methyl alcohol Phenol n-Propyl alcohol n-Propyl benzene Pyridine Methyl formate values from D. B. Macleod, Trans. Faradaay Soc. 19:38, 1923. All others from J. J. Jasper, J. Phys. Chem. Ref. Data 1:841, 1972. TABLE 2-138 Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 C1 C2 1.9703E-05 1.4230E-07 1.5640E-08 1.0939E-05 3.1005E-08 4.7754E-07 1.2025E-06 6.5230E-07 1.7154E-07 2.4910E-08 1.4250E-06 4.1855E-08 1.7531E-07 9.2121E-07 2.5082E-08 3.1340E-08 1.1184E-07 7.4266E-08 3.4647E-05 3.7790E-07 6.9022E-08 1.5600E-07 4.0138E-08 1.3874E-06 7.3534E-08 2.2320E-07 6.2597E-08 6.5411E-08 6.0259E-07 2.6960E-07 3.4387E-08 7.5626E-08 7.0728E-08 1.4031E-06 1.2114E-07 6.9744E-07 4.2898E-08 1.0500E-06 1.0060E-07 3.4205E-07 5.4539E-08 3.1378E-08 2.7856E-06 4.2200E-05 1.2566E-08 1.8178E-05 2.1480E-06 5.8204E-08 1.1127E-06 3.1370E-06 2.1709E-06 0.17646 0.7574 1.078 0.23466 0.9762 0.60273 0.4952 0.579 0.7418 0.98882 0.5039 0.9806 0.72 0.60529 0.96663 0.9676 0.8002 0.8289 0.12396 0.6005 0.84014 0.7181 0.90735 0.4434 0.93798 0.7146 0.9115 0.92914 0.5309 0.6715 0.94604 0.83521 0.84383 0.4611 0.76972 0.5462 0.91349 0.4867 0.77881 0.59764 0.88896 0.96513 0.377 0.10118 1.0939 0.17513 0.46 0.9262 0.5338 0.3742 0.45853 C3 1564.6 272.14 1209.5 23.139 327.16 291.4 410.8 138.4 108.3 30.8 176.17 83.24 7.9 152.43 91.197 3260.2 409 74.746 180 34.714 678.22 184.9 199.64 134.7 71.798 64.391 537 92.661 305.25 358.7 95.108 234.21 43.687 663.14 2840 2110.6 290 44.581 94.7 491.5 208 C4 Tmin, K Viscosity at Tmin Tmax, K Viscosity at Tmax 149.78 353.33 289.81 200.15 178.45 229.32 192.40 185.45 286.15 189.63 80.00 195.41 235.65 83.78 403.00 278.68 442.29 395.45 260.28 321.35 257.85 458.15 243.95 342.20 265.85 429.24 154.25 179.44 136.95 164.25 134.86 220.00 196.15 183.85 158.45 87.80 134.26 167.62 199.65 185.30 157.46 133.02 147.43 176.80 267.95 161.30 194.67 161.11 68.15 250.33 89.56 4.166E-06 6.842E-06 7.053E-06 5.386E-06 4.329E-06 5.208E-06 6.468E-06 4.174E-06 7.679E-06 4.455E-06 5.508E-06 6.378E-06 5.122E-06 6.742E-06 8.274E-06 7.077E-06 1.089E-05 8.578E-06 5.104E-06 5.324E-06 5.680E-06 9.122E-06 5.151E-06 6.186E-06 1.383E-05 1.187E-05 6.182E-06 8.126E-06 3.340E-06 4.553E-06 3.559E-06 5.157E-06 4.580E-06 3.961E-06 3.772E-06 1.795E-06 3.770E-06 4.044E-06 4.216E-06 3.424E-06 3.833E-06 3.520E-06 3.329E-06 4.175E-06 5.692E-06 3.144E-06 9.749E-06 5.048E-06 4.434E-06 8.361E-06 5.132E-06 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 2000 1000 1000 3273.1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 800 1000 1000 1000 1500 800 1250 1000 1000 2.600E-05 2.093E-05 2.681E-05 2.504E-05 2.571E-05 2.314E-05 1.923E-05 2.523E-05 2.532E-05 2.306E-05 6.227E-05 3.551E-05 2.154E-05 1.205E-04 1.992E-05 2.486E-05 2.441E-05 2.087E-05 1.915E-05 1.698E-05 2.129E-05 1.886E-05 2.045E-05 1.768E-05 2.967E-05 2.623E-05 3.397E-05 4.009E-05 1.966E-05 2.457E-05 2.369E-05 2.260E-05 2.259E-05 2.207E-05 2.259E-05 2.325E-05 2.360E-05 2.229E-05 1.993E-05 1.720E-05 2.427E-05 2.466E-05 1.893E-05 2.211E-05 2.404E-05 1.959E-05 5.203E-05 2.693E-05 4.654E-05 2.789E-05 4.267E-05 2-267 (Continued) 2-268 TABLE 2-138 Cmpd. no. 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone Formula Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O CAS 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 Mol. wt. 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 C1 C2 2.6000E-07 1.0650E-07 3.5554E-08 1.6960E-07 6.2860E-08 4.7100E-08 3.8802E-07 1.4427E-07 8.7371E-08 1.4305E-07 3.3699E-07 3.7385E-08 1.0881E-06 6.7700E-08 7.9581E-08 5.2312E-08 1.3326E-06 2.3619E-07 3.0260E-07 1.7578E-06 3.9150E-08 3.5018E-05 2.6400E-08 7.1748E-08 5.5065E-08 6.1192E-08 3.2720E-08 5.6914E-07 2.4999E-07 1.4125E-07 1.1379E-07 2.9444E-07 7.7147E-08 2.3340E-07 1.6030E-07 1.5913E-07 2.0135E-07 1.4321E-07 7.6787E-07 1.4906E-07 1.1989E-07 3.3628E-08 4.3184E-07 1.9480E-06 6.5492E-08 2.7228E-06 4.3934E-07 7.7484E-07 4.1380E-07 1.6910E-07 9.2797E-08 0.7423 0.7942 0.98455 0.7693 0.907 0.911 0.6367 0.7438 0.80775 0.7451 0.60751 0.98433 0.48359 0.8367 0.8376 0.89422 0.4537 0.67465 0.64991 0.4265 0.91427 0.11725 0.9487 0.7982 0.8341 0.82546 0.9302 0.50744 0.6878 0.8097 0.8502 0.728 0.79906 0.714 0.763 0.7639 0.73421 0.7785 0.5741 0.7617 0.79108 0.9426 0.6035 0.41 0.86232 0.39531 0.64867 0.57978 0.5999 0.7114 0.7819 C3 98.3 94.7 96.6 205.08 166.15 98.538 159.8 221.17 330.86 36.7 104.97 58.008 445 139 167.14 370.34 22.264 3394.6 71 109.38 79.56 77.434 39.13 273.3 0.5962 83.243 93.816 154.74 80.765 260 205 193.14 111.98 98.159 276.16 105.9 84.37 39.587 247 495.8 59.455 445.07 169.64 198.7 269.5 124 93.399 C4 Tmin, K Viscosity at Tmin Tmax, K Viscosity at Tmax 200.00 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.60 242.00 169.67 179.28 138.13 145.59 189.64 285.00 243.51 304.55 280.05 206.89 247.56 229.15 60.00 210.15 282.85 370.10 175.30 248.39 256.15 326.14 176.19 237.49 178.01 200.00 172.71 301.15 223.35 156.85 169.20 154.56 215.00 136.95 357.05 187.65 204.81 8.900E-06 5.611E-06 4.506E-06 7.091E-06 6.820E-06 4.533E-06 4.175E-06 6.113E-06 6.687E-06 6.731E-06 3.480E-06 8.411E-06 4.797E-06 6.671E-06 6.917E-06 5.714E-06 3.778E-06 4.409E-06 3.369E-06 4.150E-06 4.238E-06 5.262E-06 3.755E-06 5.070E-06 4.715E-06 3.632E-06 4.761E-06 4.091E-06 4.137E-06 7.685E-06 1.038E-05 1.538E-05 3.278E-06 5.850E-06 6.127E-06 8.313E-06 5.487E-06 7.164E-06 5.895E-06 5.515E-06 4.742E-06 6.450E-06 5.364E-06 3.720E-06 4.046E-06 5.148E-06 8.001E-06 5.478E-06 8.016E-06 4.218E-06 4.089E-06 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 900 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 480 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 3.992E-05 2.348E-05 3.195E-05 3.143E-05 3.307E-05 2.547E-05 2.618E-05 2.108E-05 2.108E-05 2.120E-05 1.834E-05 3.355E-05 2.308E-05 1.928E-05 2.346E-05 2.381E-05 2.118E-05 2.191E-05 2.309E-05 2.441E-05 2.118E-05 1.791E-05 1.729E-05 1.604E-05 1.622E-05 1.701E-05 1.944E-05 1.488E-05 1.744E-05 3.502E-05 3.696E-05 3.895E-05 1.781E-05 2.569E-05 2.588E-05 2.611E-05 2.887E-05 2.824E-05 3.175E-05 2.599E-05 2.611E-05 2.176E-05 2.239E-05 2.212E-05 2.388E-05 2.891E-05 3.317E-05 3.547E-05 2.055E-05 2.049E-05 1.881E-05 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.4172E-08 3.9833E-08 1.9377E-06 2.7570E-07 6.8567E-07 7.8220E-07 8.4576E-07 9.9104E-07 3.2282E-08 2.6800E-06 3.5538E-06 5.0372E-07 5.2195E-08 4.7238E-08 5.2854E-07 8.6101E-08 3.9554E-08 2.7334E-07 2.8451E-08 1.2900E-07 6.3440E-08 2.9236E-07 2.5906E-07 1.0613E-07 3.2140E-06 4.9340E-07 4.2231E-07 6.3441E-08 9.2371E-08 1.6175E-07 4.1070E-07 2.1696E-06 2.0789E-06 1.3744E-07 8.6706E-08 2.8132E-07 4.3403E-08 6.7610E-07 2.5704E-08 7.9129E-08 1.3974E-07 1.0498E-07 8.5992E-08 5.5300E-07 5.1539E-07 2.6635E-05 6.3600E-07 2.1174E-07 4.0868E-06 3.9346E-08 1.5948E-05 6.8290E-08 5.0702E-08 6.4320E-07 0.91098 0.91566 0.4093 0.6841 0.52542 0.4994 0.487 0.4723 0.97742 0.3975 0.3766 0.54462 0.85584 0.90849 0.6112 0.8345 0.892597 0.7393 0.93622 0.744 0.8287 0.62458 0.67988 0.8066 0.3572 0.5924 0.58154 0.8369 0.7908 0.7163 0.57143 0.3812 0.4163 0.7557 0.83923 0.6792 0.94806 0.5804 0.94738 0.79565 0.74266 0.76988 0.8427 0.6061 0.5726 0.15779 0.6638 0.7087 0.35526 1.0027 0.21516 0.8774 0.9114 0.5854 492.69 133.2 278.82 371.6 398 436.89 534 1176.1 227.44 69.036 302.85 167.86 129.93 117.03 219.5 702.84 98.902 52.7 667 239.17 239.21 73.63 102.32 142.27 230.06 577.77 352.7 122.8 75.512 238.46 354.9 83.193 98.58 100.41 58.148 273.66 288.76 2173.5 61.6 157.42 651.07 1151.1 54.864 325.3 3590 159.95 226.10 240.91 180.96 145.19 392.70 402.94 396.58 188.44 131.65 212.72 160.00 274.18 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 200.00 189.60 192.15 178.20 238.45 258.15 175.15 161.84 134.71 169.41 284.29 260.15 329.00 160.65 193.55 155.15 180.00 140.00 204.15 125.26 199.25 145.65 167.55 53.48 357.88 129.95 131.35 155.15 275.60 281.45 187.55 4.497E-06 5.701E-06 6.006E-06 5.563E-06 3.211E-06 7.936E-06 7.900E-06 7.957E-06 5.405E-06 3.688E-06 4.097E-06 3.300E-06 5.089E-06 3.739E-06 4.544E-06 6.231E-06 8.569E-06 1.226E-05 5.933E-06 4.429E-06 3.511E-06 3.214E-06 2.643E-06 6.029E-06 4.632E-06 4.953E-06 3.673E-06 4.733E-06 5.344E-06 3.392E-06 3.103E-06 2.659E-06 5.714E-06 6.863E-06 7.150E-06 8.359E-06 5.356E-06 5.069E-06 3.058E-06 3.371E-06 3.219E-06 4.224E-06 3.441E-06 5.768E-06 2.994E-06 4.277E-06 4.148E-06 9.491E-06 3.832E-06 5.237E-06 5.608E-06 7.882E-06 8.658E-06 5.037E-06 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 2.388E-05 2.224E-05 2.194E-05 2.744E-05 2.021E-05 1.796E-05 1.749E-05 1.801E-05 2.762E-05 2.722E-05 2.202E-05 1.766E-05 1.804E-05 2.511E-05 2.766E-05 2.350E-05 1.884E-05 3.995E-05 1.831E-05 1.970E-05 1.593E-05 1.284E-05 2.583E-05 2.651E-05 2.274E-05 2.384E-05 1.893E-05 1.915E-05 1.975E-05 1.989E-05 1.729E-05 1.914E-05 2.726E-05 2.264E-05 2.655E-05 2.477E-05 3.032E-05 2.750E-05 1.787E-05 1.781E-05 2.150E-05 1.946E-05 2.742E-05 2.857E-05 2.088E-05 2.496E-05 5.873E-05 2.446E-05 2.880E-05 4.009E-05 3.277E-05 2.776E-05 2.749E-05 2.768E-05 2-269 (Continued) 2-270 TABLE 2-138 Cmpd. no. 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene Formula He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 CAS Mol. wt. C1 C2 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 3.2530E-07 3.1338E-07 4.2392E-05 6.6720E-08 1.3633E-08 2.5720E-07 3.4649E-05 8.9656E-08 8.8629E-08 7.7509E-08 4.6970E-08 5.9501E-07 1.2463E-07 4.0986E-05 1.7514E-07 1.2145E-08 1.5773E-07 1.0652E-07 9.7820E-08 9.8882E-08 8.0060E-08 5.2127E-07 4.3636E-08 2.9986E-07 5.5562E-07 2.3489E-07 1.7970E-07 9.1700E-08 4.9240E-07 1.2780E-08 4.5101E-14 3.9314E-08 1.1202E-07 5.2542E-08 6.7978E-05 9.1130E-08 5.2546E-07 3.0663E-07 8.0599E-08 1.3226E-06 1.1630E-06 1.6480E-06 5.6409E-07 7.4106E-08 4.0824E-07 2.4344E-08 1.8690E-07 8.9348E-08 5.0602E-07 8.5423E-07 0.7162 0.6238 0.1011 0.82837 1.0595 0.6502 0.10705 0.78236 0.78376 0.81089 0.8932 0.52758 0.7322 0.10349 0.70737 1.0861 0.7189 0.77022 0.7772 0.7755 0.81293 0.5444 0.90747 0.62647 0.5337 0.7151 0.685 0.9273 0.6702 1.0631 3.0005 1.0134 0.7822 0.88063 0.092766 0.8222 0.59006 0.69655 0.8392 0.4885 0.4787 0.4444 0.5863 0.82436 0.5923 0.97376 0.7096 0.80197 0.55258 0.47389 C3 −9.6 692.2 3420 85.752 248.6 2900.7 100.14 100.18 69.927 57.6 274.02 395 3180.6 157.14 163.3 105.85 99.53 99.825 65.274 237.01 42.32 178.17 244.38 205.05 −0.59 157.7 340 −521.83 C4 107 6000 140 76,111 100.3 4637.3 93.57 105.67 205 77.332 504.3 316 510.66 231.9 83.086 208.22 −91.597 192 77.653 199.82 239.34 18,720 Tmin, K Viscosity at Tmin Tmax, K Viscosity at Tmax 20.00 295.13 229.80 182.57 265.83 239.15 220.00 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223.00 217.35 217.50 133.39 170.05 192.62 141.25 183.65 274.69 13.95 206.45 200.00 300.00 285.50 250.00 227.15 177.95 409.15 288.15 90.69 240.00 301.15 250.00 170.45 196.32 179.69 260.75 159.53 150.00 450.15 155.95 135.58 139.39 3.530E-06 3.254E-06 4.625E-06 3.391E-06 5.052E-06 4.440E-06 4.351E-06 4.485E-06 4.550E-06 3.169E-06 4.832E-06 3.932E-06 3.274E-06 4.523E-06 3.631E-06 5.294E-06 4.567E-06 4.650E-06 4.397E-06 4.403E-06 2.871E-06 3.567E-06 4.235E-06 2.947E-06 3.851E-06 7.460E-06 6.517E-07 1.285E-05 9.594E-06 2.576E-06 9.931E-06 1.058E-05 5.415E-06 5.037E-06 9.629E-06 7.242E-06 3.470E-06 7.523E-06 7.714E-06 6.505E-06 4.769E-06 4.781E-06 5.167E-06 5.515E-06 3.572E-06 2.621E-06 1.000E-05 3.422E-06 3.083E-06 3.263E-06 2000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1673.15 3000 800 1000 425 472.68 480 1000 1000 1000 1000 1000 1000 1000 800 800 1000 1000 1000 1000 1000 1000 1000 1000 1000 7.561E-05 1.377E-05 1.928E-05 1.878E-05 2.056E-05 1.838E-05 1.861E-05 1.812E-05 1.809E-05 1.962E-05 2.124E-05 1.787E-05 1.399E-05 2.004E-05 2.005E-05 2.201E-05 1.945E-05 1.970E-05 1.909E-05 1.907E-05 2.064E-05 1.811E-05 2.209E-05 1.928E-05 1.782E-05 4.225E-05 4.330E-05 4.512E-05 4.358E-05 4.421E-06 2.019E-05 2.050E-05 2.261E-05 2.304E-05 2.289E-05 2.440E-05 2.800E-05 3.128E-05 2.464E-05 2.125E-05 2.045E-05 2.350E-05 2.628E-05 2.034E-05 2.021E-05 2.190E-05 2.109E-05 2.111E-05 1.918E-05 1.820E-05 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 5.6844E-07 3.9342E-08 4.9950E-08 4.0748E-08 3.7330E-07 4.8806E-08 6.5281E-07 8.5736E-08 2.4000E-07 2.0000E-07 9.0798E-07 3.7026E-08 3.9771E-08 1.9770E-07 2.6098E-07 2.6552E-08 8.6219E-08 6.9755E-06 1.5035E-07 9.4257E-08 3.1573E-07 1.9250E-07 1.0826E-07 8.6077E-08 1.6370E-07 4.8890E-07 7.2131E-08 1.1164E-06 1.0546E-07 1.0871E-07 9.6050E-07 9.0981E-07 3.5642E-07 4.4941E-08 5.8223E-08 3.8926E-07 7.1455E-07 1.5779E-07 7.6460E-07 6.4318E-07 7.1900E-07 2.4391E-07 6.5592E-07 8.2005E-07 4.0700E-07 2.1150E-06 1.4670E-06 3.0465E-07 3.8518E-05 1.0344E-07 1.8105E-08 1.2000E-07 3.5879E-05 0.553 0.91086 0.89479 0.92709 0.6177 0.92549 0.5294 0.80277 0.68 0.704 0.495 0.92849 0.92242 0.7453 0.68276 0.98316 0.83591 0.3154 0.7338 0.7845 0.66404 0.7091 0.77382 0.81669 0.76706 0.6096 0.80319 0.4537 0.77106 0.78135 0.4856 0.49288 0.6327 0.90199 0.88057 0.63159 0.49832 0.73224 0.5476 0.5389 0.6659 0.702 0.6081 0.61423 0.6485 0.4642 0.5123 0.62218 0.10867 0.77301 0.99668 0.74 0.10109 227.18 44.662 256.5 310.59 100.77 210 187 355.89 131.22 133.4 72.564 1034.5 108.5 90.183 173.59 109 93.349 71.294 107.97 342.23 99.437 374.74 93.745 70.639 381 260.08 232.2 48.298 169.45 303.31 112.15 284 400.16 5.3 280 54.714 114.58 367.5 305.7 125.4 705.34 3502.7 220.47 180 3258.2 160.15 157.48 175.30 183.45 187.35 139.05 146.58 299.15 280.15 269.15 130.73 146.62 115.00 182.55 160.00 186.48 167.23 174.15 150.00 189.15 256.15 127.93 180.15 171.64 150.18 224.95 240.00 119.55 176.00 150.00 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 278.65 353.43 30.00 183.63 63.15 66.46 244.60 182.30 110.00 305.04 267.30 219.66 285.55 268.15 238.15 3.893E-06 3.947E-06 4.052E-06 5.112E-06 3.993E-06 4.698E-06 2.934E-06 6.232E-06 6.331E-06 6.062E-06 2.722E-06 3.800E-06 3.165E-06 5.574E-06 4.551E-06 4.534E-06 4.341E-06 5.117E-06 3.448E-06 3.901E-06 7.481E-06 3.242E-06 3.968E-06 4.065E-06 4.450E-06 5.265E-06 4.162E-06 2.366E-06 3.707E-06 3.707E-06 6.727E-06 3.423E-06 4.316E-06 3.725E-06 3.908E-06 3.196E-06 5.057E-06 3.938E-06 8.264E-06 7.125E-06 5.884E-06 3.752E-06 4.372E-06 3.964E-06 5.756E-06 8.854E-06 7.618E-06 3.231E-06 5.013E-06 3.335E-06 5.074E-06 4.499E-06 4.250E-06 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 1000 1000 1000 1000 1000 1000 1000 3273.1 1000 1970 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 2.112E-05 2.125E-05 2.312E-05 2.463E-05 2.118E-05 2.917E-05 1.930E-05 1.994E-05 2.175E-05 2.181E-05 2.046E-05 2.259E-05 2.327E-05 3.009E-05 2.573E-05 2.364E-05 2.588E-05 3.029E-05 2.157E-05 1.951E-05 2.642E-05 2.327E-05 2.076E-05 2.265E-05 2.956E-05 2.456E-05 1.685E-05 1.865E-05 1.983E-05 2.242E-05 1.312E-05 2.174E-05 2.288E-05 2.284E-05 2.434E-05 2.612E-05 1.714E-05 2.232E-05 2.616E-05 1.900E-05 1.573E-04 2.432E-05 6.432E-05 5.122E-05 2.625E-05 4.000E-05 5.737E-05 1.314E-05 1.812E-05 1.767E-05 1.769E-05 1.688E-05 1.694E-05 (Continued) 2-271 2-272 TABLE 2-138 Cmpd. no. 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 Vapor Viscosity of Inorganic and Organic Substances (Pa∙s) (Continued ) Name 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Formula C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 CAS 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 Mol. wt. 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 C1 C2 6.6329E-08 3.8673E-08 6.1447E-07 3.2095E-07 3.9500E-05 3.1191E-08 1.5557E-08 1.7520E-07 3.4163E-05 8.0901E-08 6.1515E-11 5.0324E-05 3.3253E-08 5.7084E-07 6.3032E-05 1.1010E-06 1.1960E-07 4.0828E-08 4.3300E-05 6.3412E-08 1.0971E-08 1.8903E-07 1.1749E-07 2.4630E-07 1.1640E-07 1.6378E-06 8.8646E-08 2.7467E-08 4.1022E-08 5.7650E-07 4.3478E-07 1.0094E-07 8.5360E-08 4.3511E-08 6.0758E-07 4.9054E-08 7.9420E-07 1.2003E-06 5.4749E-07 3.8397E-05 1.4807E-08 9.6891E-06 2.1372E-07 1.6200E-07 3.0387E-07 7.3919E-07 6.0741E-07 3.5532E-08 7.9457E-08 4.5430E-08 0.82027 0.91142 0.50705 0.61839 0.10787 0.92925 1.0299 0.6941 0.10661 0.79062 1.8808 0.077611 0.9351 0.52446 0.10487 0.5634 0.84797 0.8766 0.098676 0.84758 1.11 0.7031 0.7649 0.6653 0.7615 0.44337 0.81492 0.97555 0.90585 0.53498 0.5272 0.799 0.80872 0.908 0.53845 0.90125 0.5491 0.494 0.53893 0.10821 1.0733 0.24601 0.6894 0.7285 0.61945 0.5423 0.5863 0.95654 0.84656 0.9173 C3 C4 76.204 50.646 287.19 709.09 3390 55.092 206.8 3028 99.338 3604.6 32.426 271.76 4210.1 96.3 212.68 3090 41.718 175.9 103.78 208.7 107.94 636.11 85.198 235.2 238.27 103.1 88.273 102.73 173.45 415.8 479.78 283.52 2510.9 1537.6 178.57 117 210.35 263.73 367.29 65.878 61 –26,218 Tmin, K Viscosity at Tmin Tmax, K Viscosity at Tmax 191.91 253.05 223.15 301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.35 80.15 283.07 191.59 143.42 239.15 410.95 200.00 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 200.00 187.35 199.00 165.00 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15 3.542E-06 4.995E-06 4.170E-06 3.266E-06 4.955E-06 3.677E-06 5.338E-06 4.583E-06 4.530E-06 4.611E-06 2.075E-06 3.406E-06 4.579E-06 3.757E-06 1.188E-05 3.773E-06 4.922E-06 3.288E-06 4.246E-06 3.305E-06 4.793E-06 9.111E-06 4.452E-06 4.003E-06 5.079E-06 2.813E-06 3.638E-06 4.766E-06 4.242E-06 3.621E-06 6.010E-06 7.514E-06 5.324E-06 8.072E-06 3.788E-06 2.702E-06 4.732E-06 4.471E-06 3.914E-06 4.114E-06 5.607E-06 3.652E-06 3.802E-06 4.540E-06 3.350E-06 2.093E-06 4.203E-06 4.085E-06 4.132E-06 4.832E-06 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1.781E-05 1.996E-05 1.585E-05 1.345E-05 1.896E-05 1.813E-05 1.913E-05 1.755E-05 1.771E-05 1.733E-05 2.700E-05 1.868E-05 2.057E-05 1.681E-05 2.496E-05 6.371E-05 4.184E-05 1.436E-05 2.093E-05 2.124E-05 2.346E-05 2.068E-05 2.098E-05 2.019E-05 2.023E-05 2.176E-05 2.275E-05 2.320E-05 2.141E-05 1.879E-05 1.340E-05 2.283E-05 2.093E-05 2.090E-05 2.135E-05 2.480E-05 2.490E-05 2.461E-05 1.765E-05 2.309E-05 2.457E-05 2.089E-05 2.122E-05 2.223E-05 1.812E-05 2.477E-05 2.550E-05 2.632E-05 2.583E-05 2.418E-05 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 1.1085E-07 2.1671E-07 6.3863E-07 5.7821E-05 6.8630E-07 5.3986E-07 3.9067E-06 3.9218E-05 7.0859E-07 5.1567E-09 3.7780E-07 5.0784E-07 8.5988E-08 8.1458E-07 1.0300E-06 8.7268E-07 2.7081E-07 3.5585E-08 2.4110E-07 1.2434E-06 7.8498E-07 6.8812E-07 1.1070E-07 8.2418E-07 3.4066E-08 2.8471E-08 3.5940E-08 5.9537E-08 1.3880E-07 6.7484E-07 2.3790E-07 3.6429E-08 1.7096E-08 6.8293E-07 8.3436E-07 9.3485E-07 0.8008 0.76757 0.5254 0.099467 0.6112 0.6349 0.3845 0.12589 0.51971 1.1561 0.6533 0.5614 0.82841 0.50257 0.5497 0.49397 0.6955 0.8987 0.6845 0.4832 0.49855 0.51063 0.746 0.4931 0.95252 0.96571 0.9052 0.81842 0.7599 0.5304 0.71517 0.95924 1.1146 0.52199 0.49713 0.47683 152.51 16.28 295.1 4409.6 217 34.5 470.1 3861.1 652.24 271.01 328.55 68.172 380.29 569.4 323.79 187.93 165.3 223 447.7 362.79 330.88 72.4 371.44 43.528 30.83 125 90.245 98 230.17 102.84 324.17 365.86 371.96 19,000 388.85 250.00 242.54 460.85 197.67 205.15 297.93 700.15 329.35 279.01 164.65 237.38 176.99 373.96 234.94 178.18 236.50 267.76 158.45 156.08 247.79 229.33 165.78 387.91 398.40 354.00 247.57 288.45 180.35 173.15 119.36 178.35 273.16 225.30 247.98 286.41 9.439E-06 1.410E-05 5.158E-06 1.007E-05 8.280E-06 9.790E-06 1.355E-05 1.373E-05 4.837E-06 3.465E-06 4.006E-06 4.592E-06 4.520E-06 7.930E-06 6.049E-06 4.008E-06 6.756E-06 3.344E-06 3.210E-06 3.689E-06 4.975E-06 4.520E-06 3.488E-06 7.958E-06 9.208E-06 7.581E-06 3.506E-06 4.677E-06 4.659E-06 4.459E-06 3.907E-06 5.260E-06 8.882E-06 4.735E-06 5.225E-06 6.037E-06 1000 500 1000 1000 1000 5000 694.19 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1073.15 1000 1000 1000 2.429E-05 2.475E-05 1.858E-05 2.125E-05 3.844E-05 1.195E-04 2.883E-05 1.925E-05 1.554E-05 1.516E-05 2.710E-05 1.847E-05 2.461E-05 1.900E-05 2.926E-05 2.000E-05 2.782E-05 1.517E-05 2.230E-05 2.418E-05 1.803E-05 1.760E-05 1.786E-05 1.812E-05 2.352E-05 2.179E-05 1.660E-05 1.558E-05 2.407E-05 2.140E-05 3.016E-05 2.749E-05 4.082E-05 1.898E-05 1.894E-05 1.836E-05 The vapor viscosity is calculated by μ = C1T C2/(1 + C3/T + C4/T 2) where μ is the viscosity in Pa∙s and T is the temperature in K. Viscosities are at either 1 atm or the vapor pressure, whichever is lower. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, and N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-273 2-274 TABLE 2-139 Eqn Cmpd. no. 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 Viscosity of Inorganic and Organic Liquids (Pa∙s) Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 C1 −10.976 1.5525 −9.03 −20.457 −14.918 5.4711 6.224 −12.032 −28.12 −0.24126 −20.077 −6.743 −15.407 −8.8685 −12.632 7.5117 −8.4562 −12.947 −23.268 −148.6 −14.152 −11.46 −11.459 −9.9265 16.775 −20.611 −5.0539 −16.615 −10.143 17.844 −7.2471 −393.86 −390.03 −82.851 −16.323 −10.773 −10.346 −10.335 −17.488 −23.802 −10.807 −10.903 −3.4644 −6.4551 −9.817 −11.13 18.775 −10.306 −4.9735 C2 755.12 1376.4 1212.3 1638.6 1023.4 143.99 −151.8 867.34 2280.2 350.57 285.15 598.3 1518.7 204.29 2668.2 294.68 1024.4 2557.9 1880.5 8377.2 2652 1497 1334.4 1576.3 -314 1656.5 645.8 931.44 472.79 −310.2 534.82 19,042 18,609 4481.8 3141.7 591.61 522.3 521.39 1478.2 1887.2 966.74 932.82 334.5 744.7 1388 1084.1 −402.92 703.01 97.67 C3 −2.0126 −0.322 1.3834 0.5961 −2.4432 −2.6554 0.19534 2.3956 −1.5676 1.784 −0.7341 0.60172 −0.38305 C4 C5 −6.238E-22 −3.690E-27 10 10 −1.294E-22 10 1.7994 20.559 −0.0000133 2 −0.043397 0.00049694 −0.21119 −3.9763 1.4415 −0.87689 0.94366 −0.028241 −4.5058 −0.57469 59.978 60.014 11.182 −4.6625E-27 −0.049479 −0.055844 −0.000020943 10 1 1 2 −6.9171E-26 10 −2.794 −0.30635 −0.011847 −0.013184 0.91828 1.8479 −0.014851 0.023034 −1.0811 −0.67524 −0.238 −4.6854 −1.1088 Tmin, K Viscosity at Tmin 149.78 353.33 289.81 200.15 190 229.32 193.15 185.45 286.15 189.63 59.15 195.41 235.65 83.78 403 278.68 258.27 395.52 260.28 321.35 257.85 275.65 243.95 342.2 265.85 242.43 154.25 179.44 136.95 250 134.86 220 196.15 190 238 87.8 134.26 167.62 250 200 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.58 68.15 2.647E-03 1.728E-03 1.265E-03 7.159E-03 1.655E-03 7.616E-04 1.958E-04 1.773E-03 1.359E-03 1.340E-03 3.430E-04 5.240E-04 3.429E-03 2.950E-04 2.451E-03 7.761E-04 2.047E-03 1.534E-03 2.393E-03 5.369E-03 2.092E-02 1.886E-03 2.513E-03 1.427E-03 1.353E-03 2.842E-03 5.065E-03 1.464E-03 1.081E-03 2.547E-04 2.243E-03 2.020E+02 4.410E+04 2.602E-01 4.404E-02 1.769E-02 1.483E-03 6.810E-04 1.496E-03 1.030E-02 8.716E-03 2.287E-02 1.369E-03 3.223E-03 2.561E-03 1.217E-02 2.488E-04 2.592E-03 2.688E-04 Tmax, K 294.15 494.3 391.05 412.7 329.44 354.81 273.15 353.22 460 350.45 130 393.15 426.73 150 563.15 545 442.29 600.8 464.15 664 478.6 458.15 472.03 723.15 350 429.24 393.15 363.15 284 400 420 544 540.8 391.9 372.9 335.6 276.87 274.03 399.26 456.46 373.15 358.13 373.15 347.94 436.42 390.74 303.15 441.6 131.37 Viscosity at Tmax 2.229E-04 2.895E-04 3.890E-04 2.874E-04 2.351E-04 2.100E-04 9.819E-05 2.181E-04 2.086E-04 2.191E-04 4.276E-05 4.858E-05 2.736E-04 3.823E-05 3.730E-04 7.106E-05 3.333E-04 1.683E-04 2.836E-04 2.614E-04 1.821E-04 2.121E-04 1.788E-04 1.076E-04 6.021E-04 3.310E-04 1.751E-04 2.060E-04 1.773E-04 4.880E-05 3.566E-05 3.441E-04 2.890E-04 3.845E-04 3.715E-04 1.222E-04 1.982E-04 2.022E-04 2.521E-04 2.359E-04 2.475E-04 2.851E-04 1.271E-04 2.570E-04 3.087E-04 2.351E-04 5.652E-05 1.643E-04 6.515E-05 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 100 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Diisopropyl amine CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 −8.0738 −9.9212 −9.5412 0.15772 10.9222 −14.109 10.39 10.27183 −15.458 −914.12 −377.23 −851.12 −24.988 −11.794 −3.4968 −33.763 280.87 −44.877 −11.641 −3.2612 −4.1508 −3.524 −11.338 4.1184 −97.663 −12.305 −69.985 −15.868 −11.464 −2.3633 0.000001348 −10.457 −17.582 −10.013 10.027 −114.7 −30.6 31.63 −8.991 15.312 −13.071 −10.872 −11.269 −375.21 −17.57 10.197 −5.135 10.501 −10.072 −17.723 −1.7366 1121.1 300.5 456.62 540.5 −118.895 1049.2 −134.38 −67.2235 1086 38,855 17,909 36,686 1807.9 992.33 397.94 2497.2 −31,869 3227.7 1154.3 614.16 599.77 342.54 1304.1 629.98 4342.7 2324.1 5818.8 1434.8 1510.1 791.93 1101.1 1635.4 921.31 206 4905.4 2153.4 −1080 870.2 −41.12 940.03 1033.1 1195.3 17,177 1385.7 −63.8 667.5 −52.181 710.48 850.2 599.8 −0.4726 −1.6075 −3.305 0.5377 −3.262 −3.1664 0.654 139.11 55.565 129.13 2.0556 −1.1087 3.2236 −38.837 4.887 0.066511 −1.156 −1.0308 −1.1599 0.000092396 −2.2076 13.645 −0.055494 8.0715 0.68071 −0.012754 −1.2272 −0.00014757 −0.00004841 −0.00013329 3,994,500 2 2 2 −2.002 −0.000019319 2 −0.000020577 2 −3.6367 0.5 −1.1719E-18 7 −0.0031354 0.9932 −3.1607 16.358 2.9371 −6.114 −0.2805 −3.919 0.3733 −0.00067435 0.012736 66.66 0.85647 −3.226 −0.8553 −3.3459 −0.14677 1.0601 −1.4237 250 89.56 172.12 250 136.75 209.63 175.43 150.35 250 273.15 293.15 273.15 200 245.25 182.48 279.69 296.6 242 200 225 138.13 145.59 189.64 285 240.05 304.55 285 206.89 247.56 229.15 20.35 210.15 282.85 220.6 175.3 248.39 256.15 326.14 176.19 237.49 208.38 192.5 172.71 293.15 223.35 200 225 154.56 179.6 137 250 2.032E-03 1.408E-03 1.020E-03 1.422E-03 2.026E-03 1.970E-03 7.234E-04 2.362E-03 5.514E-04 8.438E-02 9.548E-03 9.674E-02 6.363E-03 4.317E-04 8.345E-04 1.264E-03 6.328E-02 8.960E-03 4.017E-03 1.122E-03 7.531E-03 9.601E-04 1.155E-02 2.134E-03 2.741E-03 6.798E-03 1.937E-02 4.975E-03 4.364E-03 3.786E-03 1.348E-06 5.331E-03 2.042E-03 2.919E-03 5.931E-03 2.463E-03 2.726E-03 8.543E-04 4.076E-03 1.839E-03 1.406E-03 4.051E-03 1.381E-02 8.128E-01 1.190E-03 7.359E-04 1.113E-03 1.229E-03 1.030E-03 1.832E-03 7.479E-04 455 145.1 333.72 540 423.15 353.2 416.25 423.15 308.85 564.68 558.04 563.72 400 320.12 367.94 443.04 520.08 428.58 373.15 325 405.6 318.4 431.95 481.65 494.16 543.15 503 443.75 512.35 505.6 20.35 381.15 404.51 488.8 414.15 547.16 453.57 447.21 330.45 400 373.93 361.25 369.52 589.28 329.1 373.15 365.25 343.15 283.65 343.15 357.05 2.030E-04 3.897E-04 2.822E-04 1.291E-04 8.727E-05 3.410E-04 6.726E-05 1.190E-04 2.767E-04 1.793E-05 1.514E-04 2.992E-05 2.881E-04 1.676E-04 1.278E-04 2.070E-04 1.652E-04 4.402E-04 2.877E-04 3.167E-04 1.416E-04 1.080E-04 2.440E-04 2.718E-04 1.292E-04 2.304E-04 2.727E-04 2.064E-04 1.848E-04 2.167E-04 1.348E-06 5.071E-04 5.120E-04 2.951E-04 1.989E-04 1.565E-04 3.761E-04 3.039E-04 3.407E-04 2.557E-04 2.374E-04 3.301E-04 3.495E-04 1.090E-04 2.260E-04 1.141E-04 2.354E-04 1.026E-04 2.257E-04 6.050E-05 2.193E-04 2-275 (Continued) 2-276 TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued ) Cmpd. no. Name 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Formula C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si CAS 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 Mol. wt. 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 C1 −11.5 −15.097 −10.968 −10.631 0.10842 −10.93 7.2565 −10.716 −11.796 −11.344 −10.577 −10.62 −20.425 −12.08 152.9 −17.641 −37.347 −16.0542 −46.166 −12.373 −15.404 −134.91 −18.315 −7.0046 7.875 14.354 19.822 −13.563 −40.706 −12.24 −15.485 −22.11 −6.894 1.8878 −53.908 −290.36 −11.012 −8.521 −9.8417 −13.037 −11.311 −11.331 −11.452 −9.7574 −8.9215 0.7109 −11.499 C2 993 1426.9 885.49 1086.4 300.2 699.5 221.4 1140.5 1463.5 1168.9 1172.6 448.99 1515.5 1112.2 −10,183 1067.5 2835 2221.79 3086.2 2017.5 1390 6054.2 2283.5 276.38 781.98 −154.6 −0.12598 1208.6 3035 1836.4 1325.6 1673 818.6 78.865 4030.8 14,251 967.4 634.2 876.4 2346 1337.2 908.46 1172.7 729.43 950.8 386.51 1122.6 C3 C4 C5 0.022 0.51512 −1.6831 −2.7946 −0.047736 0.04513 −0.14244 0.000083967 1.4444 0.09654 −22.709 50,373,000,000 −4 1.0317 3.7937 0.63829 5.104 0.5564 19.337 0.95485 −0.6087 −3.0418 −3.7887 −4.9793 0.377 4.2655 0.021868 0.6432 1.641 −0.5941 −2.1554 5.9704 42.486 −0.3314 −0.1708 −0.02982 0.00042478 −0.00010095 −0.14912 −0.32687 −1.7754 −0.00002443 2 −3.11E-18 7 −0.000040369 2 Tmin, K Viscosity at Tmin 187.65 204.81 159.95 226.1 240.91 200 220 239.66 223.16 184.99 188.44 131.65 240 160 274.18 2.258E-03 4.569E-03 4.375E-03 2.950E-03 3.796E-04 5.917E-04 1.103E-03 1.992E-03 5.311E-03 8.315E-03 6.093E-03 7.398E-04 2.041E-03 9.669E-03 6.023E-02 341.45 397.55 337.45 366.15 371 308.15 331.13 392.7 484.92 396.58 382.9 248.31 425.15 362.93 612.8 2.110E-04 2.194E-04 2.378E-04 4.695E-04 1.186E-04 1.734E-04 2.509E-04 3.045E-04 1.541E-04 2.956E-04 2.336E-04 1.490E-04 2.981E-04 2.147E-04 1.109E-04 225 291.67 413.79 284.95 293.15 260 262.15 309.58 90.35 200 220 192.15 178.2 250 258.15 250 200 253.15 104 284.29 260.15 250 160.65 245 155.15 180 140 204.15 125.26 250 200 167.55 6.696E-04 2.253E-03 1.071E-03 1.525E-03 4.124E-03 9.454E-04 3.002E-03 4.242E-03 1.247E-03 1.315E-02 1.132E-03 1.727E-03 8.012E-03 6.643E-03 6.705E-03 1.319E-03 6.406E-03 9.605E-04 6.334E-04 2.487E-03 1.305E-01 7.909E-04 1.918E-03 7.435E-04 8.035E+00 1.765E-02 7.908E-03 3.319E-03 9.520E-03 9.848E-04 1.156E-03 8.239E-03 310.48 464 559.2 374.65 613.44 382.35 526.4 616.93 300 440 473.15 289.73 413.1 486.55 466.95 394.65 404.94 378.15 250 483.15 576 329 283.85 345 510.1 417.15 326.15 386.55 308.15 372.25 337.01 371.05 2.528E-04 3.547E-04 3.214E-04 4.610E-04 1.134E-04 2.118E-04 1.220E-04 2.078E-04 3.587E-05 1.416E-04 9.061E-05 2.236E-04 2.326E-04 3.109E-04 2.822E-04 2.533E-04 2.956E-04 2.599E-04 6.142E-05 1.723E-04 1.276E-04 3.123E-04 2.863E-04 2.486E-04 2.165E-04 2.522E-04 1.949E-04 2.207E-04 2.626E-04 2.480E-04 2.086E-04 2.089E-04 Tmax, K Viscosity at Tmax 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 8.18 −10.064 −10.118 −10.501 −7.6591 −74.521 −48.529 −10.923 −9.6312 −19.991 −9.5468 −98.159 −40.543 −66.654 −125.81 −9.3874 −13.929 −10.819 −11.812 −2.7947 −20.182 0.1369 −56.569 −46.402 −39.324 −82.705 −11.445 −13.684 −10.903 −4.2684 −10.073 −4.7263 −3.7464 −75.781 −11.661 −11.633 −116.34 −21.927 353.99 −10.905 −11.497 −31.157 −117.73 −14.527 −6.1572 −25.317 −4.648 13.557 −2.8737 10.848 −75.6 1058.7 464.42 427.78 603.36 5081.5 3394.7 894.63 −3.841 2245.1 1147.2 3592.6 3328.3 5325.8 7996 1204.9 1321.9 841.33 1291.9 563.86 2203.5 633.77 2140.5 3448.6 3841 7404.9 1187.2 1283.4 796.19 647.6 1123.3 594.43 624.2 4175.4 24.7 316.38 3834.6 1266.5 13,928 762.11 1365.7 1926 9943.3 1497.7 178.15 1789.2 1832 −187.3 301.35 75 −3.5148 −0.17162 0.0086309 −0.53378 9.0873 5.3903 −0.00068418 −1.458 1.1982 −0.23251 14.197 4.1804 7.66 16.412 −0.32618 0.40382 0.076469 −1.1636 1.2289 −1.6659 7.5175 5.0849 3.6933 6.4721 0.0029076 0.33755 −1.0087 −0.16515 −0.86247 −1.084 9.6508 −0.261 0.56191 16.864 1.5927 −41.717 −0.11863 0.036966 2.925 14.589 0.51747 −0.95239 2.069 −1.2191 −3.6592 −1.2271 −3.297 −1.065E-08 10 −0.000029555 2 −2.2512E-28 −7.6643E-17 9.9041 6 −0.000017676 2 −2.12E-30 1.5016 10.485 0.41014 −7.27E-09 −4.10E-16 3 10 −2.5875E-10 −2962 −9.0606E-24 4 −0.5 10 53.48 232.15 129.95 131.35 155.15 273.15 281.45 200 2.2 295.13 229.8 180.15 265.83 239.15 220 234.15 250 154.12 229.92 192.22 291.31 214.93 174.65 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 158.97 259.83 189.79 187.68 250 250 409.15 288.15 90.69 175.47 301.15 250 170.45 275 7.317E-04 1.599E-03 1.438E-03 7.450E-04 1.560E-03 7.171E-03 2.319E-03 1.575E-03 3.628E-06 3.814E-03 2.971E-03 4.341E-03 9.242E-03 8.805E-02 3.856E-01 2.427E-03 1.642E-03 4.701E-03 3.097E-03 2.528E-03 3.536E-03 2.849E-03 2.379E-03 5.854E-03 8.570E-02 4.919E-01 2.561E-03 2.563E-03 7.197E-03 3.550E-03 6.035E-03 8.332E-03 2.483E-03 1.451E-03 2.546E-05 9.207E-04 1.003E-03 2.754E-04 1.545E-03 5.726E-04 2.938E-03 6.737E-04 3.386E-03 1.664E-03 2.063E-04 1.193E-02 3.995E-03 6.135E-04 6.045E-04 6.126E-04 140 453.15 235.45 194.82 253.85 493 373.71 304.5 5.1 575.3 426.15 432.16 496.15 448.6 432.9 421.15 424.18 429.92 450.09 447.2 564.15 401.15 406.08 478.85 429.9 412.4 400.7 396.65 336.63 432 425.81 412 435 522.52 33 206.45 318.15 298.85 368.92 350 450 453.15 580 434.15 188 337.85 478.15 425 373.15 400 5.954E-05 1.542E-04 2.900E-04 2.587E-04 2.645E-04 3.829E-04 5.444E-04 3.392E-04 2.532E-06 2.088E-04 2.580E-04 1.003E-04 3.754E-04 3.190E-04 2.707E-04 2.040E-04 2.318E-04 1.417E-04 2.087E-04 1.777E-04 2.054E-04 2.563E-04 1.164E-04 4.019E-04 3.343E-04 3.274E-04 2.108E-04 2.185E-04 1.959E-04 1.377E-04 2.172E-04 2.083E-04 1.368E-04 2.191E-04 3.906E-06 8.206E-04 5.777E-05 1.821E-04 1.185E-04 8.089E-05 2.649E-04 1.214E-04 4.281E-04 3.582E-04 2.262E-05 3.442E-04 2.392E-04 1.198E-04 8.846E-05 1.636E-04 (Continued) 2-277 2-278 TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 Cmpd. no. 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued ) Name Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Formula CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne CAS 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 Mol. wt. 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 C1 C2 C3 1074 2267.4 648.37 889.11 1048.5 4169.6 705.48 639.21 441.1 949.12 1067.3 433.58 1141.7 1009.7 1213.1 3219 3150.5 3173.2 612.62 679.07 788.86 745.32 627.18 520.68 863.65 2113.3 888.42 1168.7 0.84203 1.4173 −0.041947 0.20469 −1.5474 4.7 −0.011113 −0.38409 −1.0547 −0.00012343 −0.017484 −1.3238 0.15014 −11.216 −11.272 −11.075 −10.628 −0.099 −12.579 −12.86 −11.391 −13.912 400.35 −10.385 −4.841 −10.705 −10.569 737.75 1048.9 990.72 645 496 2224.2 946.91 1090.8 797.09 −30,387 599.59 696.7 788.94 952.38 0.019308 0.00030493 −11.632 −13.415 −10.34 −19.308 −17.945 1251.6 1050.5 519.61 1822.5 115.57 −17.044 −21.971 −10.481 −12.596 −1.035 −46.377 −10.755 −8.4453 −3.6585 −11.278 −10.97 −1.8842 −12.206 −12.002 −11.358 −6.1534 −6.6904 −6.6915 −1.8553 −4.8515 −6.7424 −10.517 −11.104 −1.0598 −10.842 −39.641 −11.27 −11.394 C4 C5 −1.4494 −1.392 −1.3046 −1.3774 −0.93238 −0.69862 0.036581 −1.4961 −0.00074603 4.308 0.024736 −0.007539 0.025885 −1.5939 0.26191 1.0752E-07 0.45308 −56.971 −0.046088 −0.9194 −0.048383 −0.063873 0.071692 0.33157 −0.013899 1.218 1.428 550,680,000 0 −2.14E-17 −3 0 10 Tmin, K Viscosity at Tmin 179.69 288.15 159.53 150 298.15 155.95 135.58 139.39 160.15 157.48 175.3 183.45 200 139.05 146.58 299.15 280.15 269.15 248.15 146.62 168.54 275 160 186.48 167.23 250 188 189.15 1.236E-03 2.299E-03 1.321E-03 3.542E-03 1.774E-03 5.989E+01 3.675E-03 3.164E-03 1.915E-03 5.239E-03 6.930E-03 1.628E-03 3.339E-03 8.734E-03 4.587E-02 2.584E-02 3.729E-02 1.107E-01 9.288E-04 7.669E-03 3.539E-03 4.070E-04 9.133E-04 2.266E-03 3.409E-03 6.104E-04 1.637E-03 5.222E-03 273.15 472.65 314 310 450.15 404.15 304.3 311.7 390.15 343.31 396.58 364 375.9 353.6 457.68 548.8 491.2 493.6 353.15 433.6 420.8 314.7 280.5 535.5 339.8 304.9 331.7 389.15 2.275E-04 2.149E-04 1.739E-04 1.928E-04 2.859E-04 3.891E-04 2.034E-04 1.841E-04 1.476E-04 2.006E-04 2.286E-04 2.035E-04 2.539E-04 1.066E-04 1.653E-04 8.025E-05 1.360E-04 2.356E-04 2.742E-04 1.301E-04 1.129E-04 2.891E-04 1.731E-04 7.577E-05 2.474E-04 3.134E-04 2.143E-04 2.170E-04 127.93 180.15 171.64 150.18 260 240 119.55 176 110 295.56 132.81 250 133.97 160.17 4.722E-03 4.305E-03 4.977E-03 2.022E-03 8.635E-04 3.646E-02 2.506E-02 5.554E-03 1.072E-02 5.334E-03 2.253E-03 8.002E-04 6.390E-03 7.103E-03 303.92 367.55 553.1 279.11 400 518.15 333.41 372 310.95 451.21 266.25 352.6 312.2 368.69 1.703E-04 2.212E-04 9.292E-05 2.826E-04 2.229E-04 2.519E-04 2.038E-04 2.120E-04 1.588E-04 1.006E-04 2.270E-04 2.593E-04 2.127E-04 2.333E-04 249.95 164.55 151.15 353.43 25.09 1.972E-03 4.801E-03 9.377E-04 9.077E-04 1.602E-04 438.65 328.2 278.65 633.15 44.13 2.382E-04 2.502E-04 1.929E-04 1.892E-04 2.706E-05 Tmax, K Viscosity at Tmax 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde C2H5NO2 N2 F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 −4.438 16.004 −9.5556 19.329 −246.65 −16.403 −4.3492 −68.54 −48.851 −39.863 −98.854 −11.069 −11.319 −2.3409 −22.688 −2.5373 −98.805 −60.795 −0.22128 −145.99 −11.736 −20.804 −11.19 −11.498 −3.8552 −27.978 −4.1476 −10.94 −19.299 −8.2185 −53.509 −37.067 −36.561 −16.456 −11.055 −2.8695 −10.667 −6.9168 −11.677 −1.7273 −3.7241 −22.472 −15.822 −11.31 195.25 −6.3528 −17.156 23.467 −8.8918 −11.208 −5.9402 746.5 −181.61 981.64 −381.68 3150.3 2119.5 1052.7 3165.3 4095 4089 7183.8 1081.7 1428 715.52 2466 900.91 3905.5 4617.8 3018.4 9296.7 1415.2 1834.6 1057.4 1362.1 684.22 2915.1 94.04 415.96 2088.6 919.43 1836.6 2856.7 3542.2 3209.9 1005.3 596.32 659.56 818.76 1091.2 424.34 516.54 2566.9 3301.8 1280 −11,072 240.85 646.25 116.07 2357.6 1079.8 617.95 −0.9385 −5.1551 200 63.15 3.420E-03 2.633E-04 387.22 124 3.027E-04 3.331E-05 −0.19453 −4.8618 49.98 0.6881 −1.0035 9.0919 5.294 3.7631 12.283 244.6 210 109.5 305.04 267.3 218.15 285.55 280 238.15 191.91 253.05 223.15 301.31 251.65 211.15 289.65 280 241.55 252.85 255.55 171.45 223.95 193.55 462.65 54.36 77.55 283.07 191.59 143.42 270 253.15 200 250 234.18 108.02 220 197.45 167.45 163.83 372.38 291.45 243.15 404.15 136.87 85.47 146.95 185.26 199 165 1.344E-03 2.065E-04 3.858E-04 4.012E-03 2.432E-03 3.306E-03 1.030E-02 1.733E-02 2.310E-01 4.372E-03 3.026E-03 3.206E-03 3.926E-03 2.555E-03 2.629E-03 6.652E-03 1.472E-02 1.856E-01 2.161E-03 2.039E-03 6.587E-03 4.837E-03 3.614E-03 6.539E-04 7.170E-04 3.787E-03 3.486E-03 3.532E-03 3.529E-03 3.773E-03 1.649E-02 6.660E-01 9.009E-04 1.024E-03 1.045E-02 1.643E-03 3.745E-03 2.322E-03 1.902E-03 1.920E-03 1.119E-02 2.368E-03 1.229E-03 5.772E-04 9.458E-03 2.069E+01 3.917E-01 3.083E-03 2.522E-03 374.35 283.09 180.05 603.15 465.52 593.15 528.75 486.25 471.7 420.02 492.95 487.2 589.86 445.15 454.96 512.85 468.35 452.9 446.15 440.65 453.52 472.19 468 516 150 208.8 543.84 375.15 465.15 458.95 410.95 392.2 375.46 375.14 303.22 385.15 399.79 378 415.2 610.03 555.4 522.4 557.65 298.15 360 370.35 355.3 508.8 322.15 3.078E-04 7.730E-05 3.791E-05 2.068E-04 2.606E-04 4.997E-05 3.670E-04 2.823E-04 3.334E-04 2.048E-04 1.912E-04 2.172E-04 2.057E-04 2.614E-04 1.111E-04 3.576E-04 2.902E-04 5.409E-04 1.913E-04 2.075E-04 1.422E-04 1.999E-04 1.868E-04 4.399E-04 6.990E-05 1.300E-04 2.091E-04 2.539E-04 4.796E-05 3.510E-04 3.842E-04 2.557E-04 2.354E-04 2.232E-04 2.051E-04 2.385E-04 2.463E-04 1.898E-04 9.980E-05 2.849E-04 5.134E-05 1.420E-04 1.986E-04 1.416E-04 4.275E-05 4.735E-04 4.892E-04 1.133E-04 2.470E-04 −0.022545 −1.222 1.5703 −1.2685 14.103 7.028 −2.8054 19.285 0.0003618 1.3403 −0.22541 1 −0.000013519 2 −0.000025112 2 0.000013141 2 −0.000019627 2 0.015575 −1.0071 2.3374 −1.207 1.1091 −0.42363 7.1409 3.7344 3.3364 −8.0487E-37 12.84 0.0039301 −1.2025 −0.59628 0.10658 −1.342 −1.1167 1.5749 −29.084 −0.58229 1.1101 −5.3372 −0.91376 −0.74183 −7.3439E-11 2,880,100,000 4 −4.0267 2-279 (Continued) 2-280 TABLE 2-139 Eqn 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 101 Cmpd. no. 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Viscosity of Inorganic and Organic Liquids (Pa∙s) (Continued ) Name Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene Formula C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 CAS Mol. wt. 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 C1 C2 C3 −23.931 −6.698 17.797 −9.8074 −18.282 −92.082 −73.735 −5.7244 −10.153 −804.54 −14.846 1834.6 753.58 −252.43 1010.4 1549.7 1907.3 2668.2 638.2 840.71 30,487 1829.4 1.9124 −0.63783 −4.291 −0.25697 1.0454 15.639 10.993 −0.76415 −0.093763 130.79 0.3729 −22.675 −104.32 46.223 3.8305 −88.793 −11.566 −215.09 −136.73 −10.321 −118.86 −10.843 5.5351 −16.671 −226.08 0.388 −111.98 −3.7067 10.142 −11.756 −9.6461 −12.928 −4.0309 −10.707 −11.504 52.176 −69.778 −22.407 −2.2333 0.26297 −10.37 −52.843 −11.91 −15.489 −7.381 1758 9615.1 −1378 41.21 6400.7 2843.2 11,612 6421.3 900.92 5829.5 1165.2 632.38 1342.5 6805.7 736.5 5468.6 585.78 −130.41 1483.1 1281.2 1137.5 990.76 1818.5 3301 −4951.9 5905.2 1462.8 320.37 276.55 823.31 3703.6 1094.9 1393.5 911.7 1.6701 12.587 −8.7475 −2.1342 10.709 31.849 19.493 −0.069128 16.605 −2.6576 0.8388 37.542 −1.7063 15.579 −1.0926 −3.2199 −0.040387 −0.29478 0.25725 −1.1771 −0.39102 −8.5676 8.0214 1.7006 −1.2915 −1.7282 5.866 0.13825 0.63711 −0.54152 C4 C5 −0.043098 −0.018364 1 1 −0.15449 1 −0.026882 −0.00002297 1 2 −0.000016991 2 −0.060853 1 −0.000016992 2 −3.6929E-28 10 570,980 −5.879E-29 −2 10 Tmin, K Viscosity at Tmin 252.45 180.37 250 188.36 200 87.89 180.25 142.61 159.95 213.15 388.85 2.275E-03 2.928E-03 1.002E-03 3.060E-03 6.774E-03 1.549E-02 5.852E-03 6.477E-03 4.641E-03 9.502E+02 3.642E-04 414.32 370.25 473.15 321 432.39 333.15 353.97 325.71 340.87 500.8 454 3.430E-04 2.172E-04 1.045E-04 2.908E-04 2.357E-04 5.147E-05 2.810E-04 2.784E-04 2.656E-04 3.307E-04 1.965E-04 242.54 460.85 225 223.15 289.95 700.15 329.35 277.65 164.65 237.4 293.15 373.96 250 178.18 236.5 267.67 250 200 247.79 229.33 165.78 172.22 398.4 353.15 247.57 288.45 225 173.15 130 178.35 273.16 225.3 247.98 286.41 1.919E-03 1.913E-03 6.900E-04 5.388E-04 2.477E-03 5.502E-04 1.736E-02 3.350E-03 5.505E-03 1.183E-02 1.040E-03 1.999E-04 1.269E-03 1.569E-02 2.955E-03 3.399E-03 6.135E-04 5.156E-04 2.495E-03 3.477E-03 8.636E-03 1.305E-02 2.150E-03 1.167E-02 3.240E-03 2.089E-02 1.237E-03 8.764E-04 2.425E-03 3.171E-03 1.702E-03 1.834E-03 1.735E-03 7.021E-04 418.31 591 400 318.69 318.15 795.28 723.15 554.4 373.15 576 303.15 454 393.15 383.78 387 540 359.05 308.15 449.27 442.53 541.15 387.91 676.8 625 511.2 590.15 345.65 364 400 434.52 646.15 413.1 418.1 413.1 2.268E-04 4.426E-04 6.557E-05 2.383E-04 9.456E-04 3.385E-04 1.522E-04 1.170E-04 2.446E-04 1.458E-04 9.125E-04 8.859E-05 2.625E-04 2.428E-04 3.798E-04 1.520E-04 2.028E-04 1.612E-04 1.663E-04 1.942E-04 4.530E-05 2.049E-04 3.288E-04 1.601E-04 1.569E-04 1.856E-04 2.654E-04 1.273E-04 8.272E-05 2.086E-04 5.028E-05 2.189E-04 2.459E-04 2.169E-04 Tmax, K Viscosity at Tmax Except for deuterium, the liquid viscosity is calculated by Eqn 101: µ = exp(C1 + C2/T + C3 ln T + C4T C5) where µ is the viscosity in Pa∙s and T is the temperature in K. Viscosity is either 1 atm or the vapor pressure, whichever is higher. For deuterium, liquid viscosity is calculated by Eqn 100: µ = C1 + C2T + C3T 2 + C4T 3 + C5T 4 where µ is the viscosity in Pa∙s and T is the temperature in K. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. TRAnSPORT PROPERTIES TABLE 2-140 Viscosities of Liquids: Coordinates for Use with Fig. 2-19 Liquid Acetaldehyde Acetic acid, 100% Acetic acid, 70% Acetic anhydride Acetone, 100% Acetone, 35% Acetonitrile Acrylic acid Allyl alcohol Allyl bromide Allyl iodide Ammonia, 100% Ammonia, 26% Amyl acetate Amyl alcohol Aniline Anisole Arsenic trichloride Benzene Brine, CaCl2, 25% Brine, NaCl, 25% Bromine Bromotoluene Butyl acetate Butyl acrylate Butyl alcohol Butyric acid Carbon dioxide Carbon disulfide Carbon tetrachloride Chlorobenzene Chloroform Chlorosulfonic acid Chlorotoluene, ortho Chlorotoluene, meta Chlorotoluene, para Cresol, meta Cyclohexanol Cyclohexane Dibromomethane Dichloroethane Dichloromethane Diethyl ketone Diethyl oxalate Diethylene glycol Diphenyl Dipropyl ether Dipropyl oxalate Ethyl acetate Ethyl acrylate Ethyl alcohol, 100% Ethyl alcohol, 95% Ethyl alcohol, 40% Ethyl benzene Ethyl bromide 2-Ethyl butyl acrylate Ethyl chloride Ethyl ether Ethyl formate 2-Ethyl hexyl acrylate Ethyl iodide Ethyl propionate Ethyl propyl ether Ethyl sulfide Ethylene bromide Ethylene chloride Ethylene glycol Ethylidene chloride Fluorobenzene Formic acid X Y 15.2 12.1 9.5 12.7 14.5 7.9 14.4 12.3 10.2 14.4 14.0 12.6 10.1 11.8 7.5 8.1 12.3 13.9 12.5 6.6 10.2 14.2 20.0 12.3 11.5 8.6 12.1 11.6 16.1 12.7 12.3 14.4 11.2 13.0 13.3 13.3 2.5 2.9 9.8 12.7 13.2 14.6 13.5 11.0 5.0 12.0 13.2 10.3 13.7 12.7 10.5 9.8 6.5 13.2 14.5 11.2 14.8 14.5 14.2 9.0 14.7 13.2 14.0 13.8 11.9 12.7 6.0 14.1 13.7 10.7 4.8 14.2 17.0 12.8 7.2 15.0 7.4 13.9 14.3 9.6 11.7 2.0 13.9 12.5 18.4 18.7 13.5 14.5 10.9 15.9 16.6 13.2 15.9 11.0 12.6 17.2 15.3 0.3 7.5 13.1 12.4 10.2 18.1 13.3 12.5 12.5 20.8 24.3 12.9 15.8 12.2 8.9 9.2 16.4 24.7 18.3 8.6 17.7 9.1 10.4 13.8 14.3 16.6 11.5 8.1 14.0 6.0 5.3 8.4 15.0 10.3 9.9 7.0 8.9 15.7 12.2 23.6 8.7 10.4 15.8 Liquid Glycerol, 100% Glycerol, 50% Heptane Hexane Hydrochloric acid, 31.5% Iodobenzene Isobutyl alcohol Isobutyric acid Isopropyl iodide Kerosene Linseed oil, raw Mercury Methanol, 100% Methanol, 90% Methanol, 40% Methyl acetate Methyl acrylate Methyl i-butyrate Methyl n-butyrate Methyl chloride Methyl ethyl ketone Methyl formate Methyl iodide Methyl propionate Methyl propyl ketone Methyl sulfide Naphthalene Nitric acid, 95% Nitric acid, 60% Nitrobenzene Nitrogen dioxide Nitrotoluene Octane Octyl alcohol Pentachloroethane Pentane Phenol Phosphorus tribromide Phosphorus trichloride Propionic acid Propyl acetate Propyl alcohol Propyl bromide Propyl chloride Propyl formate Propyl iodide Refrigerant R-22 Sodium Sodium hydroxide, 50% Stannic chloride Succinonitrile Sulfur dioxide Sulfuric acid, 110% Sulfuric acid, 100% Sulfuric acid, 98% Sulfuric acid, 60% Sulfuryl chloride Tetrachloroethane Thiophene Titanium tetrachloride Toluene Trichloroethylene Triethylene glycol Turpentine Vinyl acetate Vinyl toluene Water Xylene, ortho Xylene, meta Xylene, para X Y 2.0 6.9 14.1 14.7 13.0 12.8 7.1 12.2 13.7 10.2 7.5 18.4 12.4 12.3 7.8 14.2 13.0 12.3 13.2 15.0 13.9 14.2 14.3 13.5 14.3 15.3 7.9 12.8 10.8 10.6 12.9 11.0 13.7 6.6 10.9 14.9 6.9 13.8 16.2 12.8 13.1 9.1 14.5 14.4 13.1 14.1 17.2 16.4 3.2 13.5 10.1 15.2 7.2 8.0 7.0 10.2 15.2 11.9 13.2 14.4 13.7 14.8 4.7 11.5 14.0 13.4 10.2 13.5 13.9 13.9 30.0 19.6 8.4 7.0 16.6 15.9 18.0 14.4 11.2 16.9 27.2 16.4 10.5 11.8 15.5 8.2 9.5 9.7 10.3 3.8 8.6 7.5 9.3 9.0 9.5 6.4 18.1 13.8 17.0 16.2 8.6 17.0 10.0 21.1 17.3 5.2 20.8 16.7 10.9 13.8 10.3 16.5 9.6 7.5 9.7 11.6 4.7 13.9 25.8 12.8 20.8 7.1 27.4 25.1 24.8 21.3 12.4 15.7 11.0 12.3 10.4 10.5 24.8 14.9 8.8 12.0 13.0 12.1 10.6 10.9 2-281 2-282 PHYSICAL AnD CHEMICAL DATA FIG. 2-19 Nomograph for viscosities of liquids at 1 atm. For coordinates see Table 2-141. To convert centipoise to pascalseconds, multiply by 0.001. TRAnSPORT PROPERTIES 2-283 TABLE 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) Dv in cm2/s Substance Acetic acid Acetone n-Amyl alcohol sec-Amyl alcohol Amyl butyrate Amyl formate i-Amyl formate Amyl isobutyrate Amyl propionate Aniline Anthracene Argon Benzene Benzidine Benzyl chloride n-Butyl acetate i-Butyl acetate n-Butyl alcohol i-Butyl alcohol Butyl amine i-Butyl amine i-Butyl butyrate i-Butyl formate i-Butyl isobutyrate i-Butyl proprionate i-Butyl valerate Butyric acid i-Butyric acid Cadmium Caproic acid i-Caproic acid Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Chlorobenzene Chloroform Chloropicrin m-Chlorotoluene o-Chlorotoluene p-Chlorotoluene Cyanogen chloride Cyclohexane n-Decane Diethylamine 2,3-Dimethyl butane Diphenyl n-Dodecane Ethane Ethanol Ether (diethyl) Ethyl acetate Ethyl alcohol Ethyl benzene Ethyl n-butyrate Ethyl i-butyrate Ethylene Ethyl formate Ethyl propionate Ethyl valerate Eugenol Formic acid Helium n-Heptane n-Hexane Hexyl alcohol Hydrogen Temp., °C 0 0 0 30 0 0 0 0 0 0 30 0 20 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 25 500‡ 0 0 450‡ 0 30 0 25 0 0 0 0 15 45 90 0 15 0 126 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 20 38 15 0 0 25 500 Air A H2 0.1064 .109 .0589 .072 .040 .0543 .058 .0419 .046 .0610 .075 .0421 0.416 .361 .235 .077 .0298 .066 .058 .0612 .0703 .088 .0727 .0821 .0853 .0468 .0705 .0457 .0529 .0424 .067 .0679 .306 O2 N2 CO2 N2O CH4 C2H6 C2H4 n-C4H10 i-C4H10 0.0716 .0422 .171 .1914 .0347 0.194 0.0797 .0528 .2364 .2716 .0425 .0476 .2771 .0483 .185 .0327 .191 .203 .173 .264 .271 .0364 .0366 .0308 .0476 .0471 .17 .050 .0513 .138 .550 .139 0.096 .163 .0996∗ 0.153 .00215† .9 .0892 .369 .651 .293 .185 1.0 0.0636 .319 .0744 .063 .137 0.116 .075 .091 .088 .054 .059 .051 .111 0.0719 .0760 .086 .306 .0841 .0884 .0657 .301 .0753 .0751 .0610 .308 .459 .377 .298 .273 .0778 .0715 .089 .102 .0658 .0579 .0591 .0840 .068 .0512 .0377 .1308 .0813 .0686 .0546 .0487 .375 .0685 .224 .229 .486 .337 .236 .205 .0407 .0413 .0573 .0450 .0367 .510 .0874 Ref. 8 6, 16 8 5 8 8 8 8 8 8 5 8 18 8, 15 8 8 8 8 8 5 8 8 8 8 8 8 8 8 8 8 13 8 8 8 19 1, 9 18 8 8 18 16, 17 5 6 10 8 8 8 10 3 6 3 8 3 8 3 8 20 7, 8 8 5 8 8 8 8 8 8 4, 8 8 8 8 8 19 .641 .705 .066§ .0663 .0499 .611 .290 .200 .0753 .697 4.2 .0757 .674 .0351 .550 .646 .535 .625 0.459 .537 0.486 .726 0.272 0.277 3 8 8 2 18 (Continued) 2-284 PHYSICAL AnD CHEMICAL DATA TABLE 2-141 Diffusivities of Pairs of Gases and Vapors (1 atm) (Continued ) Dv in cm2/s Substance Temp., °C Air Hydrogen cyanide Hydrogen peroxide Iodine Mercury Mesitylene Methane Methyl acetate Methyl alcohol Methyl butyrate Methyl i-butyrate Methyl cyclopentane Methyl formate Methyl propionate Methyl valerate Naphthalene Nitrogen 0 60 0 0 0 500 0 0 0 0 15 0 0 0 0 0 25 0 0 30 0 0 0 0 0 0 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 25 0 30 0 0.173 .188 .07 .112 .056 Nitrous oxide n-Octane Oxygen Phosgene Propionic acid Propyl acetate n-Propyl alcohol i-Propyl alcohol n-Propyl benzene i-Propyl benzene n-Propyl bromide i-Propyl bromide Propyl butyrate Propyl formate n-Propyl iodide i-Propyl iodide n-Propyl isobutyrate i-Propyl isobutyrate Propyl propionate Propyl valerate Safrol i-Safrol Sulfur hexafluoride Toluene Trimethyl carbinol 2,2,4-Trimethyl pentane 2,2,3-Trimethyl heptane n-Valeric acid i-Valeric acid Water H2 O2 N2 CO2 N 2O CH4 C2H6 C2H4 n-C4H10 0.0731 .0872 .0735 0.0569 .0513 18 0.0567 .0879 .0446 .0451 0.0742 0.0758 .295 .0528 0.181 0.165 .096 0.535 .0505 0.0642 .178 .095 .0829 .067 .085 .0818 .101 .0481 .0489 .085 .0902 .0530 .0712 .079 .0802 .0549 .059 .057 .0466 .0434 .0455 .271 .697 0.0705 0.0710 0.181 .139 .330 .0588 .315 .0577 .206 .281 .0364 .0490 .212 .0388 .212 .189 .0395 .0341 .418 .076 .088 .087 0.071 0.0618 .288 0.0688 .270 0.050 0.0544 0.220 .212 .75 Ref. 10 11 8, 12, 14 8, 12, 13 8 1.1 .333 .506 .242 .257 .318 i-C4H10 0.070 .13 0.53 .084 .132 .0633 .0639 30 90 0 0 0 450 A 0.148 0.163 0.0960 0.0908 8 8 8 8 3 8 8 8 8 8 2 8 8 3 8 10 8 8 8 8 5 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 4, 8 5 8 0.0705 3 0.0684 3 8 8 8, 20 18 .0376 .138 1.3 ∗ 320 mmHg. † 40 atm. ‡ Also at other temperatures. § Strong function of concentration. References 1 Amdur, Irvine, Mason, and Ross, J. Chem. Phys., 20, 436 (1952). 2 Boyd, Stein, Steingrimsson, and Rumpel, J. Chem. Phys., 19, 548 (1951). 3 Cummings and Ubbelohde, J. Chem. Soc. (London), 1953, p. 3751. 4 Fairbanks and Wilke, Ind. Eng. Chem., 42, 471 (1950). 5 Gilliland, Ind. Eng. Chem., 26, 681 (1934). 6 Gorynnova and Kuvskinskii, Zhur. Tekh. Fiz., 18, 1421 (1948). 7 Hansen, Dissertation, Jena, 1907. 8 International Critical Tables, vol. 5, p. 62. 9 Jeffries and Drickamer, J. Chem. Phys., 22, 436 (1954). 10 Klotz and Miller, J. Am. Chem. Soc., 69, 2557 (1947). 11 McMurtrie and Keyes, J. Am. Chem. Soc., 70, 3755 (1948). 12 Mullaly and Jacques, Phil. Mag., 48, 6, 1105 (1924). 13 Spier, Physica, 6 (1939): 453; 7, 381 (1940). 14 Topley and Whytlaw-Gray, Phil. Mag., 4, 873 (1927). 15 Trautz and Ludwig, Ann. Physik, 5, 5, 887 (1930). 16 Trautz and Muller, Ann. Physik, 22, 353 (1935). 17 Trautz and Ries, Ann. Physik, 8, 163 (1931). 18 Walker and Westenberg, J. Chem. Phys., 32, 136 (1960). 19 Westenberg and Walker, J. Chem. Phys., 26, 1753 (1957). 20 Winkelmann, Wied. Ann., 22, 152 (1884); 23, 203 (1884); 26, 105 (1885); 33, 445 (1888); 36, 92 (1889). TRAnSPORT PROPERTIES Table 2-143 has a representative selection of diffusion coefficients. The subsection “Prediction and Correlation of Physical Properties” should be consulted for estimation techniques. TABLE 2-142 Diffusivities in Liquids (25çC) Dilute solutions and 1 atm unless otherwise noted; use DLµ/T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration. Solute Solvent DL × 105, sq cm/sec Acetal∗ Acetamide∗ Acetamide∗ Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid Acetic acid∗ Acetonitrile Acetylene Allyl alcohol∗ Allyl alcohol Ammonia∗ i-Amyl alcohol∗ i-Amyl alcohol Benzene Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzene (50 mole %) Benzoic acid Benzoic acid Benzoic acid Benzoic acid Benzoic acid Bromine Bromine Bromine Bromobenzene Bromoform∗ Bromoform Bromoform Bromoform∗ Bromoform Bromoform n-Butanol Caffeine Carbon dioxide Carbon dioxide Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 218 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %, 100 atm.) Carbon disulfide (50 mole %, 50 atm.) Carbon disulfide (50 mole %, 200 atm.) Carbon disulfide (50 mole %) Carbon tetrachloride Carbon tetrachloride∗ Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride∗ Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Carbon tetrachloride Chloral∗ Chloral hydrate Ethanol Ethanol Water Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Water Water Water Ethanol Water Water Ethanol Water Carbon tetrachloride n-Decane 2,4-Dimethyl pentane n-Dodecane n-Heptane n-Hexadecane n-Octadecane Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Benzene Carbon disulfide Water Benzene Acetone i-Amyl alcohol Ethanol Ethyl ether Methanol n-Propanol Water Water Ethanol Water n-Butanol i-Butanol Chlorobenzene 2,4-Dimethyl pentane n-Heptane Methyl cyclohexane n-Octane Toluene Benzene Cyclohexane Decalin Dioxane Ethanol n-Heptane Kerosene Methanol i-Octane Tetralin Ethanol Water 1.25 0.68 1.19 3.31 2.11 1.49 0.13 2.26 1.24 1.66 1.78, 2.11 1.06 1.19 1.7, 2.0, 2.3 0.87 1.0 1.53 1.72 2.49 1.40 2.47 0.96 0.86 2.62 1.38 0.91 0.043 1.49 2.7 4.1 1.3 2.30 2.90 0.53 1.08 3.62 2.20 0.94 0.96 0.63 4.0 1.96 3.57 2.42 3.00 3.63 3.0 3.5 3.10 2.06 2.04 1.49 0.776 1.02 1.50 3.17 0.961 2.30 2.57 0.735 0.68 0.77 Estimated possible, error, ± %1 5 5 3 3 5 5 6 5 8 5 5 6 6 1 3 2 2 2 2 2 2 2 2 2 5 7 Ref. 11 11 11 4 1, 4 4 4 4 11 11 1, 24 11 11 1, 11 11 11, 25 7 26 26 26 26 26 26 4 4 4 4 4 11 11 11 25 11 11 11 11 23 11 1, 11, 18, 25 11 11 1, 3, 5, 20, 24, 28 14 14 14 14 14 14 14 14 7, 9 9, 10∗ 9 9 9, 10∗ 9 9 9 9 9 11 11 (Continued) 2-285 2-286 PHYSICAL AnD CHEMICAL DATA TABLE 2-142 Diffusivities in Liquids (25çC) (Continued ) Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration. Solute Chlorine Chlorobenzene Chloroform Chloroform Cinnamic acid Cinnamic acid Cinnamic acid Cinnamic acid 1,1′-Dichloropropanol Dicyanodiamide∗ Diethyl ether Diethyl ether 2,4-Dimethyl pentane (50 mole %) 2,4-Dimethyl pentane (50 mole %) Ethanol∗ Ethyl acetate Ethylene dichloride Formic acid Formic acid Formic acid Formic acid Formic acid Formic acid Glucose Glycerol Glycerol Glycerol∗ n-Heptane (50 mole %) n-Heptane (50 mole %) n-Heptane (50 mole %) n-Heptane (50 mole %) Hexamethylene tetramine Hydrogen chloride∗ Hydrogen Hydrogen sulfide Hydroquinone∗ Hydroquinone∗ Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine∗ Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodine Iodobenzene Lactose∗ Maltose∗ Mannitol∗ Methanol Nicotine∗ Nitric acid∗ Nitrobenzene Nitrogen Nitrous oxide Oxalic acid∗ Solvent DL × 105, sq cm/sec Water Benzene Benzene Ethanol Acetone Benzene Carbon tetrachloride Toluene Water Water Benzene Water n-Dodecane n-Hexadecane Water Ethyl benzoate Benzene Acetone Benzene Carbon tetrachloride Ethylene glycol Toluene Water Water i-Amyl alcohol Ethanol Water n-Dodecane n-Hexadecane n-Octadecane n-Tetradecane Water Water Water Water Ethanol Water Acetic acid Anisole Benzene Bromobenzene Carbon disulfide Carbon tetrachloride Chloroform Cyclohexane Dioxane Ethanol Ethyl acetate Ethyl ether Ethylene bromide n-Heptane n-Hexane Mesitylene Methanol Methyl cyclohexane n-Octane Tetrabromoethane n-Tetradecane Toluene m-Xylene Ethanol Water Water Water Water Water Water Carbon tetrachloride Water Water Water 1.44 2.66 2.50 1.38 2.41 1.12 0.76 2.41 1.0 1.18 2.73 0.85 1.44 0.88 1.28 0.94 2.8 3.77 2.28 1.89 0.094 2.65 1.37 0.69 0.12 0.56 0.94 1.58 1.00 0.92 1.29 0.67 3.10 5.85 (4.4) 1.61 0.53 0.88, 1.12 1.13 1.25 1.98 1.25 3.2 1.45 2.30 1.80 1.07 1.30 2.2 3.61 0.93 3.4, 2.5 4.15 1.49 1.74 2.1 2.76 2.0 0.96 2.1 1.82 1.09 0.49 0.48 0.65 1.6 0.60 2.98 1.00 1.9 1.8 1.61 Estimated possible, error, ± %1 4 6 3 6 4 4 10 6 6 3 5 10 8 3 3 5 5 5 8 2 2 Ref. 1, 28 25 1, 25 11 4 4 4 4 11 11 25 2 26 26 1, 7, 9,∗ 11,∗ 22 6 1, 25 4 4 4 4 11 11 11 11 1, 11∗ 26 26 26 26 11 4, 11,∗ 12∗ 1, 11, 24(?) 1 11 2, 11∗ 11 11 9, 19, 23 4, 11, 19 11, 19, 23 9, 11, 19 11, 23 4 9 4, 11∗ 11, 19 11 11 9, 11, 19 4, 9 9 19 4 4 11 4 11 9, 11 11 11 11 11 1, 7, 11 11 11 7 1, 24 1, 11 11 TRAnSPORT PROPERTIES TABLE 2-142 Diffusivities in Liquids (25çC) (Continued ) Dilute solutions and 1 atm unless otherwise noted; use DL µ /T = constant to estimate effect of temperature; ∗ indicates that reference gives effect of concentration. Solute Oxygen Oxygen Oxygen Pentaerythritol∗ Phenol Phenol Phenol Phenol Phenol Phenol n-Propanol Pyridine∗ Pyridine Pyrogallol Raffinose∗ Resorcinol∗ Resorcinol∗ Saccharose∗ Stearic acid∗ Succinic acid∗ Sucrose Sulfur dioxide Sulfuric acid∗ Tartaric acid∗ 1,1,2,2-Tetrabromoethane Toluene Toluene Toluene Toluene Toluene Urea Urea Urethane Water Solvent Glycerol∗-water (106 poise) Sucrose∗-water (125 poise) Water Water i-Amyl alcohol Benzene Carbon disulfide Chloroform Ethanol Ethyl ether Water Ethanol Water Water Water Ethanol Water Water Ethanol Water Water Water Water Water 1,1,2,2-Tetrachloroethane n-Decane n-Dodecane n-Heptane n-Hexane n-Tetradecane Ethanol Water Water Glycerol DL × 105, sq cm/sec Estimated possible, error, ± %1 Ref. 0.24 13 0.25 13 2.5 0.77 0.2 1.68 3.7 2.0 0.89 3.9 1.1 1.24 0.76 0.74 0.41 0.46 0.87 0.49 0.65 0.94 0.56 1.7 1.97 0.80 0.61 2.09 1.38 3.72 4.21 1.02 0.73 1.37 1.06 0.021 References 1 Arnold, J. Am. Chem. Soc., 52, 3937 (1930). 2 Calvet, J. Chim. Phys., 44, 47 (1947). 3 Carlson, J. Am. Chem. Soc., 33, 1027 (1911). 4 Chang and Wilke, J. Phys. Chem., 59, 592 (1955). 5 Davidson and Cullen, Trans. Inst. Chem. Eng., 35, 51 (1957). 6 Dummer, Z. Anorg. Chem., 109, 31 (1949). 7 Gerlach, Ann. Phys. (Leipzig), 10, 437 (1931). 8 Gosting and Akeley, J. Am. Chem. Soc., 74, 2058 (1952). 9 Hammond and Stokes, Trans. Faraday Soc., 49, 890 (1953); 49, 886 (1953). 10 Hammond and Stokes, Trans. Faraday Soc., 52, 781 (1956). 11 International Critical Tables, vol. 5, p. 63. 12 James, Hollingshead, and Gordon, J. Chem. Phys., 7, 89 (1939); 7, 836 (1939). 13 Jordon, Ackermann, and Berger, J. Am. Chem. Soc., 78, 2979 (1956). 14 Koeller and Drickamer, J. Chem. Phys., 21, 575 (1953). 15 Kolthoff and Miller, J. Am. Chem. Soc., 63, 1013 (1941). 20 4 3 7 7 4 5 4 4 5 6 3 10 4 2 1, 3, 15, 21, 24 11 11 1 11 11 11 11 1, 7, 11 11 11 11 11 11 11 11 11 11 2, 27 15, 17 11 11 11 4 4 4 4 4 11 8, 11 11, 25 16 2-287 2-288 PHYSICAL AnD CHEMICAL DATA THERMAL TRAnSPORT PROPERTIES TABLE 2-143 Transport Properties of Selected Gases at Atmospheric Pressure* Thermal conductivity, W/(m ⋅ K) Temperature, K Substance Viscosity, 10–4 Pa ⋅ s Temperature, K 250 300 400 500 Acetone Acetylene Benzene 0.0080 0.0162 0.0077 0.0115 0.0213 0.0104 0.0201 0.0332 0.0195 0.0310 0.0452 0.0335 600 Bromine CCl4 Chlorine 0.0038 0.0053 0.0071 0.0048 0.0067 0.0089 0.0067 0.0099 0.0124 0.0126 0.0156 0.0190 Deuterium Propylene R 22 SO2 0.122 0.0114 0.0080 0.0078 0.141 0.0168 0.0109 0.0096 0.176 0.0226 0.0170 0.0143 0.0430 0.0230 0.0200 0.0580 0.0290 0.0256 250 0.0561 0.0524 0.111 0.073 0.109 Prandtl number, dimensionless Temperature, K 300 400 500 600 0.077 0.104 0.076 0.101 0.135 0.101 0.128 0.164 0.127 0.156 0.154 0.101 0.136 0.203 0.131 0.178 0.260 0.162 0.218 0.291 0.191 0.259 0.126 0.087 0.129 0.129 0.153 0.115 0.168 0.175 0.178 0.141 0.201 0.217 0.256 250 300 400 0.860 0.820 0.797 0.771 0.762 0.760 500 ∗An approximate interpolation scheme is to plot the logarithm of the viscosity or the thermal conductivity versus the logarithm of the absolute temperature. At 250 K the viscosity of gaseous argon is to be read as 1.95 × 10–5 Pa ⋅ s = 0.0000195 N ⋅ s/m2. TABLE 2-144 Prandtl number of Air* Pressure, bar Temperature, K 1 5 10 20 30 40 50 60 70 80 90 100 80 90 100 120 140 mix 0.796 0.786 0.773 0.763 2.31 1.76 0.872 0.813 0.782 2.32 1.77 1.54 0.89 0.82 2.35 1.78 1.53 1.44 0.94 2.37 1.79 1.53 1.65 1.20 2.40 1.81 1.53 1.54 1.59 2.42 1.82 1.53 1.48 2.14 2.45 1.83 1.53 1.43 2.43 2.48 1.85 1.53 1.40 2.07 2.51 1.87 1.54 1.38 1.78 2.54 1.89 1.54 1.36 1.62 2.57 1.91 1.55 1.34 1.52 160 180 200 240 280 0.754 0.745 0.738 0.724 0.710 0.765 0.754 0.743 0.727 0.711 0.78 0.763 0.749 0.729 0.713 0.84 0.792 0.766 0.737 0.717 0.92 0.830 0.788 0.746 0.721 1.03 0.876 0.812 0.756 0.726 1.13 0.932 0.841 0.767 0.731 1.25 1.00 0.87 0.78 0.737 1.37 1.07 0.90 0.80 0.742 1.65 1.14 0.95 0.81 0.75 1.83 1.20 0.97 0.81 0.75 1.72 1.25 1.00 0.82 0.76 300 350 400 450 500 0.705 0.699 0.694 0.691 0.689 0.707 0.699 0.694 0.691 0.689 0.708 0.699 0.694 0.691 0.689 0.712 0.701 0.695 0.691 0.689 0.715 0.703 0.696 0.692 0.689 0.717 0.705 0.697 0.692 0.690 0.721 0.707 0.698 0.693 0.690 0.725 0.709 0.699 0.693 0.690 0.728 0.711 0.700 0.694 0.690 0.732 0.712 0.701 0.695 0.691 0.737 0.714 0.703 0.695 0.691 0.742 0.716 0.704 0.696 0.691 600 700 800 900 1000 0.690 0.696 0.705 0.709 0.711 0.690 0.696 0.704 0.709 0.711 0.690 0.695 0.704 0.708 0.711 0.689 0.695 0.704 0.708 0.711 0.689 0.695 0.704 0.708 0.711 0.689 0.695 0.703 0.708 0.710 0.689 0.695 0.703 0.708 0.710 0.689 0.695 0.703 0.708 0.710 0.689 0.695 0.703 0.708 0.710 0.690 0.695 0.702 0.708 0.709 0.690 0.695 0.702 0.708 0.709 0.690 0.695 0.702 0.708 0.709 ∗Compiled by P. E. Liley from tables of specific heat at constant pressure, thermal conductivity, and viscosity given in SI units for integral kelvin temperatures and pressures in bars by Vasserman. Thermophysical Properties of Air and Its Components and Thermophysical Properties of Liquid Air and Its Components. Nauka, Moscow, and in translated form by the National Bureau of Standards, Washington. The number of significant figures given above reflects the similar numbers appearing for the constituent properties in the source references. While reasonable agreement occurs for atmospheric pressure with some other works, the fragmentary data available for the saturated, etc., states show large deviations. TABLE 2-145 Eqn Cmpd. no. 102 102 100 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102 1 2 3 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 45 46 47 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] Name Acetaldehyde Acetamide Acetic acid Acetic acid Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyric acid Butyronitrile Carbon dioxide Formula C2H4O C2H5NO C2H4O2 C2H4O2 C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H8O2 C4H7N CO2 CAS 75-07-0 60-35-5 64-19-7 64-19-7 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 107-92-6 109-74-0 124-38-9 Mol. wt. 44.05256 59.0672 60.052 60.052 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 88.1051 69.1051 44.0095 C1 1.0943E-07 0.00013195 2.4148 1.0879 3.3901E-06 3.1289E-06 −26.8 8.3653E-07 0.000075782 0.024098 0.0009265 −0.000861 0.00031417 9.6608E-06 0.00059858 0.000633 0.025389 0.00001652 0.00047951 0.0001163 1.3917E-06 0.0001235 0.00023476 0.00096451 0.00015525 2.8646E-06 1.0404E-06 0.00027085 0.00099879 5.7816E-07 0.000088221 −20890 0.051094 0.00014035 −918.39 0.0011484 4.5894E-06 0.000096809 0.000067737 0.000078576 5.86E-09 0.1807 0.00097826 0.9719 0.000037269 9.9652E-07 0.7873 9.2069E-08 1.3751E-06 3.69 C2 2.0279 0.97 −0.020867 −0.0038977 1.9588 1.4618 0.9098 1.6481 1.0327 0.3285 0.7035 0.77281 0.7786 1.3799 0.7527 0.6221 0.28547 1.3117 0.7818 0.9705 1.5389 0.9495 0.8639 0.69225 0.9446 1.4098 1.4685 0.7932 0.71894 1.6666 1.0273 0.9593 0.45253 1.0032 −0.21199 0.87647 1.4484 1.1153 1.0709 1.0565 2.376 0.0082225 0.78643 −0.111 1.1427 1.6558 −0.0036161 2.0312 1.5786 −0.3838 C3 728.3 0.000059409 3.6227E-06 36053 C4 −5.4718E-08 14,086,000 126,500,000 −36.227 1325.3 627.58 −2555.2 −0.7116 31,432 577,830 112,460 354.04 70 1018.3 491 463.4 740 241,830 778.7 187.8 519.99 715.78 −391.35 2121.7 1,228,600 189,410 193,840 278,930 156,820 278.33 2358.4 165,880 75.316 −93,820,000,000 5455.5 711.66 334420 3253.7 99,063 1,979,800 −2,884,200,000 781.82 −65.881 14.63 −401.32 −129.42 1531.5 1167.2 −43.844 129,390 105,920 69,280 1,691,500 67,115 3,163,200 79,421 5.6641E-06 −2.8451E-09 964 1,860,000 Tmin, K 294.15 494.3 391.05 458.15 541.5 412.7 329.44 339.09 189.35 325.84 414.15 298.15 70 200 426.73 90 563.15 339.15 442.29 522.4 464.15 579.24 478.6 458.15 472.03 373.15 300 429.24 311.49 273 284 268.74 272.65 469.57 481.38 370.7 372.9 266.91 273.15 274.03 273 456.46 371.61 358.13 281.22 347.94 436.42 706.95 390.74 194.67 Thermal cond. at Tmin 0.01110 0.02189 0.06749 0.06258 0.03925 0.02084 0.01363 0.01238 0.01011 0.01534 0.02027 0.00929 0.00603 0.01446 0.01809 0.00585 0.02317 0.01407 0.01861 0.02090 0.01767 0.02213 0.02167 0.01936 0.02071 0.01123 0.00452 0.01302 0.00723 0.00664 0.01172 0.01281 0.01357 0.02672 0.02110 0.02097 0.02435 0.01252 0.01105 0.01200 0.00783 0.02151 0.01832 0.01749 0.01268 0.01610 0.05147 0.05647 0.01698 0.00887 Tmax, K 1000 1000 458.15 541.5 1000 1000 1000 1000 1000 1000 1000 1000 2000 900 1000 3273.1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 500 1000 1000 1000 1000 1000 1000 1000 1000 712.94 1000 1000 1273.15 1257 800 1000 1000 1000 1000 1000 706.95 1000 1000 1500 Thermal cond. at Tmax 0.13269 0.06206 0.06259 0.03955 0.11105 0.07600 0.11362 0.07358 0.09545 0.08028 0.06867 0.11525 0.11675 0.11523 0.06796 0.09525 0.05618 0.09542 0.06427 0.05452 0.05758 0.04899 0.06636 0.06398 0.06171 0.06347 0.00956 0.04495 0.04267 0.05779 0.09071 0.16809 0.13799 0.08383 0.08332 0.06536 0.10161 0.12049 0.13926 0.13704 0.07634 0.07465 0.08610 0.08470 0.09644 0.09245 0.05647 0.11421 0.07484 0.09025 2-289 (Continued) 2-290 TABLE 2-145 Eqn Cmpd. no. 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane Formula CS2 CO CCl4 CF4 Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 CAS 75-15-0 630-08-0 56-23-5 75-73-0 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 Mol. wt. 76.1407 28.0101 153.8227 88.0043 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 C1 0.0003467 0.00059882 0.00016599 0.000092004 0.0009993 0.0004783 4.91778E-07 0.00043073 −3263.77 0.01652 0.00009154 0.00019307 0.00018648 0.00019063 1.6743E-07 0.000014433 −449910 0.000000859 0.0032207 −1095.5 0.0000901 9.5461E-06 0.0010949 −91.383 0.0000813 1.9749E-06 −668.4 3.3251E-09 −0.3072 0.000027232 0.00012058 0.000016707 0.00028527 0.00021231 0.00015878 0.00021302 0.0032694 −1067.8 −1420 −1520.8 0.0001315 0.00021054 0.0014796 0.000057603 0.000062435 −11,633 0.00001706 −0.0044894 0.0018097 0.000059249 C2 0.7345 0.6863 0.94375 1.0164 0.5472 0.8994 1.70639 0.83878 0.0675 0.44154 1.0681 0.9248 0.9302 0.9282 1.8369 1.2104 0.27364 1.7709 0.5991 −0.023408 1.0897 1.4641 0.71644 0.89718 1.0674 1.5349 0.9323 2.4876 0.489 1.257 1.0111 1.2128 0.9874 0.8052 0.8636 0.8719 0.58633 0.754 0.7614 0.754 1.0113 0.9574 0.69531 1.1148 1.103 0.4621 1.248 0.6155 0.67406 1.0713 C3 479 57.13 1449.6 270.83 458.6 1845.5 −232.008 1874.5 −46,803,200 2444.42 746.6 710 709.37 716.91 −449.46 −10,001,000,000 243 608.69 498, 780 655 632.62 175.55 −283,310,000 697.6 −4,071,000,000 −124.9 −67,500 751.7 740 −206.08 −200.51 649.51 659.5 1620 1259.9 −3,036,100,000 −4,504,000,000 −433,2800,000 1023.8 1414 2657.4 849.98 913.43 −3,793,900,000 −112.8 −3266.3 1179.7 101.84 C4 501.92 163,000 46603.4 −25,000,700,000 793,392 112,760 −9.8654E+12 509,290 −7,835,500,000 346,040 −29,400,000 153,850 21,807 300,890 77,960 174,850 45,974 Tmin, K 273.15 70 349.79 145.1 200 400 285.45 334.33 248.95 319.67 308.85 475.43 464.15 475.13 380 251.9 285.66 325 434 428.58 356.12 273 317.38 240.37 431.95 481.65 447.3 543.15 504 443.75 512.35 447.15 233.15 381.15 404.51 370.1 323.15 446.23 453.57 447.21 330.45 356.59 312.9 361.25 369.52 541.54 273.15 200 365.25 248.95 Thermal cond. at Tmin 0.00776 0.00576 0.00812 0.00505 0.00551 0.01579 0.01004 0.00854 0.00801 0.01285 0.01222 0.02316 0.02230 0.02319 0.01534 0.01164 0.01356 0.01380 0.02399 0.02291 0.01914 0.01061 0.01360 0.01061 0.02022 0.02590 0.02173 0.02746 0.02590 0.02149 0.02709 0.02092 0.11474 0.00940 0.01077 0.00687 0.01244 0.01561 0.01507 0.01564 0.01132 0.01177 0.00847 0.01220 0.01222 0.03044 0.01148 0.00764 0.01743 0.01016 Tmax, K 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 600 1000 1000 Thermal cond. at Tmax 0.03745 0.08724 0.04595 0.08108 0.03002 0.07935 0.07943 0.04920 0.07246 0.08232 0.08389 0.06716 0.06736 0.06762 0.08181 0.06174 0.14994 0.14198 0.09535 0.12704 0.10116 0.14429 0.10148 0.15854 0.07629 0.07948 0.10286 0.11029 0.09389 0.09175 0.07482 0.07667 0.44547 0.03351 0.03729 0.03356 0.07330 0.06430 0.06066 0.06417 0.07025 0.06498 0.04931 0.06881 0.06647 0.07463 0.09804 0.05181 0.08089 0.08447 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 1,2-Difluoroethane Difluoromethane Diisopropyl amine Diisopropyl ether Diisopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 2.4194E-06 0.000013015 0.00051305 0.00019879 −8.5357 0.00046265 3.7962E-06 0.00021761 1.6085 0.000034741 0.008856 0.013298 0.012144 0.00022578 0.059975 0.014449 0.000022421 0.00012822 0.0011808 0.00023614 0.00064761 0.00402358 6.4032E-07 0.00014629 0.0001123 0.000005719 −375.32 0.000073869 −0.010109 1.3575E-07 0.3935 0.000017537 0.00002012 0.00017727 829.29 0.0000748 0.0043244 8.6806E-06 0.1655 −8145800 0.00077079 −0.0003788 508 2.5804E-06 0.0052833 0.00021652 −152400 0.0015251 1.0507E-07 5.8174E-08 2.7142E-06 0.00012144 0.000053432 1.4456 1.1897 0.8076 0.9423 −0.0056423 0.81968 1.4462 0.9187 −0.1103 1.1646 0.4215 0.3692 0.3854 0.892 0.2667 0.3612 1.2137 0.9324 0.742 0.9204 0.7716 0.57548 1.7194 0.9377 0.9958 1.4699 1.0708 1.1689 0.6475 1.9681 0.0131 1.3144 1.1513 0.9428 1.0156 1.1103 0.5429 1.4559 0.1798 −0.30502 0.7713 1.115 0.9023 1.4669 0.52982 0.94192 −0.049106 0.70243 1.9854 2.0116 1.4281 0.93831 1.1576 360.19 306.8 1882.1 539.34 154,510 106,230 −65,622,000 104,530 217 2160.3 −99.956 −50.645 0.1027 52.191 697 1018.6 595.22 −146.91 752.5 1131 638 1013.3 3598.32 132,070 2,989,300 130,820 764,580 852,540 803,590 745.89 183.2 579.4 −8,783,600,000 500.73 −7332 1380 560.65 −89.583 712.4 8,955,300,000 686 333.67 299.72 3827.9 1,832,500,000 446.16 −5641 2,170,000,000 1,098,800 728,130 131,830 6400 82,563 98,000 −268,000 1,710,000 125,410 570,470 −29,403 1,600,000 −1.1842E+13 197,930 1415.7 632.16 80,955,000 1347.5 −9.3122E+11 35,085 −372.68 57,690 760.75 378,180 303.65 221.5 357.05 328.05 397.55 337.45 366.15 300.13 280.03 331.13 392.7 402.94 396.58 382.9 248.31 425.15 362.93 556.85 253.55 310.48 462.15 559.2 337.85 531.46 279.65 489.47 616.93 184.55 293.15 273.15 289.73 409.35 486.55 466.95 394.65 404.95 376.62 170 390.41 470.45 329 273.15 327.46 500.66 417.15 326.15 386.55 308.15 400 273.15 371.05 70 357.88 0.00938 0.00803 0.01836 0.01598 0.02015 0.01554 0.01936 0.01288 0.01845 0.01581 0.01884 0.01948 0.01952 0.01613 0.01139 0.02001 0.01797 0.01981 0.01291 0.01520 0.02059 0.02063 0.01427 0.02188 0.01055 0.02354 0.02563 0.00886 0.01475 0.00847 0.01622 0.02007 0.01855 0.02306 0.01583 0.02180 0.01832 0.00879 0.02272 0.02513 0.01610 0.01004 0.01426 0.02353 0.01967 0.01717 0.01889 0.01487 0.01540 0.01133 0.01268 0.00654 0.01546 993.65 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1500 1000 1000 1000 1000 1000 1000 1000 768.01 1000 1000 1000 1000 1000 1000 990.21 1000 1000 1000 1000 1000 1000 1000 590.92 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 550 1000 700 600 0.05206 0.04826 0.08967 0.09444 0.13085 0.08099 0.08279 0.09199 0.12209 0.10506 0.09500 0.09196 0.09376 0.06310 0.19458 0.07539 0.09962 0.04587 0.09296 0.08319 0.06379 0.04661 0.05855 0.05449 0.08515 0.09301 0.06968 0.15807 0.13417 0.10681 0.10532 0.09859 0.05524 0.06973 0.10314 0.09505 0.09659 0.06613 0.08915 0.09896 0.09659 0.18063 0.11921 0.06492 0.07348 0.08882 0.12768 0.08195 0.09499 0.03690 0.05223 0.05675 0.03874 2-291 (Continued) 2-292 TABLE 2-145 Eqn Cmpd. no. 102 102 102 102 100 100 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 151 152 153 154 155 155 155 156 157 158 159 160 161 161 162 163 164 165 166 167 168 169 170 171 172 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Formic acid Formic acid Furan Helium-4 Heptadecane Heptanal Heptane Heptanoic acid Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Formula C2H5F CH3F CH2O CH3NO CH2O2 CH2O2 CH2O2 C4H4O He C17H36 C7H14O C7H16 C7H14O2 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 CAS 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 64-18-6 64-18-6 110-00-9 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 Mol. wt. 48.0595 34.03292 30.02598 45.04062 46.0257 46.0257 46.0257 68.07396 4.0026 240.46774 114.18546 100.20194 130.185 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 C1 6.3522E-06 0.000048998 5.2201E-06 0.00025893 −0.8303 1.8897 0.00072291 −644950 0.00226 −114.41 1.4326E-06 −0.070028 −0.088162 4.449E-08 −0.061993 0.00018818 1348.6 2049.3 0.00002133 0.0083145 0.000060732 0.000004438 1.5427E-06 −650.5 12,049,00,000 6.1268E-08 −4935500 0.00018361 −1.2158 −0.33262 0.000064256 6.9682E-06 0.074318 0.000058116 0.000011631 0.00043196 0.002653 0.00049725 0.001865 4.6496E-06 0.000034629 1.381E-07 0.000214 0.00028183 4.8284E-06 0.00019847 8.3983E-06 5.7992E-07 0.034177 −25343 C2 1.346 1.0175 1.417 0.9083 0.0046141 −0.006901 1.8898 0.2862 0.7305 1.0566 1.5896 0.38068 0.00065022 2.133 0.2792 0.96338 1.0313 1.0323 1.2885 0.51862 1.0586 1.4949 1.5824 0.8053 −4.0059 2.0874 −0.1653 0.97199 0.026637 0.12054 1.1355 1.347 0.30035 1.0724 1.2753 0.86603 0.7452 0.63088 0.49755 1.3669 1.1224 1.8379 0.9248 0.92094 1.3599 0.9284 1.4268 1.7862 0.3312 −0.1934 C3 723.6 −5.7466E-06 6.4407E-06 4,877,600 −16,794,000,000 −18.63 −2,211,400,000 C4 −1,889,300,000 −1.7372E+13 440 −7049.9 −1.2803E-06 −2,400,500 9.1349E-10 −3336 696.02 14,832,000,000 22,983,000,000 487.8 2253 −102.79 682 −1,642,000 −1,412,100,000 −1668.8 1,563,100,000 677.05 −1711.6 −2472.6 445.15 −214.35 4470.1 −77.165 −202.84 641.48 12 331.62 358 −210.76 18.744 −352.09 698 619.17 532,590 143,140 722,550 −1.5752E+13 −13,176,000 −5,493,400 64,810 110,480 1,775,800 123,900 122,990 58,295 46,041 678.69 −49.654 2070 11,164,000 1,195,600 −67,259,000,000 Tmin, K 235.45 194.82 253.85 493 420 470 537.9 304.5 30 575.3 426.15 339.15 496.15 643.11 449.45 432.9 420.55 424.18 366.79 450.09 372.93 560.01 401.15 339.09 478.85 641.42 429.9 412.4 273 273 336.63 354.35 425.81 344.48 357.67 386.65 22 206.45 190 273.15 350 212.8 427.85 304.92 580 434.15 111.63 273 478.15 330.09 Thermal cond. at Tmin 0.00990 0.01047 0.01333 0.02930 0.09392 0.06898 0.04120 0.01367 0.03124 0.02454 0.02168 0.01583 0.03085 0.04349 0.02345 0.02501 0.01943 0.01951 0.01845 0.02289 0.01827 0.02568 0.02031 0.01704 0.03317 0.04435 0.02220 0.02421 0.00775 0.00800 0.01644 0.01485 0.02151 0.01679 0.01506 0.02828 0.01718 0.00551 0.00880 0.00985 0.02356 0.00724 0.02206 0.01804 0.02766 0.02176 0.01263 0.01303 0.02498 0.01415 Tmax, K 1000 1000 1000 1000 470 537.9 1000 1000 2000 1000 1000 1000 643.11 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 641.42 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1600 600 700 673.15 450 600 1000 1000 1000 1000 600 684.37 1000 1000 Thermal cond. at Tmax 0.06933 0.05529 0.09304 0.07973 0.06890 0.04118 0.11296 0.13631 0.58820 0.07649 0.08413 0.11493 0.04346 0.11150 0.10722 0.08616 0.11287 0.11145 0.10518 0.07899 0.08751 0.08055 0.08620 0.12003 0.04435 0.11206 0.11104 0.09022 0.10523 0.10980 0.10850 0.08546 0.08167 0.09155 0.08466 0.10430 0.64299 0.01812 0.03213 0.04185 0.03160 0.03258 0.07497 0.10081 0.05801 0.07210 0.08425 0.06726 0.07895 0.11878 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 0.00026544 0.4734 −55.13 0.000023963 0.0002509 0.0008968 0.0001799 2054.5 0.00019098 0.00021736 0.00015498 0.000023993 0.079414 0.000065855 1333.1 0.00037057 0.0000719 0.00011359 0.069565 0.075448 0.0024385 0.0040082 0.0019845 0.00041077 0.00024036 −4202700 0.0034805 −800040 0.00020053 −2483300 0.0026136 2.1191 −5935000 0.0071536 0.00002653 0.00072502 0.0001813 0.000061119 0.93312 0.089772 1.1776E-06 −488.1 −200.9 0.011136 0.0023574 12.248 0.21276 0.0002084 0.00032359 0.000091828 0.0011385 0.0011282 0.00033143 0.8921 −0.1111 1.065 1.1308 0.899 0.7742 0.9457 0.90109 0.9341 0.9171 0.9364 1.1976 0.23442 1.072 0.9962 0.81367 1.1274 1.0311 0.1633 0.155 0.61774 0.54462 0.6393 0.75688 0.93177 −0.1524 0.61906 −0.2285 0.95381 −0.046517 0.62 −0.19015 −0.089497 0.53907 1.1631 0.7395 0.92912 1.0861 −0.1172 0.18501 1.6618 0.8877 −0.1321 0.4831 0.67434 −0.5611 −0.022299 0.93034 0.8892 1.0345 0.6646 0.6895 0.7722 222.19 533.57 −448,200,000 −67.272 253.4 456 704.6 8,760,500,000 84.07 112.3 15.366 58.59 2671.9 −36.369 12,317,000,000 609.17 667 709.27 208.7 218.44 223.01 242.12 227.11 591.5 588.14 2,084,600,000 1810.8 248,100,000 644.42 1,313,100,000 1631.7 1453.4 3,098,800,000 2700.7 29.996 365.68 793.45 −59.592 1154.3 639.23 −1,448,500,000 104,000 21,70.3 1804.1 −1067 −194.68 364.832 623.22 731.78 8.7 679.11 16.323 79,869 1,649,600 125,720 149,500 230,640 155,720 177,690 137,400 35,667 1,366,100 106,430 1,209,500 1,252,500 477,570 559,040 434,120 −1.4577E+13 166,290 −1.5034E+12 −1.5798E+13 126,720 3,575,500 −2.7994E+13 241,730 32,519 204,360 141,260 2,961,700 1,114,700 −846,000,000 281,220 155,660 2,715,200 1,708,700 73,041 238,800 373.72 249.94 353.35 266.82 472.65 314 273.15 450.15 404.15 304.3 311.71 305.4 273.15 396.58 302.15 375.9 281.85 374.08 441.15 438.15 440.15 344.96 348.64 338.05 314.7 273 352.79 339.8 300 331.7 389.65 312 303.92 367.55 171.64 273.15 373.45 518.15 333.41 372 261.43 333.82 266.25 350 312.2 368.69 216.25 438.65 328.2 278.65 491.14 30 387.22 63.15 0.01154 0.01569 0.01259 0.01784 0.01326 0.01198 0.02266 0.02116 0.01348 0.01320 0.01304 0.01173 0.01966 0.01468 0.01495 0.01155 0.02056 0.02322 0.02415 0.02435 0.01592 0.01544 0.01501 0.01109 0.01419 0.01546 0.01653 0.01369 0.01729 0.01869 0.01221 0.01606 0.01760 0.00459 0.01171 0.01680 0.02383 0.01606 0.01828 0.01273 0.01839 0.01276 0.01402 0.01648 0.01802 0.01108 0.01969 0.01638 0.01493 0.02243 0.00846 0.01580 0.00602 1000 1000 650 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 766.87 1000 1000 1000 1000 1000 1000 1000 1000 1000 3273.1 1000 2000 0.09675 0.06904 0.07917 0.05588 0.08902 0.11176 0.07253 0.11843 0.09771 0.09504 0.08664 0.08586 0.07960 0.10120 0.10543 0.06357 0.10399 0.08238 0.08888 0.08908 0.10227 0.09578 0.09888 0.04813 0.09447 0.11740 0.08415 0.13148 0.08863 0.12433 0.06864 0.09451 0.12847 0.07516 0.07704 0.07637 0.06195 0.10242 0.08117 0.11701 0.07325 0.15513 0.10886 0.09079 0.08398 0.09590 0.07255 0.08958 0.09273 0.06730 0.24616 0.06887 0.11638 2-293 (Continued) 2-294 TABLE 2-145 Eqn Cmpd. no. 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 Vapor Thermal Conductivity of Inorganic and Organic Substances [W/(m∙K)] (Continued ) Name Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Octadecane Octanal Octane Octanoic acid Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Formula F3N CH3NO2 N2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 C18H38 C8H16O C8H18 C8H16O2 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O CAS 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 593-45-3 124-13-0 111-65-9 124-07-2 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 Mol. wt. 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 254.49432 128.212 114.22852 144.211 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 C1 2.1443 0.00003135 0.001096 0.0004096 0.000049571 0.00000175 −0.065771 46.08 −30.715 0.00016806 0.000021269 0.047041 0.000016681 −291.08 0.00000166 −8758 −0.20973 3.2003E-08 −0.0030238 0.00016915 −0.0020184 8.1833E-08 0.0000133 −3965.5 0.000060734 2.7969E-06 0.00044994 0.0043147 4.7796E-06 0.00000113 −684.4 0.44736 7.5284E-08 2896 0.00019575 −0.01719 22.775 2.7081E-06 0.00022307 0.00011261 0.000052415 0.00025623 0.00010167 0.038846 0.00016675 0.0000593 0.000061629 −1.12 −613.84 7.3907E-07 C4 Tmin, K 1860.3 −91.6 540 45.6 3332.3 1,216,700 128,000 −3482.3 −2460.2 8107 713.67 662.21 2460.6 −199.41 −6,019,900,000 −1,580,300 1,867,000 −156,830,000 144.09 374.35 182.3 121.38 603.05 465.52 423.97 528.75 485.2 471.7 420.02 492.95 423.85 589.86 445.15 339 512.85 637.35 468.35 452.9 446.15 440.65 394.41 472.19 399.35 516 80 161.85 543.84 375.15 273.15 458.95 706.95 410.9 392.2 273 273 303.22 385.15 399.79 313.33 329.27 610.03 454.99 439.43 557.65 238.65 231.11 370.35 355.3 C2 −0.30545 1.1119 0.667 0.7509 1.2652 1.5534 0.27198 −1.0037 −0.1075 0.96876 1.2943 0.29733 1.218 1.0615 1.5669 0.8448 0.0012201 2.18 0.8745 0.97238 1.0027 2.0418 1.3554 0.5213 1.0516 1.3164 0.7456 0.47999 1.4851 1.6323 0.764 −0.0019667 2.0589 0.8985 0.9692 0.4832 1.0019 1.5493 0.93358 1.034 1.0948 1.0073 0.988 0.2392 0.91777 1.046 1.0731 0.10972 0.7927 1.7419 C3 −27,121,000,000 −2.1843E-06 1,367,200 144,580 1.3942E-09 −13352 698.55 −20406 504.59 −1,851,900,000 −124.91 158,300 56.699 700.09 643.13 −1,055,000,000 2.9973E-06 12,735,000,000 664.04 −3798 191,000,000 41.075 794.16 693.05 −51.09 1423.7 797 985.81 730.1 765.5 1.8579 −9834.6 −1,157,400,000 −1.4141E-09 −1,235,000 8301.3 101,160 937,170 70,128 −7,535,800 Thermal cond. at Tmin 0.00648 0.01365 0.00891 0.01094 0.02502 0.02440 0.02130 0.02815 0.02436 0.02603 0.02051 0.02559 0.01981 0.02491 0.02345 0.01503 0.02955 0.04157 0.02380 0.02545 0.02046 0.02050 0.01926 0.02505 0.01967 0.01041 0.00691 0.00931 0.02529 0.01799 0.01288 0.03938 0.05537 0.02084 0.02372 0.00877 0.00898 0.01546 0.01890 0.02019 0.01517 0.01653 0.02490 0.02183 0.01669 0.01864 0.00980 0.01114 0.02135 0.02049 Tmax, K 1000 1000 1000 750 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 637.35 1000 1000 1000 1000 1000 1000 1000 1000 1000 2000 1000 1000 1000 1000 706.95 1000 990.95 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 720.25 1000 Thermal cond. at Tmax 0.06377 0.06553 0.07133 0.05567 0.07147 0.08003 0.10597 0.11042 0.09895 0.07904 0.09772 0.07598 0.07956 0.07395 0.08333 0.11053 0.04157 0.11097 0.10288 0.08229 0.10597 0.10923 0.10295 0.07845 0.08394 0.02488 0.12655 0.06990 0.08299 0.08912 0.12707 0.05536 0.11308 0.11087 0.09509 0.12002 0.12082 0.11472 0.07858 0.08412 0.09608 0.11119 0.05208 0.06936 0.05461 0.04615 0.09526 0.14599 0.07034 0.12428 102 102 100 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 102 298 299 300 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Propenylcyclohexene Propionaldehyde Propionic acid Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene C9H14 C3H6O C3H6O2 C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O2S F6S O3S C8H6O4 C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 13511-13-2 123-38-6 79-09-4 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 122.20746 58.07914 74.0785 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 0.00010242 9.0711E-07 1.0014 1.8905E-07 1.1671E-06 1325.3 0.2833 0.16992 0.0000449 740.1 0.00018367 0.0087425 0.0001666 −5678600 0.0000955 0.010048 5.5263E-06 10.527 0.00048883 1.0702 3.4082E-06 0.000078652 −163.62 9.5521E-06 0.00007754 0.00085604 0.000015235 0.00013384 0.00002392 0.0000952 5.3701E-06 0.000106 0.00027648 0.000098408 0.00008498 0.00001758 0.000020248 0.00020544 0.00018189 0.038012 2498.8 −3279500 0.000054197 −229.41 3510.8 6.2041E-06 3.0593E-09 4.9707E-06 9.9305E-08 1.0486 1.6709 −0.0045954 1.93 1.6033 1 0.055046 0.021288 1.2018 0.9732 0.9627 0.51733 0.9765 −0.045252 0.928 0.4033 1.344 −0.7732 0.6518 −0.2348 1.3647 0.95174 0.9193 1.4561 1.0778 0.7297 1.2816 0.98115 1.2694 1.0423 1.4751 1.0161 0.901 1.0452 1.061 1.3114 1.2284 0.87137 0.88744 0.68615 0.95209 −0.12941 1.0632 0.59582 0.225 1.3973 2.4182 1.3787 1.9229 701.56 7.1517E-06 12,235,000,000 1325.9 −54.484 421 5,646,000,000 646.01 2358.1 706 2,615,700,000 63.6 553.74 −3.5878E-09 1,817,600 1,624,800 334,590 −3.5415E+13 685,570 −1333 −117.08 2010.4 1,506,400 78,863 1,277,000 −282.82 −1,087,600,000 662.22 729 531.99 −111.88 645.95 537 1243.3 599.09 91 167.68 720.49 708 392.9 −174.72 807.3 803.39 34,663 20,167,000,000 1,710,400,000 −70.589 −169,430,000 401,720,000 289,490 −569.28 −225.64 −469.93 213,840 124,120 132,900 132,200 147,800 8,721,900 −1.2727E+13 90,617 121,060 66,786 113,460 431.65 322.15 414.32 616.15 370.25 374.65 321 432.39 225.45 353.97 325.71 340.87 460.75 454 333.55 418.31 591 250 273.15 317.9 795.28 373.15 526.73 339.12 480.77 394.27 379.44 357.31 383.78 387 508.62 273.15 273.15 449.27 442.53 355.15 387.91 629.6 625 469.08 520.3 345.65 278.25 259.25 363.85 273.16 320 320 320 0.02262 0.01407 0.06993 0.04578 0.01532 0.01520 0.01709 0.02022 0.01054 0.01403 0.01616 0.01654 0.02624 0.02593 0.01761 0.01837 0.02934 0.00745 0.01163 0.01386 0.03097 0.00950 0.02517 0.01564 0.02395 0.01801 0.01964 0.01525 0.01901 0.01125 0.02422 0.01018 0.01280 0.02238 0.02098 0.01846 0.02001 0.02474 0.02410 0.02259 0.02486 0.01515 0.01123 0.00963 0.01198 0.01574 0.00867 0.01492 0.01019 1000 1000 616.15 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 702.45 1000 1000 900 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1073.15 1000 1000 1000 0.08421 0.09340 0.04578 0.11657 0.07534 0.10832 0.10000 0.07658 0.12737 0.10893 0.08624 0.08439 0.08302 0.12665 0.03837 0.07276 0.05949 0.03969 0.04587 0.04930 0.04233 0.05598 0.08615 0.13419 0.07676 0.07579 0.10528 0.07139 0.10007 0.05684 0.08942 0.09680 0.10734 0.07816 0.07583 0.10847 0.10079 0.04675 0.04635 0.09798 0.08899 0.12177 0.08222 0.08300 0.04135 0.10652 0.09965 0.08084 0.09060 2-295 Except for acetic acid, butyric acid, formic acid, heptanoic acid, octanoic acid, pentanoic acid, propionic acid, the vapor thermal conductivity is calculated by Eqn 102: k = C1T C2/(1 + C3/T + C4/T 2) where k is the thermal conductivity in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure, whichever is lower. Eqn 100, used for the limited temperature ranges as noted for the associating compounds above, k = C1 + C2T + C3T 2 + C4T 3 Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. 2-296 PHYSICAL AnD CHEMICAL DATA TABLE 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids Temperature, °C Substance Property Acetaldehyde ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr Acetic acid −50 −40 −30 −20 −10 863 2.05 460 0.211 4.47 852 2.08 404 0.206 4.08 840 2.11 358 0.200 3.78 828 2.14 321 0.195 3.52 816 2.17 290 0.189 3.33 0 804 2.20 263 0.184 3.14 10 794 2.24 241 0.182 2.97 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 20 30 40 50 60 70 80 90 100 972 960 783 2.28 222 0.180 2.81 1049 2.031 1210 0.173 14.2 1039 1028 1018 1006 995 984 1102 0.170 1010 0.168 795 0.167 600 0.165 0.163 0.161 Aniline ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr — — — — — — — — — — — — — — — — — — — — — — — — — 1039 2.024 10200 0.186 111 1030 2.047 6500 0.184 72 1022 2.071 4400 0.182 50 1013 2.093 3160 0.180 36.7 1005 2.113 2370 0.177 28.3 996 2.132 1850 0.174 22.7 987 2.17 1510 0.171 19.2 978 2.20 1270 0.169 16.5 969 2.23 1090 0.168 14.5 960 2.27 935 0.167 12.7 951 2.32 825 0.167 11.5 Butanol ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 845 1.947 34700 0.175 3860 841 1.996 22400 0.174 2570 837 2.046 14700 0.173 1740 833 2.100 10300 0.172 1260 829 2.153 7400 0.171 930 825 2.202 5190 0.170 670 817 2.262 3870 0.168 120 810 2.345 2950 0.167 41 803 2.437 2300 0.166 33.8 797 2.524 1780 0.165 27.2 791 2.621 1410 0.164 22.5 784 776 768 760 753 1140 0.163 930 0.162 760 630 535 0.161 0.160 0.159 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 1362 0.988 630 0.194 3.21 1348 0.989 580 0.190 3.02 1334 0.990 535 0.186 2.85 1320 0.991 496 0.182 2.70 1306 0.993 463 0.178 2.58 1292 0.996 435 0.174 2.49 1278 1.004 405 0.170 2.39 1263 1.017 375 0.166 2.30 350 0.161 330 0.158 0.156 0.154 0.152 0.150 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 789 2.068 1175 0.122 19.9 779 2.081 980 0.120 17.0 769 2.094 820 0.119 14.4 759 2.106 710 0.118 12.7 750 2.119 605 0.117 11.0 740 731 721 540 0.116 0.114 0.112 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 2.01 6400 0.188 68.4 2.04 4790 0.186 52.5 2.08 3650 0.184 41.3 2.13 2825 0.181 33.2 2.19 2220 0.179 27.2 806 2.27 1770 0.177 22.7 798 2.35 1470 0.175 19.7 789 2.43 1200 0.173 16.9 781 2.52 1000 0.171 14.7 776 2.62 835 0.168 13.0 763 2.73 700 0.165 11.6 754 2.83 590 0.162 10.3 745 2.93 500 0.159 9.2 735 3.03 435 0.156 8.4 725 3.19 370 0.153 7.7 716 3.30 314 0.151 6.9 947 935 924 912 888 876 863 851 838 825 811 797 580 510 901 2.01 455 0.145 6.3 400 0.142 370 0.139 345 0.136 310 0.133 280 0.130 250 230 220 0.127 0.123 0.119 Carbon disulfide Cyclohexane Ethanol Ethyl acetate ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1090 k (W/m⋅K) Pr Ethylamine ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 761 2.95 580 0.204 8.39 750 2.97 500 0.201 7.39 739 2.98 435 0.199 6.51 729 3.00 390 0.196 5.97 718 3.01 350 0.194 5.43 707 3.03 320 0.191 5.08 695 683 671 658 646 633 620 607 Ethyl ether ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 790 2.135 550 0.159 7.39 780 2.156 470 0.155 6.54 769 2.179 410 0.151 5.92 758 2.205 365 0.147 5.48 747 2.233 330 0.144 5.12 736 2.265 290 0.140 4.69 725 2.299 265 0.139 4.38 714 2.332 233 0.134 4.05 702 2.36 214 0.129 3.92 689 2.39 197 0.125 3.77 676 2.43 181 0.120 3.67 666 2.47 166 0.116 3.54 653 2.51 153 0.112 3.43 640 625 611 140 129 118 Ethyl iodide ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 0.656 0.663 0.670 0.677 730 0.092 5.37 0.684 655 0.090 4.98 0.691 590 0.088 4.63 0.698 539 0.086 4.30 0.705 495 0.085 4.11 0.712 455 0.083 3.90 0.718 420 0.081 3.72 0.724 390 0.080 3.53 Ethylene glycol ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 1127 2.272 57000 0.254 510 1120 2.327 33300 0.255 305 1113 2.381 20200 0.256 190 1106 2.431 13400 0.258 126 1099 2.484 9100 0.259 87.3 1092 2.536 7070 0.260 69.0 1085 2.586 4000 1077 2.636 3450 1070 1063 1056 2.685 2.734 2.779 3000 2440 2000 Formic acid ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 1241 1231 1220 1209 1196 1184 1170 1156 1140 0.265 2260 0.261 1800 0.257 1470 0.257 1220 0.253 1030 0.250 890 0.246 780 0.243 680 615 550 0.240 0.236 0.232 1124 1108 TRAnSPORT PROPERTIES 2-297 TABLE 2-146 Thermophysical Properties of Miscellaneous Saturated Liquids (Continued ) Temperature, °C Substance Gasoline Glycerol Kerosene Property −50 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1710 k (W/m⋅K) 0.131 Pr ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr — ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) 1150 k (W/m⋅K) Pr −40 1400 0.128 — −30 −20 −10 784 1.88 1170 990 0.125 0.123 15.1 775 1.92 850 0.121 13.5 — — — 0 20 30 40 50 60 70 759 2.02 645 0.118 11.0 751 2.06 530 0.116 9.41 743 2.11 464 0.114 8.59 735 2.15 410 0.112 7.87 721 2.20 367 0.110 7.34 717 2.25 330 0.108 6.88 708 2.30 298 0.106 6.47 1276 1270 1248 2.457 1242 2.504 2.548 2.588 2.625 2.657 2.686 4.0.+6 1260 2.393 1.5.+6 0.284 12650 1254 2.406 1.2.+7 0.285 0.287 0.288 0.289 0.291 0.293 0.294 0.295 2.28 73 2.32 66 2.35 60 2.38 55 767 1.97 735 0.120 12.1 725 500 360 275 781 1.91 215 0.140 2.93 10 774 1.96 173 0.139 2.44 767 2.02 149 0.139 2.17 760 2.07 126 0.138 1.89 754 2.13 108 0.138 1.67 748 2.18 95 0.137 1.51 742 2.23 83 0.137 1.35 80 90 100 699 2.35 270 0.104 6.10 690 2.41 246 0.102 5.81 681 2.46 225 0.100 5.54 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k(W/m⋅K) Pr 2.30 2305 0.225 23.6 2.32 1800 0.222 18.8 2.35 1410 0.219 15.1 2.37 1170 0.216 12.9 2.40 975 0.212 11.0 2.42 820 0.209 9.53 2.45 692 0.206 8.23 2.47 590 0.203 7.18 783 2.49 510 0.199 6.38 774 2.52 455 0.195 5.88 766 2.55 400 0.192 5.31 756 2.65 355 0.189 4.98 746 2.78 315 0.187 4.68 736 2.94 271 0.184 4.34 725 3.13 240 0.182 4.13 711 3.30 218 0.180 3.99 Methyl formate ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 1069 1.84 830 0.217 7.04 1056 1.86 711 0.213 6.21 1043 1.88 618 0.209 5.56 1030 1.90 544 0.205 5.04 1017 1.92 481 0.200 4.62 1003 1.95 430 0.195 4.30 989 1.99 380 0.191 3.96 975 2.03 345 0.186 3.77 960 2.08 315 0.180 3.64 944 929 913 897 880 863 845 Oil, castor ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 2,420,000 0.182 986,000 451,000 231,000 125,000 74,000 43,000 0.181 0.180 0.179 0.178 0.177 0.176 0.175 0.174 0.17 Methanol Oil, olive Pentane Propanol Sulfuric acid ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 138,000 0.170 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 693 2.060 489 0.142 7.14 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 849 1.955 20,200 13,500 9500 6900 0.167 0.166 0.165 236 684 2.084 428 0.139 6.42 674 2.110 379 0.136 5.88 665 2.137 339 0.132 5.49 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr Turpentine ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr 923 1.535 1670 0.149 17.8 913 1.556 1345 0.147 14.2 904 1.579 1100 0.144 12.1 36,300 0.167 24,500 0.166 17,000 12,400 0.166 0.165 0.165 0.164 0.164 616 606 596 585 574 562 209 0.115 190 0.112 175 0.108 161 0.105 148 0.101 137 124 113 0.098 0.095 0.091 646 2.206 279 0.125 4.92 636 2.239 254 0.122 4.66 626 2.273 234 0.119 4.47 811 814 796 788 779 770 761 752 5110 819 2.219 3900 2900 2245 1720 0.171 1400 0.169 1130 0.168 921 0.167 760 0.165 630 508 447 0.164 0.163 0.162 1834 1.382 25,400 15,700 11,500 8820 7220 6090 5190 829 1.80 380 0.124 5.5 820 1.83 355 0.122 5.3 810 1.87 325 0.119 5.1 820 730 675 48,400 35,200 0.314 932 1.514 2120 0.152 21.1 52,000 0.168 656 2.167 307 0.128 5.20 ρ (kg/m3) cp (kJ/ kg⋅K) µ (10−6Pa⋅s) k (W/m⋅K) Pr Toluene 914 1.633 84,000 0.169 810 895 1.602 915 0.142 10.3 886 1.633 770 0.139 9.0 876 1.652 670 0.137 8.1 867 1.675 590 0.134 7.4 858 1.701 520 0.132 6.7 848 1.73 470 0.129 6.3 839 1.76 420 0.126 5.9 1.72 2250 0.130 29.8 1.76 1780 0.129 24.3 1.80 1490 0.128 20.9 1270 0.127 18.4 1070 0.126 16.1 1.93 925 0.125 14.3 550 747 800 1.92 295 0.117 4.8 538 743 790 1.97 270 0.114 4.7 2-298 TABLE 2-147 Cmpd. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] Name Acetaldehyde Acetamide Acetic acid Acetic anhydride Acetone Acetonitrile Acetylene Acrolein Acrylic acid Acrylonitrile Air Ammonia Anisole Argon Benzamide Benzene Benzenethiol Benzoic acid Benzonitrile Benzophenone Benzyl alcohol Benzyl ethyl ether Benzyl mercaptan Biphenyl Bromine Bromobenzene Bromoethane Bromomethane 1,2-Butadiene 1,3-Butadiene Butane 1,2-Butanediol 1,3-Butanediol 1-Butanol 2-Butanol 1-Butene cis-2-Butene trans-2-Butene Butyl acetate Butylbenzene Butyl mercaptan sec-Butyl mercaptan 1-Butyne Butyraldehyde Butyric acid Butyronitrile Carbon dioxide Carbon disulfide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Formula C2H4O C2H5NO C2H4O2 C4H6O3 C3H6O C2H3N C2H2 C3H4O C3H4O2 C3H3N Mixture H3N C7H8O Ar C7H7NO C6H6 C6H6S C7H6O2 C7H5N C13H10O C7H8O C9H12O C7H8S C12H10 Br2 C6H5Br C2H5Br CH3Br C4H6 C4H6 C4H10 C4H10O2 C4H10O2 C4H10O C4H10O C4H8 C4H8 C4H8 C6H12O2 C10H14 C4H10S C4H10S C4H6 C4H8O C4H8O2 C4H7N CO2 CS2 CO CCl4 CF4 CAS 75-07-0 60-35-5 64-19-7 108-24-7 67-64-1 75-05-8 74-86-2 107-02-8 79-10-7 107-13-1 132259-10-0 7664-41-7 100-66-3 7440-37-1 55-21-0 71-43-2 108-98-5 65-85-0 100-47-0 119-61-9 100-51-6 539-30-0 100-53-8 92-52-4 7726-95-6 108-86-1 74-96-4 74-83-9 590-19-2 106-99-0 106-97-8 584-03-2 107-88-0 71-36-3 78-92-2 106-98-9 590-18-1 624-64-6 123-86-4 104-51-8 109-79-5 513-53-1 107-00-6 123-72-8 107-92-6 109-74-0 124-38-9 75-15-0 630-08-0 56-23-5 75-73-0 Mol. wt. 44.05256 59.0672 60.052 102.08864 58.07914 41.0519 26.03728 56.06326 72.06266 53.0626 28.96 17.03052 108.13782 39.948 121.13658 78.11184 110.17684 122.12134 103.1213 182.2179 108.13782 136.19098 124.20342 154.2078 159.808 157.0079 108.965 94.93852 54.09044 54.09044 58.1222 90.121 90.121 74.1216 74.1216 56.10632 56.10632 56.10632 116.15828 134.21816 90.1872 90.1872 54.09044 72.10572 88.1051 69.1051 44.0095 76.1407 28.0101 153.8227 88.0043 C1 0.33515 0.39363 0.214 0.23638 0.2878 0.30755 0.33363 0.2703 0.2441 0.30751 0.28472 1.169 0.23494 0.1819 0.28485 0.23444 0.20996 0.2391 0.20603 0.25867 0.17847 0.2029 0.20316 0.19053 –0.2185 0.16983 0.1629 0.16143 0.21966 0.22231 0.27349 0.064621 –0.0032865 0.22888 0.18599 0.22153 0.21378 0.21153 0.21721 0.18707 0.21143 0.2069 0.22334 0.24962 0.1967 0.24077 0.4406 0.2333 0.2855 0.1589 0.20771 C2 –0.00055227 –0.00037053 –0.0001834 –0.00024263 –0.000427 –0.000402 –0.00083655 –0.0003764 –0.0002904 –0.000487 –0.0017393 –0.002314 –0.00026477 –0.0003176 –0.00025225 –0.00030572 –0.0002146 –0.0002325 –0.00021023 –0.00022516 –0.000065843 –0.0002226 –0.00019912 –0.00015145 0.0042143 –0.0001981 –0.00021198 –0.00021287 –0.0003436 –0.0003664 –0.00071267 0.00067625 0.0011463 –0.00025 –0.00017227 –0.00035023 –0.00035445 –0.00035056 –0.00026563 –0.00020037 –0.000258 –0.0002568 –0.0003515 –0.000325 –0.000168 –0.00028665 –0.0012175 –0.000275 –0.001784 –0.0001987 –0.00078883 C3 C4 C5 –0.00000411 –0.000017753 3.1041E-08 5.1555E-07 –1.0491E-06 –1.5525E-06 –2.0108E-11 Tmin, K 149.78 353.33 289.81 200.15 178.45 229.32 192.4 185.45 286.15 189.63 75 195.41 235.65 83.78 403 278.68 258.27 395.45 260.28 321.35 257.85 275.65 243.95 342.2 266 242.43 154.25 179.44 136.95 164.25 134.86 220 196.15 183.85 158.45 87.8 134.26 167.62 199.65 185.3 157.46 133.02 147.43 176.8 267.95 161.3 216.58 161.11 68.15 250.33 89.56 Thermal cond. at Tmin 0.2524 0.2627 0.1608 0.1878 0.2116 0.2154 0.1727 0.2005 0.1610 0.2152 0.1543 0.7168 0.1725 0.1264 0.1832 0.1492 0.1545 0.1472 0.1513 0.1863 0.1615 0.1415 0.1546 0.1387 0.1299 0.1218 0.1302 0.1232 0.1726 0.1621 0.1868 0.1626 0.1618 0.1829 0.1587 0.1908 0.1662 0.1528 0.1642 0.1499 0.1708 0.1727 0.1715 0.1922 0.1517 0.1945 0.1769 0.1890 0.1639 0.1092 0.1371 Tmax, K Thermal cond. at Tmax 294.15 494.3 391.05 412.7 343.15 354.81 250 325.84 484.5 350.45 125 400.05 512.5 150 563.15 413.1 442.29 596 464.15 664 478.6 528.6 472.03 723.15 584 429.24 327 413.15 284 268.74 400 469.57 481.38 391 372.9 266.91 276.87 274.03 453.75 473.15 371.61 358.13 281.22 347.94 573.15 390.74 300 319.37 125 349.79 145.1 0.1727 0.2105 0.1423 0.1362 0.1413 0.1649 0.1245 0.1477 0.1034 0.1368 0.0673 0.2433 0.0993 0.0418 0.1428 0.1081 0.1150 0.1005 0.1085 0.1092 0.1470 0.0852 0.1092 0.0810 0.0316 0.0848 0.0936 0.0735 0.1221 0.1238 0.0709 0.1508 0.1888 0.1311 0.1218 0.1281 0.1156 0.1155 0.0967 0.0923 0.1156 0.1149 0.1245 0.1365 0.1004 0.1288 0.0754 0.1455 0.0625 0.0894 0.0933 2-299 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 Chlorine Chlorobenzene Chloroethane Chloroform Chloromethane 1-Chloropropane 2-Chloropropane m-Cresol o-Cresol p-Cresol Cumene Cyanogen Cyclobutane Cyclohexane Cyclohexanol Cyclohexanone Cyclohexene Cyclopentane Cyclopentene Cyclopropane Cyclohexyl mercaptan Decanal Decane Decanoic acid 1-Decanol 1-Decene Decyl mercaptan 1-Decyne Deuterium 1,1-Dibromoethane 1,2-Dibromoethane Dibromomethane Dibutyl ether m-Dichlorobenzene o-Dichlorobenzene p-Dichlorobenzene 1,1-Dichloroethane 1,2-Dichloroethane Dichloromethane 1,1-Dichloropropane 1,2-Dichloropropane Diethanol amine Diethyl amine Diethyl ether Diethyl sulfide 1,1-Difluoroethane 1,2-Difluoroethane Difluoromethane Di–isopropyl amine Di–isopropyl ether Di–isopropyl ketone 1,1-Dimethoxyethane 1,2-Dimethoxypropane Dimethyl acetylene Dimethyl amine Cl2 C6H5Cl C2H5Cl CHCl3 CH3Cl C3H7Cl C3H7Cl C7H8O C7H8O C7H8O C9H12 C2N2 C4H8 C6H12 C6H12O C6H10O C6H10 C5H10 C5H8 C3H6 C6H12S C10H20O C10H22 C10H20O2 C10H22O C10H20 C10H22S C10H18 D2 C2H4Br2 C2H4Br2 CH2Br2 C8H18O C6H4Cl2 C6H4Cl2 C6H4Cl2 C2H4Cl2 C2H4Cl2 CH2Cl2 C3H6Cl2 C3H6Cl2 C4H11NO2 C4H11N C4H10O C4H10S C2H4F2 C2H4F2 CH2F2 C6H15N C6H14O C7H14O C4H10O2 C5H12O2 C4H6 C2H7N 7782-50-5 108-90-7 75-00-3 67-66-3 74-87-3 540-54-5 75-29-6 108-39-4 95-48-7 106-44-5 98-82-8 460-19-5 287-23-0 110-82-7 108-93-0 108-94-1 110-83-8 287-92-3 142-29-0 75-19-4 1569-69-3 112-31-2 124-18-5 334-48-5 112-30-1 872-05-9 143-10-2 764-93-2 7782-39-0 557-91-5 106-93-4 74-95-3 142-96-1 541-73-1 95-50-1 106-46-7 75-34-3 107-06-2 75-09-2 78-99-9 78-87-5 111-42-2 109-89-7 60-29-7 352-93-2 75-37-6 624-72-6 75-10-5 108-18-9 108-20-3 565-80-0 534-15-6 7778-85-0 503-17-3 124-40-3 70.906 112.5569 64.5141 119.37764 50.4875 78.54068 78.54068 108.13782 108.13782 108.13782 120.19158 52.0348 56.10632 84.15948 100.15888 98.143 82.1436 70.1329 68.11702 42.07974 116.22448 156.2652 142.28168 172.265 158.28108 140.2658 174.34668 138.24992 4.0316 187.86116 187.86116 173.83458 130.22792 147.00196 147.00196 147.00196 98.95916 98.95916 84.93258 112.98574 112.98574 105.13564 73.13684 74.1216 90.1872 66.04997 66.04997 52.02339 101.19 102.17476 114.18546 90.121 104.14758 54.09044 45.08368 0.2246 0.1841 0.23779 0.1778 0.25381 0.21851 0.21232 0.18241 0.19186 0.17971 0.1855 0.37845 0.22262 0.19813 0.1715 0.17557 0.20926 0.2066 0.21776 0.24348 0.18374 0.21363 0.2063 0.206 0.236171 0.20237 0.20134 0.20839 1.264 0.1426 0.13622 0.17558 0.19418 0.16694 0.16994 0.16977 0.18881 0.214 0.23847 0.18 0.19653 0.0218 0.2587 0.2495 0.21065 0.27019 0.23171 0.37296 0.1844 0.19162 0.22076 0.22078 0.22998 0.22773 0.2454 –0.000064 –0.0001917 –0.000395209 –0.0002023 –0.000431803 –0.00033762 –0.0003149 –0.00011109 –0.0001303 –0.00012037 –0.00020895 –0.00069945 –0.00034082 –0.0002505 –0.0001255 –0.00012392 –0.00026037 –0.0002696 –0.00027783 –0.00042568 –0.0001925 –0.00023004 –0.00025 –0.0002 –0.00025 –0.00024187 –0.00020826 –0.00023622 –0.00016402 –0.0001179 –0.00022499 –0.00022246 –0.0001667 –0.0001637 –0.0001799 –0.00026083 –0.000266 –0.00033366 –0.00023144 –0.00025012 0.0010315 –0.00054343 –0.000407 –0.0002623 –0.000661 –0.00038503 –0.00088707 –0.000239 –0.0002762 –0.00027624 –0.00031271 –0.00030372 –0.00034804 –0.000338 –0.000000788 –0.000001355 4.2097E-07 3.443E-07 2.5762E-07 172.12 227.95 136.75 209.63 175.43 150.35 155.97 285.39 304.19 307.93 177.14 245.25 182.48 279.69 296.6 242 169.67 179.28 138.13 145.59 189.64 285 243.51 304.75 280.05 206.89 247.56 229.15 20.4 210.15 282.85 220.6 175.3 248.39 262.87 326.14 176.19 253.15 178.01 192.5 172.71 301.15 223.35 156.85 169.2 154.56 179.6 136.95 176.85 187.65 204.81 159.95 226.1 240.91 180.96 0.1902 0.1404 0.1837 0.1354 0.1781 0.1677 0.1632 0.1507 0.1522 0.1426 0.1485 0.2069 0.1604 0.1281 0.1343 0.1456 0.1651 0.1583 0.1794 0.1815 0.1472 0.1481 0.1454 0.1451 0.1662 0.1523 0.1498 0.1543 1.2640 0.1081 0.1029 0.1259 0.1552 0.1255 0.1269 0.1111 0.1429 0.1467 0.1791 0.1354 0.1533 0.2095 0.1583 0.1857 0.1663 0.1763 0.1626 0.2563 0.1421 0.1398 0.1642 0.1708 0.1613 0.1439 0.1842 410 404.87 348.15 400 333 393.15 386.7 475.43 464.15 475.13 413.15 251.9 285.66 353.87 563.15 428.58 356.12 322.4 333.15 240.37 431.95 481.65 447.3 543.15 503 443.75 512.35 447.15 20.4 498.4 404.51 370.1 523.15 446.23 351.71 548 416.9 356.59 325 438 457.6 673.15 453.15 433.15 365.25 363.15 372.8 302.56 357.05 400.1 460 337.45 366.15 300.13 403.15 0.0659 0.1065 0.1002 0.0969 0.1100 0.0858 0.0906 0.1296 0.1314 0.1225 0.0992 0.2023 0.1253 0.1095 0.1008 0.1225 0.1165 0.1197 0.1252 0.1412 0.1006 0.1028 0.0945 0.0974 0.1104 0.0950 0.0946 0.1028 1.2640 0.0609 0.0885 0.0923 0.0778 0.0926 0.1124 0.0712 0.0801 0.1191 0.1300 0.0786 0.0821 0.1022 0.0989 0.0732 0.1148 0.0756 0.0882 0.1282 0.0991 0.0811 0.0937 0.1153 0.1188 0.1233 0.1091 (Continued) 2-300 TABLE 2-147 Cmpd. no. 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name 2,3-Dimethylbutane 1,1-Dimethylcyclohexane cis-1,2-Dimethylcyclohexane trans-1,2-Dimethylcyclohexane Dimethyl disulfide Dimethyl ether N,N-Dimethyl formamide 2,3-Dimethylpentane Dimethyl phthalate Dimethylsilane Dimethyl sulfide Dimethyl sulfoxide Dimethyl terephthalate 1,4-Dioxane Diphenyl ether Dipropyl amine Dodecane Eicosane Ethane Ethanol Ethyl acetate Ethyl amine Ethylbenzene Ethyl benzoate 2-Ethyl butanoic acid Ethyl butyrate Ethylcyclohexane Ethylcyclopentane Ethylene Ethylenediamine Ethylene glycol Ethyleneimine Ethylene oxide Ethyl formate 2-Ethyl hexanoic acid Ethylhexyl ether Ethylisopropyl ether Ethylisopropyl ketone Ethyl mercaptan Ethyl propionate Ethylpropyl ether Ethyltrichlorosilane Fluorine Fluorobenzene Fluoroethane Fluoromethane Formaldehyde Formamide Formic acid Furan Formula C6H14 C8H16 C8H16 C8H16 C2H6S2 C2H6O C3H7NO C7H16 C10H10O4 C2H8Si C2H6S C2H6OS C10H10O4 C4H8O2 C12H10O C6H15N C12H26 C20H42 C2H6 C2H6O C4H8O2 C2H7N C8H10 C9H10O2 C6H12O2 C6H12O2 C8H16 C7H14 C2H4 C2H8N2 C2H6O2 C2H5N C2H4O C3H6O2 C8H16O2 C8H18O C5H12O C6H12O C2H6S C5H10O2 C5H12O C2H5Cl3Si F2 C6H5F C2H5F CH3F CH2O CH3NO CH2O2 C4H4O CAS Mol. wt. C1 C2 79-29-8 590-66-9 2207-01-4 6876-23-9 624-92-0 115-10-6 68-12-2 565-59-3 131-11-3 1111-74-6 75-18-3 67-68-5 120-61-6 123-91-1 101-84-8 142-84-7 112-40-3 112-95-8 74-84-0 64-17-5 141-78-6 75-04-7 100-41-4 93-89-0 88-09-5 105-54-4 1678-91-7 1640-89-7 74-85-1 107-15-3 107-21-1 151-56-4 75-21-8 109-94-4 149-57-5 5756-43-4 625-54-7 565-69-5 75-08-1 105-37-3 628-32-0 115-21-9 7782-41-4 462-06-6 353-36-6 593-53-3 50-00-0 75-12-7 64-18-6 110-00-9 86.17536 112.21264 112.21264 112.21264 94.19904 46.06844 73.09378 100.20194 194.184 60.17042 62.134 78.13344 194.184 88.10512 170.2072 101.19 170.33484 282.54748 30.069 46.06844 88.10512 45.08368 106.165 150.1745 116.15828 116.15828 112.21264 98.18606 28.05316 60.09832 62.06784 43.0678 44.05256 74.07854 144.211 130.22792 88.14818 100.15888 62.13404 102.1317 88.14818 163.506 37.9968064 96.1023032 48.0595 34.03292 30.02598 45.04062 46.0257 68.07396 0.1774 0.1807 0.18092 0.17675 0.21373 0.31174 0.26 0.17964 0.13905 0.25547 0.23942 0.3142 0.21956 0.3027 0.18686 0.2224 0.2047 0.2178 0.35758 0.2468 0.2501 0.30059 0.1999 0.20771 0.2175 0.21043 0.17662 0.18334 0.4194 0.36434 0.088067 0.3097 0.26957 0.2587 0.20954 0.19356 0.21928 0.22873 0.23392 0.2137 0.22717 0.19653 0.2758 0.20962 0.25866 0.48162 0.336003243 0.3847 0.302 0.2198 –0.0002436 –0.0002177 –0.0002108 –0.0002077 –0.0002447 –0.0005638 –0.000255 –0.000246 0.0001509 –0.0004411 –0.0003311 –0.00030809 –0.000209955 –0.0004827 –0.00014953 –0.000314 –0.0002326 –0.0002233 –0.0011458 –0.000264 –0.0003563 –0.000581 –0.00023823 –0.00021265 –0.0002407 –0.00024903 –0.0002014 –0.0002228 –0.001591 –0.0004433 0.00094712 –0.0004023 –0.0003984 –0.00033 –0.00022251 –0.00024102 –0.00032568 –0.0002913 –0.0003206 –0.0002515 –0.0003298 –0.00016907 –0.0016297 –0.00028034 –0.000498 –0.0010709 –0.00054 –0.0001065 –0.000108 –0.00031405 C3 C4 –3.978E-07 6.1866E-07 6.602E-07 0.000001306 –1.3114E-06 –1.6698E-07 0 0 C5 Tmin, K 145.19 239.66 223.16 184.99 188.44 131.65 250 160 273.15 122.93 174.88 291.67 413.79 284.95 300.03 210.15 263.57 309.58 90.35 159.05 189.6 192.15 178.2 238.45 258.15 175.15 161.84 134.71 104 284.29 260.15 195.2 160.65 193.55 155.15 180 140 204.15 125.26 199.25 145.65 167.55 53.48 238.15 129.95 131.35 155.15 275.7 281.45 187.55 Thermal cond. at Tmin 0.1420 0.1285 0.1339 0.1383 0.1676 0.2375 0.1963 0.1403 0.1506 0.2012 0.1815 0.2243 0.1327 0.1652 0.1420 0.1564 0.1434 0.1487 0.2591 0.2048 0.1825 0.2133 0.1574 0.1570 0.1554 0.1668 0.1440 0.1533 0.2681 0.2383 0.2457 0.2312 0.2056 0.1948 0.1750 0.1502 0.1737 0.1693 0.1938 0.1636 0.1791 0.1635 0.1886 0.1429 0.1939 0.3410 0.2522 0.3553 0.2716 0.1609 Tmax, K Thermal cond. at Tmax 331.15 392.7 402.94 596.15 382.9 320.03 425.15 362.93 556.85 253.55 310.48 464 559.2 374.47 531.46 382 489.47 616.93 300 353.15 350.21 293.15 413.1 549.4 516.5 453.15 404.94 376.62 280 390.41 470.45 329 283.85 433.15 500.66 466.4 391.2 450.1 308.15 495 400.07 371.05 130 353.15 235.45 194.82 253.85 493 373.71 304.5 0.0967 0.0952 0.0960 0.0529 0.1200 0.1313 0.1516 0.0904 0.0997 0.1436 0.1366 0.1712 0.1022 0.1219 0.1074 0.1025 0.0909 0.0800 0.0695 0.1536 0.1253 0.1870 0.1015 0.0909 0.0932 0.0976 0.0951 0.0994 0.0763 0.1913 0.2434 0.1773 0.1565 0.1158 0.0981 0.0812 0.0919 0.0976 0.1351 0.0892 0.0952 0.1108 0.0639 0.1106 0.1414 0.2730 0.1989 0.3322 0.2616 0.1242 2-301 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 Helium-4 Heptadecane Heptanal Heptane Heptanoic acid 1-Heptanol 2-Heptanol 3-Heptanone 2-Heptanone 1-Heptene Heptyl mercaptan 1-Heptyne Hexadecane Hexanal Hexane Hexanoic acid 1-Hexanol 2-Hexanol 2-Hexanone 3-Hexanone 1-Hexene 3-Hexyne Hexyl mercaptan 1-Hexyne 2-Hexyne Hydrazine Hydrogen Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen sulfide Isobutyric acid Isopropyl amine Malonic acid Methacrylic acid Methane Methanol N-Methyl acetamide Methyl acetate Methyl acetylene Methyl acrylate Methyl amine Methyl benzoate 3-Methyl-1,2-butadiene 2-Methylbutane 2-Methylbutanoic acid 3-Methyl-1-butanol 2-Methyl-1-butene 2-Methyl-2-butene 2-Methyl -1-butene-3-yne Methylbutyl ether Methylbutyl sulfide 3-Methyl-1-butyne Methyl butyrate He C17H36 C7H14O C7H16 C7H14O2 C7H16O C7H16O C7H14O C7H14O C7H14 C7H16S C7H12 C16H34 C6H12O C6H14 C6H12O2 C6H14O C6H14O C6H12O C6H12O C6H12 C6H10 C6H14S C6H10 C6H10 H4N2 H2 BrH ClH CHN FH H2S C4H8O2 C3H9N C3H4O4 C4H6O2 CH4 CH4O C3H7NO C3H6O2 C3H4 C4H6O2 CH5N C8H8O2 C5H8 C5H12 C5H10O2 C5H12O C5H10 C5H10 C5H6 C5H12O C5H12S C5H8 C5H10O2 7440-59-7 629-78-7 111-71-7 142-82-5 111-14-8 111-70-6 543-49-7 106-35-4 110-43-0 592-76-7 1639-09-4 628-71-7 544-76-3 66-25-1 110-54-3 142-62-1 111-27-3 626-93-7 591-78-6 589-38-8 592-41-6 928-49-4 111-31-9 693-02-7 764-35-2 302-01-2 1333-74-0 10035-10-6 7647-01-0 74-90-8 7664-39-3 7783-06-4 79-31-2 75-31-0 141-82-2 79-41-4 74-82-8 67-56-1 79-16-3 79-20-9 74-99-7 96-33-3 74-89-5 93-58-3 598-25-4 78-78-4 116-53-0 123-51-3 563-46-2 513-35-9 78-80-8 628-28-4 628-29-5 598-23-2 623-42-7 4.0026 240.46774 114.18546 100.20194 130.185 116.20134 116.20134 114.18546 114.18546 98.18606 132.26694 96.17018 226.44116 100.15888 86.17536 116.158 102.17476 102.175 100.15888 100.15888 84.15948 82.1436 118.24036 82.1436 82.1436 32.04516 2.01588 80.91194 36.46094 27.02534 20.0063432 34.08088 88.10512 59.11026 104.06146 86.08924 16.0425 32.04186 73.09378 74.07854 40.06386 86.08924 31.0571 136.14792 68.11702 72.14878 102.1317 88.1482 70.1329 70.1329 66.10114 88.14818 104.214 68.11702 102.1317 –0.013833 0.20926 0.22841 0.215 0.202 0.234063 0.21142 0.2026 0.2108 0.19664 0.2037 0.21098 0.20749 0.22832 0.22492 0.1855 0.230656 0.21391 0.21076 0.23493 0.19112 0.20996 0.2058 0.21492 0.2119 1.3675 –0.0917 0.234 0.8045 0.43454 0.7516 0.4842 0.21668 0.237 0.28231 0.2306 0.41768 0.2837 0.23743 0.2777 0.23648 0.26082 0.33446 0.22142 0.1983 0.21246 0.22284 0.17471 0.19447 0.19636 0.20385 0.22235 0.20698 0.20348 0.21748 0.022913 –0.0002215 –0.00026273 –0.000303 –0.0002 –0.00025 –0.00024793 –0.0002234 –0.000246 –0.00016623 –0.0002252 –0.00026652 –0.00021917 –0.00026482 –0.0003533 –0.000146 –0.00025 –0.00026042 –0.00024 –0.0002912 –0.000083519 –0.0002692 –0.0002324 –0.0002899 –0.00027048 –0.0015895 0.017678 –0.0004636 –0.002102 –0.0007008 –0.0010874 –0.001184 –0.0002556 –0.000332 –0.00024019 –0.00025201 –0.0024528 –0.000281 –0.0002362 –0.000417 –0.00041639 –0.0003506 –0.00067427 –0.00022759 –0.0002822 –0.00033581 –0.0002516 –0.0001256 –0.0002901 –0.000291 –0.0002874 –0.0003044 –0.00024439 –0.0003106 –0.00025913 –0.0054872 0.0004585 –2.5241E-07 –5.1407E-07 –0.000382 3.5588E-06 8.033E-07 –3.3324E-06 1.0266E-07 2.2 295.13 229.8 182.57 265.83 239.15 220 234.15 238.15 154.12 229.92 192.22 291.31 214.93 177.83 269.25 228.55 223 217.35 217.5 133.39 170.05 192.62 141.25 183.65 274.69 13.95 185.15 273.15 259.83 189.79 193.15 227.15 177.95 409.15 288.15 90.69 175.47 301.15 175.15 170.45 196.32 179.69 260.75 159.53 113.25 357.15 155.95 135.58 139.39 160.15 157.48 175.3 183.45 187.35 0.0149 0.1439 0.1680 0.1597 0.1488 0.1743 0.1569 0.1503 0.1522 0.1650 0.1519 0.1597 0.1436 0.1714 0.1621 0.1462 0.1735 0.1558 0.1586 0.1716 0.1708 0.1642 0.1610 0.1740 0.1622 0.9309 0.0754 0.1482 0.2303 0.2525 0.5452 0.2555 0.1586 0.1779 0.1840 0.1580 0.2245 0.2344 0.1663 0.2047 0.1655 0.1920 0.2392 0.1621 0.1533 0.1744 0.1330 0.1551 0.1551 0.1558 0.1578 0.1744 0.1641 0.1465 0.1689 4.8 575.3 426.15 371.58 496.15 573.15 432.9 553.15 424.05 366.79 450.09 372.93 560.01 401.15 370 603.15 575 412.4 400.85 466 336.63 354.35 425.81 344.48 357.67 623.15 31 290.62 323.15 298.85 394.45 292.42 482.75 305.55 580 530 180 337.85 478.15 386.15 249.94 421 283.15 547.9 314 368.13 480.9 404.15 304.3 311.7 305.4 463.15 396.58 302.15 493.15 0.0204 0.0818 0.1164 0.1024 0.1028 0.0908 0.1041 0.0790 0.1065 0.1017 0.1023 0.1116 0.0848 0.1221 0.0942 0.0974 0.0869 0.1065 0.1146 0.0992 0.1048 0.1146 0.1068 0.1151 0.1152 0.3770 0.0848 0.0993 0.1252 0.2251 0.3227 0.1380 0.0933 0.1356 0.1430 0.0970 0.0915 0.1888 0.1245 0.1167 0.1324 0.1132 0.2079 0.0967 0.1097 0.0888 0.1018 0.1239 0.1062 0.1057 0.1161 0.0814 0.1101 0.1096 0.0897 (Continued) 2-302 TABLE 2-147 Cmpd. no. 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name Methylchlorosilane Methylcyclohexane 1-Methylcyclohexanol cis-2-Methylcyclohexanol trans-2-Methylcyclohexanol Methylcyclopentane 1-Methylcyclopentene 3-Methylcyclopentene Methyldichlorosilane Methylethyl ether Methylethyl ketone Methylethyl sulfide Methyl formate Methylisobutyl ether Methylisobutyl ketone Methyl Isocyanate Methylisopropyl ether Methylisopropyl ketone Methylisopropyl sulfide Methyl mercaptan Methyl methacrylate 2-Methyloctanoic acid 2-Methylpentane Methyl pentyl ether 2-Methylpropane 2-Methyl-2-propanol 2-Methyl propene Methyl propionate Methylpropyl ether Methylpropyl sulfide Methylsilane alpha-Methyl styrene Methyl tert-butyl ether Methyl vinyl ether Naphthalene Neon Nitroethane Nitrogen Nitrogen trifluoride Nitromethane Nitrous oxide Nitric oxide Nonadecane Nonanal Nonane Nonanoic acid 1-Nonanol 2-Nonanol 1-Nonene Nonyl mercaptan 1-Nonyne Formula CH5ClSi C7H14 C7H14O C7H14O C7H14O C6H12 C6H10 C6H10 CH4Cl2Si C3H8O C4H8O C3H8S C2H4O2 C5H12O C6H12O C2H3NO C4H10O C5H10O C4H10S CH4S C5H8O2 C9H18O2 C6H14 C6H14O C4H10 C4H10O C4H8 C4H8O2 C4H10O C4H10S CH6Si C9H10 C5H12O C3H6O C10H8 Ne C2H5NO2 N2 F3N CH3NO2 N 2O NO C19H40 C9H18O C9H20 C9H18O2 C9H20O C9H20O C9H18 C9H20S C9H16 CAS 993-00-0 108-87-2 590-67-0 7443-70-1 7443-52-9 96-37-7 693-89-0 1120-62-3 75-54-7 540-67-0 78-93-3 624-89-5 107-31-3 625-44-5 108-10-1 624-83-9 598-53-8 563-80-4 1551-21-9 74-93-1 80-62-6 3004-93-1 107-83-5 628-80-8 75-28-5 75-65-0 115-11-7 554-12-1 557-17-5 3877-15-4 992-94-9 98-83-9 1634-04-4 107-25-5 91-20-3 7440-01-9 79-24-3 7727-37-9 7783-54-2 75-52-5 10024-97-2 10102-43-9 629-92-5 124-19-6 111-84-2 112-05-0 143-08-8 628-99-9 124-11-8 1455-21-6 3452-09-3 Mol. wt. 80.5889 98.18606 114.18546 114.18546 114.18546 84.15948 82.1436 82.1436 115.03396 60.09502 72.10572 76.1606 60.05196 88.14818 100.15888 57.05132 74.1216 86.1323 90.1872 48.10746 100.11582 158.23802 86.17536 102.17476 58.1222 74.1216 56.10632 88.10512 74.1216 90.1872 46.14384 118.1757 88.1482 58.07914 128.17052 20.1797 75.0666 28.0134 71.00191 61.04002 44.0128 30.0061 268.5209 142.23862 128.2551 158.238 144.2545 144.255 126.23922 160.3201 124.22334 C1 C2 0.24683 0.1791 0.21558 0.21839 0.21828 0.1929 0.20023 0.1994 0.21956 0.27304 0.2197 0.22136 0.3246 0.222 0.2301 0.2822 0.24154 0.2332 0.20978 0.26119 0.2583 0.20911 0.19334 0.21698 0.20455 0.21258 0.2802 0.22534 0.24817 0.21103 0.2774 0.19657 0.22526 0.28035 0.17096 0.2971 0.247 0.2654 –0.00038854 –0.0002291 –0.00022728 –0.00025776 –0.0002557 –0.0002492 –0.00025581 –0.00026149 –0.00032153 –0.0004518 –0.0002505 –0.00028938 –0.000468 –0.00032217 –0.00028899 –0.00042037 –0.0003774 –0.0003044 –0.00026468 –0.00038345 –0.000379 –0.00021852 –0.00028038 –0.00028998 –0.00036589 –0.00029864 –0.000786 –0.0002683 –0.0003774 –0.00025985 –0.00054608 –0.0002118 –0.00037235 –0.0004646 –0.00010059 –0.017356 –0.0002814 –0.001677 0.3276 0.10112 0.1878 0.21229 0.21905 0.209 0.204 0.240538 0.2081 0.20468 0.20244 0.20954 –0.000405 0.0010293 –0.00022 –0.00024013 –0.000264 –0.0002 –0.00025 –0.00022869 –0.00025738 –0.00021343 –0.00024588 C3 C4 C5 6.516E-07 1.1689E-07 0 0.0005911 –0.000007421 –0.00000943 0 Tmin, K Thermal cond. at Tmin Tmax, K Thermal cond. at Tmax 139.05 273.15 299.15 280.15 269.15 130.73 146.62 168.54 182.55 160 186.48 167.23 174.15 188 189.15 256.15 127.93 180.15 171.64 150.18 290.15 208.2 119.55 176 113.54 298.97 132.81 185.65 133.97 160.17 116.34 249.95 164.55 151.15 353.43 25 183.63 63.15 0.1928 0.1165 0.1476 0.1462 0.1495 0.1603 0.1627 0.1553 0.1609 0.2008 0.1730 0.1730 0.2431 0.1614 0.1754 0.1745 0.1933 0.1784 0.1644 0.2036 0.1483 0.1636 0.1598 0.1659 0.1630 0.1233 0.1873 0.1755 0.1976 0.1694 0.2139 0.1436 0.1672 0.2101 0.1354 0.1167 0.1953 0.1595 281.85 374.08 548.8 484.2 484.8 344.95 348.64 338.05 314.7 341.34 352.79 339.8 373.15 390 451.42 312 370 435.9 357.91 279.11 363.45 555.2 389.25 432.3 400 404.96 395.2 475 373 368.69 216.25 438.65 328.2 341.1 646.97 44 387.22 124 0.1373 0.0934 0.0909 0.0936 0.0943 0.1069 0.1110 0.1110 0.1184 0.1188 0.1313 0.1230 0.1500 0.0964 0.0996 0.1510 0.1019 0.1005 0.1150 0.1542 0.1206 0.0878 0.0842 0.0916 0.0582 0.0916 0.0713 0.0979 0.1074 0.1152 0.1593 0.1037 0.1156 0.1219 0.1059 0.0457 0.1380 0.0575 244.6 277.59 110 305.04 267.3 219.66 285.55 268.15 238.15 191.91 253.05 223.15 0.2285 0.1011 0.1869 0.1452 0.1549 0.1510 0.1469 0.1735 0.1536 0.1553 0.1484 0.1547 374.35 277.59 176.4 603.05 465.52 423.97 528.75 578.65 471.7 420.02 492.95 423.85 0.1760 0.1011 0.0759 0.0796 0.1073 0.0971 0.0983 0.0959 0.1002 0.0966 0.0972 0.1053 2-303 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 Octadecane Octanal Octane Octanoic acid 1-Octanol 2-Octanol 2-Octanone 3-Octanone 1-Octene Octyl mercaptan 1-Octyne Oxalic acid Oxygen Ozone Pentadecane Pentanal Pentane Pentanoic acid 1-Pentanol 2-Pentanol 2-Pentanone 3-Pentanone 1-Pentene 2-Pentyl mercaptan Pentyl mercaptan 1-Pentyne 2-Pentyne Phenanthrene Phenol Phenyl isocyanate Phthalic anhydride Propadiene Propane 1-Propanol 2-Propanol Propenylcyclohexene Propionaldehyde Propionic acid Propionitrile Propyl acetate Propyl amine Propylbenzene Propylene Propyl formate 2-Propyl mercaptan Propyl mercaptan 1,2-Propylene glycol Quinone Silicon tetrafluoride Styrene Succinic acid Sulfur dioxide Sulfur hexafluoride Sulfur trioxide Terephthalic acid C18H38 C8H16O C8H18 C8H16O2 C8H18O C8H18O C8H16O C8H16O C8H16 C8H18S C8H14 C2H2O4 O2 O3 C15H32 C5H10O C5H12 C5H10O2 C5H12O C5H12O C5H10O C5H10O C5H10 C5H12S C5H12S C5H8 C5H8 C14H10 C6H6O C7H5NO C8H4O3 C3H4 C3H8 C3H8O C3H8O C9H14 C3H6O C3H6O2 C3H5N C5H10O2 C3H9N C9H12 C3H6 C4H8O2 C3H8S C3H8S C3H8O2 C6H4O2 F4Si C8H8 C4H6O4 O 2S F6S O 3S C8H6O4 593-45-3 124-13-0 111-65-9 124-07-2 111-87-5 123-96-6 111-13-7 106-68-3 111-66-0 111-88-6 629-05-0 144-62-7 7782-44-7 10028-15-6 629-62-9 110-62-3 109-66-0 109-52-4 71-41-0 6032-29-7 107-87-9 96-22-0 109-67-1 2084-19-7 110-66-7 627-19-0 627-21-4 85-01-8 108-95-2 103-71-9 85-44-9 463-49-0 74-98-6 71-23-8 67-63-0 13511-13-2 123-38-6 79-09-4 107-12-0 109-60-4 107-10-8 103-65-1 115-07-1 110-74-7 75-33-2 107-03-9 57-55-6 106-51-4 7783-61-1 100-42-5 110-15-6 7446-09-5 2551-62-4 7446-11-9 100-21-0 254.49432 128.212 114.22852 144.211 130.22792 130.228 128.21204 128.21204 112.21264 146.29352 110.19676 90.03488 31.9988 47.9982 212.41458 86.1323 72.14878 102.132 88.1482 88.1482 86.1323 86.1323 70.1329 104.21378 104.21378 68.11702 68.11702 178.2292 94.11124 119.1207 148.11556 40.06386 44.09562 60.09502 60.095 122.20746 58.07914 74.0785 55.0785 102.1317 59.11026 120.19158 42.07974 88.10512 76.16062 76.16062 76.09442 108.09476 104.07911 104.14912 118.08804 64.0638 146.0554192 80.0632 166.13084 0.2137 0.22273 0.2156 0.203 0.235281 0.20955 0.2132 0.21732 0.20467 0.2012 0.2095 0.26335 0.2741 0.17483 0.20649 0.23894 0.2537 0.1848 0.223042 0.21875 0.2161 0.21569 0.21361 0.20597 0.2086 0.22102 0.21282 0.13753 0.18831 0.16326 0.22946 0.23081 0.26755 0.23144 0.20161 0.1831 0.31721 0.1954 0.26743 0.2332 0.2632 0.18707 0.24719 0.2247 0.21706 0.2202 0.2152 0.26524 –0.0002252 –0.00025037 –0.00029483 –0.0002 –0.00025 –0.00023733 –0.0002494 –0.00024969 –0.0002675 –0.0002142 –0.00025334 –0.00022461 –0.00138 0.00075288 –0.00021911 –0.00029724 –0.000576 –0.0001434 –0.00025 –0.00027849 –0.00024866 –0.00024081 –0.00030777 –0.00024518 –0.00024536 –0.000322 –0.0002856 –0.000025247 –0.0001 –0.00017777 –0.00021345 –0.0004078 –0.00066457 –0.00025 –0.00021529 –0.00020275 –0.000528 –0.000164 –0.00033418 –0.0003096 –0.0004278 –0.00019846 –0.00048824 –0.000264 –0.00028952 –0.00028535 –0.0000497 –0.00028676 0.20215 0.27216 0.38218 0.2544 0.92882 0.3063 –0.0002201 –0.00023183 –0.0006254 –0.0006595 –0.0030803 –0.00028541 –2.5228E-06 0.000000344 2.774E-07 0.000000412 0.00000266 301.31 251.65 216.38 289.65 257.65 241.55 252.85 255.55 171.45 223.95 193.55 462.65 60 77.35 283.07 191.59 143.42 239.15 273.15 200 196.29 234.18 108.02 160.75 197.45 167.45 163.83 372.38 314.06 243.15 404.15 136.87 85.47 200 185.26 199 165 252.45 180.37 178.15 188.36 173.55 87.89 180.25 142.61 159.95 213.15 388.85 0.1458 0.1597 0.1518 0.1451 0.1709 0.1522 0.1501 0.1535 0.1588 0.1532 0.1605 0.1594 0.1913 0.2180 0.1445 0.1820 0.1782 0.1505 0.1548 0.1631 0.1673 0.1593 0.1804 0.1666 0.1602 0.1671 0.1660 0.1281 0.1569 0.1200 0.1432 0.1750 0.2128 0.1814 0.1617 0.1428 0.2301 0.1540 0.2072 0.1780 0.1972 0.1526 0.2043 0.1771 0.1758 0.1746 0.2046 0.1537 589.86 445.15 398.83 512.85 570.15 452.9 499 440.65 394.41 472.19 399.35 516 150 161.85 543.84 375.15 445 458.65 353.15 392.2 375.46 375.14 303.22 385.15 399.79 313.33 329.27 610.03 454.99 439.43 557.65 238.65 350 370.35 425 431.65 322.15 543.15 370.25 434.82 333.15 583.15 340.49 483.15 325.71 340.87 460.75 545 0.0809 0.1113 0.0980 0.1004 0.0927 0.1021 0.0888 0.1073 0.0992 0.1001 0.1083 0.1475 0.0671 0.2306 0.0873 0.1274 0.0655 0.1190 0.1348 0.1095 0.1227 0.1254 0.1203 0.1115 0.1105 0.1201 0.1188 0.1221 0.1428 0.0851 0.1104 0.1335 0.0689 0.1389 0.1101 0.0956 0.1471 0.1063 0.1437 0.0986 0.1664 0.0713 0.0810 0.0972 0.1228 0.1229 0.1923 0.1090 242.54 460.85 197.67 223.15 289.95 700.15 0.1488 0.1653 0.2586 0.1072 0.2593 0.1065 418.31 591 400 318.69 481.47 795.28 0.1101 0.1351 0.1320 0.0442 0.0624 0.0793 (Continued) 2-304 TABLE 2-147 Cmpd. no. 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 Thermal Conductivity of Inorganic and Organic Liquids [W/(m∙K)] (Continued ) Name o-Terphenyl Tetradecane Tetrahydrofuran 1,2,3,4-Tetrahydronaphthalene Tetrahydrothiophene 2,2,3,3-Tetramethylbutane Thiophene Toluene 1,1,2-Trichloroethane Tridecane Triethyl amine Trimethyl amine 1,2,3-Trimethylbenzene 1,2,4-Trimethylbenzene 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 1,3,5-Trinitrobenzene 2,4,6-Trinitrotoluene Undecane 1-Undecanol Vinyl acetate Vinyl acetylene Vinyl chloride Vinyl trichlorosilane Water m-Xylene o-Xylene p-Xylene Formula C18H14 C14H30 C4H8O C10H12 C4H8S C8H18 C4H4S C7H8 C2H3Cl3 C13H28 C6H15N C3H9N C9H12 C9H12 C8H18 C8H18 C6H3N3O6 C7H5N3O6 C11H24 C11H24O C4H6O2 C4H4 C2H3Cl C2H3Cl3Si H2O C8H10 C8H10 C8H10 CAS 84-15-1 629-59-4 109-99-9 119-64-2 110-01-0 594-82-1 110-02-1 108-88-3 79-00-5 629-50-5 121-44-8 75-50-3 526-73-8 95-63-6 540-84-1 560-21-4 99-35-4 118-96-7 1120-21-4 112-42-5 108-05-4 689-97-4 75-01-4 75-94-5 7732-18-5 108-38-3 95-47-6 106-42-3 Mol. wt. 230.30376 198.388 72.10572 132.20228 88.17132 114.22852 84.13956 92.13842 133.40422 184.36142 101.19 59.11026 120.19158 120.19158 114.22852 114.22852 213.10452 227.1311 156.30826 172.30766 86.08924 52.07456 62.49822 161.48972 18.01528 106.165 106.165 106.165 C1 0.16853 0.20293 0.19428 0.14563 0.20414 0.17835 0.20571 0.20463 0.20731 0.20447 0.1918 0.23813 0.18854 0.19216 0.1659 0.16815 0.18421 0.19898 0.20515 0.218744 0.256 0.22838 0.2333 0.21831 –0.432 0.20044 0.19989 0.20003 C2 –0.00010817 –0.00021798 –0.000249 –0.0000536 –0.00021217 –0.00023704 –0.00020028 –0.00024252 –0.00024997 –0.00022612 –0.0002453 –0.00038397 –0.0001963 –0.0002105 –0.00022686 –0.00020535 –0.00016097 –0.00017659 –0.00023933 –0.00025 –0.0003542 –0.00035173 –0.00039223 –0.00029122 0.0057255 –0.00023544 –0.0002299 –0.00023573 C3 C4 –0.000008078 1.861E-09 C5 Tmin, K 329.35 279.01 164.65 237.38 176.98 373.96 234.94 178.18 236.5 267.76 158.45 156.08 247.79 229.33 165.78 172.22 398.4 354 247.57 281 180.35 173.15 119.36 178.35 273.16 225.3 247.98 286.41 Thermal cond. at Tmin 0.1329 0.1421 0.1533 0.1329 0.1666 0.0897 0.1587 0.1614 0.1482 0.1439 0.1529 0.1782 0.1399 0.1439 0.1283 0.1328 0.1201 0.1365 0.1459 0.1485 0.1921 0.1675 0.1865 0.1664 0.5672 0.1474 0.1429 0.1325 Tmax, K Thermal cond. at Tmax 723.15 526.73 339.12 480.77 394.27 426 357.31 474.85 482 508.62 483.15 276.02 449.27 442.53 372.39 387.91 629.6 625 469.08 561.2 410 278.25 345.6 434.52 633.15 413.1 417.58 413.1 0.0903 0.0881 0.1098 0.1199 0.1205 0.0774 0.1341 0.0895 0.0868 0.0895 0.0733 0.1321 0.1003 0.0990 0.0814 0.0885 0.0829 0.0886 0.0929 0.0784 0.1108 0.1305 0.0978 0.0918 0.4272 0.1032 0.1039 0.1026 The liquid thermal conductivity is calculated by k = C1 + C2T + C3T2 + C4T3 + C5T4 where k is the thermal conductivity in W/(m∙K) and T is the temperature in K. Thermal conductivities are at either 1 atm or the vapor pressure, whichever is higher. Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. TRAnSPORT PROPERTIES TABLE 2-148 FIG. 2-20 and TABLE 2-148 Nomograph (right) for thermal conductivity of organic liquids. (From B.V. Mallu and Y.J. Rao, Hydroc. Proc. 78, 1988.) 2-305 2-306 PHYSICAL AnD CHEMICAL DATA TABLE 2-149 Thermal-Conductivity-Temperature Table for Metals and nonmetals* Thermal conductivities tabulated in watts per meter-kelvin Temperature, K Substance 20 40 60 80 7 38,000 470 47 240 32 13,500 230 196 100 300 400 500 121 2,300 110 810 45 174 850 80 1,400 31 160 380 60 1,650 24 125 300 48 1,490 22 55 237 32 480 18 36 273 26 272 16 26 240 22 196 14 20 237 20 146 12 165 900 400 250 4 305 250 570 450 9 400 150 450 380 16 327 120 250 250 18 230 110 180 190 19 170 110 158 160 20 45 105 111 120 23 25 104 90 100 25 15 101 87 85 27 Copper Gallium Gold Graphite† Graphite‡ 19,000 2,200 2,800 27 81 10,700 640 1,500 108 420 2,100 250 520 135 1,630 850 200 380 81 2,980 570 170 350 54 4,290 483 140 345 39 4,980 413 100 327 15 3,250 398 85 315 10 2,000 Hastelloy Inconel Iridium Iron Lead 1 2 1,300 710 175 3 4 1,900 1,000 57 4 8 750 560 43 5 10 360 270 42 6 11 230 170 41 7 11 172 132 40 9 14 147 94 37 10 15 145 80 35 Magnesium Magnesium oxide Manganese Manganin Mercury 1,200 1,100 2 2 54 1,300 3,100 2 4 40 620 2,200 4 9 35 290 950 5 11 33 190 460 5 13 33 169 260 6 13 32 159 75 7 17 32 Molybdenum Nickel Nylon Palladium Platinum 150 2,600 0.04 1,200 1,200 280 1,700 0.10 610 490 350 570 0.17 160 130 250 290 0.20 100 92 210 200 0.23 88 82 179 158 0.25 80 79 PTFE§ Pyrex Quartz Rhodium Rubber 0.94 0.12 1,200 2,900 1.43 0.20 480 3,900 1.94 0.33 82 1,000 0.13 2.1 0.42 40 370 0.15 2.15 0.51 30 250 0.16 140 57 25 15 16,500 108 300 5,200 146 93 1,100 88 29 14 320 28 130 39 880 100 110 59 Alumina Aluminum Antimony Beryllium oxide Bismuth Boron Cadmium Chromium Cobalt Constantan Selenium (axis) Silica Silver Tantalum Tellurium Tin Titanium Tungsten Uranium Zinc Zirconium 10 100 200 1000 1200 16 232 10 220 8 93 7 99 6 105 111 70 47 33 25 12 99 85 70 30 81 71 65 62 61 392 388 383 371 357 342 312 7 1,460 309 5 1,140 304 4 930 292 3 680 278 3 530 262 2 440 2 370 11 13 143 69 34 140 61 33 55 31 43 19 33 22 28 24 31 26 156 48 8 22 8 153 36 9 28 10 151 27 9 34 11 149 21 146 13 84 10 98 8 112 7 40 12 13 14 143 106 0.28 78 75 138 91 0.30 78 73 134 80 130 72 126 66 118 67 112 72 105 76 100 80 78 72 80 72 72 73 78 78 81 2.16 0.57 2.20 0.88 2.25 1.1 190 0.17 160 0.20 10 8 6 630 68 17 500 62 13 430 59 11 358 61 62 101 37 330 20 150 42 90 33 310 22 135 38 84 31 280 23 130 34 2.3 1.6 2.5 2.1 150 0.22 145 0.24 140 0.25 425 58 6 4 1.34 424 57 4 3 1.52 420 58 3 2 1.70 413 58 3 72 26 190 26 123 25 67 21 180 28 120 23 62 20 170 30 116 22 60 20 150 32 110 21 600 1.87 405 59 800 2.22 389 59 2.60 374 60 1400 19 140 110 21 ∗ Especially at low temperatures, the thermal conductivity can often be markedly reduced by even small traces of impurities. This table, for the highest-purity specimens available, should thus be used with caution in applications with commercial materials. From Perry, Engineering Manual, 3d ed., McGraw-Hill, New York, 1976. A more detailed table appears as Section 5.5.6 in the Heat Exchanger Design Handbook, Hemisphere Pub. Corp., Washington, DC, 1983. † Parallel to basal plane. ‡ Perpendicular to basal plane. § Also known as Teflon, etc. TRAnSPORT PROPERTIES TABLE 2-150 Thermal Conductivity of Chromium Alloys* TABLE 2-151 Thermal Conductivity of Some Alloys at High Temperature* k = Btu/(h⋅ft2)(°F/ft) American iron and steel institute type no. 301, 302, 302B, 303, 304, 316† 308 309, 310 321, 347 403, 406, 410, 414, 416† 430, 430F† 442 501, 502† k at 212°F k at 932°F 9.4 8.8 8.0 9.3 14.4 15.1 12.5 21.2 12.4 12.5 10.8 12.8 16.6 15.2 14.2 19.5 2-307 Thermal conductivity, Btu/( ft)(hr)(°R) °R ∗ Table 2-150 is based on information from manufacturers. † Shelton and Swanger (National Bureau of Standards), Trans. Am. Soc. Steel Treat., 21, 1061–1078 (1933). Kovar Advance Monel Hastelloy A Inconel Nichrome V 5.6 6.2 6.8 7.3 7.8 6.0 6.5 7.0 7.6 8.1 5.5 6.1 6.7 7.3 7.8 500 600 700 800 900 7.8 8.3 8.6 8.7 8.7 11.4 12.6 13.9 15.1 9.0 10.2 11.2 12.3 13.4 1000 1100 1200 1300 1400 8.9 9.2 9.5 9.8 10.2 16.4 17.6 18.8 20.0 21.2 14.4 15.4 16.5 17.6 18.7 8.4 9.0 9.5 10.1 10.7 8.6 9.1 9.7 10.2 10.8 8.4 9.0 9.5 10.1 10.7 1500 1600 1700 1800 1900 10.5 10.8 11.1 11.3 11.5 22.5 23.8 25.0 26.2 27.4 19.8 20.8 21.9 23.0 24.0 11.3 11.8 12.3 12.9 13.4 11.3 11.8 12.4 13.0 13.6 11.3 11.9 12.4 13.0 13.5 2000 2100 2200 11.8 12.1 12.3 28.7 30.0 25.1 26.1 27.2 14.0 14.6 15.1 14.0 14.5 15.0 14.1 14.7 15.3 ∗Silverman, J. Metals, 5, 631 (1953). Copyright American Institute of Mining, Metallurgical and Petroleum Engineers, Inc. TABLE 2-152 Thermophysical Properties of Selected nonmetallic Solid Substances Material Density, kg/m3 Alumina Asphalt Bakelite Beryllia Brick 3975 2110 1300 3000 1925 Brick, fireclay Carbon, amorphous Clay Coal Cotton 2640 1950 1460 1350 80 Diamond Granite Hardboard Magnesite Magnesia 3500 2630 1000 3025 3635 Emissivity Specific heat, kJ/(kg⋅K) Thermal conductivity, W/(m⋅K) 0.82 0.93 0.765 0.920 1.465 1.030 0.835 36 0.06 1.4 270 0.72 11.9 0.03 0.74 88 0.45 0.960 0.724 0.880 1.26 1.30 1.0 1.6 1.3 0.26 0.06 0.39 1.13 1.01 0.15 0.58 0.509 0.775 1.38 1.13 0.943 2300 2.79 0.15 4.0 48 1290 1.37 0.11 1.2 14 0.93 0.86 0.91 0.80 0.38 0.72 Oak Paper Pine Plaster board Plywood 770 930 525 800 540 0.90 0.83 0.84 0.91 Pyrex Rubber Rubber, foam Salt Sandstone 2250 1150 70 2150 0.92 0.92 0.90 0.34 0.59 Silica Sapphire Silicon carbide Soil 3975 3160 2050 Teflon Thoria Urethane foam Vermiculite 2200 4160 70 120 2.38 1.34 2.75 Thermal diffusivity, m2/s × 106 0.18 0.011 0.12 0.17 0.12 0.10 0.01 0.54 0.74 0.09 0.854 0.745 1.4 0.2 0.03 7.1 2.9 0.79 0.48 0.86 0.38 0.743 0.765 0.675 1.84 1.3 46 110 0.52 15 230 0.14 0.92 0.28 0.35 0.71 1.05 0.84 0.26 14 0.03 0.06 0.34 4.7 0.36 0.60 1.22 0.835 2.00 0.18 1.8 note: Difficulties of accurately characterizing many of the specimens mean that many of the values presented here must be regarded as being of order of magnitude only. For some materials, actual measurement may be the only way to obtain data of the required accuracy. To convert kilograms per cubic meter to pounds per cubic foot, multiply by 0.062428; to convert kilojoules per kilogram-kelvin to British thermal units per pounddegree Fahrenheit, multiply by 0.23885. 2-308 TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons LFL UFL Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Paraffin hydrocarbons Olefins Olefins Olefins Olefins Olefins Olefins Acetylenes Group Methane Ethane Propane n-Butane Isobutane n-Pentane Isopentane Neopentane n-Hexane n-Heptane 2,3-Dimethylpentane n-Octane 2,2,4-Trimethylpentane n-Nonane n-Decane Ethylene Propylene 1-Butene cis-2-Butene trans-2-Butene 1-Pentene Acetylene Compound 74-82-8 74-84-0 74-98-6 106-97-8 75-28-5 109-66-0 78-78-4 463-82-1 110-54-3 142-82-5 565-59-3 111-65-9 540-84-1 111-84-2 124-18-5 74-85-1 115-07-1 106-98-9 590-18-1 624-64-6 109-67-1 74-86-2 CAS CH4 C2H6 C3H8 C4H10 C4H10 C5H12 C5H12 C5H12 C6H14 C7H16 C7H16 C8H18 C8H18 C9H20 C10H22 C2H4 C3H6 C4H8 C4H8 C4H8 C5H10 C2H2 Formula 5.00 3.00 2.10 1.60 1.80 1.40 1.40 1.40 1.20 1.05 1.10 0.96 0.95 0.85 0.75 2.70 2.15 1.60 1.70 1.70 1.40 2.50 15.00 12.40 9.50 8.40 8.40 7.80 7.60 7.50 7.20 6.70 6.70 6.50 6.00 5.60 5.40 36.00 11.20 10.00 9.70 9.70 8.70 80.00 Flash point (K) 87.12 139.00 171.00 199.15 191.00 224.15 218.00 205.00 250.15 269.00 261.00 287.15 265.00 304.15 322.85 129.00 169.00 198.00 205.00 203.00 222.00 151.00 Acetylenes Acetylenes Aromatics Aromatics Aromatics Aromatics Aromatics Aromatics Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Cyclic hydrocarbons Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Alcohols Aldehydes Aldehydes Aldehydes Vinylacetylene Methylacetylene Benzene Toluene o-Xylene Ethylbenzene Cumene Anthracene Cyclopropane Furan Cyclopentadiene Cyclohexane Methylcyclohexane Phenol Dicyclopentadiene Methanol Ethanol Allyl Alcohol 1-Propanol Isopropanol 1-Butanol 2-Butanol 2-Methyl-1-propanol 2-Methyl-2-propanol Cyclohexanol Formaldehyde Acetaldehyde Acrolein 689-97-4 74-99-7 71-43-2 108-88-3 95-47-6 100-41-4 98-82-8 120-12-7 75-19-4 110-00-9 542-92-7 110-82-7 108-87-2 108-95-2 77-73-6 67-56-1 64-17-5 107-18-6 71-23-8 67-63-0 71-36-3 78-92-2 78-83-1 75-65-0 108-93-0 50-00-0 75-07-0 107-02-8 C4H4 C3H4 C6H6 C7H8 C8H10 C8H10 C9H12 C14H10 C3H6 C4H4O C5H6 C6H12 C7H14 C6H6O C10H12 CH4O C2H6O C3H6O C3H8O C3H8O C4H10O C4H10O C4H10O C4H10O C6H12O CH2O C2H4O C3H4O 2.20 1.70 1.20 1.10 1.10 1.00 0.88 0.60 2.40 2.00 1.70 1.30 1.15 1.70 0.80 7.18 3.30 2.50 2.10 2.00 1.70 1.70 1.70 1.84 1.20 7.00 4.00 2.80 31.70 57.30 8.00 7.10 6.40 6.70 6.50 5.20 10.40 23.00 14.60 7.80 6.70 8.60 6.30 36.50 19.00 18.00 14.00 12.70 11.30 9.80 11.00 9.00 11.10 73.00 30.00 31.00 211.00 192.00 262.00 279.15 305.15 296.15 309.15 458.15 180.00 237.00 227.00 255.93 269.15 352.15 318.15 284.15 286.15 294.00 297.59 285.15 310.50 296.15 302.32 284.26 334.15 219.80 232.00 247.15 Autoignition T (K) 810.00 745.00 723.00 561.00 733.15 516.00 693.15 723.15 498.00 477.00 608.15 479.00 684.15 478.00 474.00 723.15 728.15 657.00 598.00 597.00 546.00 578.15 Decomposes violently on heating. Forms explosive peroxides with air or oxygen. 613.15 833.15 753.15 736.15 703.15 697.00 813.15 771.00 663.15 913.15 518.15 523.15 988.00 783.15 737.00 696.00 651.00 644.00 728.75 616.00 663.15 681.15 751.00 573.15 697.15 449.15 507.00 Aldehydes Aldehydes Aldehydes Aldehydes Aldehydes Aldehydes Ethers Ethers Ethers Ethers Ketones Ketones Ketones Acids Acids Acids Esters Esters Esters Esters Esters Esters Esters Esters Esters Esters Inorganic Inorganic Inorganic Oxides Oxides Oxides Oxides Oxides Peroxides Sulfur containing Sulfur containing Sulfur containing Sulfur containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Chlorine containing Bromides Glycols Glycols Propanal trans-Crotonaldehyde cis-Crotonaldehyde 2-Methylpropanal Butanal Furfural Dimethyl ether Methyl vinyl ether Diethyl ether Diphenyl ether Acetone Methyl ethyl ketone Acetophenone Acetic acid Hydrogen cyanide Formic acid Methyl formate Ethyl formate Methyl acetate Vinyl acetate Ethyl acetate n-Propyl acetate Isopropyl acetate n-Butyl acetate Isobutyl acetate n-Pentyl acetate Hydrogen Ammonia Cyanogen Carbon monoxide Ethylene oxide 1,2-Propylene oxide 1,4-Dioxane Mesityl oxide Di-t-Butyl peroxide Carbon disulfide Hydrogen sulfide Carbonyl sulfide Dimethyl sulfide Methyl chloride Ethyl chloride Isopropyl chloride 1,2-Dichloroethane 1,2-Dichloropropane Dichloromethane 2-Chloroethanol Trichloroethylene Hexachloro-1,3-Butadiene Vinyl chloride Monochlorobenzene Benzyl chloride Bromomethane Ethylene glycol Diethylene glycol 123-38-6 123-73-9 15798-64-8 78-84-2 123-72-8 98-01-1 115-10-6 107-25-5 60-29-7 101-84-8 67-64-1 78-93-3 98-86-2 64-19-7 74-90-8 64-18-6 107-31-3 109-94-4 79-20-9 108-05-4 141-78-6 109-60-4 108-21-4 123-86-4 110-19-0 628-63-7 1333-74-0 7664-41-7 460-19-5 630-08-0 75-21-8 75-56-9 123-91-1 141-79-7 110-05-4 75-15-0 7783-06-4 463-58-1 75-18-3 74-87-3 75-00-3 75-29-6 107-06-2 78-87-5 75-09-2 107-07-3 79-01-6 87-68-3 75-01-4 108-90-7 100-44-7 74-83-9 107-21-1 111-46-6 C3H6O C4H6O C4H6O C4H8O C4H8O C5H4O2 C2H6O C3H6O C4H10O C12H10O C3H6O C4H8O C8H8O C2H4O2 CHN CH2O2 C2H4O2 C3H6O2 C3H6O2 C4H6O2 C4H8O2 C5H10O2 C5H10O2 C6H12O2 C6H12O2 C7H14O2 H2 H3N C2N2 CO C2H4O C3H6O C4H8O2 C6H10O C8H18O2 CS2 H2S COS C2H6S CH3Cl C2H5Cl C3H7Cl C2H4Cl2 C3H6Cl2 CH2Cl2 C2H5ClO C2HCl3 C4Cl6 C2H3Cl C6H5Cl C7H7Cl CH3Br C2H6O2 C4H10O3 2.60 2.10 2.10 1.60 1.90 2.10 3.30 2.60 1.70 0.80 2.60 1.80 1.10 4.00 5.60 12.00 5.20 2.76 3.13 2.60 2.18 1.80 1.76 1.40 1.42 1.10 4.00 15.00 6.60 12.50 3.00 2.20 2.00 1.30 0.74 1.30 4.00 12.00 2.20 8.10 3.80 2.80 4.50 3.30 14.00 4.90 12.00 2.90 3.60 1.30 1.10 10.10 3.10 1.70 17.00 15.50 15.50 11.00 12.50 19.30 26.20 39.00 46.00 6.00 13.00 11.00 6.70 19.90 40.00 38.00 23.00 15.70 14.00 13.40 11.50 8.00 7.20 7.60 8.00 7.10 75.00 28.00 32.00 74.20 100.00 35.50 22.00 8.80 8.20 50.00 44.00 29.00 19.70 17.20 15.40 10.70 16.00 14.50 22.00 15.90 29.00 15.70 33.00 9.60 7.10 16.00 42.00 37.00 243.15 286.15 285.93 254.15 262.15 333.15 193.00 217.15 228.15 388.15 253.15 264.15 350.15 312.04 255.00 323.15 247.00 254.15 260.15 265.37 269.00 283.71 274.82 298.15 291.00 310.15 14.00 209.00 214.00 71.00 225.00 236.00 284.15 301.00 277.15 243.15 167.00 186.00 237.15 203.00 223.15 238.15 286.00 286.15 265.00 328.15 305.15 389.00 205.00 301.15 333.15 230.00 384.15 413.15 500.15 505.00 505.00 478.00 503.15 589.00 499.15 560.15 433.15 891.15 738.15 789.00 843.15 700.00 811.00 753.00 729.00 728.15 775.00 700.00 700.00 723.00 733.15 694.00 696.00 633.15 793.15 924.00 984.00 882.00 702.00 703.15 453.15 618.00 Organic peroxides can ignite easily 363.15 533.15 477.00 478.15 905.00 802.00 866.00 686.00 830.00 888.15 698.15 683.15 883.15 745.00 911.00 858.15 800.00 669.00 636.15 2-309 (Continued) 2-310 TABLE 2-153 Lower and Upper Flammability Limits, Flash Points, and Autoignition Temperatures for Selected Hydrocarbons (Continued ) Group Glycols Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Amines Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Miscellaneous Compound Triethylene glycol Methylamine Ethylamine Dimethylamine Isopropylamine Trimethylamine Allylamine Diethylamine Tert-Butylamine Triethylamine Cyclohexylamine Monoethanolamine Diethanolamine Dimethylethanolamine Acrylonitrile Aniline Diborane Methyl methacrylate Styrene Biphenyl Methyl acrylate Phthalic anhydride CAS 112-27-6 74-89-5 75-04-7 124-40-3 75-31-0 75-50-3 107-11-9 109-89-7 75-64-9 121-44-8 108-91-8 141-43-5 111-42-2 108-01-0 107-13-1 62-53-3 19287-45-7 80-62-6 100-42-5 92-52-4 96-33-3 85-44-9 Formula C6H14O4 CH5N C2H7N C2H7N C3H9N C3H9N C3H7N C4H11N C4H11N C6H15N C6H13N C2H7NO C4H11NO2 C4H11NO C3H3N C6H7N B2H6 C5H8O2 C8H8 C12H10 C4H6O2 C8H4O3 LFL UFL 0.90 4.90 2.70 2.80 2.00 2.00 2.03 1.70 1.70 1.20 0.66 3.00 1.70 1.40 3.05 1.30 0.80 1.70 1.10 0.70 2.18 1.20 9.20 20.70 14.00 14.40 10.40 11.60 24.30 10.10 8.90 8.00 9.40 13.10 9.80 12.20 17.00 11.00 88.00 12.50 6.10 5.80 14.40 9.20 Flash point (K) 429.15 217.00 227.00 223.15 236.15 207.00 252.00 245.15 236.00 262.15 299.65 366.55 445.15 312.15 268.15 344.15 142.00 284.15 305.00 383.15 270.00 425.00 Autoignition T (K) 644.00 703.15 657.00 595.00 673.15 463.15 647.039 583.15 648.15 522.15 566.15 683.15 935.00 568.15 754.00 890.00 325.00 708.15 763.15 813.15 741.15 857.00 Values in this table were taken from the Design Institute for Physical Properties (DIPPR) of the American Institute of Chemical Engineers (AIChE), 801 Critically Evaluated Gold Standard Database, copyright 2016 AIChE, and reproduced with permission of AIChE and of the DIPPR Evaluated Process Design Data Project Steering Committee. Their source should be cited as “R. L. Rowley, W. V. Wilding, J. L. Oscarson, T. A. Knotts, N. F. Giles, DIPPR Data Compilation of Pure Chemical Properties, Design Institute for Physical Properties, AIChE, New York, NY (2016)”. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES 2-311 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES* InTRODUCTIOn Physical property values, sufficiently accurate for many engineering applications, can be estimated in the absence of reliable experimental data. The purpose of this section is to provide a set of recommended prediction methods for general engineering use. It is not intended to be a comprehensive review, and many additional methods are available in the literature. Methods recommended in this section were selected on the basis of accuracy, generality, and, in most cases, simplicity or ease of use. They generally correspond to the methods tested and given priority in the DIPPR 801 database project.* Properties included in this subsection are divided into 10 categories: (1) physical constants including critical properties, normal melting and boiling points, acentric factor, radius of gyration, dipole moment, refractive index, and dielectric constant; (2) liquid and solid vapor pressure; (3) thermal properties including enthalpy and Gibbs energy of formation and ideal gas entropy; (4) latent enthalpies of vaporization, fusion, and sublimation; (5) heat capacities for ideal and real gases, liquids, and solids; (6) densities of gas, liquid, and solid phases; (7) gas and liquid viscosity; (8) gas and liquid thermal conductivity; (9) surface tension; and (10) flammability properties including flash point, flammability limits, and autoignition temperature. Each of the 10 subsections gives a definition of the properties and a description of one or more recommended prediction methods. Each description lists the type of method, its uncertainty, its limitations, and the expected *The Design Institute for Physical Properties (DIPPR) is an industrial consortium under the auspices of AIChE; Project 801, Evaluated Process Design Data, is a purecomponent database of industrially important compounds. Values and procedures used with permission of the DIPPR 801 Technical Committee. uncertainty of the predicted value. A numerical example is also given to illustrate use of the method. For brevity, symbols used for physical properties and for variables and constants in the equations are defined under Nomenclature and are not necessarily defined after their first use except where doing so clarifies usage. A list of equation and table numbers in which variables appear is included in the Nomenclature section for quick crossreferencing. Although emphasis is on pure-component properties, some mixture estimation techniques have been included for physical constants, density, viscosity, thermal conductivity, surface tension, and flammability. Correlation and estimation of properties that are inherently multicomponent (e.g., diffusion coefficients, mixture excess properties, activity coefficients) are treated elsewhere in this handbook. UnITS The International System (SI) of metric units has been used throughout this section. Where possible, the estimation equations are set up in dimensionless groups to eliminate the need to specify units of variables and to facilitate unit conversions. For example, rather than use Pc as an equation variable, the dimensionless group (Pc/Pa) is used. When a value for Pc expressed in any units (say, Pc = 6.53 MPa) is inserted into this group, the result is dimensionless with an explicit indication of conversion factors that must be included, such as Pc 6.53 MPa  6.53 MPa   10 6 Pa  = = = 6.53 × 10 6   Pa Pa Pa   MPa  Appropriate unit conversion factors are found in Sec. 1 of this handbook. nomenclature Physical constants h k NA R Properties Definition Planck’s constant Boltzmann’s constant Avogadro’s number Gas constant Value 6.626 × 10−34 J ⋅ s 1.3806 × 10−23 J/(molecule ⋅ K) 6.022 × 1026 molecule/kmol 8314.3 Pa ⋅ m3/(kmol ⋅ K) Definition Typical units A, B, C AIT Avdw B, B(T) CP C op Molecular principal moments of inertia Autoignition temperature Van der Waals area Second virial coefficient Isobaric molar heat capacity Ideal gas isobaric molar heat capacity kg ⋅ m2 K m2/kmol m3/kmol J/(kmol ⋅ K) J/(kmol ⋅ K) Cv Hi k LFL M n P P Pc Pr P* P*meas Pr* Pt* RD Rg So Ss Sr Svib Constant-volume molar heat capacity Enthalpy of compound i Thermal conductivity Lower flammability limit Molecular weight Refractive index Pressure Parachor Critical pressure Reduced pressure; Pr = P/Pc Vapor pressure Measured vapor pressure value Reduced vapor pressure; Pr* = P*/Pc Vapor pressure at triple point Molar refraction Radius of gyration Ideal gas entropy Standard state entropy Rotational contribution to entropy Vibrational contribution to entropy J/(kmol ⋅ K) J/kmol W/(m ⋅ K) % kg/kmol unitless Pa unitless Pa unitless Pa Pa unitless Pa cm3/mol m J/(kmol ⋅ K) J/(kmol ⋅ K) J/(kmol ⋅ K) J/(kmol ⋅ K) 2-312 PHYSICAL AnD CHEMICAL DATA nomenclature (Continued ) Properties Definition Typical units T Tad Tb Tbr Tc TFP Tm Tmeas Tr UFL V Vc Vr wi xi yi Z Zc Zi ∆G of Temperature Adiabatic flame temperature Normal boiling point temperature Reduced temperature at Tb; Tbr = Tb/Tc Critical temperature Flash point temperature Melting temperature T at which a dependent property was measured Reduced temperature; Tr = T/Tc Upper flammability limit Molar volume Critical volume Reduced volume; Vr = ZTr/Pr Mass fraction of component i Mole fraction of component i Mole fraction of component i in vapor phase Compressibility factor; Z = PV/RT Critical compressibility factor; Zc = PcVc/RTc Compressibility factor of reference fluid i Ideal gas standard Gibbs energy of formation K K K unitless K K K K unitless % m3/kmol m3/kmol unitless unitless unitless unitless unitless unitless unitless J/kmol ∆G sf Standard state Gibbs energy of formation J/kmol ∆H of Ideal gas standard enthalpy of formation J/kmol ∆H sf Standard state enthalpy of formation J/kmol DHfus DHrxn DHsub DHu ∆S sf Enthalpy of fusion Enthalpy change per mole of reaction as written Enthalpy of sublimation Enthalpy of vaporization Standard state entropy of formation J/kmol J/kmol J/kmol J/kmol J/(kmol ⋅ K) ∆S of Ideal gas entropy of formation J/(kmol ⋅ K) DSfus DZv d e h ho m mr r ρc ρr ρS, ρL, ρV σ σm t tb fi w Latent entropy of fusion Change in compressibility factor upon vaporization Solubility parameter Dielectric constant Viscosity Viscosity at low pressure Dipole moment Reduced dipole moment [defined in Eq. (2-66)] Molar density; r = V −1 Critical molar density; ρc = Vc−1 Reduced molar density; ρr = ρ/ρc Density of solid, liquid, vapor, respectively Surface tension Surface tension of mixture Complementary reduced temperature (1 − Tr) t at the normal boiling point (1 − Tbr) Volume fraction of component i Acentric factor J/(kmol ⋅ K) unitless J1/2 ⋅ m−3/2 unitless Pa ⋅ s Pa ⋅ s D unitless kmol/m3 kmol/m3 unitless kmol/m3 mN/m mN/m unitless unitless unitless unitless Equation variables Definition a a, b, c, . . . a, b, c ai a, b a, b ai, bi, di aα A, B, C, . . . EoS constant GC values for Cp and h Correlation coefficients GC values Terms in second virial correlation Chickos correlation parameters GC values for liquid Cp EoS constant for mixture Correlation constants/parameters A Ai b bi, ci, . . . bi Factor in liquid k correlation o Constants in C p correlation EoS constant Reference EoS constants GC value for AIT Appears in (Eq. 2-?) or [Table 2-?] (70), [172] (54), (57), (96), [174] (25), (27), (42), (43), (44), (69) (46), (96), [164], [174] (65) (42), (43), (44) (54), [166] (78) (2), (23), (24), (26), (28), (28a), (38), (40), (53), (54), (56), (69), (71), (82), (84), (86), (87), (94), (95), (100), (101), (102) (110), [176] (48), (49), (70) (70), [172] (69), [171] (129), [180] PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES nomenclature (Continued ) Equation variables Definition Appears in (Eq. 2-?) or [Table 2-?] b B(i) C EoS constant for mixture Second virial expansion term Number of components in mixture C Ci Parameter in modified Pachaiyappan method GC values for some methods Cij (Cop)i Csj Cst Ctj fi F(i) F GI Gij gEc gEr h K m nhvy nA nE NG ni Group-group intramolecular interaction pair GC values for ideal gas heat capacity Chickos GC value for C—H group Fuel concentration for stoichiometric combustion Chickos GC value for functional group Halogen correction for DHsub correlation Vapor pressure deviation function Factor in surface tension equation Group-group interaction correction term Adjustable mixture viscosity parameter UNIFAC combinatorial excess Gibbs energy UNIFAC residual excess Gibbs energy Parameter in Riedel vapor pressure equation Parameter in Riedel vapor pressure equation Parameter in modified Pachaiyappan method Number of non-hydrogen atoms Number of atoms in the molecule Number of occurrences of element E in compound Number of interacting groups Number of occurrences of group i nf ns nx N Number of different functional groups Number of C—H groups bonded to functional groups Number of halogen and H atoms Total number of groups in molecule NC Nfi Ngi NH NCR NO NR NS Nsi NSi NX Pc q qi Qk ri r* Rk (So)i t tm1,i tm2,i Tc Tc,ij xP U* UFLi Z(0) Z(1) Zc,ij ZRA ZRA α, b, g, . . . Number of C atoms Number of functional groups of type i Number of C—H groups of type i bonded to C Number of H atoms Number of CH2 groups forming cyclic paraffin Number of O atoms Number of nonaromatic rings Number of S atoms Number of C—H groups bonded to functional group Number of Si atoms Number of halogen atoms Pseudocritical pressure for mixture (77) (62), (63), (64), (65) (74), (75), (76), (77), (78), (79), (80), (81), (98) (109) (9), (10), (11), (18), (86), [175], [173] (12), [156] (52), [165] (44), [162] (127), (128) (44), [163] (46), [164] (29) (118), (119) (9), (10), (11), (12) (97) (98) (98) (28a) (28a) (109) (11), (12), (18) (1), (34), (35), (51) (58) (12) (9), (10), (11), (13), (15), (16), (31), (46), (52), (54), (55), (86), (117), (124), (127), (129) (44) (44) (46) (18), (31) (46), (54), (57), (58), (86), (96), (117), (124), (127), (129) (123) (44) (44) (123) (43) (123) (43) (123) (44) (123) (123) (75) Rackett equation power for Zc UNIFAC molecular surface area UNIFAC group surface area UNIFAC molecular volume Dimensionless separation distance UNIFAC group volume GC value for entropy Total number of functional groups First-order GC contribution for Tm Second-order GC contribution for Tm Pseudocritical temperature for mixture (72), (80) following (99) following (99) following (99) (4) following (99) (31), [161] (44) (16), [158] (16), [159] (74), (75), (79) Cross term in mixing rule Term in the Pailhes method [= log(1 atm/P)] Dimensionless intermolecular potential GC contribution Compressibility factor of simple fluid Acentric deviation term for Z Cross term in mixing rule Modified Rackett correlation parameter Modified Rackett parameter for mixture Correlation parameters for k (79) (17) (4) (127), [178] (68), [169] (68), [170] (79) following (72) (80), (81) (107), (108), (110), [176] 2-313 2-314 PHYSICAL AnD CHEMICAL DATA nomenclature (Continued ) Equation variables Appears in (Eq. 2-?) or [Table 2-?] Definition EoS temperature-dependent function Parameter in Riedel vapor pressure equation Viscosity group-group interactions Reference EoS constant Stoichiometric coefficient for combustion Nonlinear correction term in correlation Reference EoS constant α(Tr) αc αmn b b bi g d d DE DP DT DV (DHfo)i DPi Dpci Dsi DTad,i Dtci e e f n ni = 0 for nonlinear molecules; = 1 for linear EoS parameter Contribution of element E to heat capacity GC contribution to Pc GC contribution to Tc GC contribution to Vc GC value for enthalpy of formation GC for Parachor Group i contribution to critical pressure GC value for group i Group i contribution to adiabatic flame temperature Group i contribution to critical temperature Lennard-Jones well depth parameter EoS parameter UNIFAC molecular volume fraction LFL enthalpic term Stoichiometric coefficient (+ for product and − for reactant) for compound i in reaction Frequency of vibrational mode j UNIFAC molecular surface fraction UNIFAC group surface fraction Characteristic rotational T of molecule Characteristic vibrational T of mode j Lennard-Jones size parameter Rotational external symmetry number Modified reduced dipole moment Parameter in Riedel vapor pressure equation Parameter in correlation of k for gases UNIFAC interaction factor Viscosity de-dimensionalizing factor Pseudo-acentric factor for mixture nj q Q QA, QB, QC Qj σ σ µ*r y y ymn x ω (70), [172] (28a) (99), [175] (69), [171] (122), (123), (128) (46), (57), [164], [167] (69), [171] (1), (35), before (50), (51) (70), [172] (58), [168] (7), [154] (6), [154] (8), [154] (31), [161] (117), [177] (15) (44), [162, 163] (124) (13) following (4) (70), [172] following (99) (126) (32), (33), (34) (50) following (99) following (99) before and following (35) (1), (35) following (4) following (35) (84), (85) (28a) (106), (107) (99) (88), (89), (90), (91), (92), (93) (76) Acronyms and abbreviations Definition CC CS DIPPR EoS GC LJ MC MD QSPR Computational chemistry Corresponding states Design Institute for Physical Properties Equation of state Group contributions Lennard-Jones Monte Carlo Molecular dynamics Quantitative structure-property relationships GEnERAL REFEREnCES Prediction Methods [PGL4] Reid, R. C., J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, 4th ed., McGraw-Hill, New York, 1987. [PGL5] Poling, B. E., J. M. Prausnitz, and J. P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001. Property Databases [DIPPR] Rowley, R. L., et al., DIPPR Data Compilation of Pure Chemicals Properties, Design Institute for Physical Properties, AIChE, New York, 2007. [TRC] TRC Thermodynamic Tables—Non-Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004; TRC Thermodynamic Tables—Hydrocarbons, Thermodynamics Research Center, The Texas A&M University System, College Station, Tex., extant 2004. [JANAF] Chase, M. W., Jr., et al., “JANAF Thermochemical Tables,” J. Phys. Chem. Ref. Data, 14, suppl. 1, 1985. [SWS] Stull, D. R., F. F. Westrum, Jr., and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds, John Wiley & Sons, New York, 1969. [TDS] Daubert, T. E., and R. P. Danner, Technical Data Book—Petroleum Refining, 5th ed., American Petroleum Institute, Washington, extant 1994. CLASSIFICATIOn OF ESTIMATIOn METHODS Physical property estimation methods may be classified into six general areas: (1) theory and empirical extension of theory, (2) corresponding states, (3) group contributions, (4) computational chemistry, (5) empirical and quantitative structure-property relations (QSPR) correlations, and (6) molecular simulation. A quick overview of each class is given below to provide context for the methods and to define the general assumptions, accuracies, and limitations inherent in each. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Theory and Empirical Extension of Theory Methods based on theory generally provide better extrapolation capability than empirical fits of experimental data. Assumptions required to simplify the theory to a manageable equation suggest accuracy limitations and possible improvements, if necessary. For example, the ideal gas isobaric heat capacity, rigorously obtained from statistical mechanics under the assumption of independent harmonic vibrational modes, is (Rowley, R. L., Statistical Mechanics for Thermophysical Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994) C op R = 8 − δ 3 n A −6+δ + ∑ 2 j =1 2 Θ /T e j  Θj   T  Θ j /T − 1)2 (e (2-1) 0 nonlinear molecules δ = 1 linear molecules where Qj is the characteristic temperature for the jth vibrational frequency in a molecule of nA atoms. The temperature dependence of this equation is exact to the extent that the frequencies are harmonic. Extension of theory often requires introduction of empirical models and parameters in lieu of terms that cannot be rigorously calculated. Good accuracy is expected in the region where the model parameters were fitted to experimental data, but only limited accuracy when an empirical model is extrapolated to other conditions. For example, a simplified theory suggests that vapor pressure should have the form ln P * = A − B T (2-2) where the empirical parameter B is given by B= ∆ Hυ R ∆ Zυ (2-3) and ∆Hυ and ∆Zυ are differences between the vapor and liquid enthalpies and compressibility factors, respectively. Equation (2-2) can be used to correlate vapor pressures over a moderate temperature range, but it is inadequate to represent vapor pressures over the whole liquid temperature range because ∆Hυ also varies with temperature. Corresponding States (CS) The principle of CS applies to conformal fluids [Leland, T. L., Jr., and P. S. Chappelear, Ind. Eng. Chem., 60 (1968): 15]. Two fluids are conformal if their intermolecular interactions are equivalent when scaled in dimensionless form. For example, the Lennard-Jones (LJ) intermolecular pair potential energy U can be written in dimensionless form as U* = 4(r∗−12 − r∗−6) (2-4) where r∗ = r/σ, U ∗ = U/ε, σ is the LJ size parameter, and ε is the LJ attractive well depth parameter. At equivalent scaled temperatures kT/ε (k is Boltzmann’s constant) and pressures Pσ3/ε, all LJ fluids will have identical dimensionless properties because the molecules interact through the identical scaled intermolecular potential given by Eq. (2-4). Generalization of this scaling principle is commonly done using critical temperature Tc and critical pressure Pc as scaling factors. At the same reduced coordinates (Tr = T/Tc and Pr = P/Pc) conformal fluids will have the same dimensionless properties. For example, Z = Z(Tr, Pr) where the compressibility factor is defined as Z = PV/RT. A correlation of experimental data for one fluid can then be used as the reference for the properties of all conformal fluids. Nonconformality is the main accuracy limitation. For instance, interactions between nonspherical or polar molecules are not adequately represented by Eq. (2-4), and so the scaled properties of these fluids will not conform to those of a fluid with interactions well represented by Eq. (2-4). A correction for nonconformality is usually made by the addition of one or more reference fluids whose deviations from the first reference fluid are used to characterize the effect of nonconformality. For example, in the Lee-Kesler method [Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510] n-octane is used as a second, nonspherical reference fluid, and deviations of n-octane scaled properties from those of the spherical reference fluid at equivalent reduced conditions are assumed to be a linear function of the acentric factor. Group Contributions (GCs) Physical properties generally correlate well with molecular structure. GC methods assume a summative behavior of the structural groups of the constituent molecules. For example, ethanol (CH3—CH2—OH) properties would be obtained as the sum of contributions from the —CH3, —CH2, and —OH groups. The contribution of each group is obtained by regression of experimental data that include as many different compounds containing that group as possible. Structural groups must be used exactly as defined in the original correlation of the groups. A general principle when parsing a structure into constituent groups is that 2-315 the more specific the group, the higher its priority. For example, the structural piece —COOCH3 in a methyl ester could be divided in more than one way, but if the —COO— and —CH3 groups are available in the method, then they should be used rather than the combination of the two less specific groups —(C == O)— and —O—. These latter group values were most likely regressed only from ketone and ether data, respectively. Excellent accuracy can usually be expected from GC methods in which the group values were regressed from large quantities of experimental data. However, if the ratio of the number of groups to regressed experimental data is large, significant errors can result when the method is applied to new compounds (extrapolation). Such excessive specificity in the group definitions leads to poor extrapolation capabilities even though the fit of the regressed data may have been excellent. First-order GC methods assume simple summations of the group values are adequate to represent the molecular value. Second-order effects, caused by steric and electron induction effects from neighboring groups, can alter group values. Second-order GC methods require considerably more experimental data to tune the method, and large tables of group values are required because differences in bonded neighbors require separate groups. Computational Chemistry (CC) Commercial software is available that solves the Schrödinger equation by using approximate forms of the wave function. Various levels of sophistication (termed model chemistry) for the wave function can be chosen at the expense of computational time. Results include structural information (bond lengths, bond angles, dihedral angles, etc.), electron/charge distribution information, internal vibrational modes ( for ideal gas properties), and energy of the molecule, valid for the chosen model chemistry. Because calculations are usually performed on individual molecules, the results are best suited for ideal gas properties. Relative energies for the same model chemistry are more accurately obtained than absolute energies, so enthalpies and entropies of reaction are also common industrial uses of CC predictions. Empirical QSPR Correlations Quantitative structure-property relationship (QSPR) methods correlate physical properties with molecular descriptors that characterize the structural and electronic character of the molecule. Large amounts of experimental data are used to statistically determine the most significant descriptors to be used in the correlation and their contributions. The resultant correlations are simple to apply if the descriptors are available. Descriptors must be generated by the user with computational chemistry software or obtained from some tabulation. QSPR methods are often very accurate for specific families of compounds for which the correlation was developed, but extrapolation to other families generally results in considerable loss of accuracy. Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton’s equations of motion for a small number (on the order of 103) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the potential energy between molecules to simulate configurations of the molecules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not commonly available. PHYSICAL COnSTAnTS Critical Properties The critical temperature Tc, pressure Pc, and volume Vc of a compound are important, widely used constants. They are important in determining the phase boundaries of a compound and (particularly Tc and Pc) are required input parameters for many property estimation methods, particularly CS methods. The critical temperature of a compound is the temperature above which a liquid phase cannot be formed, regardless of the system pressure. The critical pressure is the vapor pressure of the compound at the critical temperature. The molar critical volume is the volume occupied by 1 mol of a chemical at its critical temperature and pressure. The critical compressibility factor Zc is determined from the experimental or predicted values of the critical properties by its definition Zc = PcVc RTc (2-5) Recommended Methods The Ambrose method is recommended for all three critical properties of hydrocarbons and n-alcohols. The Nannoolal method is recommended for all three critical properties of all other organic molecules. The Wilson-Jasperson method is a simple method also recommended for estimating Tc and Pc for organic and some inorganic chemicals. 2-316 PHYSICAL AnD CHEMICAL DATA The first-order Wilson-Jasperson method often gives better results than the second-order method except strongly polar, hydrogen-bonding, and associating fluids. Method: Ambrose method. Reference: Ambrose, D., Natl. Phys. Lab. Report Chem. 92 (1978); Natl. Phys. Lab Report Chem. 98 (1979). Classification: Group contributions. Expected uncertainty: ~6 K for Tc (about 1 percent), ~2 bar for Pc (about 5 percent), ~8 cm3/mol for Vc (about 3 percent). Applicability: Organic compounds. Input data: Tb, M, group contributions DT, DP, and DV from Table 2-154. Description: A GC method with first-order contributions and corrections (delta Platt number) for branched alkanes. Variables Tc, Pc, and Vc are given by the following relations: ( ) −1   Pc M 0.339 + ∑ ∆ P = bar kg/kmol ) Tc = Tb 1 + 1.242 + ∑ ∆T  ( Description: A GC method with first-order contributions. Variables Tc, Pc, and Vc are given by the following relations:     1  Tc = Tb  0.6990 + 0.8607      0.9889 +  ∑ niC i + GI   i    (2-9) −0.14041  M   kg/kmol  Pc = 2 kPa    0.00939 + ∑ niC i + GI  (2-10) i (2-6) −2 Vc = 10 m3 /mol (2-7) Vc = 40 + ∑ ∆V cm /mol (2-8) 3 i i i n -0.2266 hvy + 86.1539 (2-11) where ni is the number of groups of type i; Ci are group contributions from Table 2-155; M is molecular weight; and GI is the total correction for groupgroup interactions calculated using GI = Example Use the Ambrose method to estimate the critical constants of 2,2,4-trimethylpentane. Required data: From the DIPPR 801 database, Tb = 372.39 K and M = 114.229 kg/kmol. Structure: ∑n C + GI -6 1 nhvy NG NG i =1 j =1 C ij ∑ ∑ NG − 1 (2-12) where Cji = Cij. The values for the interactions are shown in this format in Table 2-156. The sum of all group pairs within the molecule is divided by the number of nonhydrogen atoms, nhvy, and by 1 less than the number of interacting groups NG. In the example below, there are no group-group interactions. The calculation of GI using Eq. (2-12) is illustrated later in an example calculation for the normal boiling point. Group contributions from Table 2-154: Example Estimate the critical constants of o-xylene using the Nannoolal Group ni Alkyl carbons >CH— (correction) >C< (correction) Delta Platt no. 8 1 1 0 DT DP 0.138 −0.043 −0.120 −0.023 0.226 −0.006 −0.030 −0.026 DV 55.1 −8 −17 — Calculations using Eqs. (2-6), (2-7), and (2-8): ∑∆ T Required input data: From the DIPPR 801 database, Tb = 417.58 K. From Table 2-155: = (8) (0.138) + (1)(−0.043) + (1)(−0.120) = 0.941 Tc = Tb(1.4581) = (372.39 K)(1.4581) = 543.0 K ∑∆ P = (8)(0.226) + (1)(−0.006) + (1)(−0.030) = 1.772 ( Pc M 0.339 + ∑ ∆ P = bar kg/kmol ∑∆ V method. Structure: ) −2 = 114.229 = 25.63 (0.339 + 1.772)2 Pc = 25.63 bar = (8)(55.1) + (1)(−8) + (1)(−17) = 415.8 Group ni Ci (TC) Ci (PC) =C(a)} CH3−(a) =C(a)<(ne) ortho GI 4 2 2 1 — 0.0161154 −0.001071 0.0682045 0.0012823 0 0.00021064 0.0004166 0.00041826 0.00007061 0 19.402 26.7237 25.0434 −3.5964 0 From Eqs. (2-9), (2-10), and (2-11): Vc = (40 + 415.8) cm3/mol = 455.8 cm3/mol ∑C (T ) = (4)(0.0161154) + (2)(−0.001071) + (2)(0.0682045) i c Results: Property Ci (VC) + (1)(0.0012823) = 0.20001 DIPPR recommended value Ambrose estimation % Difference −0.15 Tc /K 543.8 543.0 Pc /bar 25.70 25.63 Vc /(cm3/mol) 468.0 455.8   1 Tc = Tb  0.6990 + 0.8607  = 1.5060Tb 0.9889 + ( 0.20001)   Tc = (1.5060)(417.58 K) = 628.87 K 0.27 −2.6 ∑C ( P ) = (4)(0.00021064) + (2)(0.0004166) + (2)(0.00041826) i c +(1)(0.00007061) = 0.0025829 Method: Nannoolal method. Reference: Nannoolal, Y., J. Rarey, and D. Ramjugernath, Fluid Phase Equilib. 252 (2007): 1. Classification: Group contributions. Expected uncertainty: ~6 K or 1 percent for Tc; ~2 bar or 5 percent for Pc; ~8 cm3/mol or 3 percent for Vc. Applicability: Organic compounds. Input data: Tb, group contributions Ci from Table 2-155, intramolecular group-group interactions Cij, from Table 2-156, and the number of nonhydrogen atoms in the molecule nhvy. Pc (106.165 ) 0.14041 = 2 = 3623.55 kPa ( 0.00939 + 0.00258289 ) − ∑C (V ) = (4)(19.402) + (2)(26.7237) + (2)(25.0434) i c + (1)(−3.5964) = 177.5458 nhvy = 8 Vc 177.5458 177.5458 = −0.2266 + 86.1539 = + 86.1539 = 370.57 10 −6 m 3 /mol nhvy (8)−0.2266 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-154 Ambrose Groupa Contributions for Critical Constants Group Carbon atoms in alkyl groups Corrections >CH} (each) >C< (each) Double bonds (nonaromatic) Triple bonds Delta Platt number,b multiply by Aliphatic functional groups: }O} >CO }CHO }COOH }CO}O}OC} }CO}O} }NO2} }NH2 }NH} >N} }CN }S} }SH }SiH3 }O}Si(CH3)2 }F }Cl }Br }I Halogen correction in aliphatic compounds: F is present F is absent, but Cl, Br, I are present Aliphatic alcoholsc Ring compound increments (listed only when different from aliphatic values): }CH2}, >CH}, >C< >CH} in fused ring Double bond }O} }NH} }S} Aromatic compounds: Benzene Pyridine C4H4 ( fused as in naphthalene) }F }Cl }Br }I }OH Corrections for nonhalogenated substitutions: First Each subsequent Ortho pairs containing }OH Ortho pairs with no }OH Highly fluorinated aliphatic compounds: }CF3, }CF2}, >CF} }CF2}, >CF} (ring) >CF} (in fused ring) }H (monosubstitution) Double bond (nonring) Double bond (ring) (other increments as in nonfluorina ted compounds) DT DP DV 0.138 0.226 55.1 −0.043 −0.120 −0.050 −0.200 −0.023 −0.006 −0.030 −0.065 −0.170 −0.026 −8 −17 −20 −40 — 0.138 0.220 0.220 0.578 1.156 0.330 0.370 0.208 0.208 0.088 0.423 0.105 0.090 0.200 0.496 0.055 0.055 0.055 0.055 0.160 0.282 0.220 0.450 0.900 0.470 0.420 0.095 0.135 0.170 0.360 0.270 0.270 0.460 — 0.223 0.318 0.500 — 20 60 55 80 160 80 78 30 30 30 80 55 55 119 — 14 45 67 90 0.125 0.055 d e 0.090 0.030 −0.030 0.090 0.090 0.090 0.182 0.182 — — — — 0.448 0.448 0.220 0.080 0.080 0.080 0.080 0.198 0.924 0.850 0.515 0.183 0.318 0.600 0.850 −0.025 0.010 0.030 −0.080 −0.040 0 0.020 −0.050 −0.050 0.200 0.140 0.030 −0.050 −0.150 −0.030 0.550 0.420 — −0.350 −0.500 — 15 44.5 44.5 −15 10 — 30 f a Ambrose, D., Correlation and Estimation of Vapour-Liquid Critical Properties. I. Critical Temperatures of Organic Compounds, Natl. Phys. Lab Report Chem. 92 (1978); Correlation and Estimation of Vapour-Liquid Critical Properties. II. Critical Pressures and Volumes of Organic Compounds, Natl. Phys. Lab Report Chem. 98 (1979). b The delta Platt number is defined as the Platt number of the isomer minus the Platt number of the corresponding alkane. (For n-alkanes the Platt number is n − 3.) The Platt number is the total number of groups of four carbon atoms three bonds apart [Platt, J. R., J. Chem. Phys., 15(1947): 419; 56(1952): 328]. This correction is used only for branched alkanes. c Includes naphthenic alcohols and glycols but not aromatic alcohols such as xylenol. d First determine the hydrocarbon homomorph, i.e., substitute }CH3 for each }OH and calculate ∑DT for this compound. Subtract 0.138 from ∑DT for each }OH substituted. Next, add 0.87 − 0.11n + 0.003n2 where n = [Tb/K (alcohol) − 314]/19.2. Exceptions include methanol (∑DT = 0), ethanol (∑DT = 0.939), and any alcohol whose value of n exceeds 10. e Determine the hydrocarbon homomorph as in footnote d. Calculate ∑Dp and subtract 0.226 for each }OH substituted. Add 0.100 − 0.013n, where n is computed as in footnote d. f When estimating the critical volumes of aromatic substances, use ring compound values, if available, and correct for double bonds. 2-317 2-318 PHYSICAL AnD CHEMICAL DATA TABLE 2-155 Group Contributions for the nannoolal et al. Method for Critical Constantsa and normal Boiling Pointb Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon; (Ca) = aromatic carbon; b = any nonhydrogen atom ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 74 Group CH3—(ne) CH3—(e) CH3—(a) —C(c)H2— >C(c)H— >C(c)< >C(c)<(e) >C(c)<(Ca) —C(r)H2— >C(r)H— >C(r)< >C(r)<(e, c) >C(r)<(e, r) >C(r)<(Ca) =C(a)H— =C(a)<(ne) =C(a)<(e) (a) = C(a)<2(a) F—(C, Si) —CF= C< F—(C,Si)(F)(2b) F—(C,Si)([F, Cl])(b) F—(C,Si)([F, Cl]2) F—(Ca) Cl—(C,Si) Cl—(C,Si)([F, Cl]) Cl—(C, Si)([F, Cl]2) Cl—(Ca) —CCl=C< Br—(C,Si) Br—(Ca) I—(C, Si) —OH tert HO—(C,Si) sec HO—(C,Si) long HO—(C,Si) short —OH (Ca) (C,Si)—O—(C,Si) >(OC2)< NH2—(C, Si) NH2—(Ca) (C,Si)—NH—(C,Si) (C,Si)2>N—(C,Si) COOH—(C) (C)—COO—(C) HCOO—(C) —C(r)OO— —CON< —CONH— —CONH2 O=C<(Can)2 CHO—(Can) SH—(C) (C)—S—(C) (C)—S—S—(C) —S(a)— (C)—C≡N >C(c)=C(c)< >C(c)=C(c)<(Ca) —(e)C(c)=C(c)< H2C(c)=C< >C(r)=C(r)< —C≡C— HC≡C— (Ca)—O(a)—(Ca) =N(a)—(r5) =N(a)—(r6) NO2—(C) NO2—(Ca) >Si< >Si<(O) NO3— O=N—O—(C) Description CH3— not connected to N, O, F, or Cl CH3— connected to N, O, F, or Cl CH3— connected to an aromatic atom (not necessarily C) —CH2— in a chain >CH— in a chain >C< in a chain >C< in a chain connected to at least one F, Cl, N, or O >C< in a chain connected to at least one aromatic carbon —CH2— in a ring >CH— in a ring >C< in a ring >C< in a ring; connected to at least one N, O, Cl, or F not in the ring >C< in a ring connected to at least one N or O which is part of the ring >C< in a ring connected to at least one aromatic carbon aromatic =CH— aromatic =C< not connected to O, N, Cl, or F aromatic =C< connected to O, N, Cl, or F aromatic =C< with three aromatic neighbors F— connected to C or Si F— on a C=C (vinyl fluoride) F— connected to C or Si substituted with at least one F and two other atoms F— connected to a C or Si substituted with one F or Cl and one other atom F— connected to C or Si already substituted with two F or Cl atoms F— connected to an aromatic carbon Cl— connected to C or Si not already substituted with F or Cl Cl— connected to C or Si already substituted with one F or Cl Cl— connected to C or Si already substituted with at least two F or Cl Cl— connected to aromatic C Cl— on a C=C (vinyl chloride) Br— connected to a nonaromatic C or Si Br— connected to an aromatic C I— connected to C or Si —OH connected to tertiary carbon —OH connected to secondary C or Si —OH connected to primary C or Si; chain >4 C or Si —OH connected to primary C or Si; chain <5 C or Si —OH connected to an aromatic C (phenols) ether —O— connected to two C or Si >(OC2)< (epoxide) NH2— connected to either C or Si NH2— connected to an aromatic C —NH— connected to two C or Si (secondary amine) >N— connected to three C or Si (tertiary amine) —COOH connected to C —COO— connected to two C (ester) HCOO— connected to C ( formic acid ester) —COO— in ring, C is connected to C (lactone) —CON< disubstituted amide —CONH— (monosubstituted amide) —CONH2 (amide) —CO— connected to two nonaromatic C (ketones) CHO— connected to nonaromatic C (aldehydes) —SH connected to C (thiols) —S— connected to two C —S—S— (disulfide) connected to two C —S— in an aromatic ring —C≡N (cyanide) connected to C >C=C< (both C have at least one non-H neighbor) noncyclic >C=C< connected to at least one aromatic C noncyclic >C=C< with at least one F, Cl, N, or O H2C=C< (1-ene) cyclic >C=C< —C≡C— HC≡C— (1-yne) —O—in an aromatic ring with aromatic C neighbors aromatic —N— in a five-member ring, free electron pair aromatic =N— in a six-member ring NO2— connected to aliphatic C NO2— connected to aromatic C >Si< >Si< connected to at least one O nitrate (esters of nitric acid) nitrites (esters of nitrous acid) TC × 103 PC × 104 VC NBP 41.8682 33.1371 −1.0710 40.0977 30.2069 −3.8778 52.8003 9.4422 21.2898 26.3513 −17.0459 51.7974 18.9549 −29.1568 16.1154 68.2045 68.1923 29.8039 15.6068 11.0757 18.1302 19.1772 20.8519 −24.0220 −1.3329 2.6113 15.5010 −16.1905 60.1907 5.2621 −21.5199 −8.6881 84.8567 79.3047 49.5968 130.1320 14.0159 12.5082 41.3490 18.3404 −50.6419 17.1780 −0.5820 199.9042 75.7089 58.0782 109.1930 102.1024 8.1620 5.5262 4.1660 5.2623 2.3009 −2.9925 3.4310 2.3665 3.4027 3.6162 −5.1299 4.1421 0.8765 −0.1320 2.1064 4.1826 3.5500 1.0997 0.7328 4.3757 3.4933 2.6558 1.6547 0.5236 −2.2611 −1.4992 0.4883 −0.9280 11.8687 −4.3170 −2.2409 −4.7841 −7.4244 −4.4735 −1.8153 −6.8991 −12.1664 2.0592 0.1759 −4.4164 −9.0065 −0.4086 2.3625 3.9873 4.3592 1.0266 0.4329 0.5172 28.7855 28.8811 26.7237 32.0493 32.1108 28.0534 33.7577 28.8792 24.8517 30.9323 5.9550 29.5901 20.2325 10.5669 19.4020 25.0434 5.6704 16.4118 −5.0331 1.5646 3.3646 1.0897 1.1084 19.3190 22.0457 23.9279 26.2582 36.7624 34.4110 36.0223 30.7004 48.2989 10.6790 5.6645 2.0869 3.7778 25.6584 11.6284 46.7680 13.2571 73.7444 20.5722 6.0178 40.3909 42.6733 36.1286 56.1572 44.2000 −7.1070 0.5887 0.1190 −2.3615 −9.4154 −8.2595 30.9229 25.5034 34.7699 38.0185 −7.7181 117.1330 45.1531 −4.9259 5.1666 7.1581 20.3127 43.7983 67.9821 45.4406 56.4059 −19.9737 36.0883 10.4146 18.9903 10.9495 82.6239 −6.2791 9.6413 3.4731 −2.2718 2.4489 −0.5403 8.3052 −4.7101 −5.0929 51.0710 48.1957 34.1240 40.9263 29.8612 4.7476 −25.3680 23.6094 34.8472 25.4209 72.5587 5.7270 2.7602 75.7193 69.5645 177.3066 251.8338 157.9527 239.4531 240.6785 249.5809 266.8769 201.0115 239.4957 222.1163 209.9749 250.9584 492.0707 244.3581 235.3462 315.4128 348.2779 367.9649 106.5492 49.2701 53.1871 78.7578 103.5672 −19.5575 330.9117 287.1863 267.4170 205.7363 292.5816 419.4959 377.6775 556.3944 349.9409 390.2446 443.8712 488.0819 361.4775 146.4836 820.7118 321.1759 441.4388 223.0992 126.2952 1080.3139 636.2020 642.0427 1142.6119 1052.6072 1364.5333 1487.4109 618.9782 553.8090 434.0811 461.5784 864.5074 304.3321 719.2462 475.7958 586.1413 500.2434 412.6276 475.9623 512.2893 422.2307 37.1936 453.3397 306.7139 866.5843 821.4141 282.0181 207.9312 920.3617 494.2668 64.3506 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-155 2-319 Group Contributions for the nannoolal Method for Critical Constantsa and normal Boiling Point b (Continued ) Table-specific nomenclature: (e) = connected to N, O, F, Cl; (ne) = not connected to N, O, F, Cl; (r) = in a ring; (c) = in a chain; (a) = aromatic, not necessarily carbon; (Ca) = aromatic carbon; b = any nonhydrogen atom ID 76 77 78 79 80 81 82 83 87 88 89 90 91 92 93 94 97 99 100 101 102 103 104 107 109 111 113 115 Group Description —C=O—O—C=O— COCl— >Si<(F,Cl) O=C(—O—)2 OCN— SCN—(C) (C)—SO2—(C) (C)2>Sn<(C)2 >C=C=C< >C=C—C=C<(r) >C=C—C=C<(c) CHO—(Ca) (C,Si) =N— (O= C< (C)2)a >Si<(C,H)2 —O—O— (C,Si)a—NH—(Ca,Si)a —OCON< >N—(C=O)—N< (C,Si)2>N< (C,Si)2 F—(C,Si)(Cl)(b)2 —OCOO— >SO4 >S=O >N(C=O) (N)—C≡N >P< —ON=(C,Si) TC × 103 anhydride connected to two C COCl— connected to C (acid chloride) >Si< connected to at least one F or Cl noncyclic carbonate OCN— connected to C or Si (cyanate) SCN— (thiocyanate) connected to C noncyclic sulfone connected to two C (sulfones) >Sn< connected to four carbons cumulated double bond conjugated double bond in a ring conjugated double bond in a chain CHO— connected to aromatic C (aldehydes) double-bonded amine connected to at least one C or Si —CO— connected to two C with at least one aromatic C (ketones) >Si< attached to two carbon or hydrogen peroxide —NH— connected to two C or Si, at least one aromatic (secondary amines) —CO connected to O and N (carbamate) —CO connected to two N (urea) Quaternary amine connected to four C or Si F— connected to C or Si with at least one Cl and two other atoms —CO connected to two O (carbonates) S(= O)2 connected to two O (sulfates) sulfoxide —CO connected to N —C≡N (cyanide) connected to N phosphorus connected to at least 1 C or S (phosphine) —ON= connected to C or Si (isoazole) PC × 104 VC NBP 164.3355 4.0458 157.3401 97.2830 153.7225 12.6786 0.2822 90.9726 62.3642 53.6350 24.7302 −23.9221 0.7043 12.6128 −10.2451 68.0701 38.4681 −4.0133 20.0440 63.6504 34.2058 −5.0403 3.2023 28.7127 55.3822 27.3441 −4.3834 29.3068 1.3231 764.9595 3.3971 58.9190 1.3597 36.0361 −5.1116 16.2688 32.1829 11.4437 −1.3023 −34.3037 −1.3798 −2.7180 11.3251 −4.7516 1.2823 6.7099 7.3149 4.1439 0.4387 −4.2678 4.8944 2.8103 −0.3035 0.0930 0.7061 −0.7246 −3.8033 27.5326 1.5807 −2.6235 −5.3091 −6.1909 3.2219 −6.3900 −3.5964 1.5196 −33.8201 −18.4815 −23.6024 −24.5802 −35.6113 −8.8457 −2.2542 −3.2460 −5.3113 1.0934 −4.6483 −5.0563 −6.3267 4.9392 2.8889 52.8789 27.1026 64.4616 1251.2675 778.9151 540.0895 879.7062 660.4645 1018.4865 1559.9840 510.4223 664.0903 957.6388 928.9954 560.1024 229.2288 606.1797 273.1755 201.3224 886.7613 1045.0343 –109.6269 111.0590 1573.3769 1483.1289 1379.4485 492.0707 971.0365 428.8911 612.9506 Corrections 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 (C=O)—C([F,Cl]2,3) (C=O)—C([F,Cl]2,3)2 C—[F,Cl]3 (C)2—C—[F,Cl]2 No hydrogen One hydrogen (3,4) ring 5-ring Ortho pair(s) Meta pair(s) Para pair(s) ((C= )(C)C—CC3) C2C—CC2 C3C—CC2 C3C—CC3 C=C—C=O carbonyl connected to C with two or more halogens carbonyl connected to two C, each with at least two halogens carbon with three halogens secondary carbon with two halogens component has no hydrogen component has one hydrogen a three- or four-member nonaromatic ring a five-member nonaromatic ring ortho- position counted only once and only if no meta or para pairs meta- position counted only once and only if no para or ortho pairs para- position counted only once and only if no meta or ortho pairs carbon with four carbon neighbors and one double-bonded carbon neighbor carbon with four carbon neighbors, two on each side carbon with five carbon neighbors carbon with six carbon neighbors —C=O connected to sp3 carbon –82.2328 –247.8893 –20.3996 15.4720 –172.4201 –99.8035 –62.3740 –40.0058 –27.2705 –3.5075 16.1061 25.8348 35.8330 51.9098 111.8372 40.205 Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1. Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45. a b Description: A GC method with first- and some second-order contributions. Variables Tc, Pc, and Vc are given by the following relations: Results: Property Tc /K Pc /bar Vc /(cm3/mol) DIPPR 801 recommendation 630.3 37.32 370 Nannoolal estimation % Difference 628.9 36.24 370.6 −0.2 −2.9 0.2 Method: Wilson-Jasperson method. Reference: Wilson, G. M., and L. V. Jasperson, “Critical Constants Tc, Pc, Estimation Based on Zero, First and Second Order Methods,” AIChE Spring Meeting, New Orleans, La., 1996. Classification: Group contributions. Expected uncertainty: ~6 K or 1 percent for Tc; ~2 bar or 5 percent for Pc. Applicability: Organic and some inorganic compounds. Input data: M, Tb, group contributions Ci from Table 2-157, and molecular structure. Tc = Tb    0.048271 − 0.019846nr + ∑ nk ∆tc k + ∑ n j ∆tc j    k j 0.2 Pc 0.0186233(Tc /K) = bar exp(Y ) − 0.96601   Y = − 0.00922295 − 0.0290403nr + 0.041  ∑ nk ∆pc k + ∑ n j ∆pc j   k  j (2-13) (2-14) (2-15) where nr is the number of rings in the molecule; Dtck and Dpck are the firstorder group contributions tabulated in Table 2-157 with nk the number of such occurrences in the molecule; and Dtcj and Dpcj are the second-order 2-320 PHYSICAL AnD CHEMICAL DATA TABLE 2-156 Intermolecular Interaction Corrections for the nannoolal et al. Method for Critical Constantsa and normal Boiling Pointb —OH :: —OH —OH :: —COOH —OH :: —O— —OH :: >(OC2)< —OH :: —COOC— —OH :: —CO— —OH :: —O(a)— —OH :: —S(na)— —OH :: —SH —OH :: —NH2 —OH :: >NH —OH :: —CN —OH :: =N(a)–(r6) —OH(a) :: —OH(a) —OH(a) :: —COOH —OH(a) :: —O— —OH(a) :: —COOC— —OH(a) :: —CHO —OH(a) :: —NH2 —OH(a) :: Nitrate —OH(a) :: =N(a)–(r6) —COOH :: —COOH —COOH :: —O— —COOH :: —COOC— —COOH :: —CO— —O— :: —O— —O— :: >(OC2)< —O— :: —COOC— —O— :: —CO— —O— :: —CHO —O— :: —O(a)— —O— :: —S(na)— —O— :: —NH2 —O— :: >NH —O— :: —CN —O— :: Nitrate >(OC2)< :: >(OC2)< >(OC2)< :: —CO— >(OC2)< :: —CHO —COOC— :: —COOC— —COOC— :: —CO— —COOC— :: —O(a)— —COOC— :: —NH2 —COOC— :: >NH —COOC— :: —CN —COOC— :: Nitrate —CO— :: —CO— —CO— :: —CHO —CO— :: —O(a)— —CO— :: —S(a)— —CO— :: >NH —CO— :: —CN —CO— :: Nitrate —CO— :: =N(a)–(r6) —CHO— :: —CHO— —CHO— :: —O(a)— —CHO— :: —S(a)— —CHO— :: Nitrate —O(a)— :: —NH2 —O(a)— :: =N(a)–(r5) —S(na)— :: —S(na)— —S(na)— :: —NH2 —S(a)— :: —CN —S(a)— :: =N(a)–(r5) —SH :: —SH —NH2 :: —NH2 —NH2 :: >NH —NH2 :: Nitrate —NH2 :: =N(a)–(r6) >NH :: >NH >NH :: =N(a)–(r6) —OCN :: —OCN —OCN :: Nitrate —CN :: =N(a)–(r6) Nitrate :: Nitrate =N(a)–(r6) :: =N(a)–(r6) PC × 104 −434.8568 −5.6023 −146.7881 7.3373 19.7707 120.9166 −30.4354 69.8200 6.1331 −8.0423 144.4697 57.8350 97.5425 162.6878 707.4116 128.2740 2.6751 88.8752 −1.0295 −23.6366 −329.5074 −55.5112 −654.1363 −738.0515 25.8246 −125.5983 −37.2468 0.5195 −74.8680 1605.564 −78.2743 −413.3976 24.0243 −861.1528 −35.1998 43.9001 217.9243 −403.1196 131.7924 −19.7033 164.2930 −60.9217 −0.6754 −49.7641 22.1871 741.8565 366.2663 −32.3208 −57.1233 44.1062 −1866.097 Nannoolal, Y., et al., Fluid Phase Equilib. 252 (2007): 1. b Nannoolal, Y., et al., Fluid Phase Equilib. 226 (2004): 45. a VC TC × 103 12.5371 −26.4556 NBP 291.7985 146.7286 135.3991 226.4980 211.6814 46.3754 435.0923 –74.0193 38.6974 314.6126 286.9698 306.3979 1334.6747 288.6155 –1477.9671 130.3742 −1184.9784 43.9722 797.4327 –1048.124 –614.3624 117.2044 612.8821 −183.2986 −55.9871 91.4997 178.7845 322.5671 15.6980 17.0400 329.0050 394.5505 124.3549 101.8475 293.5974 963.6518 1006.388 22.5208 163.5475 431.0990 22.5208 707.9404 182.6291 317.0200 517.0677 –205.6165 −303.9653 −391.3690 176.5481 381.0107 −215.3532 −574.2230 –3628.903 124.1943 562.1763 674.6858 397.575 140.9644 395.4093 –888.612 –11.9406 −562.306 −101.232 –348.740 217.6360 174.0258 510.3473 663.8009 27.2735 239.8076 758.9855 −356.5017 –263.0807 –370.9729 65.1432 –271.9449 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES group contributions, also tabulated in Table 2-157, with nj occurrences of these second-order groups in the molecule. TABLE 2-157 Wilson-Jasperson First- and Second-Order Contributions for Critical Temperature and Pressurea First-order atom Example Estimate Tc and Pc of sec-butanol by using the Wilson-Jasperson method. Required input data: From DIPPR 801 database, Tb = 372.9 K. Structure: Group contributions from Table 2-157: Group nk Dtck Dpck nj Dtcj Dpcj H 10 0.002793 0.12660 — — — O 1 0.020341 0.43360 — — — C 4 0.008532 0.72983 — — — −OH, C4 or less — — 1 — 0.0350 0 From Eqs. (2-13), (2-14), and (2-15): ∑ n ∆tc k k = (10)(0.002793) + (1)(0.020341) + (4)(0.008532) = 0.082399 Tc = ∑ n ∆pc k k Tb 372.9 K = = 534.25 K (0.048271 + 0.082399 + 0.0350)0.2 0.6980 = (10)(0.12660) + (1)(0.43360) + (4)(0.72983) = 4.61892 Y = − 0.00922295 + 0.041(4.61892) = 0.18015 Pc 0.0186233(Tc /K) (0.0186233)(534.25) = = = 43.00 bar exp(Y ) − 0.96601 exp(0.18015) − 0.96601 Results: Property DIPPR 801 recommendation Wilson-Jasperson estimation % Difference Tc /K 536.2 534.25 −0.4 43.00 2.3 Pc /bar 42.02 Normal Melting Point The normal melting point is defined as the temperature at which melting occurs at atmospheric pressure. Methods to estimate the melting point are not particularly effective because the melting point depends strongly on solid crystal structure and that structure is not effectively correlated with standard GC or CS methods. Recommended Method The method of Constantinou and Gani is recommended with caution. Reference: Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697. Classification: Group contributions. Expected uncertainty: 25 percent. Applicability: Organic compounds. Input data: First- and second-order group contributions from molecular structure. Description: A group contribution method given by  Tm = (102.425 K) ⋅ ln  ∑ ni t m1, i +  i ∑n t j m 2, j j ni 2 1 1 tm1,i Second-order group }OH, C4 or less }OH, C5 or more }O} }NH2, >NH, >N} }CHO >CO }COOH }COO} }CN }NO2 Organic halides (once per molecule) }SH, }S}, }SS} Siloxane bond Dpck 0.12660 0.43400 0.91000 0.72983 0.44805 0.43360 0.32868 0.12600 6.05000 1.34000 1.22000 1.04713 0.97711 0.79600 1.19000 — — 1.42000 2.68000 1.20000 0.97151 1.11000 — 1.11000 2.71000 1.69000 1.95000 — 0.43000 1.31593 1.66000 6.33000 1.07000 — 1.08000 — — −0.08000 0.69000 2.05000 2.04000 Dtcj Dpcj 0.0350 0.0100 −0.0075 −0.0040 0.0000 −0.0550 0.0170 −0.0150 0.0170 −0.0200 0.0020 0.00 0.00 0.00 0.00 0.50 0.00 0.50 0.00 1.50 1.00 0.00 0.0000 −0.0250 0.00 −0.50 As cited in PGL5. Calculation using Eq. (2-16): Tm = (102.425 K) ln [(2)(0.4640) + 12.6275 + 1.5656] = 278 K Example Estimate the melting point of 2,6-dimethylpyridine. Structure and group contributions: Group Dtck 0.002793 0.320000 0.019000 0.008532 0.019181 0.020341 0.008810 0.036400 0.088000 0.020000 0.012000 0.007271 0.011151 0.016800 0.014000 0.018600 0.059000 0.031000 0.007000 0.010300 0.012447 0.013300 −0.027000 0.175000 0.017600 0.007000 0.020000 0.010000 0.000000 0.005900 0.017000 −0.027500 0.219000 0.013000 0.011000 0.014000 −0.050000 0.000000 0.000000 0.007000 0.015000 (2-16) where ni, nj = number of first- and second-order groups, respectively tm1,i = first-order group contributions from Table 2-158 tm2,i = second-order group contributions from Table 2-159 −CH3 −C5H3(N)− Six-member ring H, D, T He B C N O F Ne Al Si P S Cl Ar Ti V Ga Ge As Se Br Kr Rb Zr Nb Mo Sn Sb Te I Xe Cs Hf Ta W Re Os Hg Bi Rn U a    2-321 tm2,i 0.4640 12.6275 1.5656 The predicted value is 4 percent higher than the recommended experimental value of 267 K in the DIPPR 801 database. Normal Boiling Point The normal boiling temperature Tb is the temperature at which the vapor pressure of the liquid equals 101.325 kPa (1.0 atm). If there are sufficient vapor pressure data available, then Tb may be found from a regression of the data using an appropriate vapor pressure equation [e.g., Eqs. (2-24) to (2-28)]. If two or more vapor pressure values are available in the approximate temperature range of Tb, they can be used to obtain Tb by using Eq. (2-2) to linearly interpolate ln P* versus 1/T values. When one or more low-temperature vapor pressure points are available, a common occurrence, then the method of Pailhes can be used to estimate Tb. 2-322 PHYSICAL AnD CHEMICAL DATA TABLE 2-158 Group First-Order Groups and Their Contributions for Melting Point * Group tm1,i TABLE 2-159 Group tm1,i }CH3 0.4640 }COOCH2} >CH2 0.9246 }OOCH >CH} 0.3557 }OCH3 >C< 1.6479 }OCH2} }CH=CH2 1.6472 }OCH< }CH=CH} 1.6322 }OCH2F >C=CH2 1.7899 }CH2NH2 >C=CH} 2.0018 >CHNH2 >C=C< 5.1175 }NHCH3 }CH=C=CH2 3.3439 }CH2NH} >ACH 1.4669 >CHNH} >AC} 0.2098 >NCH3 >ACCH3 1.8635 }NCH2} >ACCH2} 0.4177 >ACNH2 >ACCH< −1.7567 }C5H3(N)} }OH 3.5979 }CH2CN >ACOH 13.7349 }COOH }COCH3 4.8776 }CH2Cl }COCH2} 5.6622 >CHCl }CHO 4.2927 >CCl} }COOCH3 4.0823 }CHCl2 *Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697. 3.5572 4.2250 2.9248 2.0695 4.0352 4.5047 6.7684 4.1187 4.5341 6.0609 3.4100 4.0580 0.9544 10.1031 12.6275 4.1859 11.5630 3.3376 2.9933 9.8409 5.1638 }CCl3 >ACCl }CH2NO2 >CHNO2 >ACNO2 }CH2SH }I }Br }C≡CH }C≡C} >C=CCl} >ACF }CF3 }COO} }CCl2F }CClF2 }F (other) }CONH2 }CON(CH3)2 }CH3S >CH2S tm1,i 10.2337 2.7336 5.5424 4.9738 8.4724 3.0044 4.6089 3.7442 3.9106 9.5793 1.5598 2.5015 3.2411 3.4448 7.4756 2.7523 1.9623 31.2786 11.3770 5.0506 3.1468 Second-Order Groups and Their Contributions for Melting Point* Group tm21,i }CH(CH3)2 }C(CH3)3 }CH(CH3)CH(CH3)} }CH(CH3)C(CH3)2} }C(CH3)2C(CH3)2} Three-member ring Five-member ring Six-member ring Seven-member ring CHn=CHm}CHp=CHk [k, n, m, p = 0, 1, 2] CH3CHm=CHn [m, n = 0, 1, 2] 0.0381 −0.2355 0.4401 −0.4923 6.0650 1.3772 0.6824 1.5656 6.9709 1.9913 CH2CHm=CHn [m, n = 0, 1, 2] −0.5870 CHCHm=CHn or CCHm=CHn [m, n = 0, 1, 2] Alicyclic side chain: CcyclicCm [m > 1] CH3CH3 −0.2361 CHCHO; CCHO Group 0.2476 1.4880 2.0547 −0.2951 CH3COCH; CH3COC −0.2986 Ccyclic(=O) 0.7143 ACCHO −0.6697 *Constantinou, L., and R. Gani, AIChE J., 40 (1994): 1697. The most accurate method for prediction of normal boiling temperatures without experimental data is the Nannoolal method. Recommended Method Pailhes method. Reference: Pailhes, F., Fluid Phase Equilib., 41 (1988): 97. Classification: Group contributions. Expected uncertainty: ~3 K (1 to 2 percent). Applicability: Organic compounds. Input data: Molecular structure and one measured vapor pressure value * Pmeas (often at a low pressure). The method requires estimation of the reduced normal boiling point, Tbr, and Pc, which in the example below are obtained using the Wilson-Jasperson first-order method and the Ambrose method, respectively. Description: A simple group contribution method is given by  log(Pc /bar) + (1 − Tbr ) x P  2 Tb = Tmeas   − 3 x p − 1.49 x p log(Pc /bar)   where Tb = estimated normal boiling point Pc = critical pressure estimated from group contributions −3.1034 28.4324 0.4838 0.0127 −2.3598 −2.0198 −0.5480 0.3189 0.9124 9.5209 CHm(OH)CHn(NHp) [m, n, p = 0, 1, 2, 3] CHm(NH2)CHn(NH2) [m, n = 0, 1, 2] CHm cyclic}NHp}CHn cyclic [m, n, p = 0, 1, 2] CHm}O}CHn=CHp [m, n, p = 0, 1, 2] AC}O}CHm [m = 0, 1, 2, 3] CHm cyclic}S}CHn cyclic [m, n = 0, 1, 2] CHm=CHn}F [m, n = 0, 1, 2] CHm=CHn}Br [m, n = 0, 1, 2] ACBr ACl −2.8298 CH3COCH2 tm21,i CHCOOH; CCOOH ACCOOH CH3COOCH; CH3COOC COCH2COO or COCHCOO or COCCOO CO}O}CO ACCOO CHOH COH CHm(OH)CHn(OH) [m, n = 0, 1, 2] CHm cyclic}OH [m = 0, 1] (2-17) 2.7826 2.5114 1.0729 0.2476 0.1175 −0.2914 −0.0514 −1.6425 2.5832 −1.5511 xP = log(1 atm/P*meas) Tmeas = temperature at which experimental vapor pressure P*meas is known Example The vapor pressure of n-decylacetate (M = 200.32 kg/kmol) at 348.65 K is 106.66 Pa. Estimate the normal boiling point of this compound, using the Paihles method. Structure and group contributions from Tables 2-154 and 2-157: Wilson-Jasperson Groups ni ni DP,i H 24 0.002793 −COO− 1 0.470 O 2 0.020341 C (alkyl) 11 0.226 C 12 0.008532 Δtci Ambrose Groups PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES CHARACTERIZInG AnD CORRELATInG COnSTAnTS Group contribution calculations using Eq. (2-13) for Tbr and Eq. (2-7) for Pc : ∑ n ∆tc i i = (24)(0.002793) + (2)(0.020341) + (12)(0.008532) = 0.210098 Acentric Factor The acentric factor of a compound w is defined in terms of the reduced vapor pressure evaluated at a reduced temperature of 0.7 as Tbr = (0.048271 + 0.210098)0.2 = 0.7629 ∑n ∆ i P ,i ω = − log Pr* = (1)(0.470) + (11)(0.226) = 2.956 Pc = 200.32 bar = 18.450 bar (0.339 + 2.956)2 Calculation of auxiliary quantities:  101,325 Pa   1 atm  x P = log  ∗  = log   = 2.9777  Pmeas   106.66 Pa  Calculation of normal boiling point using Eq. (2-17):  log (18.450) + (1 − 0.7629)(2.9777)  Tb 2 = (348.65)   − 3(2.9777) − 1.49(2.9777) log(18.450) K   Tb = 520.94 K The estimated value is 0.7 percent higher than the DIPPR 801 recommended value of 517.15 K. Recommended Method: Nannoolal method. Reference: Nannoolal, Y., J. Rarey, D. Ramjugernath, and W. Cordes, Fluid Phase Equilib., 226 (2004): 45. Classification: Group contributions. Expected uncertainty: ~7 K (about 2 percent). Applicability: Organic compounds. Input data: Ci values in Table 2-155; intramolecular group-group interactions Cij in Table 2-156; and the number of nonhydrogen atoms in the molecule. Description: A GC method that includes second-order corrections for steric effects and intramolecular interactions. Tb is calculated from (2-18) where nhvy = number of nonhydrogen (heavy) atoms ni = number of occurrences of group i Ci = group contribution from Table 2-155 GI = total group-group interaction as calculated using Eq. (2-12) and Table 2-156 −1.0000 (2-19) Example Calculate the acentric factor of chlorobenzene with a known value for Tb. Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and Pc = 45.1911 bar. Calculation of auxiliary quantities (see Eq. (2-28a) for these equations): Tbr = Tb 404.87 = = 0.64 Tc 632.35 ψ = −35 + αc = = Example Estimate the normal boiling point of di-isopropanolamine by using the Nannoolal method. Structure: Tr = 0.7 It is primarily used as a third parameter (in addition to Tc and Pc) in CS predictions as a measure of deviations from nonspherical molecular shape, hence the name, suggesting molecular interactions that are not between centers of molecules. However, as defined in Eq. (2-19), w also contains polarity information, and it increases with increasing polarity for molecules of similar size and shape. The value of w is close to zero for small, spherically shaped, nonpolar molecules (argon, methane, etc.). It increases in value with larger deviations of molecular shape from spherical (longer chain lengths, less chain branching, etc.) and with increasing molecular polarity. When possible, w should be obtained from experimental vapor pressure correlations by using Eq. (2-19), but an accurate estimation of w can be made by using the critical constants and a single vapor pressure point by application of CS vapor pressure equations. Recommended Method 1 Definition. Classification: Theory and empirical extension of theory. Expected uncertainty: Within 3 percent if an experimental vapor pressure correlation is available; within 10 percent from a predicted vapor pressure correlation. Applicability: Most organic compounds. Input data: Vapor pressure correlation or Tc, Pc, and Tb if an experimental vapor pressure correlation is unavailable. Description: Equation (2-19) is applied directly to the appropriate vapor pressure equation. A predictive vapor pressure equation can also be used as in the second example. N ∑n ⋅ C + GI Tb i =1 i i + 84.3395 = 0.6583 K nhvy + 1.6868 2-323 K = 0.0838 36 36 + 42 ⋅ ln(Tbr ) − Tbr6 = −35 + + 42 ⋅ ln(0.64) − (0.64)6 = 2.4312 Tbr 0.64 (3.758) K ψ + ln( PC /1.01325bar) K ψ − ln(Tbr ) 45.1911  (3.758)( 0.0838 )(2.4312) + ln   1.01325  = 7.025 (0.0838)(2.4312) − ln(0.64) D = K (α c − 3.758) = (0.0838)(7.025 − 3.758) = 0.2738 A = 35 D = 9.581 B = −36 D = −9.855 C = α c − 42 D = −4.473 Calculation using Eq. (2-28) at Tr = 0.7: ln( Pr ) = 9.581 − Group contributions and values: Group ni Ci Group total }CH3 2 177.3066 354.6132 >C(c)<(e) 4 266.8769 1067.508 }OH sec 2 390.2446 780.4892 }NH} 1 223.0992 223.0992 }OH:: }OH 2/(9 × 2) 291.7985 32.42206 }OH:: }NH} 4/(9 × 2) 286.9698 63.77107 Total 2521.902 GI Note that the frequencies of the interaction correction terms are calculated in the following manner: There are three interacting groups (}OH, }OH, }NH}) in the molecule, so NG − 1 = 2. The four }OH:: }NH} interactions and two }OH:: }OH interactions are each divided by 2 and by the number of nonhydrogen atoms nhvy = 9, according to Eq. (2-12). Calculation using Eq. (2-18): 2521.902 Tb = + 84.3395 = 509.3 K 9 0.6583 + 1.6868 Tb = 509.3 K This value differs by −2.4 percent from the DIPPR 801 recommended value of 521.9 K. 9.855 − 4.473 ⋅ ln(0.7) + 0.2738 ⋅ (0.7)6 = −2.870 0.7 Calculation using Eq. (2-19): ω=− ln( Pr ) 2.870 − 1.0000 = − 1.0000 = 0.246 2.303 2.303 This value differs by −1.5 percent from DIPPR 801 recommended value of 0.2499. Recommended Method 2 Corresponding states. Reference: [PGL5]. Classification: Corresponding states. Expected uncertainty: Generally within 5 percent, worse for strongly polar fluids. Applicability: Most organic compounds. Input data: Tc, Pc, and a single vapor pressure point (e.g., the normal boiling point Tb). Description: See Eq. (2-29) for the equations used in this method. The vapor pressure equation is inverted to obtain the acentric factor from a single vapor pressure point. Example Repeat the above calculation of the acentric factor of chlorobenzene, using the Walton-Ambrose modification of the Lee-Kesler vapor pressure equation, Eq. (2-29). Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and Pc = 45.1911 bar. 2-324 PHYSICAL AnD CHEMICAL DATA This is 3.8 percent below the DIPPR 801 database value of 1.564 × 10−10 m which was obtained from spectral principal moments of inertia. Calculation of auxiliary quantities: Tbr = Tb 404.87 = = 0.64 Tc 632.35 τ = 1 − 0.64 = 0.36 (−5.97616)(0.36) + (1.29874)(0.36)1.5 − (0.60394)(0.36)2.5 − (1.06841)(0.36)5 f (0) = 0.64 = −3.0034 (−5.03365)(0.36) + (1.11505)(0.36)1.5 − (5.41217)(0.36)2.5 − (7.46628)(0.36)5 0.64 = −3.1788 f (1) = (−0.64771)(0.36) + (2.41539)(0.36)1.5 − (4.26979)(0.36)2.5 − (3.25259)(0.36)5 0.64 = −0.037 f (2) = Example Calculate the dipole moment for methanol. Draw structure and optimize molecule by using computational chemistry software: The dipole moment obtained from a geometry optimized with the HF/6-31G model chemistry for methanol is 2.288 D. This value is 35 percent larger than the experimental gas-phase value of 1.700 D in the DIPPR 801 database. Calculation using Eq. (2-29) at the normal boiling point: ln 1.01325 = −3.798 = f (0) + ωf (1) + ω 2 f (2) = −3.0034 − 3.1788ω − 0.037ω 2 45.1911 Back solution of the quadratic equation for ω: ω = 0.249 Radius of Gyration The radius of gyration Rg is a measure of the mass distribution about the center of mass of a molecule. Radius Rg increases with molecular size. It is useful in CS applications to separate molecular size and shape effects from polar effects. It is defined in terms of the principal moments of inertia of a molecule (A, B, and C) as Rg = (AB )1/2 N A M (2-20) 2π(ABC )1/3 N A M (2-21) for planar molecules and as Rg = Dipole Moment The dipole moment of a molecule is the first moment of the electric charge density expansion. All normal paraffins have a value of zero. Charge separation within the molecule due to electronegativity differences between bonded atoms increases the dipole moment. Computational chemistry software uses the electron density distribution of the optimized molecule to calculate dipole moments. Recommended Method Electron density distribution. Classification: Computational chemistry. Expected uncertainty: Uncertainty varies depending upon the model chemistry chosen, but it can be as large as 60 percent. Applicability: All molecules. Input data: Molecular structure. for nonplanar molecules. Radii of gyration can be calculated from these defining equations using principal moments of inertia obtained from spectral data or from computational chemistry software. Recommended Method Principal moments of inertia. Classification: Computational chemistry. Expected uncertainty: Less than 5 percent. Applicability: All molecules. Input data: M and molecular structure. Description: Computational chemistry software is used to optimize the geometry of the molecule and obtain the principal moments of inertia to be used in Eqs. (2-20) and (2-21). Example Calculate the radius of gyration for hydrazine. Input information: From the DIPPR 801 database, M = 32.0452 kg/kmol. The structure of hydrazine is Refractive Index Refractive index is the ratio of the speed of light in a vacuum to the speed of light in the medium. The incident light is the sodium D line (5.896 × 10−7 m). Refractive index is dimensionless and generally ranges between 1.3 and 1.5 for organic liquids. Recommended Method Wildman-Crippen method. Reference: Wildman, S. A., and G. M. Crippen, J. Chem. Inf. Comput. Sci. 39 (1999): 868. Classification: Theory and group contribution. Expected uncertainty: Generally less than 3 percent for liquids. Applicability: Most organic molecules (currently not applicable to organic acids). Input data: Molecular structure, molecular weight, and density at the desired temperature. Description: This method is based on the Lorentz-Lorenz relation between the molar refraction RD and the refractive index, which can be written in the form   ρ M + 2 RD  gm ⋅ cm −3  n=   ρ M − RD  gm ⋅ cm −3  (2-22) where n is refractive index at the same temperature as the density r. Wildman and Crippen developed a GC method for RD with the atomic contributions shown in Table 2-160 for each type of atom with its bonded neighbors. Example Calculate the refractive index of m-ethylphenol at 298.15 K. The various types of atoms corresponding to the descriptions in Table 2-160 are identified in the 2-D structural diagram shown here. H2N—NH2 H1 Calculation of the principal moments of inertia: Optimizing hydrazine with HF/6-31G model chemistry gives the following principal moments of inertia: H1 C18 A = 12.24050 amu ⋅ Bohr2 H1 B = 72.41081 amu ⋅ Bohr2 C = 79.16893 amu ⋅ Bohr2 C18 H1 H1 C1 C1 H1 H1 C21 C18 C23 C18 H1 Conversion from atomic units to SI gives  5.29177 × 10 −11 m  A = (12.24050 amu ⋅ Bohr 2 )    Bohr −2  1.66054 × 10 −27 kg    amu = 5.692 × 10 −47 kg ⋅ m 2  4.65010 −48 kg ⋅ m2  = 3.367 × 10 −46 kg ⋅ m 2 B = (72.41081 amu ⋅ Bohr 2 )   amu ⋅ Bohr 2   4.65010 −48 kg ⋅ m2  −46 2 C = (79.16893 amu ⋅ Bohr 2 )   = 3.681 × 10 kg ⋅ m 2  amu ⋅ Bohr  Calculation using Eq. (2-21): (ABC)1/3 = [(5.692 × 10−47)(3.367 × 10−46)(3.681 × 10−46)]1/3 kg ⋅ m2 = 1.918 × 10−46 kg ⋅ m2 Rg = 2π (1.918 × 10 − 46 kg ⋅ m 2 )(6.022 ⋅10 26 kmol −1 ) = 1.505 × 10 −10 m 32.0452 kg/kmol H2 02 H1 The molecular weight of m-ethylphenol is 122.16 kg/kmol, and its liquid density at 298.15 K is given in the DIPPR database as 1.00651 g/cm3. The group contributions are summed up as shown in this table: Type C1 C18 C21 C23 O2 H1 H2 Description 1° & 2° aliphatic aromatic 4° aromatic –aliphatic C 4° aromatic –O attached alcohol hydrocarbon alcohol Group Sum Number 2 4 1 1 1 9 1 19 Value Contribution 2.503 3.350 3.509 3.853 0.8238 1.057 1.395 5.006 13.40 3.509 3.853 0.8238 9.513 1.395 RD 37.4998 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-160 2-325 Wildman-Crippen Contributions for Refractive Indexa Table-specific nomenclature: e = N, O, P, S, F, Cl, Br, or I; ! = not (e.g., !e = not any of the e elements); c = aromatic carbon; n = aromatic nitrogen; o = aromatic oxygen; A = any nonhydrogen atom; a = aromatic, not necessarily carbon; bond types are single (}), double (=), triple (#), and aromatic (:) Type Description C1 1°, 2° aliphatic C2 3°, 4° aliphatic C3 1°, 2° aliphatic e C4 3º, 4º aliphatic e C5 olefin e C6 olefin C7 acetylene C8 1° aromatic c C9 1° aromatic e C10 2° aromatic C11 3° aromatic C12 4° aromatic C13 aromatic e C14 aromatic F C15 aromatic Cl C16 aromatic Br C17 aromatic I C18 aromatic C19 bridgehead C20 4° aromatic C21 4° aromatic C22 4° aromatic C23 4° aromatic C24 4° aromatic C25 4° aromatic C26 C=C aromatic C27 aliphatic e CS supplemental C H1 hydrocarbon H2 alcohol H3 amine/amide H4 acid HS supplemental H MR C(4H), C(3H)(C), C(2H)(2C) C(H)(3C), C(4C) C(3H)(e), C(2H)(2e) C(H)(3e), C(4e) C(=e) C(2H)(=A), C(H)(=A), C(=A) C(#A) C(3H)(c) C(3H)(ae) C(2H)(a) C(H)(a) C(a) c(!e) c(F) c(Cl) c(Br) c(I) c(H) c(3:a) c(2:a)(a) c(2:a)(C) c(2:a)(N) c(2:a)(O) c(2:a)(S) c(2:a)(=C), c(2:a)(=N, =O) C(=C)(a) C(4!e) any other C H(H), H(C) H(O) H(N), H(O)(N) H(COO), H(COS), H(OO) any other H 2.503 2.433 2.753 2.731 5.007 3.513 3.888 2.464 2.412 2.488 2.582 2.576 4.041 3.257 3.564 3.180 3.104 3.350 4.346 3.904 3.509 4.067 3.853 2.673 3.135 4.305 2.693 3.243 1.057 1.395 0.9627 1.805 1.112 Type Description MR N(2H)(A) N1 1° amine N(H)(2A) N2 2° amine N(2H)(a) N3 1° aromatic amine N(H)(a)(A, a) N4 2° aromatic amine N5 imine N(H)(=A, =a) N6 substituted imine N[2(=A, =a)] N(3A) N7 3° amine N(a)[2(a, A)] N8 3° aromatic amine N9 nitrile N(#A) N11 aromatic N n N13 4° amine N(4A,), N(=A)[2(A, a)] NS supplemental N any other N O1 aromatic o O2 alcohol O(H), O(2H) O3 aliphatic ether O[2(C, A)] O4 aromatic ether O(a)(A, a) O5 oxide O(=O, =N), O(A)(N) O6 oxide O(A)(S) O7 oxide O(A)(!N, !S) O8 aromatic carbonyl O(=c) O9 aliphatic carbonyl O(=C)[2(C, H, N, A] O10 aromatic carbonyl O(=C)(c)(C, H, A, a) O11 carbonyl (e) O(=C)(A, a) O12 acid O(C=O) OS supplemental O any other O F fluorine F(A) Cl chlorine Cl(A) Br bromine Br(A) I iodine I(A) P phosphorous P(A) S1 aliphatic S S(A) S3 aromatic S s(A) pblk all remaining p-block elements 2.262 2.173 2.827 3.000 1.757 2.428 1.839 2.819 1.725 2.202 0.2604 2.134 1.080 0.8238 1.085 1.182 3.367 0.7774 0.000 3.135 0.000 0.2215 0.3890 — 0.6865 1.108 5.853 8.927 14.02 6.920 7.591 6.691 5.754 Wildman, S. A., and G. M. Crippen, J. Chem. Inf. Comput. Sci. 39 (1999): 868. a This value for RD is used in Eq. (2.22) to obtain n= with the coefficients given by 122.16 + 2(1.00651)(37.4998) = 1.530 122.16 − (1.00651)(37.4998) Applicability The predicted value differs by 0.3 percent from the experimental value of 1.535 given in the DIPPR database. Dielectric Constant The dielectric constant is the ratio of the electric field strength in vacuum to that in the material for the same charge distribution. Equivalently, it is the ratio of the capacitance between two parallel charged plates when filled with the material to that of a vacuum with identical charges on the plates. Recommended Method Liu method. Reference: Liu, J-P, W. V. Wilding, N. F. Giles, and R. L. Rowley, J. Chem. Eng. Data 55 (2010): 41–45. Classification: QSPR. Expected uncertainty: Generally less than 1 percent for nonpolar organic liquids and less than 20 percent for polar organic liquids. Applicability: Organic liquids. Not valid if the predicted dielectric constant is greater than 50. Input data: For hydrocarbons and nonpolar molecules, the dipole moment μ, solubility parameter δ, and refractive index n are required. For polar and nonhydrocarbon molecules, the van der Waals area Avdw and number of oxygen-containing groups are additionally required. Description: The general correlation for the dielectric constant ε is Hydrocarbons and nonpolar C1 0.1283 0 C2 2.8251 × 10−5 C3 0.2150 C4 −0.3416 0.5239 4.072 × 108 7.408 × 10−5 −0.3248 The summation term shown in Eq. (2.23) is only for oxygen-containing groups in the molecule in which Gi is the contribution shown below and ki (ki > 1) is the number of occurrences of that group in the molecule. Group Example Group Gi Example Gi 0.2879 –OH(na) alcohol 0.2230 [S, N, P] = O thionyl chloride ketone 0.3615 –OH(a) phenol 0.0990 >C=O 0.3348 2-pyrrolidone 0.0075 >C=O ring –OH(C < 5)* ethanol –COO– ester −0.0650 –CHO aldehyde 0.1617 –COOH acid −0.5900 *Applied in addition to regular −OH group for molecules with fewer than 5 C atoms. Example Calculate the dielectric constant of salicylaldehyde at 303 K. The structure of salicylaldehyde is shown below with the two different oxygen-containing groups and their contributions that are to be used in Eq. (2.23). O −1 O Groups   A G µ δ ln ε = C 0 + C1   + C 2  2 vdw −1  + C 3  1/2 -3/2  + C 4 n 2 + ∑ i  m ⋅ kmol   D  J ⋅m  ki i (2-23) C0 −0.1694 HO Group Gi ki −CHO 0.1617 1 −OH(a) 0.0990 1 2-326 PHYSICAL AnD CHEMICAL DATA Values of the input properties for Eq. (2.23) obtained from the DIPPR database are μ = 3.08794 D, Avdw = 8.43 × 108 m2/kmol, d = 21330 J1/2∙m−3/2, n = 1.57017. Equation (2.23) is then used to obtain the dielectric constant: 4.072 ln ε = −0.3416 + (0.5239) ( 3.08794 ) + 8.43 + (7.408 × 10 −5 )(21330) − (0.3248)(1.57017)2 + 0.1617 + 0.0990 C = αc − 42D B = −36D A = 35D Values of the constant K [Vetere, A., Ind. Eng. Chem. Res., 30 (1991): 2487] are as follows: Class ln e = 2.799 and e = 16.43 A few reported experimental values are 13.9 at 293 K, 17.1 at 303 K, and 18.35 at 293.15 K. Value Acids K = −0.120 + 0.025h Alcohols K = 0.373 − 0.030h All other organic compounds K = 0.0838 VAPOR PRESSURE Liquids Vapor pressure is the equilibrium pressure at a given temperature of pure, coexisting liquid and vapor phases. The vapor pressure curve is a monotonic function of temperature from its minimum value (the triple point pressure) at the triple point temperature Tt, to its maximum value, Pc, at Tc. Liquid vapor pressure data over a limited temperature range can be correlated with the Antoine equation [Antoine, C., C.R., 107 (1888): 681, 836] In P∗ B = A− T /K + C Pa aτ + bτ1.5 + cτ 2.5 + d τ 5 1− τ K = 0.0838 D = (0.0838)(7.0248 − 3.758) = 0.2738 C = 7.0248 − (42)(0.2738) = −4.4729 B = −(36)(0.2738) = −9.8552 A = −(35)(0.2738) = 9.5814 Calculation using Eq. (2-28) at each T (detailed calculation shown for T = 500 K): Tr = 500/632.35 = 0.7907 (2-25) where τ ≡ 1 − Tr ln Pr = 9.5814 − or the Riedel equation [Riedel, L., Chem. Ing. Tech., 26 (1954): 679] ln T T P∗ B = A+ + C ln + D    K Pa T /K K aτ + bτ1.5 + cτ 2.5 + d τ5 + eτ 6 1− τ Pr = exp(−1.7651) = 0.1712 (for alcohols) (2-27) B + C ln Tr + DTr6 Tr (2-28) is used with the constants for this equation determined from the following set of relationships: ψ = −35 + h = Tbr 36 + 42 ln Tbr − Tbr6 Tbr ln ( Pc /1.01325 bar) 1 − Tbr αc = P = PrPc = (0.1712)(45.1911 bar) = 7.74 bar (2-26) Correlation of experimental data within a few tenths of a percent over the entire fluid range can usually be obtained with either the Wagner or Riedel equations. Two prediction methods are recommended for liquid vapor pressure. The first method is based on the Riedel equation; the second is a CS method. Both methods require Tc and Pc as input, but these can be estimated by the methods shown earlier if experimental values are unavailable. Recommended Method 1 Riedel method. Reference: Riedel, L., Chem. Ing. Tech., 26 (1954): 679. Classification: Empirical extension of theory and corresponding states. Expected uncertainty: Varies strongly depending upon relative T, but 1 percent or less above Tb is typical with uncertainties of 5 to 30 percent near the triple point. Applicability: Most organic compounds. Input data: Tb, Tc, Pc. Description: Equation (2-26) in reduced form ln Pr = A + 9.8552 − 4.4729 ln 0.7907 + (0.2738)(0.7907) 6 = −1.7651 0.7907 E In its original form, E in Eq. (2-26) was assigned a value of 6, but other integer values of E from 1 to 6 have been found to be more effective for different families of chemicals in representing the vapor pressure over the whole liquid range. With the best value of E, either the Riedel or the Wagner equation can be used to correlate most fluids over the whole liquid range, but a fifth term is used in the Wagner equation for alcohols [Poling, B. E., Fluid Phase Equilib., 116 (1996): 102]: ln Pr∗ = Tbr = 404.87/632.35 = 0.640 36 ψ = −35 + + 42 ln(0.640) − (0.640) 6 = 2.431 0.640 (3.758) (0.0838)(2.431) + ln (45.191/1.01325) = 7.0248 αc = (0.0838)(2.431) − ln (0.640) (2-24) Data from the triple point to the critical point can be correlated with either a modified form of the Wagner equation [Wagner, W., A New Correlation Method for Thermodynamic Data Applied to the Vapor-Pressure Curve of Argon, Nitrogen, and Water, J. T. R. Watson (trans. and ed.), IUPAC Thermodynamic Tables Project Centre, London, 1977; Ambrose, D., J. Chem. Thermodyn., 18 (1986): 45; Ambrose, D., and N. B. Ghiassee, J. Chem. Thermodyn., 19 (1987): 903, 911] ln Pr∗ = Example Estimate the vapor pressure of chlorobenzene at 50 K intervals from 300 to 600 K. Input information: From the DIPPR 801 database, Tb = 404.87 K, Tc = 632.35 K, and Pc = 45.1911 bar. Auxiliary Quantities: 3.758 K ψ + ln(Pc /1.01325 bar) K ψ − ln Tbr D = K (α c − 3.758) (2-28a) T/K Tr ln Pr P/bar PDIPPR/bar % Error 300 350 400 450 500 550 600 0.4744 0.5535 0.6326 0.7116 0.7907 0.8698 0.9488 −7.8532 −5.5704 −3.9323 −2.7101 −1.7651 −1.0067 −0.3705 0.0176 0.172 0.886 3.01 7.74 16.51 31.20 0.0175 0.172 0.880 2.98 7.67 16.39 31.11 0.3 0.1 0.6 0.9 0.9 0.8 0.3 Recommended Method 2 Ambrose-Walton method. References: Ambrose, D., and J. Walton, Pure & Appl. Chem., 61 (1989): 1395; Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510. Classification: Corresponding states. Expected uncertainty: Varies strongly with relative T, but less than 1 percent is typical above Tb if the acentric factor is known. Applicability: Most organic compounds. Input data: Tb, Tc, Pc, and w. Description: The acentric factor is used to interpolate within the simplefluid and deviation terms for ln P*. The f (i) terms have been obtained from correlations of the reference fluid vapor pressures with the Wagner vapor pressure equation ln Pr* = f (0) + ωf (1) + ω 2 f (2) −5.97616 τ + 1.29874 τ1.5 − 0.60394 τ 2.5 − 1.06841τ 5 1− τ −5.03365 τ + 1.11505 τ1.5 − 5.41217 τ 2.5 − 7.46628 τ 5 (1) f = 1− τ −0.64771τ + 2.41539 τ1.5 − 4.26979 τ 2.5 + 3.25259 τ 5 (2) f = 1− τ f (0) = (2-29) where t = 1 − Tr. Example Repeat the calculation of the liquid vapor pressure of chlorobenzene at 50-K intervals from 300 to 600 K using the Ambrose-Walton method. Input information: From the DIPPR 801 database, Tc = 632.35 K, Pc = 45.1911 bar, and w = 0.249857. Auxiliary quantities: Tr = 500/632.35 = 0.7907 t = 1 − 0.7907 = 0.2093 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Simple-fluid and deviation vapor pressure terms at each T (shown for T = 500 K): ( − 5.97616)(0.2093) + (1.29874)(0.2093)1.5 − (0.60394)(0.2093) 2.5 − (1.06841)(0.2093)5 0.7907 = −1.4405 f (0) = ( − 5.03365)(0.2093) + (1.11505)(0.2093)1.5 − (5.41217)(0.2093) 2.5 − (7.46628)(0.2093)5 0.7907 = −1.3383 Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure. Description: GC values from Table 2-161 are directly additive for both enthalpy of formation and absolute third-law entropies: ∆H of f (1) = (−0.64771)(0.2093) + (2.41539)(0.2093)1.5 − (4.26979)(0.2093) 2.5 + (3.25259)(0.2093)5 0.7907 = 0.0145 f (2) = Calculation using Eq. (2-29): * ln Pr = −1.4405 + (0.249857)(−1.3383) + (0.249857)2(0.0145) = −1.774 P* = (45.1911 bar)[exp(−1.774)] = 7.667 bar T t f (0) 300 350 400 450 500 550 600 0.5256 0.4465 0.3674 0.2884 0.2093 0.1302 0.0512 −5.9228 −4.3006 −3.1036 −2.1800 −1.4405 −0.8289 −0.3068 f (1) −7.5966 −5.0017 −3.3106 −2.1576 −1.3383 −0.7318 −0.2612 f (2) −0.3050 −0.1439 −0.0437 0.0043 0.0145 0.0036 −0.0081 ln P*r P*/bar P*DIPPR/ bar % Error −7.840 −5.559 −3.933 −2.719 −1.774 −1.012 −0.373 0.0178 0.174 0.885 2.98 7.67 16.43 31.14 0.0175 0.172 0.880 2.98 7.67 16.39 31.11 1.4 1.5 0.5 0.0 0.0 0.3 0.1 2-327 kJ/mol N = ∑ ni (∆H of )i i =1 N So = ∑ ni (S o )i −1 −1 J ⋅ mol K i =1 (2-31) where ( ∆H of )i = enthalpy of formation GC value and (So)i = entropy GC value, both obtained from Table 2-161. Group values in Table 2-161 are defined by the central, nonhydrogen group and the atoms bonded to that group. Thus, C—(2H)(2C) represents a C atom to which 2 H and 2 C atoms are bonded. For example, propane (CH3—CH2—CH3) is composed of three groups: two C—(3H)(C) and one C—(2H)(2C). Example Estimate the standard and ideal gas enthalpies of formation of o-toluidine. Input information: Because the melting point (256.8 K) and boiling point (473.49 K) for o-toluidine bracket 298.15 K, the standard state phase at 298.15 K and 1 bar is liquid. Structure: Group contributions: Solids Below the triple point, the pressure at which the solid and vapor phases of a pure component are in equilibrium at any given temperature is the vapor pressure of the solid. It is a monotonic function of temperature with a maximum at the triple point. Solid vapor pressures can be correlated with the same equations used for liquids. Estimation of solid vapor pressure can be made from the integrated form of the Clausius-Clapeyron equation ln P ∗ ∆H sub  Tt  = 1−  Pt∗ RTt  T  Group ni Cb—(H)(2Cb) Cb—(C)(2Cb) Cb—(N)(2Cb) C—(3H)(C) N—(2H)(Cb) 4 1 1 1 1 Total DH of gas DH of liq. So gas Ss liq. 13.81 23.64 −1.30 −42.26 19.25 54.57 8.16 19.16 1.50 −47.61 −11.00 −5.31 48.31 −35.61 −43.53 127.32 126.90 368.32 28.87 −19.50 −24.43 83.30 71.71 226.56 (2-30) where Tt = triple point temperature Pt* = triple point pressure DHsub = enthalpy of sublimation The liquid and solid vapor pressures are identical at the triple point. A good vapor pressure correlation that is valid at the triple point may be used to obtain the triple point pressure. Estimating solid vapor pressures by using Eq. (2-30) generally requires an estimation of DHsub, and so the illustrative example is combined with the example on enthalpy of sublimation in the section on latent enthalpy. THERMAL PROPERTIES Enthalpy of Formation The standard enthalpy (heat) of formation is the enthalpy change upon formation of 1 mole of the compound in its standard state from its constituent elements in their standard states. Two different standard enthalpies of formation are commonly defined based on the chosen standard state. The standard enthalpy of formation ∆H sf uses the naturally occurring phase at 298.15 K and 1 bar as the standard state while the ideal gas enthalpy (heat) of formation ∆H of uses the compound in the ideal gas state at 298.15 K and 1 bar as the standard state. In both cases, the standard state for the elements is their naturally occurring state of aggregation at 298.15 K and 1 atm. Sources for data include DIPPR, TRC, SWS, JANAF, and TDB. The Domalski-Hearing method is the most accurate general method for estimating either ∆H sf or ∆H of if the appropriate GC values are available, but a CC method is also as accurate for estimating ∆H of if an isodesmic reaction can be formulated and used. The Domalski-Hearing method also applies to entropies, and the entropy predictive equations are listed in this section for convenience because they are equivalent in form to the enthalpy equations. However, discussion and illustration of the estimation methods for entropy are delayed to the next subsection. Recommended Method Domalski-Hearing method. Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805. Classification: Group contributions. Expected uncertainty: 3 percent. Calculation from Eq. (2-31): ∆H of kJ/mol = 54.57 So = 368.32 J/(mol ⋅ K) ∆H Sf kJ/mol = −5.31 Ss = 226.56 J/(mol ⋅ K) o The recommended DIPPR 801 standard enthalpies of formation are ∆H f = 53.20 kJ/mol s and ∆H f = −4.72 kJ/mol. The estimated values are higher than the recommended values by 2.6 and 12.5 percent, respectively. The recommended DIPPR 801 standard entropies are So = 355.8 J/(mol ⋅ K) and Ss = 231.2 J/(mol ⋅ K). The estimated values differ from these by 3.5 and −2.0 percent, respectively. Recommended Method Isodesmic reaction. Reference: Foresman, J. B., and A. Frisch, Exploring Chemistry with Electronic Structure Methods, 2d ed., Gaussian Inc., Pittsburgh, Pa., 1996. Classification: Computational chemistry. Expected uncertainty: 5 to 10 percent depending upon the level of theory and basis set size used. Applicability: Compounds for which an isodesmic reaction can be formulated. Input data: Experimental ∆H of values for all other participants in the isodesmic reaction. Description: While ab initio calculations of absolute enthalpies are not currently as accurate as GC methods, relative enthalpies of molecules calculated with the same level of theory and basis set can be very accurate, as in the case of isodesmic reactions. An isodesmic reaction is one in which the number and type of bonds are preserved during the reaction. For example, the reaction of acetaldehyde with ethane to form acetone and methane is 2-328 PHYSICAL AnD CHEMICAL DATA TABLE 2-161 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group ∆Hfo So ∆Hfs liq. S s liq. ∆Hfs solid S s solid 56.69 23.01 −16.89 0.00 −33.19 0.00 0.00 0.00 21.75 CH Groups C}(3H)(C) C}(2H)(2C) C}(H)(3C) }CH3 corr (tertiary) C}(4C) }CH3 corr (quaternary) }CH3 corr (tert/quat) }CH3 corr (quat/quat) Cd}(2H) Cd}(H)(C) Cd}(2C) Cd}(H)(Cd) Cd}(C)(Cd) Cd}(Cd)(Cb) Cd}(H)(Cb) Cd}(C)(Cb) Cd}(H)(Ct) C}(4H), Methane Cd}(2Cb) C}(2H)(C)(Cd) C}(H)(2C)(Cd) }CH3 corr (tertiary) C}(3C)(Cd) }CH3 corr (quaternary) C}(H)(C)(2Cd) C}(2H)(2Cd) C}(2H)(Cd)(Cb) C}(H)(C)(Cd)(Cb) cis (unsat) corr tert}Butyl cis corr Ct}(H) Ct}(C) Ct}(Cd) Ct}(Cb) Ct}(Ct) C}(2H)(C)(Ct) C}(H)(2C)(Ct) }CH3 corr (tertiary) C}(3C)(Ct) }CH3 corr (quaternary) C}(2H)(2Ct) C}(2C)(2Ct) Ca Cb}(H)(2Cb) Cb}(C)(2Cb) Cb}(Cd)(2Cb) Cb}(Ct)(2Cb) Cb}(3Cb) C}(2C)(2Cb) C}(2H)(C)(Cb) C}(H)(2C)(Cb) C}(Cb)(3C) C}(2H)(2Cb) C}(H)(C)(2Cb) C}(H)(3Cb) C}(3Cb)(C) C}(4Cb) Cbf}(Cbf)(2Cb) Cbf}(Cb)(2Cbf) Cbf}(3Cbf) Cb}(2Cb)(Cbf) Cb}(Cb)(2Cbf) ortho corr, hydrocarbons meta corr, hydrocarbons Cyclopropane rsc (unsub) Cyclobutane rsc Cyclopentane rsc (unsub) Cyclohexane rsc (unsub) Cycloheptane rsc Cyclooctane rsc Cyclononane rsc Cyclodecane rsc −42.26 −20.63 −1.17 −2.26 19.20 −4.56 −1.80 −0.64 26.32 36.32 44.14 28.28 36.78 127.32 39.16 −53.60 0.00 −149.49 0.00 0.00 0.00 115.52 33.05 −50.84 27.74 −61.33 −47.61 −25.73 −4.77 −2.18 17.99 −4.39 −1.77 −0.64 21.75 31.05 39.16 22.18 30.42 83.30 32.38 −23.89 0.00 −98.65 0.00 0.00 0.00 86.19 28.58 −29.83 13.30 −41.92 28.28 37.95 28.28 −74.48 32.88 −20.88 −1.63 −2.26 22.13 −4.56 −1.17 −18.92 27.74 −51.97 27.74 206.92 22.18 38.58 22.18 13.30 −46.74 −29.41 −5.98 −2.34 12.47 −4.35 −2.70 −2.24 22.43 25.48 32.97 17.53 27.91 56.07 17.53 13.30 17.53 38.20 −50.38 0.00 −150.23 0.00 −53.60 42.08 31.67 −28.07 0.00 −108.20 0.00 −23.89 19.32 49.91 −24.35 −6.49 −2.34 12.51 −4.35 −5.98 −21.60 4.85 17.24 113.50 115.10 121.42 120.76 120.76 −19.70 −3.16 −2.26 5.06 0.00 101.96 26.32 39.92 17.77 25.94 42.80 −45.69 0.00 0.00 0.00 67.57 14.25 5.73 17.57 110.34 101.66 32.36 103.28 103.28 −29.41 −4.56 −41.14 0.00 142.67 13.81 23.64 24.17 24.17 21.66 26.28 48.31 −35.61 −33.85 −33.85 −36.57 −21.34 −4.52 18.28 −46.43 42.59 −48.00 −147.19 30.83 −25.73 −5.02 −2.18 20.79 −4.39 −4.77 −24.43 −24.73 −6.90 5.27 17.48 104.47 107.15 114.77 119.00 104.80 −22.13 −2.18 22.83 −4.39 −39.08 20.67 134.68 8.16 19.16 19.12 19.12 17.21 −24.81 −5.82 18.70 −26.50 −21.47 0.00 0.00 14.39 28.87 −19.50 −9.04 −9.04 47.40 −13.90 −96.10 51.97 28.12 −6.86 27.04 20.10 16.00 3.59 22.46 1.26 −0.63 115.15 110.89 26.75 0.68 26.34 40.65 52.91 51.99 0.00 15.83 11.50 −0.90 −5.54 −2.50 0.00 134.86 126.04 116.22 78.18 73.97 70.78 3.26 0.00 111.58 106.64 22.84 −1.77 23.50 38.10 50.40 50.61 0.00 0.00 51.48 42.24 10.07 15.89 2.96 −2.34 26.38 −4.35 131.08 6.53 13.90 20.27 20.07 17.03 52.81 −22.10 −3.50 21.57 −21.44 16.40 34.48 116.25 64.89 14.10 12.00 1.94 −8.77 47.93 5.00 2.00 114.43 34.00 10.94 21.75 21.75 0.00 0.00 −16.89 0.00 0.00 0.00 0.00 22.75 −5.50 −10.00 −10.00 −6.00 26.90 22.85 −12.62 −6.00 2.00 7.00 0.00 0.00 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161 2-329 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued ) This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group DHfo DHfs liq. So S s liq. DHfs solid S s solid CHO Groups CO}(2H), formaldehyde CO}(C)(CO) CO}(H)(CO) CO}(CO)(Cb) CO}(O)(CO) CO}(Cd)(O) CO}(C)(O) CO}(H)(O) CO}(2O) CO}(H)(Cd) CO}(2Cb) CO}(C)(Cb) CO}(H)(Cb) CO}(O)(Cb) CO}(2C) CO}(H)(C) CO}(C)(Cd) O}(2CO), aliphatic O}(2CO), aromatic O}(Cd)(CO) O}(C)(CO) O}(H)(CO) O}(Cb)(CO) O}(C)(O) O}(H)(O) O}(2Cd) O}(H)(Cd) O}(C)(Cd) O}(2Cb) O}(C)(Cb) O}(H)(Cb) O}(2C) O}(H)(C) Cd}(H)(CO) Cd}(C)(CO) Cd}(O)(Cd) Cd}(O)(C) Cd}(O)(H) Ct}(CO) Cb}(CO)(2Cb) Cb}(O)(2Cb) C}(2H)(2CO) C}(CO)(3C) C}(H)(CO)(2C) C}(2H)(CO)(C) C}(3H)(CO) C}(2H)(CO)(Cd) C}(2H)(CO)(Ct) C}(2H)(CO)(Cb) C}(H)(CO)(C)(Cb) C}(H)(O)(CO)(C) C}(4O) C}(H)(3O) C}(3O)(C) C}(2O)(2C) C}(H)(2O)(C) C}(2H)(2O) C}(2H)(O)(Cb) C}(2H)(O)(Cd) C}(H)(CO)(C)(Cb) C}(H)(CO)(2Cb) C}(O)(3Cb) C}(O)(3C) (ethers, esters) C}(H)(O)(2C) (ethers, esters) C}(O)(3C) (alcohols, peroxides) C}(H)(O)(2C) (alcohols, peroxides) C}(2H)(O)(C) C}(3H)(O) O}(CO)(O) C}(2C)(O)(Cb) C}(H)(C)(2O) −108.60 −121.29 −105.98 −112.30 −123.75 −136.73 −137.24 −124.39 −111.88 −126.96 −110.00 −148.82 −121.35 −125.00 −132.67 −124.39 224.54 −214.50 −238.30 −198.03 −188.87 −254.30 −167.00 −20.75 −72.26 −139.29 34.16 −135.04 62.59 62.59 147.03 64.31 147.03 36.03 101.71 −123.30 −155.56 −149.37 −142.42 −122.00 −153.05 −119.00 −145.22 −138.12 −140.00 −152.76 −142.42 −230.50 −220.90 −201.42 −196.02 −285.64 −165.50 −23.50 −101.75 −137.32 −129.33 −77.66 −92.55 −160.30 −101.42 −159.33 32.30 121.50 29.33 121.50 35.19 −133.72 −85.27 −104.85 −191.75 −110.83 −191.50 26.61 36.78 44.14 36.32 −61.34 −50.84 33.05 30.42 39.08 31.05 15.50 −4.75 −30.74 23.93 −0.25 −21.84 −42.26 −16.95 −25.48 −16.20 126.63 −152.46 −113.97 −114.39 −53.56 −57.78 −62.22 −33.76 −27.49 9.50 −19.46 −13.50 −26.10 −32.90 −42.26 −88.00 15.30 −43.72 39.58 127.32 37.49 −141.92 −52.80 −144.60 −43.05 43.43 127.32 10.50 −5.61 −23.06 26.15 −3.89 −24.14 −47.61 −19.62 −26.61 −11.67 123.43 −133.34 −107.74 −99.54 −41.30 −51.42 −62.89 −29.17 −28.62 0.79 −21.00 −11.13 −27.60 −35.80 −47.61 −90.00 25.80 −140.75 32.72 94.68 33.81 93.55 −117.75 −120.81 −134.10 −153.60 32.90 32.13 −123.00 −42.92 −116.00 −143.70 −160.18 −145.00 −157.95 23.72 32.13 −235.00 −207.00 38.28 38.28 −210.60 −282.15 −170.00 −30.20 −105.30 12.09 21.78 45.32 23.31 −96.20 −122.87 −199.25 −119.00 −199.66 7.82 3.14 43.89 26.78 43.89 28.62 28.62 27.53 −85.98 −24.52 39.87 83.30 27.91 32.97 25.48 144.52 8.15 1.00 −19.10 24.02 −9.83 −27.90 −46.74 24.73 56.69 −46.71 14.81 −14.39 8.08 −41.92 −29.83 28.58 −10.59 0.08 1.59 23.85 −94.68 −25.31 −122.48 −29.83 32.59 83.30 −14.39 3.72 60.46 −0.50 −20.08 −12.25 −29.08 −33.00 −46.74 −80.50 29.30 −52.50 −14.77 6.95 24.73 56.69 (Continued ) 2-330 PHYSICAL AnD CHEMICAL DATA TABLE 2-161 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued ) This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group DHfo So DHfs liq. S s liq. DHfs solid −47.61 −30.80 −14.65 −2.18 5.10 −4.39 83.30 32.38 −20.00 0.00 −87.99 0.00 −26.09 0.33 0.33 51.50 112.00 25.30 75.00 119.00 71.71 71.71 32.09 −38.62 60.58 22.05 −26.94 −46.74 −34.00 −13.90 −2.34 1.00 −4.35 −26.00 −33.31 −6.30 −46.00 47.80 101.00 18.97 S s solid CHN and CHNO Groups C}(3H)(N) C}(2H)(C)(N) C}(H)(2C)(N) }CH3 corr (tertiary) C}(3C)(N) }CH3 corr (quaternary) C}(2H)(2N) C}(2H)(Cb)(N) N}(2H)(C) ( first, amino acids) N}(2H)(C) (second, amino acids) N}(H)(2C) N}(3C) N}(2H)(N) N}(H)(C)(N) N}(2C)(N) N}(2Cb)(N) N}(H)(Cb)(N) N}(2CO)(N) N}(H)(2Cd) N}(C)(2Cd) N}(2H)(Cb) N}(H)(C)(Cb) N}(2C)(Cb) N}(C)(2Cb) N}(H)(2Cb) N}(3Cb) NI}(C) NI}(Cb) NA}(C) NA}(Cb) NA}(oxide)(C) C}(2H)(C)(NA) C}(H)(2C)(NA) C}(3C)(NA) Cd}(H)(N) Cd}(C)(N) Cb}(N)(2Cb) Cb}(NO)(2Cb) Cb}(NO2)(2Cb) Cb}(CNO)(2Cb) Cb}(CN)(2Cb) Cb}(NA)(2Cb) Cb}(H)(2NI) CO}(H)(N) CO}(C)(N) CO}(Cb)(N) (amides) CO}(Cb)(N) (amino acids) CO}(Cd)(N) CO}(2N) N}(2H)(CO) (amides, ureas) N}(2H)(CO) (amino acids) N}(H)(C)(CO) (amides, ureas) N}(H)(C)(CO) (amino acids) N}(2C)(CO) N}(H)(Cb)(CO) N}(H)(2CO) N}(C)(2CO) N}(Cb)(2CO) N−(2Cb)(CO) N}(C)(Cb)(CO) C}(3H)(CN), acetonitrile C}(2H)(C)(CN) C}(H)(2C)(CN) C}(3C)(CN) C}(2C)(2CN) C}(2H)(Cd)(CN) Cd}(H)(CN) Ct}(CN) C}(3H)(NO2), nitromethane C}(2H)(2NO2), dinitromethane C}(H)(3NO2), trinitromethane C}(4NO2), tetranitromethane C}(2H)(C)(NO2) −42.26 −28.30 −16.70 −2.26 0.29 −4.56 −30.00 −24.14 19.25 19.25 67.55 116.50 47.70 89.16 120.71 127.32 42.26 −63.55 0.00 −152.59 0.00 124.40 126.90 33.96 −61.71 122.18 87.50 73.40 83.55 120.64 19.25 59.00 126.40 120.44 83.55 123.15 81.46 69.00 109.50 109.50 40.80 −20.70 −2.66 11.50 −16.00 −5.74 −1.30 21.50 −1.45 −177.63 151.00 22.55 6.30 −124.39 −133.26 50.50 97.38 −11.00 26.25 109.40 97.38 50.50 121.80 73.68 54.50 104.85 104.85 22.65 −25.70 −5.42 15.50 −15.50 −5.62 1.50 −171.80 −111.00 −63.00 −63.00 −16.28 −16.28 45.00 −20.84 −91.00 −11.64 9.12 74.04 94.52 113.50 137.96 95.31 146.65 264.60 −74.86 −58.90 −0.30 82.30 −60.50 126.90 47.01 −43.53 71.71 36.40 −24.43 −28.30 79.95 122.38 20.08 64.75 147.03 56.70 −188.00 −185.00 93.55 96.00 88.25 −190.50 −63.90 −63.90 −17.10 −17.10 62.00 56.20 158.41 284.14 203.60 40.56 66.07 81.50 116.20 66.40 117.28 250.20 −112.60 −104.90 −32.80 38.30 −93.50 0.00 0.00 39.00 48.75 70.00 57.00 103.00 103.00 −29.41 85.25 252.60 167.25 67.86 137.35 66.90 73.62 45.40 88.92 −21.60 36.55 96.50 89.30 45.40 107.50 56.69 23.01 149.62 106.02 −17.91 10.50 −13.00 −3.95 9.75 23.00 −32.50 155.69 121.20 18.65 0.25 −37.57 110.46 50.45 −194.60 −177.75 −177.75 40.00 −203.10 −65.25 −59.75 −9.80 5.50 55.00 −3.50 −30.80 64.00 69.00 18.00 33.03 60.85 72.00 69.85 69.00 102.07 92.72 171.75 −48.00 −99.00 96.15 74.57 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161 2-331 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued ) This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group DHfo So DHfs liq. S s liq. DHfs solid S s solid CHN and CHNO Groups C}(H)(2C)(NO2) C}(3C)(NO2) C}(2H)(Cb)(NO2) C}(H)(C)(2NO2) C}(2C)(2NO2) C}(H)(C)(CO)(N) C}(2H)(CO)(N) C}(H)(Cb)(CO)(N) O}(C)(NO) O}(C)(NO2) N}(H)(C)(NO2) N}(H)(Cb)(NO2) N}(H)(CO)(NO2) N}(C)(2NO2) N}(C)(Cb)(NO2) N}(2C)(NO) N}(2C)(NO2) C}(2H)(C)(N3) C}(H)(2C)(N3) C}(2H)(Cb)(N3) C}(3Cb)(N3) Cb}(N3)(2Cb) −53.00 −36.65 −62.00 −36.80 −28.50 −18.70 −3.10 115.32 −24.23 −79.71 166.11 191.92 100.30 183.00 90.00 88.00 −82.50 −61.20 −82.76 −88.80 −77.20 −46.50 −108.96 −89.00 −76.55 −81.00 −91.50 −90.30 −11.65 −30.95 127.50 −124.00 16.50 −14.00 53.50 167.00 59.00 50.00 321.70 255.00 327.40 274.00 347.00 328.60 320.00 −4.00 24.00 150.50 55.00 40.00 346.50 303.50 CHS and CHSO Groups C}(3H)(S) C}(2H)(C)(S) C}(H)(2C)(S) }CH3 corr (tertiary) C}(3C)(S) }CH3 corr (quaternary) }CH3 corr (tert/quat) }CH3 corr (quat/quat) C}(2H)(Cb)(S) C}(2H)(Cd)(S) C}(2H)(2S) Cb}(S)(2Cb) Cd}(H)(S) Cd}(C)(S) S}(C)(H) S}(Cb)(H) S}(2C) S}(H)(Cd) S}(C)(Cd) S}(2Cd) S}(Cb)(C) S}(C)(S) S}(Cb)(S) S}(2S) S}(2Cb) S}(H)(S) S}(H)(CO) CO}(C)(S) C}(3H)(SO) C}(2H)(C)(SO) C}(H)(2C)(SO) }CH3 corr (tertiary) C}(3C)(SO) }CH3 corr (quaternary) C}(2H)(Cd)(SO) cis correction Cb}(SO)(2Cb) O}(SO)(H) O}(C)(SO) SO}(2C) SO}(2Cb) SO}(2O) SO}(C)(Cb) C}(3H)(SO2) C}(2H)(C)(SO2) C}(H)(2C)(SO2) }CH3 corr (tertiary) C}(3C)(SO2) }CH3 corr (quaternary) −42.26 −23.17 −5.88 −2.26 13.52 −4.56 −1.80 −0.64 −18.53 −25.93 −25.10 −4.75 36.32 45.73 18.64 48.10 46.99 25.52 54.39 102.60 76.21 27.62 57.45 12.59 102.60 7.95 −5.90 −132.67 −42.26 −29.16 127.32 41.87 −47.36 0.00 −145.38 0.00 0.00 0.00 −47.61 −26.77 −6.07 −2.18 16.69 −4.39 −1.77 −0.64 −23.82 −32.44 83.30 41.09 −16.61 0.00 −86.86 0.00 0.00 0.00 −46.74 56.69 −2.34 0.00 −4.35 −2.70 −2.24 0.00 0.00 0.00 43.72 33.05 −51.92 137.67 57.34 55.19 −5.61 31.05 −10.59 28.58 1.00 25.48 1.59 0.06 28.51 29.82 85.95 89.04 29.80 50.50 58.20 14.36 35.44 30.84 56.07 68.59 93.02 −2.26 4.56 −4.56 −27.56 4.11 15.48 −158.60 −92.60 −66.78 −62.26 −213.00 −72.00 −42.26 −27.03 −14.00 −2.26 1.52 −4.56 0.00 68.59 130.54 64.31 127.32 0.00 5.06 42.00 40.60 −152.76 −47.61 −36.88 33.81 83.30 −46.74 56.69 −2.18 0.97 −4.39 −32.63 5.27 25.44 0.00 −2.34 0.00 0.00 −4.35 0.00 0.00 5.73 7.55 0.00 0.08 75.73 −108.98 22.18 127.32 −47.61 −33.76 83.30 −46.74 −35.96 56.69 0.00 −2.18 2.00 −4.39 0.00 −2.34 3.78 −4.35 0.00 0.00 0.00 0.00 (Continued ) 2-332 PHYSICAL AnD CHEMICAL DATA TABLE 2-161 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued ) This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group DHfo So DHfs liq. S s liq. DHfs solid S s solid CHN and CHNO Groups }CH3 corr (quat/quat) C}(2H)(Cd)(SO2) C}(H)(C)(Cd)(SO2) C}(2H)(Cb)(SO2) C}(2H)(Ct)(SO2) Cb}(SO2)(2Cb) Cd}(H)(SO2) Cd}(C)(SO2) Ct}(SO2) SO2}(Cd)(Cb) SO2}(2Cd) SO2}(2C) SO2}(C)(Cb) SO2}(2Cb) SO2}(SO2)(Cb) SO2}(2O) SO2}(C)(Cd) SO2}(Ct)(Cb) O}(SO2)(H) O}(C)(SO2) −0.64 −29.49 −71.99 −29.80 16.36 15.48 51.58 64.01 177.10 −291.55 −306.70 −288.58 −289.10 −287.76 −325.18 −417.30 −316.80 −296.30 −158.60 −91.40 C}(3H)(F), methyl fluoride C}(3H)(Cl), methyl chloride C}(3H)(Br), methyl bromide C}(3H)(I), methyl iodide C}(C)(3F) C}(2H)(C)(F) C}(H)(2C)(F) C}(3C)(F) C}(H)(C)(2F) C}(2C)(2F) C}(C)(Cl)(2F) C}(H)(C)(Cl)(F) C}(C)(3Cl) C}(H)(C)(2Cl) C}(2H)(C)(Cl) C}(2C)(2Cl) C}(H)(2C)(Cl) C}(3C)(Cl) C}(C)(3Br) C}(H)(C)(2Br) C}(2H)(C)(Br) C}(2C)(2Br) C}(H)(2C)(Br) C}(3C)(Br) C}(C)(3I) C}(H)(C)(2I) C}(2H)(C)(I) C}(2C)(2I) C}(H)(2C)(I) C}(3C)(I) C}(H)(C)(Br)(Cl) N}(C)(2F) C}(H)(C)(Cl)(O) C}(2H)(I)(O) C}(C)(2Cl)(F) C}(C)(Br)(2F) C}(C)(2Br)(F) C}(Br)(Cl)(F) Cd}(H)(F) Cd}(H)(Cl) Cd}(H)(Br) Cd}(H)(I) Cd}(C)(Cl) Cd}(2F) Cd}(2Cl) Cd}(2Br) Cd}(2I) Cd}(Cl)(F) Cd}(Br)(F) Cd}(Cl)(Br) Ct}(F) −247.00 −81.90 −37.66 14.30 −673.81 −221.12 −204.46 −202.92 −454.74 −411.39 −462.70 −271.14 −81.98 −79.10 −69.45 −79.56 −55.61 −43.70 87.37 −0.64 −49.05 −2.24 25.44 7.55 0.08 −341.14 −356.62 32.10 −305.40 −361.75 CHX and CHXO Groups 231.93 243.60 254.94 263.14 178.22 146.80 55.76 −61.10 −11.70 −709.07 135.56 164.32 74.48 169.45 −487.23 −400.37 −466.00 138.31 202.14 183.28 159.24 95.41 71.34 −24.26 233.05 −112.93 −102.60 −86.90 −101.80 −71.17 −56.78 145.91 128.45 104.27 −21.78 173.31 −42.65 113.00 −10.75 7.26 84.69 −13.46 −27.31 −7.40 108.78 33.54 228.45 177.78 48.74 68.46 −18.45 −32.64 −90.37 15.90 −322.54 −394.55 88.10 −3.21 191.21 4.14 −343.87 −165.12 4.37 50.94 102.36 −5.06 −329.90 −11.51 137.24 147.85 159.91 169.45 62.76 155.63 175.41 199.16 −235.10 175.61 177.82 188.70 141.71 149.70 −12.67 −2.23 −32.08 −85.65 3.65 24.78 48.60 66.53 170.29 −428.77 115.35 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-161 2-333 Domalski-Hearing* Group Contribution Values for Standard State Thermal Properties (Continued ) This table is a partial listing of GC values available from the original Domalski-Hearing tables. Table-specific nomenclature: Cd = carbon with double bond; Ct = carbon with triple bond; Cb = carbon in benzene ring; Ca = allenic carbon; corr = correction term; Cbf = fused benzene ring; NA = azo nitrogen; NI = imino nitrogen. Group DHfs liq. So DHfo S s liq. DHfs solid S s solid −191.20 −32.20 19.90 73.70 0.00 −58.41 −55.11 −419.59 −696.66 −44.06 −7.24 −92.56 −225.29 −216.67 −175.49 −117.09 −35.46 54.19 55.47 74.85 61.08 0.00 −194.00 −32.00 13.50 70.40 0.00 −74.75 39.79 43.37 54.45 6.96 25.00 14.00 6.30 0.00 0.00 18.50 40.60 83.55 0.00 0.00 0.00 112.00 6.00 −6.00 8.00 8.00 6.00 10.00 8.50 0.00 34.43 23.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 CHX and CHXO Groups Ct}(Cl) 140.00 Ct}(Br) 151.30 Ct}(I) 35.53 Cb}(F)(2Cb) −181.26 67.52 Cb}(Cl)(2Cb) −17.03 77.08 Cb}(Br)(2Cb) 36.35 88.60 Cb}(I)(2Cb) 94.50 98.26 3.00 0.00 cis corr}(I)(I) C}(2H)(CO)(Cl) −44.26 C}(H)(CO)(2Cl) −40.40 CO}(C)(F) −379.84 C}(Cb)(3F) −691.79 179.08 C}(2H)(Cb)(Br) −29.49 C}(2H)(Cb)(I) 7.31 C}(2H)(Cb)(Cl) −73.79 CO}(C)(Cl) −200.54 176.66 CO}(Cb)(Cl) CO}(C)(Br) −148.54 CO}(C)(I) −83.94 C}(H)(C)(CO)(Cl) −39.88 C}(C)(CO)(2Cl) ortho corr}(I)(I) 7.56 0.00 ortho corr}(F)(F) 20.90 0.00 ortho corr}(Cl)(Cl) 9.50 0.00 ortho corr}(alkyl)(X) 2.51 0.00 cis corr}(Cl)(Cl) −4.00 0.00 cis corr}(CH3)(Br) −4.00 0.00 ortho corr}(F)(Cl) 13.50 0.00 ortho corr}(F)(Br) 37.25 0.00 ortho corr}(F)(I) 85.40 0.00 meta corr}(I)(I) 0.00 0.00 meta corr}(COCl)(COCl) 0.00 0.00 ortho corr}(COCl)(COCl) 0.00 0.00 ortho corr}(F)(CF3) 111.00 0.00 meta corr}(F)(CF3) 2.00 0.00 ortho corr}(F)(CH3) −3.30 0.00 ortho corr}(F)(F’) 8.00 0.00 ortho corr}(Cl)(Cl’) 8.00 0.00 meta corr}(F)(F) 0.00 0.00 meta corr}(Cl)(Cl) −5.00 0.00 ortho corr}(Cl)(CHO) −6.75 0.00 ortho corr}(F)(COOH) 20.00 0.00 ortho corr}(Cl)(COCl) 0.00 0.00 ortho corr}(F)(OH) 25.50 0.00 ortho corr}(Cl)(COOH) 0.00 0.00 ortho corr}(Br)(COOH) 0.00 0.00 ortho corr}(I)(COOH) 0.00 0.00 ortho corr}(NH2)(NH2) −10.00 0.00 meta corr}(NH2)(NH2) 0.00 0.00 ortho corr}(OH)(Cl) 7.50 0.00 cis corr}(CH3)(I) −4.00 0.00 *Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805. isodesmic with 12 single bonds and 1 double bond in both reactants and products. To use this method, one devises an isodesmic reaction involving the compound for which ∆H of is to be determined with other compounds for which experimental ∆H of values are available. Ab initio calculations are performed on all the participating compounds, all at the same level of theory and basis set size, to obtain the enthalpy for each at 298.15 K. The enthalpy of reaction is then calculated from ∆H rxn = ∑ν i H i (2-32) where ni = stoichiometric coefficient of i (+ for products, − for reactants). The enthalpy of reaction is also related to DHfo by 0.00 −212.99 5.50 25.50 8.50 0.00 0.00 0.00 19.50 42.50 85.20 20.08 16.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 8.00 8.00 8.50 4.00 0.00 20.00 0.00 20.00 20.00 20.00 20.00 0.00 14.00 11.00 0.00 Input information: The isodesmic reaction shown above will be used. The recommended DHfo values from DIPPR 801 for the other three compounds are as follows: Acetone Methane Ethane −215.70 kJ/mol −74.52 kJ/mol −83.82 kJ/mol Ab initio calculations of enthalpy: With structures optimized using HF/6-31G(d) model chemistry and energies calculated with B3LYP/6-311+G(3df,2p), the following enthalpies are obtained (including the zero-point energy): Acetone Methane Ethane Acetaldehyde −5.071 × 105 kJ/mol −1.063 × 105 kJ/mol −2.095 × 105 kJ/mol −4.039 × 105 kJ/mol Calculation using Eq. (2-32): DHrxn = (−1.063 − 5.071 + 2.095 + 4.039) × 105 kJ/mol = − 41.67 kJ/mol ∆H rxn = ∑ν i (∆H of )i (2-33) Calculation using Eq. (2-33): ∆H of ,acetaldehyde = ∆H of ,acetone + ∆H of ,methane − ∆H of ,ethane − ∆H rxn o f With experimental values available for all ∆H except the desired compound, its value can be back-calculated from Eq. (2-33). Example Estimate the standard ideal gas enthalpy of formation of acetaldehyde. ∆H of ,acetaldehyde = ( − 215.70 − 74.52 + 83.82 + 41.67) kJ kJ = −164.73 mol mol The estimated value is 1.0 percent above the DIPPR 801 recommended value of −166.40 kJ/mol. 2-334 PHYSICAL AnD CHEMICAL DATA Entropy Absolute or third-law entropies (relative to a perfectly ordered crystal at 0 K) of a compound in its standard state Ss or of an ideal gas So at 298.15 K and 1 bar can be found in various literature sources (DIPPR, JANAF, TRC, SWS, and TDB). Very good estimates for Ss or So can be obtained by using the Domalski-Hearing method. Excellent So values can also be obtained from statistical mechanics by using experimental vibrational frequencies or values of the frequencies generated from computational chemistry. The standard ∆S sf and ideal gas ∆S of entropies of formation at 298.15 K and 1 bar are related to the standard entropies by nA s s ∆S sf = Scompound − ∑ν i Selement, i i =1 nA o s ∆S of = Scompound − ∑ν i Selement, i (2-34) i =1 where S is the absolute entropy of element i in its standard state at 298.15 K and 1 bar. Recommended Method Domalski-Hearing method. Reference: Domalski, E. S., and E. D. Hearing, J. Phys. Chem. Ref. Data, 22 (1993): 805. Classification: Group contributions. Expected uncertainty: 3 percent. Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure. Description: See description given under Enthalpy of Formation above. s element,i Example Calculate So for ammonia. Structure: NH3. Input data: M = 17 kg/kmol. McQuarrie [McQuarrie, D. A., Statistical Mechanics, Harper & Row, New York, 1976] gives the following 3nA − 6 + d = 12 − 6 + 0 = 6 characteristic vibrational temperatures (in K): 1360, 2330, 2330, 4800, 4880, 4880. The characteristic rotational temperatures given by McQuarrie are QA = 13.6 K, QB = 13.6 K, and QC = 8.92 K. For NH3, s = 3. Vibrational contribution: The table below shows a spreadsheet calculation of the vibrational terms inside the summation sign in Eq. (2-35). Qj/K Qj/(298.15 K) 1207.91 1850.16 1850.16 3688.19 3821.36 3821.36 4.051 6.205 6.205 12.370 12.817 12.817 Svib 0.08929 0.01457 0.01457 0.00006 0.00004 0.00004 Sum 0.1186 Rotational contribution: 1/2  1    (298.15 K)3π e 3 Sr = ln  ⋅    = 5.81593 R 3 (13.6 K)(13.6 K)(8.92 K)      Calculation using Eq. (2-35): Example Estimate the standard and ideal gas entropies of formation of o-toluidine. Standard state entropies: Estimation of Ss and So using the Domalski-Hearing method was illustrated above in the Enthalpy of Formation section. The standard entropies of formation can be obtained from the values determined in that example. Formula: C7H9N. The standard entropies of the elements from the DIPPR 801 database are as follows: Compound νi Sis/[J(kmol ⋅ K)] N2 H2 C, graphite 1/2 1.9151 × 105 9/2 1.3057 × 105 7 5740 5 1 9   10 J ∆S sf =  2.2656 −   (1.9151) −   (1.3057) − (7)(0.0574)   2  2   kmol ⋅ K J kmol ⋅ K 5 1 9   10 J ∆S of =  3.6832 −   (1.9151) −   (1.3057) − (7)(0.0574)      2 2  kmol ⋅ K  J = −3.552 ⋅10 5 kmol ⋅ K = −4.969 ⋅10 5 ∆G of = ∆H of − T ∆S of Recommended Method Statistical mechanics. Classification: Theory and computational chemistry. Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; uncertainty depends upon model chemistry if frequencies are determined from computational chemistry, but generally within about 5 percent. Applicability: Ideal gases. Input data: M; σ (external symmetry number); characteristic rotational temperature(s) (ΘA for linear molecules; ΘA, ΘB, and ΘC for nonlinear molecules); and 3nA − 6 + d characteristic vibrational temperatures Qj. Description: For harmonic frequencies, the rigorous temperature dependence of So is given by So 3  M  Sr = ln 6175 + kg/kmol  R R 2  + ∑ j =1  Θ j  Θ j /T −Θ /T  − 1)−1 − ln (1 − e j )   T  (e   0 nonlinear where δ =  1 linear   1  πT 3e 3  1/2  ln     nonlinear S r   σ  Θ A Θ B ΘC   and =  R   Te   linear ln     σΘ A   The calculated value differs from the DIPPR 801 recommended value of 1.927 × 105 J/(kmol ⋅ K) by 0.5 percent. Gibbs Energy of Formation The standard Gibbs energy of formation is the Gibbs energy change upon formation of 1 mole of the compound in its standard state from its constituent elements in their standard states. The standard Gibbs energy of formation DGfs uses the naturally occurring phase at 298.15 K and 1 bar as the standard state, while the ideal gas Gibbs energy of formation DGfo uses the compound in the ideal gas state at 298.15 K and 1 bar as the standard state. In both cases, the standard state for the elements is their naturally occurring state of aggregation at 298.15 K and 1 bar. Sources for data include DIPPR, TRC, JANAF, and TDB. The Gibbs energies of formation are related to the corresponding enthalpies and entropies of formation by Entropies of formation can be calculated from these values by using Eq. (2-34): 3 n A − 6+δ o S 298 3 = ln (6175.17) + 5.81593 + 0.1186 = 23.277 R 2 J o = 1.935 × 10 5 S 298 kmol ⋅ K (2-35) and ∆G sf = ∆H sf − T ∆S sf (2-36) and predicted values of ∆G sf and ∆G of are obtained from Eq. (2-36) by estimating the enthalpies and entropies of formation as shown above. LATEnT EnTHALPY Enthalpy of Vaporization The enthalpy (heat) of vaporization DHυ is the difference between the molar enthalpies of the saturated vapor and saturated liquid at a temperature between the triple point and critical point (at the corresponding vapor pressure). Variable ∆Hυ is related to the vapor pressure P* by the thermodynamically exact Clapeyron equation ∆H υ = − R ∆Zυ d ln P ∗ d ln P ∗ = RT 2 ∆Zυ dT d (1/T ) (2-37) where ∆Zυ = ZG − ZL, ZG = Z of saturated vapor, and ZL = Z of saturated liquid. Experimental heats of vaporization can be effectively correlated with 2 ∆H υ = A (1 − Tr ) B + CTr + DTr + ETr3 (2-38) A simple method for obtaining DHυ at one temperature from a known value at a reference temperature, say at the normal boiling point, is to truncate Eq. (2-38) after the B term, set B = 0.38, and take a ratio of the ∆Hυ values at the two conditions to give the Watson [Thek, R. E., and L. I. Stiel, AIChE J., 12 (1966): 599; 13 (1967): 626] correlation  1 − Tr  ∆H υ = ∆H υ , ref    1 − Tr , ref  0.38 (2-39) PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES If an accurate correlation for P* and accurate values for ZG and ZL are available, Eq. (2-37) is the preferred method for obtaining enthalpies of vaporization. Otherwise, the CS methods shown below should be used. Recommended Method 1 Vapor pressure correlation. Classification: Extension of theory. Expected uncertainty: The uncertainty varies significantly with temperature and with the quality and temperature range of the vapor pressure data used in the correlation. Applicability: Organic compounds for which group contributions have been regressed. Input data: Correlations for P*, ZG, and ZL. Description: An expression for DHυ can be obtained from Eq. (2-37) by using an appropriate vapor pressure correlation. If one differentiates the Riedel vapor pressure correlation, Eq. (2-26), in accordance with Eq. (2-37), one obtains the heat of vaporization as DHυ = R DZυ (−B + CT + DET E+1) (2-40) The ZG and ZL values can be evaluated using the methods given in the section on densities below. Example Calculate DHυ for anisole at 452 K. Input data: The vapor pressure coefficients in the DIPPR 801 database for Eq. (2-26) are A = 128.06 B = −9307.7 C = −16.693 D = 0.014919 E=1 The vapor pressure at 452 K is therefore  P∗  9307.7 − 16.693 ln ( 452 ) + 0.014919 (452)1 = 12.155 ln   = 128.06 −  Pa  452 2-335 Auxiliary quantities: From the previous example, the reduced temperature variables are Tr = 0.7 t = 1 − 0.7 = 0.3 Calculation using Eq. (2-41): ∆H υ = 7.08(0.3)0.354 + 10.95 (0.35017)(0.3)0.456 = 6.838 RTc J  kJ ∆H υ = (6.838)  8.314  (645.6 K) = 36.70  mol ⋅ K  mol ⋅ K This value is 2.2 percent below the DIPPR 801 recommended value of 37.51 kJ/(mol ⋅ K). Enthalpy of Fusion The enthalpy (heat) of fusion DHfus is the difference between the molar enthalpies of the equilibrium liquid and solid at the melting temperature and 1.0 atm pressure. There is no generally applicable, high-accuracy estimation method for DHfus, but the GC method of Chickos can be used to obtain approximate results if the melting temperature is known. Recommended Method Chickos method. Reference: Chickos, J. S., C. M. Braton, D. G. Hesse, and J. R. Liebman, J. Org. Chem., 56 (1991): 927. Classification: QSPR and group contributions. Expected uncertainty: Considerable variation but generally less than 50 percent. Applicability: Only valid at the melting temperature. The method is based on the DSfus between a solid at 0 K and the liquid at the Tm so no solid-solid transitions are taken into account. Values of DHfus will be overestimated if there are solid-solid transitions for the actual material. Input data: Tm and molecular structure. Description: P ∗ = exp (12.155) ⋅ Pa = 1.901 × 10 5 Pa Determine DZ: Required data from the DIPPR 801 database for this calculation are Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017. These values are used to determine the reduced conditions, Tr = 452 = 0.7 645.6 Pr = no nonaromatic rings  0 a= N N N 35.19 + 4.289( − 3 ) nonaromatic rings R CR R  0.1901 = 0.045 4.25 and the values of ZG and ZL from the Lee-Kesler corresponding states method as discussed in the section on density. Interpolation of the Pr values in Tables 2-169 and 2-170 at a Tr of 0.7 gives ZG(0) = 0.9904 + 0.045 - 0.010 (0.9504 − 0.9904) = 0.9554 0.050 - 0.010 ZG(1) = − 0.0064 + 0.045 − 0.010 ( − 0.0507 + 0.0064) = −0.0452 0.050 − 0.010 ZG = ZG(0) + ω ZG(1) = 0.9554 + (0.35017)( − 0.0452) = 0.94 At this low pressure, ZL is very small compared to ZG and may be neglected; so DZV = ZG − ZL = 0.94 Calculation using Eq. (2-40): J  2 ∆H υ =  8.314  (0.94)[9307.7 − (16.693) (452) + (0.014919) (1)(452) ]  mol ⋅ K  = 37.59 kJ mol ⋅ K This value is 0.2 percent higher than the value of 37.51 kJ/(mol ⋅ K) obtained from the DIPPR 801 database. Recommended Method 2 Corresponding states correlation. Reference: [PGL5], p. 7.18. Classification: Corresponding states. Expected uncertainty: Less than about 6 percent. Applicability: Organic compounds. Input data: Tc, Pc, and w. Description: The following correlation is used: ∆H υ = 7.08τ 0.354 + 10.95ωτ 0.456 RTc where τ = 1 − Tr Example Repeat the above calculation for anisole’s DHυ at 452 K. Input data: Tc = 645.6 K, Pc = 4.25 MPa, and w = 0.35017. ∆H fus ∆S fus  Tm  =   = (Tm /K) (a + b) J/mol J/(mol ⋅ K)  K  ng ns nf i =1 j =1 k =1 b = ∑ Ng i ∆si + ∑ Ns jCs j ∆s j + ∑ Nf kCt k ∆s k (2-42) (2-43) (2-44) where Ngi = number of C—H groups of type i bonded to other carbon atoms ng = number of different nonring or aromatic C—H groups bonded to other carbon atoms Nsj = number of C—H groups of type j bonded to at least one functional group or atom ns = number of different nonring or aromatic C—H groups bonded to at least one functional group or atom Nf k = number of functional groups of type k nf = number of different functional groups or atoms t = total number of functional groups or atoms with the exception that F atoms count as one regardless of number of occurrences Csj = value from Table 2-162 for C—H group j bonded to at least one functional group or atom Ctk = value from Table 2-163 for functional group k NR = number of nonaromatic rings NCR = number of —CH2— groups in nonaromatic ring(s) required to form cyclic paraffin of same ring size(s) Dsi = contribution from Table 2-162 for group i Dsk = contribution from Table 2-163 for group k Note that nonaromatic ring —CH2 groups are accounted for in the a term and are not included in the b term. Example Calculate DHfus at the melting point for (a) benzothiophene, (b) furfuryl alcohol, and (c) cis-crotonaldehyde. Structures: (2-41) 2-336 PHYSICAL AnD CHEMICAL DATA TABLE 2-162 Cs (C}H) Group Values for Chickos Estimation* of DHfus Group Description Group Ds Cs }CH3 methyl 1.0 >CH2 methylene 1.0 >CH} secondary C 0.69 >C< tertiary C 0.67 CH2= terminal alkene 1.0 }CH= alkene 3.23 >C= subst. alkene 1.0 ≡CH term. alkyne 1.0 ≡C} alkyne 1.0 *Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927. 18.33 9.41 −16.91 −38.70 14.56 4.85 −11.38 10.88 2.18 }CHAr }CAr} }CAr} }CAr} >CrH} >Cr < }CrH= >Cr= ≡Cr} or =Cr= Description aromatic C ar. C bonded to paraffinic C ar. C bonded to olefinic C or non-C group ar. C bonded to acetylinic C ring structure ring structure ring structure ring structure ring structure (a) t = 1 (1 total “functional group”), so the C1 column in Table 2-163 is used. NR = 1 Group =CH} =C} =C} =CH} =CH} }S} NCR = 5 a = 35.19 + (5 − 3)(4.289) = 43.77 Description N C aromatic (Ng type) ring (Ng type) ring (Ns type) ring (Ng type) ring (Ns type) ring 4 1 1 1 1 1 1 1 0.86 1 0.62 1 Tm = 258.52 K Cs Ds 1.0 1.0 1.0 1.0 0.76 1.0 0.62 0.86 1.0 6.44 −10.33 −4.27 −2.51 −15.98 −32.97 −4.35 −11.72 −5.36 from DIPPR 801 database DHfus = (Tm/K)(a + b) J/mol = (258.52)(43.77 + 3.51) J/mol = 12.22 kJ/mol Ds Total 6.44 −11.72 −11.72 −4.35 −4.35 2.18 25.76 −11.72 −10.08 −4.35 −2.70 2.18 Total −0.91 This value is 7 percent lower than the DIPPR 801 recommended value of 13.13 kJ/mol. (c) t = 1 a=0 NR = 0 Group Description N C Ds Total }CH3 =CH} =CH} }CHO nonring (Ng type) nonring (Ng type) nonring (Ns type) aldehyde 1 1 1 1 1 1 3.23 1 18.33 4.85 4.85 19.66 18.33 4.85 15.67 19.66 Total Tm = 304.5 K from DIPPR 801 database DHfus = (Tm /K)(a + b) J/mol = (304.5)(43.77 − 0.91) J/mol = 13.05 kJ/mol This value is 10 percent higher than the DIPPR 801 recommended value of 11.83 kJ/mol. (b) t = 2 (2 total “functional groups”), so the C2 column in Table 2-163 is used. NR = 1 Group =CH} =CH} =C< =O} }CH2} }OH NCR = 5 a = 35.19 + (5 − 3)(4.289) = 43.77 Description ring (Ng type) ring (Ns type) ring (Ns type) ring ether Ns type alcohol N C 2 1 1 1 1 1 1 0.62 0.86 1 1 12.6 Total −4.35 −4.35 −11.72 1.34 9.41 1.13 −8.70 −2.70 −10.08 1.34 9.41 14.24 Group Ct (Functional) Group Values for Chickos Estimation* Description C1 C2 }OH alcohol 1.0 12.6 }OH phenol 1.0 1.0 }O} nonring ether 1.0 1.0 }O} ring ether 1.0 1.0 nonring ketone 1.0 1.0 >C=O >C=O ring ketone 1.0 1.0 }CHO aldehyde 1.0 1.0 }COOH acid 1.0 1.83 }COO} ester 1.0 1.0 aliphatic 1.0 1.0 }NH2 }NH2 aromatic 1.0 1.0 >NH nonring 1.0 1.0 >NH ring 1.0 1.0 >N} nonring 1.0 1.0 >N} ring 1.0 1.0 =N} ring 1.0 1.0 =N} aromatic 1.0 1.0 }CN nitrile 1.0 1.4 }NO2 nitro 1.0 1.0 }CONH2 primary amide 1.0 1.0 }CONH} secondary amide 1.0 1.0 }SH 1.0 1.0 }S} nonring 1.0 1.0 }S} ring 1.0 1.0 nonring 1.0 1.0 }SO2 }F on aliph. C 1.0 1.0 }F on olefinic C 1.0 1.0 }F on ring C 1.0 1.0 }Cl 1.0 2.0 }Br 1.0 1.0 }I 1.0 1.0 *Chickos, J. S., et al., J. Org. Chem., 56 (1991): 927. C3 C4 Ds 18.9 1.0 1.0 1.0 26.4 1.0 1.0 1.0 1.13 16.57 1.09 1.34 3.14 −1.88 19.66 14.90 3.68 16.23 15.48 −2.18 1.84 −15.90 −17.07 1.67 7.32 9.62 17.36 26.19 −0.42 17.99 7.20 2.18 3.26 14.73 13.01 15.90 8.37 17.95 16.95 1.88 1.0 1.72 1.0 1.0 1.0 0.36 1.0 1.0 1.0 2.0 1.0 1.0 1.0 1.0 1.93 0.82 from DIPPR 801 database DHfus = (Tm/K)(a + b) J/mol = (158.38)(0 + 58.51) J/mol = 9.27 kJ/mol This value is 5 percent higher than the DIPPR 801 recommended value of 8.86 kJ/mol. Ds Total 3.51 TABLE 2-163 of DH fus Tm = 158.38 K 58.51 Enthalpy of Sublimation The enthalpy (heat) of sublimation DHsub is the difference between the molar enthalpies of the equilibrium vapor and solid along the sublimation curve below the triple point. The effects of pressure on DHsub and melting temperature are very small so that Tt and the normal melting point are nearly equal and DHsub(Tt) = DHυ (Tt) + DHfus(Tt) (2-45) Equation (2-45) can be used to estimate DHsub at the triple point if DHυ is accurately known at Tt. Because DHυ is usually obtained from Eq. (2-37), DHυ(T) correlations may be less accurate near Tt where P*(Tt) is very small and difficult to measure. In this case, it is better to estimate DHsub directly by using the following recommended method. DHsub is only a weak function of temperature and can generally be treated as a constant from the triple point temperature down to the first solid-solid phase transition. Recommended Method Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, Int. J. Thermophys. 25 (2004): 337. Classification: QSPR and group contributions. Expected uncertainty: 6 percent. Applicability: Organic compounds for which group contributions have been regressed. Input data: Molecular structure and radius of gyration RG. Description: N N N R n ∆H sub (Tt ) = 698.04 + 3.83798 × 1012  G  + ∑ ni ai + ∑ ni2βi + ∑ i f i  m  i =1 RK n i =1 x i =1 (2-46) where ai = GC values from Table 2-164 bi = nonlinear corrections for >CH2 and Ar—CH = groups fi = halogen corrections nx = total number of all halogen and hydrogen atoms attached to C and Si atoms Example Calculate DHsub and the solid vapor pressure for 1,2,3-trichlorobenzene at 301.15 K. Structure: PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-164 Group Contributions and Corrections* for DHsub Group Description 736.5889 561.3543 111.0344 −800.517 572.6245 541.2918 117.9504 626.7621 348.8092 763.284 1317.056 911.2903 970.4474 3278.446 2402.093 Nonlinear terms >C=O }COO} }COOH }NH2 }NH} >N} }NO2 }SH }S} }SS} }F }Cl }Br >Si< >Si(O})} 9.5553 −2.21614 Description ai ketone ester acid primary amine sec. amine tertiary amine nitro thiol/mercaptan sulfide disulfide fluoride chloride bromide silane siloxane 1816.093 2674.525 5006.188 2219.148 1561.222 325.9442 3661.233 1921.097 1930.84 2782.054 626.4494 1243.445 669.9302 −83.7034 −16.0597 Halogen correction terms bi methylene aromatic C >CH2 Ar}CH= Group ai methyl methylene secondary C tertiary C terminal alkene alkene substituted alkene aromatic C subst. aromatic C furan O pyridine N thiophene S ether alcohol aldehyde }CH3 >CH2 >CH} >C< CH2= }CH= >C= Ar }CH= Ar >C= Ar }O} Ar }N= Ar }S} }O} }OH }COH 2-337 fi F fraction Cl fraction Br fraction }F }Cl }Br −1397.4 −1543.66 5812.49 *Goodman, B., et al., Int. J. Thermophys., 25 (2004): 337. Group contributions: 2 Linear groups  A4 /T   A2 /T  C Po = A0 + A1    + A3   cosh(A4 /T )   sinh(A2 /T )  Nonlinear and correction terms Group ni ai Group ni bi Ar}CH= 3 626.7621 Ar }CH= 3 −2.21614 Ar >C= 3 348.8092 }Cl 3 }Cl 3 nx 6 1243.445 (2-48) fi −1543.66 and a polynomial form (generally fourth-order) ∑ ni ai = 6657.049 C Po = 4 ∑ AT i (2-49) i i = 0 i Input data: The value of RG from the DIPPR 801 database is 4.455 × 10−10 m. Calculation using Eq. (2-46): ∆H sub (Tt ) = 698.04 + (3.838 × 1012 )(4.455 × 10 −10 ) RK 3 + 6657.05 + (3 2 )(−2.21614) +   (−1543.66)  6  kJ  kJ = 68.78 ∆H sub (Tt ) = (8273 K)  0.008314 mol ⋅ K  mol  The estimated value is 5.6 percent above the DIPPR 801 recommended value of 65.11 kJ/mol. Estimate the solid vapor pressure at 301.15 K: The solid vapor pressure can be calculated from Eq. (2-30) by using the estimated DHsub and one additional solid vapor pressure point. In this example the triple point temperature and vapor pressure (Tt = 325.65 K; Pt* = 182.957 Pa) from the DIPPR 801 database are used in Eq. (2-30): ln 2 Ideal gas heat capacities may also be estimated from several techniques, of which two of the most accurate and commonly used are recommended here. Recommended Method 1 Statistical mechanics. Reference: Rowley, R. L., Statistical Mechanics for Thermophysical Property Calculations, Prentice-Hall, Englewood Cliffs, N.J., 1994. Classification: Theory and computational chemistry. Expected uncertainty: 0.2 percent if vibrational frequencies (or their characteristic temperatures) are experimentally available; accuracy depends upon model chemistry if frequencies are determined from computational chemistry, but generally within 3 percent. Applicability: Ideal gases. Input data: 3nA − 6 + d vibrational frequencies nj, or the corresponding characteristic vibrational temperatures Qj. The two are related by (2-50) Qj = hnj /k Description: For harmonic frequencies, the rigorous temperature dependence of C Po is given by 68.78 kJ/mol P∗  1 − 325.65  = −2.067 =   182.957 Pa [0.008314 kJ/(mol ⋅ K)](325.65 K)  301.15  2 P* = (182.957 Pa) [exp(−2.067)] = 23.16 Pa The estimated value is 0.3 percent above the DIPPR 801 recommended value of 23.09 Pa. HEAT CAPACITY Θ /T  C Po 8 − δ 3 n A −6+δ  Θ j   e j = + ∑    Θ j /T 2    R 2 T − e ( 1) j =1   0 δ = 1 nonlinear linear (2-51) Example Calculate the ideal gas heat capacity of ammonia at 300 K. The isobaric heat capacity CP is defined as the energy required to change the temperature of a unit mass (specific heat) or mole (molar heat capacity) of the material by one degree at constant pressure. Typical units are J/(kg ⋅ K). Gases The isobaric heat capacity of a gas is related rigorously to the ideal gas value C Po by 2 P ∂ V  C P = C Po − T ∫  2  dP 0  ∂T  P (2-47) The second term, giving the deviation of the real fluid heat capacity from the ideal gas value, can be neglected at low to moderate pressures, or it can be calculated directly from an appropriate EoS. Ideal gas heat capacities are available from several sources (DIPPR, JANAF, TRC, and SWS). Two common correlating equations for C Po are the Aly-Lee equation [Aly, F. A., and L. L. Lee, Fluid Phase Equilib., 6 (1981): 169] Structure: Input data: McQuarrie (McQuarrie, D. A., Statistical Mechanics, Harper & Row, New York, 1976) gives the following 3nA − 6 + d = 12 − 6 + 0 = 6 characteristic vibrational temperatures (in K): 1360, 2330, 2330, 4800, 4880, and 4880. Alternatively, a computational chemistry package gives the following scaled frequencies for HF/6-31G+ model chemistry (1013 Hz): 3.24, 4.97, 4.97, 9.90, 10.26, and 10.26. Calculation: The table on the left uses the experimental Q values to determine the individual terms in the summation of Eq. (2-51). The table on the right uses the scaled frequencies from computational chemistry software and Eq. (2-50) to obtain Q values and the individual terms in Eq. (2-51). 2-338 PHYSICAL AnD CHEMICAL DATA HF/6-31G+ scaled frequencies* Experimental frequencies Q/K 1360 2330 2330 4800 4880 4880 Q/(300 K) 4.533 7.767 7.767 16.000 16.267 16.267 Term nscaled/10 Hz Q/K 0.2256 0.0256 0.0256 0.0000 0.0000 0.0000 3.24 4.97 4.97 9.90 10.26 10.26 1555.0 2385.3 2385.3 4751.4 4924.2 4924.2 13 Q/(300 K) 5.183 7.951 7.951 15.838 16.414 16.414 Term 0.1524 0.0223 0.0223 0.0000 0.0000 0.0000 Sum: 0.2768 Sum: 0.1970 *Empirical scaling factors have been developed for each model chemistry to help correct theoretical frequencies for anharmonic effects [Scott, A. P., and L. Radom, J. Phys. Chem., 100 (1996): 16502]. Danner, AIChE J., 23 (1977): 944] and thermodynamic differentiation. The Ruzicka-Domalski method is generally accurate at low temperature, but the cubic behavior can overestimate the temperature rise at higher temperatures. The Lee-Kesler method is accurate for nonpolar and slightly polar fluids, but has less accuracy for strongly polar or associating fluids. Recommended Method 1 Ruzicka-Domalski. References: Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619. Classification: Group contributions. Expected uncertainty: 4 percent. Applicability: Organic compounds for which group values are available. Input data: Molecular structure and Table 2-166 values. Description: Groups are summed to find the temperature coefficients for a cubic polynomial correlation: From experimental frequencies:  T   T  = A+ B   + D  100 K  R    100 K  Cp 8 J  J C Po =  + 0.2768  R = (4.2768)  8.3143  = 35.56   2 mol ⋅ K  mol ⋅ K N A = ∑ ni ai From computational chemistry frequencies: i =1 8 J  J C Po =  + 0.197  R = (4.197)  8.3143  = 34.90   2 mol ⋅ K  mol ⋅ K The value calculated from experimental frequencies is 0.1 percent lower than the DIPPR 801 recommended value of 35.61 J/(mol ⋅ K); the value calculated from frequencies generated from computational chemistry software is 2.0 percent lower than the DIPPR 801 value. Recommended Method 2 Benson method as implemented in CHETAH program. References: Benson, S. W., et al., Chem. Rev., 69 (1969): 279; CHETAH Version 8.0: The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16). Classification: Group contributions. Expected uncertainty: 4 percent. Applicability: Ideal gases of organic compounds. Input data: Table 2-165 group values at the seven specified temperatures. Description: Groups are summed at each individual temperature: N C Po = ∑ ni ⋅ (C op )i (2-52) N B = ∑ ni bi i =1 2 (2-53) N D = ∑ ni di (2-54) i =1 where ni = number of occurrences of group i and ai, bi, di = individual group contributions. Example Estimate the liquid heat capacity for 2-methyl-2-propanol at 340 K. Structure: Group contributions: Group ni C } (3C, O) (alcohol) O } (H)(C) C } (3H)(C) 1 1 3 ai −44.690 12.952 3.8452 Sum −20.202 i =1 where ni = number of occurrences of group i and (C Po )i = individual group contribution. Either Eq. (2-48) or Eq. (2-49) can be used to interpolate between the discrete temperatures. J  C p =  8.3143   mol ⋅ K  = 254.16 Example Calculate the ideal gas heat capacity of isoprene (2-methyl-1,3-butadiene) at 400 K. Structure: bi di 31.769 −10.145 −0.33997 −4.8791 2.6261 0.19489 20.604 −1.668 2   304  − 1.668  340        −20.202 + 20.604     100  100  J mol ⋅ K This value is 0.7 percent higher than the DIPPR 801 recommended value of 252.40 J/(mol ⋅ K). Group identification and values: Group No. Value, J/(mol ⋅ K) Contribution, J/(mol ⋅ K) =CH2 2 26.62 =C}(2C) 1 19.3 53.24 19.3 }CH3}(=C) 1 32.82 32.82 =CH}(C) 1 21.05 Recommended Method 2 Lee-Kesler. References: [PGL5] Classification: Corresponding states. Expected uncertainty: 4 percent. Applicability: Organic compounds other than those that are strongly polar or associate. Input data: Tc, w, and the ideal gas heat capacity at the same temperature. Description: The isobaric liquid heat capacity is calculated at the reduced temperature Tr using 21.05 Total Cp 126.41 R = C op R + 1.586 +  6.3(1 − Tr )1/3 0.4355  0.49 + ω  4.2775 + +  1 − Tr  1 − Tr Tr  (2-55) The value of 126.4 J/(mol ⋅ K) is 3.1 percent below the DIPPR 801 recommended value of 130.4 J/(mol ⋅ K). Example Calculate the isobaric liquid heat capacity for 1,4-dioxane at 320 K. Liquids Liquid isobaric heat capacity increases with increasing temperature, although a minimum occurs near the triple point for many compounds. Usually liquid heat capacity is correlated as a function of temperature with a polynomial equation; a third-order polynomial is usually adequate. Estimation of liquid heat capacity can be done by using a number of methods [Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619; Chueh, C. F., and A. C. Swanson, Chem. Eng. Prog., 69, 7 (1973): 83; Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510; Tarakad, R. R., and R. P. Auxiliary data: From the DIPPR 801 database: Tc = 597.0 K, w = 0.2793, and C /R = 11.94. The reduced temperature is therefore Tr = (320 K)/(597.0 K) = 0.536. From Eq. (2.55), o p Cp R = 11.94 + 1.586 + 1/3  0.49 6.3 (1 − 0.536 ) 0.4355  + (0.2793)  4.2775 + +  = 18.58 1 − 0.536 0.536 1 − 0.536   and Cp = 154.5 J/(mol ∙ K). This is 4.6 percent below the DIPPR recommended value of 162.0 J/(mol ∙ K). PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165 2-339 Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group 298 K 400 K 500 K 600 K 800 K 1000 K 1500 K 45.17 45.17 45.17 45.17 45.21 45.17 45.17 45.17 45.17 45.17 45.17 45.17 45.17 45.17 54.5 54.5 54.5 54.5 54.42 54.54 54.54 54.54 54.54 54.5 54.5 54.5 54.5 54.5 61.83 61.83 61.83 61.83 61.95 61.83 61.83 61.83 61.83 61.83 61.83 61.83 61.83 61.83 73.59 73.59 73.59 73.59 73.67 73.59 73.59 73.59 73.59 73.59 20.59 19.42 17.12 20.59 38.51 37.67 35.79 28.76 38.93 53.16 22.35 20.93 19.25 22.35 39.77 39.35 38.3 31.27 40.18 56.93 23.02 21.89 20.59 23.02 40.6 40.18 39.85 33.32 41.02 59.86 24.28 23.32 26.58 24.28 37.8 39.14 38.17 40.18 40.98 40.98 63.71 40.18 41.9 39.77 38.01 39.35 39.47 36.84 38.34 41.73 39.72 41.36 40.1 38.72 40.85 45.46 46.34 43.2 47.3 49.35 49.77 72.58 47.3 48.1 46.46 45.46 46.46 46.5 44.58 45.84 51.32 46.97 48.3 47.17 45.92 50.98 51.74 51.65 47.26 52.74 55.25 55.25 78.82 52.74 52.49 51.07 51.03 51.49 51.61 49.94 51.15 59.23 52.24 53.29 52.49 51.28 59.48 36.63 35.12 32.57 35.16 36.54 35.5 36.38 34.28 33.7 31.77 40.73 41.11 38.09 40.18 41.06 40.35 41.44 39.6 38.97 35.41 42.9 43.99 41.44 42.7 43.53 43.11 44.24 42.65 42.07 38.97 25.53 36.75 27.17 19.97 33.07 32.23 27.17 27.63 34.11 34.58 33.99 27.63 38.47 30.43 25.2 35.58 34.32 30.43 31.56 36.5 37.34 36.71 28.46 37.51 31.69 26.71 35.58 34.49 31.23 33.32 33.91 37.51 36.67 CH3 Groups CH3}(Cb) CH3}(CO) CH3}(Ct) CH3}(C) CH3}(N) CH3}(O) CH3}(PO) CH3}(P) CH3}(P=N) CH3}(Si) CH3}(SO2) CH3}(SO) CH3}(S) CH3}(=C) 25.91 25.91 25.91 25.91 25.95 25.91 25.91 25.91 25.91 25.91 25.91 25.91 25.91 25.91 32.82 32.82 32.82 32.82 32.65 32.82 32.82 32.82 32.82 32.82 32.82 32.82 32.82 32.82 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 39.35 73.59 Ct Groups Ct}(Cb) Ct}(Ct) Ct}(C) Ct}(=C) CtBr CtCl CtF CtH CtI Ct(CN) 10.76 14.82 13.1 10.76 34.74 33.07 28.55 22.06 35.16 43.11 14.82 16.99 14.57 14.82 36.42 35.16 31.65 25.07 36.84 47.3 14.65 18.42 15.95 14.65 37.67 36.42 33.99 27.17 38.09 50.65 41.77 37.04 64.04 CH2 Groups CH2}(2CO) CH2}(2C) CH2}(2O) CH2}(2=C) CH2}(Cb,O) CH2}(Cb,SO2) CH2}(Cb,S) CH2}(Cb,=C) CH2}(C,Cb) CH2}(C,CO) CH2}(C,Ct) CH2}(C,N) CH2}(C,O) CH2}(C,SO2) CH2}(C,SO) CH2}(C,S) CH2}(C,=C) CH2}(=C,O) CH2}(=C,SO2) CH2}(=C,SO) CH2}(=C,S) 16.03 23.02 11.85 19.67 15.53 15.53 38.09 19.67 24.45 25.95 20.72 21.77 20.89 17.12 19.05 22.52 21.43 19.51 20.34 18.42 22.23 26.66 29.09 21.18 28.46 26.26 27.5 49.02 28.46 31.85 32.23 27.46 28.88 28.67 24.99 26.87 29.64 28.71 29.18 28.51 26.62 28.59 CH}(2C,Cb) CH}(2C,CO) CH}(2C,Ct) CH}(2C,N) CH}(2C,O) CH}(2C,SO2) CH}(2C,S) CH}(2C,=C) CH}(3C) CH}(C,2O) 20.43 18.96 16.7 19.67 20.09 18.5 20.3 17.41 19 22.02 27.88 25.87 23.48 26.37 27.79 26.16 27.25 24.74 25.12 23.06 C}(2C,2O) C}(3C,Cb) C}(3C,CO) C}(3C,Ct) C}(3C,N) C}(3C,O) C}(3C,SO2) C}(3C,SO) C}(3C,S) C}(3C,=C) C}(4C) 19.25 19.72 9.71 0.33 18.42 18.12 9.71 12.81 19.13 16.7 18.29 19.25 28.42 18.33 7.33 25.95 25.91 18.33 19.17 26.25 25.28 25.66 32.15 34.53 31.48 35.16 34.66 34.66 57.43 35.16 37.59 36.42 33.19 34.74 34.74 31.56 33.28 36 34.83 36.21 34.95 29.05 34.45 59.65 60.28 60.28 57.6 59.44 61.11 60.11 CH Groups 33.07 30.89 28.67 31.81 33.91 31.65 32.57 30.72 30.01 27.67 44.7 46.55 47.22 46.76 C Groups 23.02 33.86 23.86 14.36 30.56 30.35 23.86 20.26 31.18 31.1 30.81 31.94 34.45 33.99 (Continued ) 2-340 PHYSICAL AnD CHEMICAL DATA TABLE 2-165 Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued ) Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group 298 K 400 K 500 K 600 K 800 K 1000 K 1500 K 25.32 Aromatic (Cb and Cp Groups) Cb}(Cb) Cb}(CO) Cb}(Ct) Cb}(C) Cb}(N) Cb}(O) Cb}(Si) Cb}(SO2) Cb}(SO) Cb}(S) Cb}(=C) Cb}(=Nim) CbBr CbCl CbF CbH CbI Cb(CHN2) Cb(CN) Cb(N3) Cb(NCO) Cb(NCS) Cb(NO2) Cb(SO2OH) Cp}(2Cb,Cp) Cp}(3Cp) Cp}(Cb,2Cp) 13.94 11.18 15.03 11.18 16.53 16.32 11.18 11.18 11.18 16.32 15.03 16.53 32.65 30.98 26.37 13.56 33.49 47.3 41.86 34.74 55.25 32.23 38.93 65.42 12.56 8.37 12.56 17.66 13.14 16.62 13.14 21.81 22.19 13.14 13.14 13.14 22.19 16.62 21.81 36.42 35.16 31.81 18.59 37.25 20.47 15.4 18.33 15.4 24.86 25.95 15.4 15.4 15.4 25.95 18.33 24.86 39.35 38.51 35.58 22.85 40.18 22.06 17.37 19.76 17.37 26.45 27.63 17.37 17.37 17.37 27.63 19.76 26.45 41.44 40.6 38.09 26.37 41.44 24.11 20.76 22.1 20.76 27.33 28.88 20.76 20.76 20.76 28.88 22.1 27.33 43.11 42.7 41.02 31.56 43.11 24.91 22.77 23.48 22.77 27.46 28.88 22.77 22.77 22.77 28.88 23.48 27.46 43.95 43.53 42.7 35.2 43.95 48.14 52.74 55.67 59.86 62.79 64.04 70.32 74.51 79.95 82.88 50.23 79.49 15.49 12.14 15.49 59.44 84.51 17.58 14.65 17.58 66.56 97.61 19.25 16.74 19.25 76.18 109.25 21.77 19.67 21.77 80.37 113.31 23.02 21.35 23.02 =C}(2C) =C}(CO,O) =C}(C,Cb) =C}(C,CO) =C}(C,O) =C}(C,SO2) =C}(C,S) =C}(C,=C) =CC}(=C,O) =CH}(Cb) =CH}(CO) =CH}(Ct) =CH}(C) =CH}(O) =CH}(SO2) =CH}(S) =CH}(=C) =CH2 =C= 17.16 23.4 18.42 22.94 17.16 15.49 14.65 18.42 18.42 18.67 31.73 18.67 17.41 17.41 12.72 17.41 18.67 21.35 16.32 19.3 29.3 22.48 29.22 19.3 26.04 14.94 22.48 22.9 24.24 37.04 24.24 21.05 21.05 19.55 21.05 24.24 26.62 18.42 22.02 32.44 25.87 31.98 22.02 38.51 17.12 25.87 26.29 31.06 40.31 31.06 27.21 27.21 28.63 27.21 31.06 35.58 20.93 24.28 33.57 27.21 33.53 24.28 44.62 18.46 27.21 27.21 34.95 43.45 34.95 32.02 32.02 32.94 32.02 34.95 42.15 22.19 25.45 34.03 27.71 34.32 25.45 47.47 20.93 27.71 27.71 37.63 46.21 37.63 35.37 35.37 36.29 35.37 37.63 47.17 23.02 O}(2C) O}(2O) O}(2=C) O}(Cb,CO) O}(CO,O) O}(C,Cb) O}(C,CO) O}(C,O) O}(C,=C) O}(=C,CO) OH}(Cb) OH}(CO) OH}(C) OH}(O) O(CN)}(Cb) O(CN)}(C) O(CN)}(=C) O(NO2)}(C) O(NO)}(C) (CO)Cl}(C) (CO)H}(Cb) (CO)H}(CO) 14.23 15.49 14.02 8.62 1.51 2.6 11.64 15.49 12.72 6.03 18 15.95 18.12 21.64 34.74 41.86 54.42 39.93 38.09 42.28 33.53 28.13 15.49 15.49 16.32 11.3 6.28 3.01 15.86 15.49 13.9 12.47 18.84 20.85 18.63 24.24 15.49 15.49 17.58 13.02 9.63 4.94 18.33 15.49 14.65 16.66 20.09 24.28 20.18 26.29 15.91 15.49 18.84 14.32 11.89 7.45 19.8 15.49 15.49 18.79 21.77 26.54 21.89 27.88 18.42 17.58 21.35 16.24 15.28 11.89 20.55 17.58 17.54 20.8 25.12 30.01 25.2 29.93 19.25 17.58 22.6 17.5 17.33 14.99 21.05 17.58 18.96 21.77 27.63 32.44 27.67 31.44 48.3 43.11 46.04 44.2 32.78 55.5 46.88 49.39 48.77 37.25 65.3 50.23 51.9 59.48 41.4 68.61 55.67 55.67 68.56 47.84 72.75 58.18 57.76 74.01 50.73 24.07 25.03 25.03 24.07 40.73 85.81 =C=,=C},=CH}Groups 20.89 31.31 24.82 31.02 20.89 33.32 16.03 24.82 24.82 28.25 38.8 28.25 24.32 24.32 24.82 24.32 28.25 31.44 19.67 26.62 28.13 28.13 41.77 41.77 40.27 40.27 41.77 55.21 23.86 Oxygen Groups 20.09 20.09 37.34 33.65 34.2 60.69 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165 2-341 Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued ) Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group 298 K 400 K 500 K 600 K 800 K 1000 K 40.52 40.52 40.52 48.77 21.05 46.71 46.71 46.71 63.12 26.32 51.07 51.07 51.07 74.68 29.54 55.25 85.64 49.52 68.98 82.88 77.86 46.71 57.85 77.44 74.93 68.52 57.3 57.35 59.86 56.09 54.42 59.9 58.18 56.72 53.75 68.23 53.41 46.88 69.07 48.39 63.21 54.42 74.17 56.3 59.86 59.02 56.51 58.18 55.67 53.16 47.72 46.88 43.95 48.56 56.93 88.66 52.07 70.99 86.23 82.88 52.03 63.46 84.14 80.79 76.06 65.26 64.88 67.81 64.04 63.62 68.15 66.14 64.25 58.81 74.93 59.82 56.09 89.66 53.12 71.24 87.9 85.39 53.24 65.84 87.9 83.72 79.99 69.95 70.32 73.67 69.9 69.49 73.8 72 69.36 61.62 79.53 64.38 74.93 54.83 69.9 59.31 79.7 57.72 62.37 61.53 59.86 61.11 59.44 57.76 51.9 51.49 49.39 52.74 78.28 58.64 74.51 61.95 81.58 56.93 63.62 62.79 61.53 62.79 61.53 60.69 55.25 54.83 53.16 55.67 17.29 26.16 34.45 27.33 29.05 24.99 20.3 20.93 17.66 45.63 21.35 30.93 28.59 13.94 26.29 14.57 29.3 33.78 34.7 33.78 38.93 22.35 28.34 21.89 28.42 37.8 28.59 30.93 27.46 22.1 22.94 20.05 50.9 28.3 33.28 33.07 16.91 30.1 17.75 32.65 39.39 41.69 39.39 43.95 23.82 28.71 23.4 28.76 38.47 34.91 38.68 27.92 22.14 27.08 21.43 53.54 32.98 34.28 36.21 18.21 32.36 18.96 34.74 43.83 46.97 43.83 48.14 23.9 29.51 1500 K Oxygen Groups (CO)H}(C) (CO)H}(N) (CO)H}(O) (CO)H}(=C) CO}(Cb)(O) 29.43 29.43 29.43 24.32 9.12 32.94 32.94 32.94 30.22 11.51 CBr}(3C) CBr3}(C) CCl}(3C) CCl2}(2C) CCl3}(C) CClF2}(C) CF}(3C) CF2}(2C) CF3}(Cb) CF3}(C) CF3}(S) CH2Br}(Cb) CH2Br}(C) CH2Br}(=C) CH2Cl}(C) CH2F}(C) CH2I}(Cb) CH2I}(C) CH2I}(O) CHBr}(2C) CHBrCl}(C) CHCl}(2C) CHCl}(C,O) CHCl2}(C) CHF}(2C) CHF2}(C) CHI}(2C) CHI2}(C) CI}(3C) =CBr2 =CBrCl =CBrF =CCl2 =CClF =CF2 =CHBr =CHCl =CHF =CHI 39.35 72.12 36.96 51.07 68.23 57.35 28.46 39.01 52.32 53.16 41.36 30.51 38.09 40.6 37.25 33.91 33.91 38.51 34.41 37.38 51.9 35.45 37.67 50.65 30.56 41.44 38.64 56.93 41.15 51.49 50.65 45.21 47.72 43.11 40.6 33.91 33.07 28.46 36.84 47.72 78.65 43.87 62.29 75.35 67.39 37.09 46.97 64.04 62.79 54.46 46.46 46.04 47.72 44.79 41.86 45.17 46.04 43.91 44.62 58.6 42.7 41.44 58.6 37.84 50.23 45.67 63.42 49.18 55.25 53.16 50.23 52.32 48.97 46.04 39.77 38.51 35.16 41.86 CH2(N3)}(C) =CH(N3) N}(2C,Cb) N}(2C,CO) N}(2C,SO2) N}(2C,SO) N}(2C,S) N}(3C) N}(Cb,2CO) N}(C,2CO) Nb pyrid}N NF2}(C) NH}(2Cb) NH}(2CO) NH}(2C) NH}(Cb,CO) NH}(C,Cb) NH}(C,CO) NH}(C,N) NH2}(Cb) NH2}(CO) NH2}(C) NH2}N =Naz}(C) =Naz}(N) 64.46 54.42 2.6 13.02 25.2 17.58 15.99 14.57 4.1 4.48 10.88 26.5 9.04 15.03 17.58 2.39 15.99 2.76 20.09 23.94 17.04 23.94 25.53 11.3 8.87 36.92 36.92 36.92 39.77 16.65 Halide Groups 52.74 82.92 47.72 66.76 79.95 73.25 42.7 53.24 72 68.65 62.08 52.2 52.74 54.42 51.49 50.23 53.7 54 51.19 50.06 63.3 48.89 43.95 64.46 43.83 57.35 50.9 69.61 54.08 58.18 56.51 53.58 55.67 52.74 50.23 44.37 43.11 39.77 45.63 Nitrogen Groups 8.46 19.17 26.58 24.61 21.64 19.09 12.81 12.99 13.48 34.58 13.06 23.19 21.81 6.32 20.47 6.49 24.28 27.25 24.03 27.25 30.98 17.16 17.5 13.69 23.52 31.56 25.62 25.99 22.73 17.71 18.04 15.95 40.9 17.29 28.05 25.66 9.96 23.9 10.3 27.21 30.64 29.85 30.64 35.16 20.59 23.06 27.21 39.97 37.67 51.4 51.4 55.25 (Continued ) 2-342 PHYSICAL AnD CHEMICAL DATA TABLE 2-165 Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued ) Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group 298 K 400 K 500 K 600 K 800 K 1000 K 1500 K Nitrogen Groups =NazH =Nim}(Cb) =Nim}(C) =NimH 18.33 12.56 10.38 12.35 20.47 22.77 24.86 28.34 31.06 13.98 19.17 16.53 27 17.96 32.27 19.21 38.22 19.25 41.52 S}(2Cb) S}(2C) S}(2S) S}(2=C) S}(Cb,S) S}(C,Cb) S}(C,S) S}(C,=C) SH}(Cb) SH}(CO) SH}(C) SO}(2Cb) SO}(2C) SO2}(2Cb) SO2}(2C) SO2}(2=C) SO2}(Cb,SO2) SO2}(Cb,=C) SO2}(C,Cb) S(CN)}(Cb) S(CN)}(C) S(CN)}(=C) 8.37 20.89 19.67 20.05 12.1 12.64 21.89 17.66 21.43 31.94 24.53 23.94 37.17 34.99 48.22 48.22 41.06 41.4 41.61 39.77 46.88 59.44 8.41 20.76 20.93 23.36 14.19 14.19 22.69 21.26 22.02 33.86 25.95 38.05 41.98 46.17 50.1 50.1 48.14 48.14 48.14 11.47 21.22 21.77 26.33 17.37 16.91 23.06 24.15 25.24 34.2 28.38 47.93 45.17 62.54 59.77 59.77 61.66 61.16 60.74 15.91 22.65 22.19 33.24 20.01 19.34 22.52 24.57 29.26 35.58 30.56 47.97 45.96 66.39 64.38 64.38 65.76 65.8 65.38 19.72 23.98 22.6 40.73 21.35 20.93 21.43 24.57 32.82 34.49 32.27 47.09 46.76 66.81 66.47 66.47 67.1 66.64 66.64 113.23 −39.64 134.95 198.62 219.72 47.72 61.95 52.7 45.21 50.19 80.79 36.21 61.62 41.4 72.42 43.11 51.90 51.49 56.93 56.93 64.04 70.74 80.79 85.81 66.22 54 63.67 101.3 46.71 74.47 55.84 77.52 60.69 74.17 117.2 53.96 83.72 66.39 86.48 66.14 82.08 129.76 58.81 90.46 73.75 99.58 72 92.84 146.09 64.92 99.54 82.92 108.41 79.11 99.2 156.13 67.77 104.48 87.32 50.23 56.09 61.11 68.65 73.67 63.21 69.28 72.83 78.19 80.37 84.76 90.41 93.51 97.11 98.74 −11.05 −7.03 −7.95 −10.88 −12.64 −16.37 −14.56 −7.87 −6.2 −7.41 −9.63 18.09 −19.25 −10.88 −5.78 −5.57 −6.78 −8.63 24.35 −23.86 0.84 −10.97 −5.44 −5.99 −6.91 −15.91 −17.33 −12.56 −3.77 −16.74 −15.91 −2.89 −15.32 −15.32 −6.4 4.6 −1.21 −5.36 −11.72 −12.26 −10.88 9.21 −12.01 −11.3 3.6 −18.46 −18.46 −1.8 9.21 0.33 −4.35 −8.08 −9.46 −10.05 17.58 −9.08 −7.53 5.4 −23.32 −23.32 35.33 Sulfur Groups 9.38 21.01 21.35 23.15 15.57 15.53 23.06 23.27 23.32 33.99 27.25 40.6 43.95 56.72 55.88 55.88 56.59 55.88 56.3 Boron and Silicon Groups Si}(4C) SiH3}(C) 154.5 171.2 252.91 Monovalent Ligands CH2(CN)}(C) CH2(NCS)}(C) CH2(NO2)}(C) CH(CN)}(2C) CH(NO2)}(2C) CH(NO2)2}(C) C(CN)}(3C) C(CN)2}(2C) C(NO2)}(3C) =CH(CHN2) =CH(CN) =CH(NCS) =CH(NO2) =C(CN)2 105.9 3,4 Member Ring Corrections cyclobutane ring cyclobutene ring cyclopropane ring ethylene oxide ring ethylene sulfide ring thietane ring trimethylene oxide ring −19.3 −10.59 −12.77 −8.37 −11.93 −19.21 −19.25 −16.28 −9.17 −10.59 −11.72 −10.84 −17.5 −20.93 1,4 dioxane ring cyclohexane ring cyclohexene ring cyclopentadiene ring cyclopentane ring cylopentene ring furan ring piperidine ring pyrrolidine ring tetrahydrofuran ring thiacyclohexane ring thiolane ring thiophene ring −19.21 −24.28 −17.92 −14.44 −27.21 −25.03 −20.51 −24.7 −25.83 −25.12 −26.04 −20.51 −20.51 −20.8 −17.16 −12.72 −11.85 −23.02 −22.39 −18 −19.67 −23.36 −24.28 −17.83 −19.55 −19.55 −13.14 −7.91 −8.79 −12.56 −11.13 −16.37 −17.58 −2.8 −5.11 −6.36 5,6 Member Ring Corrections −15.91 −12.14 −8.29 −8.96 −18.84 −20.47 −15.07 −12.14 −20.09 −20.09 −9.38 −15.4 −15.4 13.81 3.39 −1.55 −4.52 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-165 2-343 Benson* and CHETAH† Group Contributions for Ideal Gas Heat Capacity (Continued ) Table-specific nomenclature: Cb = carbon in benzene ring; Ct = carbon with a triple bond, (=C) = carbon with a double bond; Cp = carbon in fused ring; Naz = azide; Nim = imino. Group 298 K 400 K 500 K 600 K 800 K 1000 K −1.63 −1.63 −1.63 −1.63 −1.63 −1.26 2.93 3.68 −1.09 −1.09 −1.09 −1.09 −1.09 1500 K 7 and 8 Member Ring Corrections cycloheptane ring cyclooctane ring −38.01 −44.16 Gauche and 1,5 Repulsion Corrections but-2-ene structure C}C=C}C but-3-ene structure C}C}C=C cis- between 2 t-butyl groups cis- involving 1 t-butyl group cis-(not with t-butyl group) ortho- between Cl atoms ortho- between F atoms other ortho- (nonpolar-nonpolar) −5.61 −5.61 −5.61 −5.61 −5.61 −2.09 −4.56 −4.56 −4.56 −4.56 −4.56 5.02 −0.84 5.65 4.69 −3.39 −3.39 −3.39 −3.39 −3.39 2.09 −0.42 5.44 −2.55 −2.55 −2.55 −2.55 −2.55 −2.51 1.26 4.9 2.76 −0.21 *Benson, S. W., et al., Chem. Rev., 69 (1969): 279. † CHETAH Version 8.0: The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16). TABLE 2-166 Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method* Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond; Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom. Group Definition a b d T range (K) Group Definition Hydrocarbon Groups C}(3H,C) C}(2H,2C) C}(H,3C) C}(4C) =C}(2H) =C}(H,C) =C}(2C) =C}(H,=C) =C}(C,=C) C}(3H,=C) C}(2H,C,=C) C}(H,2C,=C) C}(3C,=C) C}(2H,2=C) Ct}(H) Ct}(C) =C= Ct}(Cb) Cb}(H) Cb}(C) Cb}(=C) Cb}(Cb) C}(2H,C,Ct) C}(3H,Ct) C}(3H,Cb) C}(2H,C,Cb) C}(H,2C,Cb) C}(3C,Cb) C}(2H,2Cb) C}(H,3Cb) =C}(H,Cb) =C}(C,Cb) Cp}(Cp,2Cb) Cp}(2Cp,Cb) Cp}(3Cp) 3.8452 2.7972 −0.42867 −2.9353 4.1763 4.0749 1.9570 3.6968 1.0679 3.8452 2.0268 −0.87558 −4.8006 1.4973 9.1633 1.4822 3.0880 12.377 2.2609 1.5070 −5.7020 5.8685 2.0268 3.8452 3.8452 1.4142 −0.10495 1.2367 −18.583 −46.611 3.6968 1.0679 −3.5572 −11.635 26.164 −0.33997 −0.054967 0.93805 1.4255 −0.47392 −1.0735 −0.31938 −1.6037 −0.50952 −0.33997 −0.20137 0.82109 2.6004 −0.46017 −4.6695 1.0770 −0.62917 −7.5742 −0.2500 −0.13366 5.8271 −0.86054 −0.20137 −0.33997 −0.33997 0.56919 1.0141 −1.3997 11.344 24.987 −1.6037 −0.50952 2.8308 6.4068 −11.353 15.423 −8.9527 8.5430 10.880 9.6663 9.6663 −2.0600 6.3944 10.784 0.037620 13.532 7.2295 8.7956 7.1564 7.6646 9.3249 −9.2464 10.550 2.6966 −0.35391 −1.8601 −1.8601 5.3281 −0.10298 −2.4754 5.6204 −3.2794 0.41759 −0.19165 −0.84442 −2.0750 −1.2478 b d T range (K) Halogen Groups 0.19489 0.10679 0.0029498 −0.085271 0.099928 0.21413 0.11911 0.55022 0.33607 0.19489 0.11624 0.18415 −0.040688 0.52861 1.1400 −0.19489 0.25779 1.3760 0.12592 0.011799 −1.2013 −0.063611 0.11624 0.19489 0.19489 0.0053465 −0.071918 0.41385 −1.4108 −3.0249 0.55022 0.33607 −0.39125 −0.78182 1.2756 80–490 80–490 85–385 145–395 90–355 90–355 140–315 130–305 130–305 80–490 90–355 110–300 165–295 130–300 150–275 150–285 140–315 230–550 180–670 180–670 230–550 295–670 90–355 80–490 80–490 180–470 180–670 220–295 300–420 375–595 130–305 130–305 250–510 370–510 385–480 =C}(Cl,F) Cb}(F) Cb}(Cl) Cb}(Br) Cb}(I) C}(Cb,3F) C}(2H,Cb,Cl) 7.8204 3.0794 4.5479 2.2857 2.9033 7.4477 16.752 C}(3H,N) C−(2H,C,N) C}(2H,Cb,N) C}(H,2C,N) C}(3C,N) N}(2H,C) N}(2H,Cb) N}(H,2C) N}(3C) N}(H,C,Cb) N}(2C,Cb) N}(C,2Cb) Cb}(N) N}(2H,N) N}(H,C,N) N}(2C,N) N}(H,Cb,N) C}(2H,C,CN) C}(3C,CN) =C}(H,CN) Cb}(CN) C}(2H,C,NO2) O}(C,NO2) Cb}(NO2) N}(H,2Cb) (pyrrole) Nb}(2Cb) 3.8452 2.4555 2.4555 2.6322 1.9630 8.2758 8.2758 −0.10987 4.5942 0.49631 −0.23640 4.5942 −0.78169 6.8050 1.1411 −1.0570 −0.74531 11.976 2.5774 9.0789 1.9389 18.520 −2.0181 15.277 −7.3662 0.84237 2.8647 −1.9986 −0.42564 0.08488 0.41360 0.41360 −0.82721 0.19403 0.33288 −0.92054 0.80145 0.15892 0.24596 0.27199 0.82003 0.44241 125–345 125–345 245–310 180–355 140–360 140–360 275–360 168–360 190–420 245–340 240–420 180–420 165–415 120–300 120–240 155–300 O}(H,C) O}(H,C) (diol) O}(H,Cb) (diol) O}(H,Cb) C–(3H,O) C–(2H,C,O) C–(2H,Cb,O) C–(2H,=C,O) C}(H,2C,O) (alcohol) C}(H,2C,O) (ether, ester) C}(3C,O) (alcohol) C}(3C,O) (ether, ester) O}(2C) O}(C,Cb) O}(2Cb) C}(2H,2O) −0.69005 0.46959 0.22250 2.2573 2.9763 −0.92230 −6.7938 0.19165 −0.0055745 −0.0097873 −0.40942 −0.62960 0.39346 1.2520 120–240 210–365 230–460 245–370 250–320 210–365 245–345 0.19489 −0.24054 −0.24054 0.45109 0.31086 0.035272 0.035272 0.89325 0.55316 −0.57161 −2.5258 0.55316 −0.25287 0.15634 −0.69350 −0.71494 −0.53306 0.52358 −0.58466 0.32986 −0.47276 1.05080 −1.83980 0.71161 −0.68137 −0.20336 80−490 190–375 190–375 240–370 255–375 185–455 185–455 170–400 160–360 240–380 285–390 160–360 240–455 215–465 205–300 205–300 295–385 185–345 295–345 195–345 265–480 190–300 180–350 280–415 255–450 210–395 2.6261 0.54075 0.54075 −0.87263 0.19489 −0.27140 −4.9593 −4.9593 0.69508 −0.016124 −4.8791 −0.44354 0.37860 −1.44210 0.31655 −0.31693 155–505 195–475 195–475 285–400 80–490 135–505 260–460 260–460 185–460 130–170 200–355 170–310 130–350 320–350 300–535 170–310 Nitrogen Groups Halogen Groups C}(C,3F) C}(2C,2F) C}(C,3Cl) C}(H,C,2Cl) C}(2H,C,Cl) C}(2H,=C,Cl) C}(H,2C,Cl) C}(2H,C,Br) C}(H,2C,Br) C}(2H,C,I) C}(C,2Cl,F) C}(C,Cl,2F) C}(C,Br,2F) =C}(H,Cl) =C}(2F) =C}(2Cl) a −0.33997 1.0431 1.0431 −2.0135 −1.7235 −0.18365 −0.18365 0.73024 −2.2134 3.4617 16.260 −2.2134 1.5059 −0.72563 3.5981 4.0038 3.6258 −2.4886 3.5218 −0.86929 3.0269 −5.4568 10.505 −4.4049 6.3622 1.25560 Oxygen Groups 12.952 5.2302 5.2302 −7.9768 3.8452 1.4596 −35.127 −35.127 2.2209 0.98790 −44.690 −3.3182 5.0312 −22.5240 −4.5788 1.0852 −10.145 −1.5124 −1.5124 8.10450 −0.33997 1.4657 28.409 28.409 −1.4350 0.39403 31.769 2.6317 −1.5718 13.1150 0.94150 1.5402 (Continued ) 2-344 PHYSICAL AnD CHEMICAL DATA TABLE 2-166 Liquid Heat Capacity Group Parameters for Ruzicka-Domalski Method* (Continued ) Table-specific nomenclature: Ct refers to a carbon atom with a triple bond; Cb refers to a carbon atom in benzene ring; =C refers to a carbon atom with a double bond; Cp refers to a carbon atom in a fused benzene ring; =C= refers to an allenic carbon atom. Group Definition a b d T range (K) Group Definition a Oxygen Groups C}(2C,2O) Cb}(O) C}(3H,CO) C}(2H,C,CO) C}(H,2C,CO) C}(3C,CO) CO}(H,C) CO}(H,=C) CO}(H,Cb) CO}(2C) CO}(C,=C) CO}(C,Cb) CO}(H,O) CO}(C,O) CO}(=C,O) CO}(O,CO) O}(C,CO) O}(H,CO) =C}(H,CO) =C}(C,CO) Cb}(CO) CO}(Cb,O) −12.955 −1.0686 3.8452 6.6782 3.92380 −2.2681 −3.82680 −8.00240 −8.00240 5.4375 41.507 −47.21100 13.11800 29.24600 41.61500 23.99000 −21.43400 −27.58700 −9.01080 −12.81800 12.15100 16.58600 9.10270 3.52210 −0.33997 −2.44730 −2.12100 1.75580 7.67190 3.63790 3.63790 0.72091 −32.632 24.36800 16.12000 3.42610 −12.78900 6.25730 −4.01640 −0.16485 15.14800 15.99700 −1.67050 5.44910 −1.53670 −0.79259 0.19489 0.47121 0.49646 −0.25674 −1.27110 −0.15377 −0.15377 −0.18312 6.0326 −2.82740 −5.12730 −2.89620 0.53631 −3.24270 3.05310 2.74830 −3.04360 −3.05670 −0.12758 −2.68490 275–335 285–530 80–490 180–465 185–375 225–360 180–430 220–430 220–430 185–380 275–355 300–465 280–340 180–445 195–350 320–345 175–440 230–500 195–355 195–430 175–500 175–500 0.19489 −0.08349 −0.31234 −0.72356 −0.75674 0.47368 0.47368 0.45625 0.45625 0.17938 0.45625 −0.06131 80–490 130–390 150–390 190–365 260–375 130–380 130–380 165–390 165–390 170–350 165–390 205–345 Sulfur Groups C}(3H,S) C}(2H,C,S) C}(H,2C,S) C}(3C,S) Cb}(S) S}(H,C) S}(H,Cb) S}(2C) S}(2Cb) S}(C,S) S}(Cb,S) S}(2Cb) (thiophene) 3.84520 1.54560 −1.64300 −5.38250 −4.45070 10.99400 10.99400 9.23060 9.23060 6.65900 9.23060 3.84610 −0.33997 0.88228 2.30700 4.50230 4.43240 −3.21130 −3.21130 −3.00870 −3.00870 −1.35570 −3.00870 0.36718 *Ruzicka, V., and E. S. Domalski, J. Phys. Chem. Ref. Data, 22 (1993): 597, 619. Solids Solid heat capacity increases with increasing temperature and is proportional to T 3 near absolute zero. The heat capacity at a solid-solid phase transition becomes large, and there can be a substantial difference in the heat capacity of the two equilibrium solid phases that exist on either side of the transition temperature. The heat capacity generally rises steeply with increasing temperature near the triple point. For a quick estimation of solid heat capacity specifically at 298.15 K, the very simple modification of Kopp’s rule [Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362] by Hurst and Harrison [Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21] can be used. At other temperatures and to obtain the temperature dependence of the solid heat capacity, the method given below by Goodman et al. should be used. Recommended Method 1 Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 24. Classification: Group contributions. Expected uncertainty: 10 percent. Applicability: Organic compounds for which group values are available. Input data: Molecular structure and Table 2-167 group values. Description: CP A T  =   J/(mol ⋅ K) 1000  K  b d T range (K) Ring Strain Contributions 4.4297 −4.3392 1.2313 −2.8988 −0.33642 −2.8663 0.21983 −1.5118 −2.0097 −0.72656 −11.460 4.9507 −4.1696 0.52991 5.9700 −3.7965 0.21433 −2.5214 −1.2086 −1.5041 −5.6817 1.5073 −14.885 7.4878 −8.9683 6.4959 −7.2890 3.1119 −8.7885 8.2530 −12.914 13.583 −6.1414 3.5709 −3.6501 2.4707 −6.3861 2.6257 −6.8984 0.66846 −3.9271 −0.29239 −19.687 8.8265 −0.67632 −1.4753 61.213 −30.927 1.0222 0.75099 0.70123 0.28172 0.14758 −0.74754 −0.018423 0.74612 0.63136 0.42863 −0.19810 −1.0879 −1.5272 −0.43040 −2.4573 −4.0230 −0.48620 −0.60531 −0.19578 −0.070012 0.048561 −1.4031 −0.13087 3.2269 155–240 140–300 180–300 135–365 145–485 270–300 295–320 175–310 140–300 160–320 220–300 260–330 170–300 205–320 200–310 275–330 170–395 280–375 250–320 235–485 210–425 315–485 315–485 310–485 15.281 12.703 25.681 −2.3360 1.3109 −7.0966 −0.13720 −1.18130 0.14304 195–330 170–400 265–370 6.8459 −7.0148 −2.3985 9.6704 3.2842 −13.017 −5.8759 7.3764 −0.48585 −2.8138 −5.8260 3.7416 1.2408 −2.1901 0.10253 0.11376 1.2681 −0.15622 135–325 185–300 175–300 190–305 160–320 295–325 −0.73127 −3.2899 −12.766 −1.3426 0.38399 5.2886 0.40114 0.089358 −0.59558 200–320 170–390 295–340 Example Estimate the solid heat capacity for p-cresol at 307.93 K. Structure: Group contributions: Group ni 1 4 2 1 }CH3 Ar }CH= Ar >C= }OH ai 0.20184 0.082478 0.012958 0.10341 bi 0 −0.00033 0 0 From Eq. (2-57): A = exp [6.7796 + 0.20184 + (4) (0.082478) + (2)(0.012958) + 0.10341+ (4)2 (−0.00033)] = 1694.9 From Eq. (2-56): 0.79267 N N   A = exp  6.7796 + ∑ ni ai + ∑ ni2βi    i =1 i =1 Hydrocarbons (ring strain) cyclopropane cyclobutane cyclopentane (unsub) cyclopentane (sub) cyclohexane cycloheptane cyclooctane spiropentane cyclopentene cyclohexene cycloheptene cyclooctene cyclohexadiene cyclooctadiene cycloheptatriene cyclooctatetraene indan 1H-indene tetrahydronaphthalene decahydronaphthalene hexahydroindan dodecahydrofluorene tetradecahydrophenanthrene hexadecahydropyrene Nitrogen compounds ethyleneimine pyrrolidine piperidine Oxygen compounds ethylene oxide trimethylene oxide 1,3-dioxolane furan tetrahydrofuran tetrahydropyran Sulfur compounds thiacyclobutane thiacyclopentane thiacyclohexane (2-56) CP = (2-57) where ni = number of occurrences of group i ai = individual group i contribution bi = nonlinear correction terms for chain and aromatic carbons 1694.9 J J = 159.1 (307.93) 0.79267 1000 mol ⋅ K mol ⋅ K This value is 2.5 percent higher than the DIPPR 801 recommended value of 155.2 J/(mol ⋅ K). Recommended Method 2 Modified Kopp’s rule. Reference: Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362; Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES 2-345 TABLE 2-167 Group Values and nonlinear Correction Terms for Estimation of Solid Heat Capacity with the Goodman et al.* Method Group Description ai }CH3 >CH2 >CH} >C< CH2= }CH= >C= =C= #CH #C} Ar }CH= Ar >C= Ar }O} Ar }N= Ar >N} Ar }NH} Ar }S} }O} }OH }COH >C=O }COO} }COOH }COOCO} methyl methylene secondary C tertiary C terminal alkene alkene subst. alkene allene terminal alkyne alkyne arom. C subst. arom. C furan O pyridine N subst. pyrrole N pyrrole N thiophene S ether alcohol aldehyde ketone ester acid anhydride 0.20184 0.11644 0.030492 −0.04064 0.18511 0.11224 0.028794 0.053464 −0.02914 0.13298 0.082478 0.012958 0.066027 0.056641 0.008938 −0.05246 0.090926 0.064068 0.10341 0.15699 0.12939 0.13686 0.21019 0.33091 Group }CO3} }NH2 >NH >N} =NH #N }N=N} }NO2 }N=C=O }SH }S} }SS} =S >S=O }F }Cl }Br }I >Si< >Si(O})} cyc >Si(O})} P(=O)(O})3 >P} >P(=O)} Description ai carbonate primary amine secondary amine tertiary amine double -bond NH nitrile diazide nitro isocyanate thiol/mercaptan sulfide disulfide sulfur double bond sulfoxide fluoride chloride bromide iodide silane linear siloxane cyclic siloxane phosphate phosphine phosphine oxide 0.2517 0.056138 −0.00717 −0.01661 0.17689 0.015355 0.3687 0.23327 0.2698 0.21123 0.14232 0.31457 0.13753 0.040002 0.15511 0.16995 0.19112 0.11318 0.12213 0.10125 0.063438 0.15016 0.069602 0.21875 Nonlinear Terms Groups Usage bi Methylene Aromatic carbon >CH2 −0.00188 Ar=CH} −0.00033 *Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 24. Classification: Group contributions. Expected uncertainty: 10 percent. Applicability: At 298.15 K; organic compounds that are solids at 298.15 K. Input data: Compound chemical formula and element contributions of Table 2-168. Description: N CP = ∑ nE ∆ E J/(mol ⋅ K) E = 1 C C P , m = ∑ x iC P ,i DEnSITY Structure: C12H8S. Group values from Table 2-168: DS = 12.36 Calculation using Eq. (2-54): CP = (12)(10.89) + (8)(7.56) + (1)(12.36) = 203.52 J/(mol ⋅ K) TABLE 2-168 Element Contributions to Solid Heat Capacity for the Modified Kopp’s Rule*† Element DE Element DE Element DE C H O N S F Cl Br I Al B 10.89 7.56 13.42 18.74 12.36 26.16 24.69 25.36 25.29 18.07 10.10 Ba Be Ca Co Cu Fe Hg K Li Mg Mn 32.37 12.47 28.25 25.71 26.92 29.08 27.87 28.78 23.25 22.69 28.06 Mo Na Ni Pb Si Sr Ti V W Zr All others 29.44 26.19 25.46 31.60 17.00 28.41 27.24 29.36 30.87 26.82 26.63 *Kopp, H., Ann. Chem. Pharm. (Liebig), 126 (1863): 362. † Hurst, J. E., and B. K. Harrison, Chem. Eng. Comm., 112 (1992): 21. (2-59) i =1 This neglects the excess heat capacity, which, if available, can be added to the mole fraction average to improve the estimated value. Example Estimate the solid heat capacity at 298.15 K for dibenzothiophene. DH = 7.56 Mixtures The molar heat capacity of liquid and vapor mixtures can be estimated as a mole fraction average of the pure-component values (2-58) where N = number of different elements in compound nE = number of occurrences of element E in compound DE = contribution of element E from Table 2-168 DC = 10.89 This value is 2.5 percent higher than the DIPPR 801 recommended value of 198.45 J/(mol ⋅ K). Density is defined as the mass of a substance per unit volume. Density is given in kg/m3 in SI units, but lbm/ft3 and g/cm3 are common AES and cgs units, respectively. Other commonly used forms of density include molar density (density divided by molecular weight) in kmol/m3, relative density (density relative to water at 15°C), and the older term specific gravity (density relative to water at 60°F). Often the inverse of density, specific volume, and the inverse of molar density, molar volume, are correlated and used to convey equivalent information. Gases Gases/vapors are compressible and their densities are strong functions of both temperature and pressure. Equations of state (EoS) are commonly used to correlate molar densities or molar volumes. The most accurate EoS are those developed for specific fluids with parameters regressed from all available data for that fluid. Super EoS are available for some of the most industrially important gases and may contain 50 or more constants specific to that chemical. Different predictive methods may be used for gas densities depending upon the conditions: 1. At very low densities (high temperatures, generally above the critical, and very low pressures, generally below a few bar), the ideal gas EoS Z ≡ PV =1 RT (2-60) may be applied. 2. At moderate densities (below 40 percent of the critical density), the virial equation truncated after the second virial coefficient Z =1+ B (T ) V (2-61) 2-346 PHYSICAL AnD CHEMICAL DATA may be used. Second virial coefficients B(T) are available in the DIPPR 801 database for many chemicals and can be estimated using the Tsonopoulos method. Recommended Method Tsonopoulos method. Reference: Tsonopoulos, C., AIChE J., 20 (1974): 263; 21 (1975): 827; 24 (1978): 1112. Classification: Corresponding states. Expected uncertainty: 8 percent for B(T). Applicability: Nonpolar organic compounds and some classes of polar compounds. Input data: Class of fluid, w, Pc, Tc, and m. Description: BPc = B (0) + ωB (1) + B (2) RTc (2-62) where B (0) = 0.1445 − 0.330 0.1385 0.0121 0.000607 − − − Tr3 Tr8 Tr Tr2 (2-63) (2-64) a b − Tr6 Tr8 2 µ P T µ r =    c   c   D   bar   K  3. For higher gas densities, the Lee-Kesler method described below provides excellent predictions for nonpolar and slightly polar fluids. Extended four-parameter corresponding-states methods are available for polar and slightly associating compounds. Recommended Method Lee-Kesler method. Reference: Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510. Classification: Corresponding states. Expected uncertainty: 1 percent except near the critical point where errors can be up to 30 percent. Applicability: Nonpolar and moderately polar compounds. An extended Lee-Kesler method, not described here, may be used for polar and slightly associating compounds [Wilding, W. V., and R. L. Rowley, Int. J. Thermophys., 8 (1986): 525]. Input data: Tc, Pc, w, Z(0), Z(1). Description: Z = Z(0) + wZ(1) 0.331 0.423 0.008 B = 0.0637 + 2 − 3 − 8 Tr Tr Tr (1) B (2) = r = V −1 = 0.86 kmol/m3 is much less than 40 percent of the critical density (the DIPPR 801 recommended value for the critical density is 13.8 kmol/m3). (2-65) where Z = compressibility factor Z(0) = compressibility factor of simple fluid obtained from Table 2-169 Z(1) = deviation from simple fluid obtained from Table 2-170 Analytical expressions for Z(0) and Z(1) can also be generated by using Z (0) = Z0 −2 (2-66) and m = dipole moment. The values of a and b used in Eq. (2-65) depend upon the class of fluid, as given in the table below: Class a b Nonpolar fluids Ketones, aldehydes, nitriles, ethers, esters, NH3, H2S, HCN Monoalkylhalides, mercaptans, sulfides 1-Alcohols except methanol Methanol 0 −21.4mr − 4.308 × 1019mr8 0 0 −2.188 × 1016mr4 − 7.831 × 1019mr8 0 0.0878 0.0878 0.00908 + 69.57mr 0.0525 Example Estimate the molar volume of ammonia at 430 K and 2.82 MPa. Input properties: Recommended values from the DIPPR 801 database are Tc = 405.65 K, Pc = 11.28 MPa, m = 1.469 D, and w = 0.252608. Reduced conditions: Tr = (430 K)/(405.65 K) = 1.06 Pr = (2.82 MPa)/(11.28 MPa) = 0.25 Z (1) = Z1 − Z0 0.3978 (2-68) where Z0 and Z1 are determined from Zi = PrVr B C D c γ −γ = 1 + + 2 + 5 + 3 4 2  β + 2  exp  2  Tr Vr Vr Vr Tr Vr  Vr   Vr  b2 b3 b4 − − Tr Tr2 Tr3 c c C = c1 − 2 + 32 Tr Tr d D = d1 + 2 Tr B = b1 − (2-69) as applied to the simple reference fluid and to the acentric reference fluid (n-octane), respectively. The constants for Eq. (2-69) for the two reference fluids are given in Table 2-171. Example Estimate the molar volume of saturated n-decane vapor at 540.5 K. Input properties: Recommended values from the DIPPR 801 database are Tc = 617.7 K, Pc = 2.11 MPa, P*(540.5 K) = 0.6799 MPa, and w = 0.492328. Reduced conditions: mr = (1.469)2(112.8)/(405.65)2 = 0.0014793 Second virial coefficient from Eqs. (2-63) to (2-66): (2-67) Tr = (540.5 K)/(617.7 K) = 0.875 and Pr = (0.6799 MPa)/(2.11 MPa) = 0.322 LK compressiblity factor: Since vapor phase values are needed, the appropriate values from Tables 2-169 and 2-170 that can be used to double-interpolate are as follows: B(0) = 0.1445 – 0.330/1.06 – 0.1385/(1.06)2 − 0.0121/(1.06)3 − 0.000607/(1.06)8 = −0.301 B(1) = 0.0637 + 0.331/(1.06)2 − 0.423/(1.06)3 − 0.008/(1.06)8 = −0.00189 a = (−21.4)(0.0014793) − (4.308 × 1019)(0.0014793)8 = −0.033 b=0 B(2) = (−0.033)/(1.06)6 = −0.023 From Eq. (2-62) : BPc/(RTc) = −0.301 − (0.252608)(0.00189) − 0.023 = −0.324 B = (−0.324)[0.008314 m3 ⋅ MPa/(kmol ⋅ K)](405.65 K)/(11.28 MPa) = −0.097 m3/kmol Molar volume from Eq. (2-61) : 3  m 3 ⋅ MPa  0.0083143 (430 K)  −0.097 m    kmol ⋅ K  RT  B   m3 kmol V= 1+  =  = 1.162 1+ P  V 2.82 M Pa V kmol     Note that the ideal gas value, 1.268 m3/kmol, deviates by 9.1 percent from this more accurate value. The truncated virial EoS should be valid for this density since Z(0) Tr\Pr 0.85 0.90 Z(1) 0.2 0.8810 0.9015 0.4 0.2 Tr\Pr (0.7222) 0.7800 0.85 0.90 −0.0715 −0.0442 0.4 (−0.1503) −0.1118 Double linear interpolation within these values gives Z(0) = 0.8058 and Z(1) = −0.1025. From Eq. (2-67): Z = 0.8058 + (0.492328)(−0.1025) = 0.7553 Note: If the analytical form available in Eq. (2-69) is used, the following more accurate values are obtained: Z(0) = 0.8131, Z(1) = − 0.1067, and Z = 0.7606. Molar volume: ZRT V= = P  m 3 ⋅ MPa  (0.7553)  0.0083143 (540.5 K)  kmol ⋅ K  0.6799 M Pa = 4.992 m3 kmol 4. Cubic EoS can be used to obtain both vapor and liquid densities as an alternative method to those mentioned above. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-169 2-347 Simple Fluid Compressibility Factors Z(0) Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J. Thermophys., 8(1987):717]. Tr\Pr 0.010 0.050 0.100 0.200 0.400 0.600 0.800 1.000 1.200 1.500 2.000 3.000 5.000 7.000 10.000 0.30 0.35 0.40 0.45 0.0029 0.0026 0.0024 0.0022 0.0145 0.0130 0.0119 0.0110 0.0290 0.0261 0.0239 0.0221 0.0579 0.0522 0.0477 0.0442 0.1158 0.1043 0.0953 0.0882 0.1737 0.1564 0.1429 0.1322 0.2315 0.2084 0.1904 0.1762 0.2892 0.2604 0.2379 0.2200 0.3470 0.3123 0.2853 0.2638 0.4335 0.3901 0.3563 0.3294 0.5775 0.5195 0.4744 0.4384 0.8648 0.7775 0.7095 0.6551 1.4366 1.2902 1.1758 1.0841 2.0048 1.7987 1.6373 1.5077 2.8507 2.5539 2.3211 2.1338 0.50 0.0021 0.0103 0.0207 0.0413 0.0825 0.1236 0.1647 0.2056 0.2465 0.3077 0.4092 0.6110 1.0094 1.4017 1.9801 (0.9741) (0.8699) 0.9804 0.0098 0.0195 0.0390 0.0778 0.1166 0.1553 0.1939 0.2323 0.2899 0.3853 0.5747 0.9475 1.3137 1.8520 (0.0020) (0.9000) (0.7995) 0.9849 0.0093 0.0186 0.0371 0.0741 0.1109 0.1476 0.1842 0.2207 0.2753 0.3657 0.5446 0.8959 1.2398 1.7440 (0.0019) (0.9211) (0.8405) 0.9881 0.9377 0.0178 0.0356 0.0710 0.1063 0.1415 0.1765 0.2113 0.2634 0.3495 0.5197 0.8526 1.1773 1.6519 (0.0018) (0.0089) (0.8707) (0.7367) 0.9904 0.9504 0.8958 0.0344 0.0687 0.1027 0.1366 0.1703 0.2038 0.2538 0.3364 0.4991 0.8161 1.1241 1.5729 (0.0086) (0.0172) (0.7805) 0.9598 0.9165 0.0336 0.0670 0.1001 0.1330 0.1656 0.1981 0.2464 0.3260 0.4823 0.7854 1.0787 1.5047 (0.0085) (0.0169) (0.8181) (0.6122) 0.9669 0.9319 0.8539 0.0661 0.0985 0.1307 0.1626 0.1942 0.2411 0.3182 0.4690 0.7598 1.0400 1.4456 (0.0168) (0.0332) (0.6659) (0.4746) 0.9436 0.8810 0.0661 0.0983 0.1301 0.1614 0.1924 0.2382 0.3132 0.4591 0.7388 1.0071 1.3943 (0.0336) (0.7222) (0.5346) 0.9015 0.7800 0.1006 0.1321 0.1630 0.1935 0.2383 0.3114 0.4527 0.7220 0.9793 1.3496 (0.0364) (0.0685) (0.6040) (0.4034) 0.9115 0.8059 0.6635 0.1359 0.1664 0.1963 0.2405 0.3122 0.4507 0.7138 0.9648 1.3257 (0.7350) (0.1047) (0.4499) 0.8206 0.6967 0.1410 0.1705 0.1998 0.2432 0.3138 0.4501 0.7092 0.9561 1.3108 (0.0822) (0.1116) 0.4853) 0.8338 0.7240 0.5580 0.1779 0.2055 0.2474 0.3164 0.4504 0.7052 0.9480 1.2968 (0.1312) (0.1532) 0.7360 0.5887 0.1844 0.2097 0.2503 0.3182 0.4508 0.7035 0.9442 1.2901 0.1959 0.2154 0.2538 0.3204 0.4514 0.7018 0.9406 1.2835 0.2901 0.4648 0.5146 0.6026 0.6880 0.7443 0.7858 0.8438 0.8827 0.9103 0.9308 0.9463 0.9583 0.9678 0.9754 0.9865 0.9941 0.9993 1.0031 1.0057 1.0097 1.0115 0.2237 0.2370 0.2629 0.4437 0.5984 0.6803 0.7363 0.8111 0.8595 0.8933 0.9180 0.9367 0.9511 0.9624 0.9715 0.9847 0.9936 0.9998 1.0042 1.0074 1.0120 1.0140 0.2583 0.2640 0.2715 0.3131 0.4580 0.5798 0.6605 0.7624 0.8256 0.8689 0.9000 0.9234 0.9413 0.9552 0.9664 0.9826 0.9935 1.0010 1.0063 1.0101 1.0156 1.0179 0.3229 0.3260 0.3297 0.3452 0.3953 0.4760 0.5605 0.6908 0.7753 0.8328 0.8738 0.9043 0.9275 0.9456 0.9599 0.9806 0.9945 1.0040 1.0106 1.0153 1.0221 1.0249 0.4522 0.4533 0.4547 0.4604 0.4770 0.5042 0.5425 0.6344 0.7202 0.7887 0.8410 0.8809 0.9118 0.9359 0.9550 0.9827 1.0011 1.0137 1.0223 1.0284 1.0368 1.0401 0.7004 0.6991 0.6980 0.6956 0.6950 0.6987 0.7069 0.7358 0.7761 0.8200 0.8617 0.8984 0.9297 0.9557 0.9772 1.0094 1.0313 1.0463 1.0565 1.0635 1.0723 1.0741 0.9372 0.9339 0.9307 0.9222 0.9110 0.9033 0.8990 0.8998 0.9112 0.9297 0.9518 0.9745 0.9961 1.0157 1.0328 1.0600 1.0793 1.0926 1.1016 1.1075 1.1138 1.1136 1.2772 1.2710 1.2650 1.2481 1.2232 1.2021 1.1844 1.1580 1.1419 1.1339 1.1320 1.1343 1.1391 1.1452 1.1516 1.1635 1.1728 1.1792 1.1830 1.1848 1.1834 1.1773 (0.9648) 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.93 0.95 0.97 0.98 0.9922 0.9935 0.9946 0.9954 0.9959 0.9961 0.9963 0.9965 0.9725 0.9768 0.9790 0.9803 0.9815 0.9821 0.9528 0.9573 0.9600 0.9625 0.9637 0.9174 0.9227 0.9253 0.8398 (0.1703) 0.99 0.9966 0.9826 0.9648 0.9277 0.8455 0.7471 0.6138 (0.2324) 1.00 1.01 1.02 1.05 1.10 1.15 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00 0.9967 0.9968 0.9969 0.9971 0.9975 0.9978 0.9981 0.9985 0.9988 0.9991 0.9993 0.9994 0.9995 0.9996 0.9997 0.9998 0.9999 1.0000 1.0000 1.0000 1.0001 1.0001 0.9832 0.9837 0.9842 0.9855 0.9874 0.9891 0.9904 0.9926 0.9942 0.9954 0.9964 0.9971 0.9977 0.9982 0.9986 0.9992 0.9996 0.9998 1.0000 1.0002 1.0004 1.0005 0.9659 0.9669 0.9679 0.9707 0.9747 0.9780 0.9808 0.9852 0.9884 0.9909 0.9928 0.9943 0.9955 0.9964 0.9972 0.9983 0.9991 0.9997 1.0001 1.0004 1.0008 1.0010 0.9300 0.9322 0.9343 0.9401 0.9485 0.9554 0.9611 0.9702 0.9768 0.9818 0.9856 0.9886 0.9910 0.9929 0.9944 0.9967 0.9983 0.9994 1.0002 1.0008 1.0017 1.0021 0.8509 0.8561 0.8610 0.8743 0.8930 0.9081 0.9205 0.9396 0.9534 0.9636 0.9714 0.9775 0.9823 0.9861 0.9892 0.9937 0.9969 0.9991 1.0007 1.0018 1.0035 1.0043 0.7574 0.7671 0.7761 0.8002 0.8323 0.8576 0.8779 0.9083 0.9298 0.9456 0.9575 0.9667 0.9739 0.9796 0.9842 0.9910 0.9957 0.9990 1.0013 1.0030 1.0055 1.0066 0.6353 0.6542 0.6710 0.7130 0.7649 0.8032 0.8330 0.8764 0.9062 0.9278 0.9439 0.9563 0.9659 0.9735 0.9796 0.9886 0.9948 0.9990 1.0021 1.0043 1.0075 1.0090 2-348 PHYSICAL AnD CHEMICAL DATA TABLE 2−170 Acentric Deviations Z (1) from the Simple Fluid Compressibility Factor Values in parentheses are for the opposite phase and may be used to interpolate to or near the phase boundary [PGL4; Wilding, W. V., J. K. Johnson, and R. L. Rowley, Int. J. Thermophys., 8(1987):717]. Tr\Pr 0.010 0.050 0.100 0.200 0.400 0.600 0.800 1.000 1.200 1.500 0.30 0.35 0.40 0.45 −0.0008 −0.0009 −0.0010 −0.0009 −0.0040 −0.0046 −0.0048 −0.0047 −0.0081 −0.0093 −0.0095 −0.0094 −0.0161 −0.0185 −0.0190 −0.0187 −0.0323 −0.0370 −0.0380 −0.0374 −0.0484 −0.0554 −0.0570 −0.0560 −0.0645 −0.0738 −0.0758 −0.0745 −0.0806 −0.0921 −0.0946 −0.0929 −0.0966 −0.1105 −0.1134 −0.1113 −0.1207 −0.1379 −0.1414 −0.1387 −0.0009 −0.0045 −0.0090 −0.0181 −0.0360 −0.0539 −0.0716 −0.0893 (−0.0457) (−0.2270) −0.0172 −0.0343 −0.0513 −0.0682 −0.0164 −0.0326 −0.0487 −0.0309 2.000 3.000 5.000 7.000 10.000 −0.2407 −0.2738 −0.2799 −0.2734 −0.3996 −0.4523 −0.4603 −0.4475 −0.5572 −0.6279 −0.6365 −0.6162 −0.7915 −0.8863 −0.8936 −0.8606 −0.1069 −0.1330 −0.1762 −0.2611 −0.4253 −0.5831 −0.8099 −0.0849 −0.1015 −0.1263 −0.1669 −0.2465 −0.3991 −0.5446 −0.7521 −0.0646 −0.0803 −0.0960 −0.1192 −0.1572 −0.2312 −0.3718 −0.5047 −0.6928 −0.0461 −0.0611 −0.0759 −0.0906 −0.1122 −0.1476 −0.2160 −0.3447 −0.4653 −0.6346 −0.0294 −0.0438 −0.0579 −0.0718 −0.0855 −0.1057 −0.1385 −0.2013 −0.3184 −0.4270 −0.5785 −0.0417 −0.0550 −0.0681 −0.0808 −0.0996 −0.1298 −0.1872 −0.2929 −0.3901 −0.5250 −0.0526 −0.0648 −0.0767 −0.0940 −0.1217 −0.1736 −0.2682 −0.3545 −0.4740 −0.0509 −0.0622 −0.0731 −0.0888 −0.1138 −0.1602 −0.2439 −0.3201 −0.4254 −0.0604 −0.0701 −0.0840 −0.1059 −0.1463 −0.2195 −0.2862 −0.3788 −0.0602 −0.0687 −0.0810 −0.1007 −0.1374 −0.2045 −0.2661 −0.3516 −0.0607 −0.0678 −0.0788 −0.0967 −0.1310 −0.1943 −0.2526 −0.3339 −0.0623 −0.0669 −0.0759 −0.0921 −0.1240 −0.1837 −0.2391 −0.3163 −0.0641 −0.0661 −0.0740 −0.0893 −0.1202 −0.1783 −0.2322 −0.3075 −0.0680 −0.0646 −0.0715 −0.0861 −0.1162 −0.1728 −0.2254 −0.2989 −0.0879 −0.0223 −0.0062 0.0220 0.0476 0.0625 0.0719 0.0819 0.0857 0.0864 0.0855 0.0838 0.0816 0.0792 0.0767 0.0719 0.0675 0.0634 0.0598 0.0565 0.0497 0.0443 −0.0609 −0.0678 −0.0473 −0.0621 0.0227 −0.0524 0.1059 0.0451 0.0897 0.1630 0.0943 0.1548 0.0991 0.1477 0.1048 0.1420 0.1063 0.1383 0.1055 0.1345 0.1035 0.1303 0.1008 0.1259 0.0978 0.1216 0.0947 0.1173 0.0916 0.1133 0.0857 0.1057 0.0803 0.0989 0.0754 0.0929 0.0711 0.0876 0.0672 0.0828 0.0591 0.0728 0.0527 0.0651 −0.0824 −0.0778 −0.0722 −0.0432 0.0698 0.1667 0.1990 0.1991 0.1894 0.1806 0.1729 0.1658 0.1593 0.1532 0.1476 0.1374 0.1285 0.1207 0.1138 0.1076 0.0949 0.0849 −0.1672 −0.1615 −0.1556 −0.1370 −0.1021 −0.0611 −0.0141 0.0875 0.1737 0.2309 0.2631 0.2788 0.2846 0.2848 0.2819 0.2720 0.2602 0.2484 0.2372 0.2268 0.2042 0.1857 −0.2185 −0.2116 −0.2047 −0.1835 −0.1469 −0.1084 −0.0678 0.0176 0.1008 0.1717 0.2255 0.2628 0.2871 0.3017 0.3097 0.3135 0.3089 0.3009 0.2915 0.2817 0.2584 0.2378 −0.2902 −0.2816 −0.2731 −0.2476 −0.2056 −0.1642 −0.1231 −0.0423 0.0350 0.1058 0.1673 0.2179 0.2576 0.2876 0.3096 0.3355 0.3459 0.3475 0.3443 0.3385 0.3194 0.2994 −0.1608 −0.1834 −0.1879 −0.1840 (−0.0740) 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.93 0.95 0.97 0.98 −0.0314 −0.0043 −0.0086 (−0.0009) (−0.1438) (−0.2864) −0.0205 −0.0041 −0.0082 (0.0008) (0.0949) (−0.1857) −0.0137 −0.0772 −0.0078 −0.0156 (−0.0008) (0.0039) (−0.1262) (−0.2424) −0.0093 −0.0064 −0.0044 −0.0029 −0.0019 −0.0015 −0.0012 −0.0010 −0.0009 −0.0507 −0.1161 −0.0148 (−0.0038) (−0.0075) (−0.1685) −0.0339 −0.0744 −0.0143 −0.0282 (−0.0037) (−0.0072) (−0.1298) (−0.2203) −0.0228 −0.0152 −0.0099 −0.0075 −0.0062 −0.0050 −0.0044 −0.0487 −0.1160 −0.0272 −0.0401 (−0.0073) (−0.0139) (−0.1682) (−0.2185) −0.0319 −0.0205 −0.0154 −0.0126 −0.0101 −0.0090 −0.0715 −0.0268 −0.0391 (−0.0144) (−0.1503) (−0.1692) −0.0442 −0.1118 −0.0396 −0.0503 (−0.0179) (−0.0286) (−0.1580) (−0.1464) −0.0326 −0.0262 −0.0208 −0.0184 −0.0763 −0.1662 −0.0514 (−0.0340) (−0.0424) (−0.1418) −0.0589 −0.1110 −0.0540 (−0.0444) (−0.0490) (−0.1532) −0.0450 −0.0390 −0.0770 −0.1647 (−0.0714) (−0.0643) −0.0641 −0.1100 (−0.0828) 0.99 −0.0008 −0.0039 −0.0079 −0.0161 −0.0335 −0.0531 −0.0796 (−0.1621) 1.00 1.01 1.02 1.05 1.10 1.15 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.20 2.40 2.60 2.80 3.00 3.50 4.00 −0.0007 −0.0006 −0.0005 −0.0003 0.0000 0.0002 0.0004 0.0006 0.0007 0.0008 0.0008 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 0.0007 0.0006 0.0006 0.0005 0.0005 −0.0034 −0.0030 −0.0026 −0.0015 0.0000 0.0011 0.0019 0.0030 0.0036 0.0039 0.0040 0.0040 0.0040 0.0040 0.0039 0.0037 0.0035 0.0033 0.0031 0.0029 0.0026 0.0023 −0.0069 −0.0060 −0.0051 −0.0029 0.0001 0.0023 0.0039 0.0061 0.0072 0.0078 0.0080 0.0081 0.0081 0.0079 0.0078 0.0074 0.0070 0.0066 0.0062 0.0059 0.0052 0.0046 −0.0140 −0.0120 −0.0102 −0.0054 0.0007 0.0052 0.0084 0.0125 0.0147 0.0158 0.0162 0.0163 0.0162 0.0159 0.0155 0.0147 0.0139 0.0131 0.0124 0.0117 0.0103 0.0091 −0.0285 −0.0240 −0.0198 −0.0092 0.0038 0.0127 0.0190 0.0267 0.0306 0.0323 0.0330 0.0329 0.0325 0.0318 0.0310 0.0293 0.0276 0.0260 0.0245 0.0232 0.0204 0.0182 −0.0435 −0.0351 −0.0277 −0.0097 0.0106 0.0237 0.0326 0.0429 0.0477 0.0497 0.0501 0.0497 0.0488 0.0477 0.0464 0.0437 0.0411 0.0387 0.0365 0.0345 0.0303 0.0270 −0.0588 −0.0429 −0.0303 −0.0032 0.0236 0.0396 0.0499 0.0612 0.0661 0.0677 0.0677 0.0667 0.0652 0.0635 0.0617 0.0579 0.0544 0.0512 0.0483 0.0456 0.0401 0.0357 −0.1118 −0.1072 −0.1021 −0.0838 −0.0373 0.0332 0.1095 0.2079 0.2397 0.2433 0.2381 0.2305 0.2224 0.2144 0.2069 0.1932 0.1812 0.1706 0.1613 0.1529 0.1356 0.1219 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-171 Constants for the Two Reference Fluids Used in Lee-Kesler Method* Constant b1 b2 b3 b4 c1 c2 c3 c4 d1 × 104 d2 × 104 b g 2-349 Tr = (353.15 K)/(405.65 K) = 0.871 Simple reference fluid Acentric reference fluid 0.1181193 0.265728 0.154790 0.030323 0.0236744 0.0186984 0.0 0.042724 0.155488 0.623689 0.65392 0.060167 0.2026579 0.331511 0.027655 0.203488 0.0313385 0.0503618 0.016901 0.041577 0.48736 0.0740336 1.226 0.03754 α = {1 + [0.48 + (1.574) (0.252608) − (0.176) (0.252608)2] [1 − (0.871)0.5]}2 = 1.119 Rearrange and solve Eq. (2-70) for V: P= RT aα − V − b V (V + b) PV 3 − RTV 2 + (aα − bRT − Pb2)V − abα = 0 or 3 m3   V   V   − 0.029 41.352  3    m /mol   mol   m 3 /mol  2  m6   V  −10 +  4.037 × 10 −6   − 1.25 × 10 = 0  mol 2   m 3 /mol  Vapor root (initial guess of V = 7.1 × 10−7 m3/mol from ideal gas equation): *Lee, B. I., and M. G. Kesler, AIChE J., 21 (1975): 510. Vvap = 5.395 × 10−4 m3/mol and rvap = 1/Vvap = 1.854 kmol/m3 Liquid root (initial guess of V = 2.72 × 10−5 m3/mol from 1.05b): Recommended Method Cubic EoS. Classification: Empirical extension of theory. Expected uncertainty: Varies depending upon compound and conditions, but a general expectation is 10 to 20 percent. Applicability: Nonpolar and moderately polar compounds. Input data: Tc, Pc, w. Description: The more common cubic EoS can be written in the form a α (Tr ) V V − Z= V − b V 2 + δV + ε RT Vliq = 4.441 × 10−5 m3/mol The corresponding values and equation for the Peng-Robinson EoS are a = 4.611 × 106 cm6 ⋅ bar/mol2 P= or (2-70) 353.15 K, using the Soave and Peng-Robinson EoS. Required properties: Recommended values in the DIPPR 801 database are w = 0.252608 P*(353.15 K) = 41.352 bar (vapor pressure at 353.15 K) EoS parameters (shown for Soave EoS): 2   bar ⋅ cm 3  0.42748  83.145 (405.65 K)  6  mol ⋅ K  0.42748 (RTc )   = 4.311 × 10 6 cm ⋅ bar a= = 112.8 bar Pc mol 2 2 0.08664 (RTc ) b= = Pc bar ⋅ cm 3   0.08664  83.145 (405.65 K)  mol ⋅ K  cm 3 = 25.906 112.8 bar mol TABLE 2-172 EoS RT aα − V − b V 2 + 2bV − b 2 PV 3 + (bP − RT)V 2 + (aα − 2bRT − 3Pb2)V + (bP 3 + RTb2 − abα) = 0 m3   V   V   − 0.0284 41.352  3    m /mol   mol   m 3 /mol  2  m6   V  −10 +  3.651 × 10 −6  − 1.018 × 10 = 0   mol 2   m 3 /mol  Solve for the two physical roots of this equation: Vvap = 5.286 × 10−4 m3/mol and rvap = 1.892 kmol/m3 Vliq = 3.914 × 10−5 m3/mol and rliq = 25.55 kmol/m3 The liquid density calculated from the Soave EoS is 24.2 percent below the DIPPR 801 recommended value of 29.69 kmol/m3; that calculated from the Peng-Robinson EoS is 13.9 percent below the recommended value. Liquids For most liquids, the saturated molar liquid density r can be effectively correlated with ρ= Example Estimate the molar density of liquid and vapor saturated ammonia at Pc = 112.8 bar b = 23.262 cm3/mol α = 1.103 3 where a, b, d, and e are constants that depend upon the model EoS chosen, as does the temperature dependence of the function α(Tr). Definitions of these constants and α(Tr) for some of the more commonly used EoS models are shown in Table 2-172. The corresponding relations for many other EoS models in this same form are available [Soave, G., Chem. Eng. Sci., 27 (1972): 1197]. The independent parameters a and b in these models can be regressed from experimental data to correlate densities or can be obtained from known critical constants to predict density data. Of the cubic EoS given in Table 2-172, the Soave and Peng-Robinson are the most accurate, but there is no general rule for which EoS produces the best estimated volumes for specific fluids or conditions. The Peng-Robinson equation has been better tuned to liquid densities, while the Soave equation has been better tuned to vapor-liquid equilibrium and vapor densities. In solving the cubic equation for volume, a convenient initial guess to find the vapor root is the ideal gas value, while an initial value of 1.05b is convenient to locate the liquid root. Tc = 405.65 K rliq = 1/Vliq = 22.516 kmol/m3 and A D B [1+(1−T /C ) ] (2-71) adapted from the Rackett prediction equation [Rackett, H. G., J. Chem. Eng. Data, 15 (1970): 514]. The regression constants A, B, and D are determined from the nonlinear regression of available data, while C is usually taken as the critical temperature. The liquid density decreases approximately linearly from the triple point to the normal boiling point and then nonlinearly to the critical density (the reciprocal of the critical volume). A few compounds such as water cannot be fit with this equation over the entire range of temperature. The recommended method for estimation of saturated liquid density for pure organic compounds is the Rackett prediction method. Recommended Method Rackett method. Reference: Rackett, H. G., J. Chem. Eng. Data, 15 (1970): 514. Classification: Corresponding states. Expected uncertainty: 15 percent as purely predictive equation; 2 percent if a liquid density value is available. Relationships for Eq. (2-70) for Common Cubic EoS d e α(Tr) van der Waals* 0 0 1 Relich-Kwong† 0 0 Tr−0.5 Soave‡ b 0 [1 + (0.48 + 1.574w − 0.176w2)(1 − Tr0.5)]2 Peng-Robinson§ 2b −b2 [1 + (0.37464 + 1.54226w − 0.2699w2)(1 − Tr0.5)]2 *van der Waal, J. H., Z. Phys. Chem., 5 (1890): 133. † Redlich, O., and J. N. S. Kwong, Chem. Rev., 44 (1949): 233. ‡ Soave, G., Chem. Eng. Sci., 27 (1972): 1197. § Peng, D. Y., and D. B. Robinson, Ind. Eng. Chem. Fundam., 15 (1976): 59. aPc/(RTc)2 bPc/(RTc) 0.42188 0.42748 0.42748 0.45724 0.125 0.08664 0.08664 0.0778 2-350 PHYSICAL AnD CHEMICAL DATA Applicability: Saturated liquid densities of organic compounds. Input data: Tc, Pc, and Zc (or, equivalently, Vc). Description: A predictive form of the equation is given by  RT  1 = V =  c  Zcq ρ  Pc  Example Estimate the density of solid naphthalene at 281.46 K. Required properties: The recommended values from the DIPPR 801 database for Tt and the liquid density at Tt are where q = 1 + (1 − Tr ) (2-72) When one or more liquid density data points are available, Zc in Eq. (2-72) can be replaced with an adjustable parameter fitted from the data (ZRA in the notation of Spencer and Danner [Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data 17 (1972): 236]). This produces densities in good agreement with experiment and permits accurate interpolation of the densities over most of the liquid temperature range, but it does not give the correct critical density unless ZRA = Zc. Example Estimate the saturated liquid density of acetonitrile at 376.69 K. Required properties: The recommended values from the DIPPR 801 database are Tc = 545.5 K rL(Tt) = 7.6326 kmol/m3 Tt = 353.43 K 2/7 Pc = 4.83 MPa Zc = 0.184 Calculate supporting quantities: From Eq. (2-73):  281.46 K   kmol  kmol ρs =  1.28 − 0.16  7.6326 3  = 8.797 3 353.43 K   m m  The estimated value is 4.3 percent lower than the DIPPR 801 recommended value of 9.1905 kmol/m3. Mixtures Both liquid and vapor densities can be estimated using purecomponent CS and EoS methods by treating the fluid as a pseudo-pure component with effective parameters calculated from the pure-component parameters using ad hoc mixing rules. To apply the Lee-Kesler CS method to mixtures, pseudo-pure fluid constants are required. One of the simplest set of mixing rules for these quantities is [Prausnitz, J. M., and R. D. Gunn, AIChE J., 4 (1958): 430, 494; Joffe, J., Ind. Eng. Chem. Fundam., 10 (1971): 532]: Tr = (376.69 K)/(545.5 K) = 0.691 C Tc = ∑ x iTc ,i q = 1 + (1 − 0.691)2/7 = 1.715 Calculate saturated liquid density from Eq. (2-72): C ∑x Z i Pc =     4.83 × 10 6 Pa   (0.184)− 1.715 = 19.42 kmol ρ=   m3 Pa ⋅ m 3  8.314 (545.5 K)     mol ⋅ K    RTc (2-75) i =1 ω = ∑ xiωi 1/1.798 (2-76) i =1 The procedures are identical to those for pure components with the replacement of Tc, Pc, and w with the effective mixture values obtained from the above equations. To use a cubic EoS for a mixture, mixing rules are used to calculate effective mixture parameters in terms of the pure-component values. Although more complex mixing rules may improve prediction accuracy, the simple forms recommended here provide reasonable accuracy without adjustable parameters: = 0.202 C b = ∑ x i bi (2-77) i =1     6 × 4.83 10 Pa  (0.202)−1.715 = 16.577 kmol ρ=    m3 Pa ⋅ m 3  (545.5 K)    8.314 mol ⋅ K    2 The value obtained by the modified Rackett method is 0.9 percent below the DIPPR 801 recommended value. Note, however, that with ZRA = 0.202 instead of Zc, Eq. (2-72) gives rc = 5.28 kmol/m3 instead of rc = Pc/(ZcRTc) = 5.79 kmol/m3. Solids Solid density data are sparse and usually available only within a narrow temperature range. For most solids, density decreases approximately linearly with increasing temperature. No accurate method for prediction of solid densities is available, but an approximate correlation has been found between the density of the liquid phase at the triple point and the solid that is stable at the triple point conditions. Recommended Method Goodman method. Reference: Goodman, B. T., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 49 (2004): 1512. Classification: Empirical correlation. Expected uncertainty: 6 percent. Applicability: Organic compounds; applicable to the stable solid phase at the triple point temperature Tt; applicable T range is from Tt down to either the first solid-phase transition temperature or to approximately 0.3Tt. Input data: Liquid density at the triple point. Description: The density for the solid phase that is stable at the triple point has been correlated as a function of temperature and the liquid density at Tt as  T ρs =  1.28 − 0.16  ρL (Tt ) Tt   ∑x V C q = 1 + (1 – 0.546)2/7 = 1.798     4.83 × 10 6 Pa   Z RA =  Pa ⋅ m 3  kmol    (545.5 K) 18.919     8.314   kmol ⋅ K  m3    c ,i i =1 C i c ,i The estimated density is 16 percent above the DIPPR 801 value of 16.73 kmol/m3. Calculate rsat from Eq. (2-72) with a known liquid density: Kratzke and Muller [Kratzke, H., and S. Muller, J. Chem. Thermo., 17 (1985): 151] reported an experimental density of 18.919 kmol/m3 at 298.08 K. Use of this experimental value in Eq. (2-72) to calculate ZRA gives Tr = (298.08 K)/(545.5 K) = 0.546 (2-74) i =1 (2-73) C  (2-78) aα =  ∑ x i (ai α i )1/2   i =1  Mixture calculations are then identical to the pure-component calculations using these effective mixture parameters for the pure-component aα and b values. The modified Rackett method has also been extended to liquid mixtures [Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972): 236] using the following combining and mixing rules as modified by Li [Li, C. C., Can. J. Chem. Eng., 19 (1971): 709]: Tc ,ij = Tc ,iTc , j φi = x iVc ,i C ∑x V j c, j C C Tc = ∑ ∑ φi φ jTc ,ij (2-79) i =1 j =1 j =1 Recommended Method Spencer-Danner-Li mixing rules with Rackett equation. References: Spencer, C. F., and R. P. Danner, J. Chem. Eng. Data, 17 (1972): 236; Li, C. C., Can. J. Chem. Eng., 19 (1971): 709. Classification: Corresponding states. Expected uncertainty: About 7 percent on average; higher near the Tc of any of the components. Applicability: Saturated (at the bubble point) liquid mixtures. Input data: Tc, Vc, and xi. Description: The predictive form of the equation is given by  C xT  q 1 = V = R  ∑ i c ,i  Z RA ρ  i =1 Pc ,i  q = 1.0 + (1.0 − Tr )2/7 (2-80) PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES where C Z RA = 0.29056 − 0.08775 ∑ x i ω i and Tr = i =1 T Tc (2-81) 2-351 Input data: Tc, Pc, and M. Description: The correlation for viscosity as a function of reduced temperature is 46.1Tr0.618 - 20.4 exp( - 0.449Tr ) + 19.4 exp( − 4.058 Tr ) + 1 ηo = 2.173424 × 1011 (Tc /K)1/6 (M /g ⋅ mol −1 )−1/2 (Pc / Pa)−2/3 Pa ⋅ s Example Estimate the saturated liquid density of a liquid mixture of 50 mol% ethane(1) and 50 mol% n-decane(2) at 377.6 K. Required properties: The recommended values from the DIPPR 801 database for the required properties are as follows: Example Estimate the low-pressure vapor viscosity of propane at 353 K. Required constants: The DIPPR 801 database recommends the following values: Tc = 369.83 K Tc/K Vc /(m3 ⋅ kmol−1) Pc /bar w Ethane 305.32 0.1455 48.72 0.0995 Decane 617.7 0.617 21.1 0.4923 (2-83) Pc = 4.248 MPa M = 44.0956 g/mol Reduced temperature: Tr = (353 K)/(369.83 K) = 0.9545 Calculation using Eq. (2-83): Auxiliary quantities from Eq. (2-79): φ1 = (0.5) (0.1455) = 0.191; (0.5)(0.1455) + (0.5)(0.617) (46.1) (0.9545)0.618 − 20.4 exp[ − (0.449) (0.9545)] + 19.4 exp[ − 4.058(0.9545)] + 1 ηo = Pa ⋅ s (2.173424 × 1011 ) (369.83) −1/6 (44.0956) −1/2 (4.248 × 10 6 )−2/3 = 9.84 × 10 −6 φ2 = 0.809 This value is 1.5 percent higher than the DIPPR 801 recommended value of 9.70 × 10−6 Pa ⋅ s. Tc ,12 = (305.32 K) (617.7 K) = 434.3 K Tc = φ12Tc ,1 + 2φ1φ2Tc ,12 + φ22Tc ,2 K = (0.191)2 (305.32) + (2)(0.191)(0.809)(434.3) + (0.809)2 (617.7) Recommended Method 2 Reichenberg method. Reference: Reichenberg, D., AIChE J., 21 (1975): 181. Classification: Group contributions and corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and polar organic and inorganic vapors. Input data: Tc, Pc, M, m, and molecular structure. Description: The temperature dependence of the viscosity is given by Tc = 549.68 K Calculations from Eqs. (2-80) and (2-81): Tr = (377.6 K)/(549.63 K) = 0.687 q = 1 + (1 − 0.687)2/7 = 1.718  1 + 270(µ ∗r ) 4  ATr2 ηo =   Pa ⋅ s [1 + 0.36 Tr (Tr − 1)]1/6  Tr + 270(µ ∗r ) 4  ZRA = 0.29056 − 0.08775[(0.5)(0.0995) + (0.5)(0.4923)] = 0.2646  m 3 ⋅ bar   (0.5)(305.32 K) (0.5) (617.7 K)  m3 1.718 + V =  0.08314   (0.2646) = 0.151   K ⋅ kmol   48.72 bar 21.1 bar  kmol The experimental value [Reamer, H. H., and B. H. Sage, J. Chem. Eng. Data, 7 (1962): 161] is 0.149 m3/kmol, and the error in the estimated value is 1.3 percent. where the parameter A is determined from group contributions and the modified reduced dipole µ∗r is found from µ∗r = 52.46mr ηo = AT B 1 + C /T + D /T 2 (2-82) Over smaller temperature ranges, parameters C and D may not be necessary as ln(h) is often reasonably linear with ln(T). Care should be taken in extrapolating using Eq. (2-82) as there can be unintended mathematical poles where the denominator approaches zero. Numerous methods have been developed for estimation of vapor viscosity. For nonpolar vapors, the Yoon-Thodos CS method works well, but for polar fluids the Reichenberg method is preferred. Both methods are illustrated below. Recommended Method 1 Yoon-Thodos method. Reference: Yoon, P., and G. Thodos, AIChE J., 16 (1970): 300. Classification: Corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and slightly polar organic vapors. (2-85) and Eq. (2-66). For organic compounds, A is found from the group values Ci, listed in Table 2-173, using VISCOSITY Viscosity is defined as the shear stress per unit area at any point in a confined fluid, divided by the velocity gradient in the direction perpendicular to the direction of flow. The absolute viscosity h is the shear stress at a point, divided by the velocity gradient at that point. The SI unit of viscosity is Pa ⋅ s [1 kg/(m ⋅ s)], but the cgs units of poise (P) [1 g/(cm ⋅ s)] and centipoise (cP = 0.01 P) are also frequently used (1 cP = 1 mPa ⋅ s). The kinematic viscosity n is defined as the ratio of the absolute viscosity to density at the same temperature and pressure. The SI unit for n is m2/s, but again cgs units are very common and n is often given in stokes (1 St = 1 cm2/s) or centistokes (1 cSt = 0.01 cm2/s). Gases Experimental data for gases and vapors at low density are often correlated with (2-84) A = 10  M    −7  kg/kmol  1/2 (Tc /K) (2-86) N ∑n C i i i =1 For inorganic gases, A is obtained from  M  1/2  P  2/3  T  −1/6  c c A = 1.6104 × 10 −10         g/mol   Pa   K   TABLE 2-173 Group (2-87) Reichenberg* Group Contribution Values Ci Group }CH3 9.04 }F >CH2 6.47 }Cl >CH} 2.67 }Br >C< −1.53 }OH alcohol =CH2 7.68 >O =CH} 5.53 >C=O >C= 1.78 }CHO ≡CH 7.41 }COOH ≡C} 5.24 }COO} or HCOO} >CH2 ring 6.91 }NH2 >CH} ring 1.16 >NH >C< ring 0.23 =N} ring =CH} ring 5.90 }CN >C= ring 3.59 >S ring *Reichenberg, D., AIChE J., 21 (1975): 181. Ci 4.46 10.06 12.83 7.96 3.59 12.02 14.02 18.65 13.41 9.71 3.68 4.97 18.13 8.86 2-352 PHYSICAL AnD CHEMICAL DATA Example Estimate the low-pressure vapor viscosity of ethyl acetate at 401.25 K. Required constants: The DIPPR 801 database recommends the following values: Tc = 523.3 K M = 88.1051 g/mol Pc = 3.88 MPa where rc = Pc /(ZcRTc) and m = 1.78 D T ξ = 2173.4  c   K Supporting quantities: Structural groups:  M   kg/kmol  −1/2  Pc    MPa  −2/3 (2-93) Example Estimate the vapor viscosity of CO2 at 350 K and 20 MPa if h° = 0.0174 mPa ⋅ s and Z = 0.4983 (estimated from Lee-Kesler method, see section on density). Required properties: From the DIPPR 801 database, M = 44.01 kg/kmol Group ni Ci Contribution —CH3 2 9.04 18.08 >CH2 1 6.47 6.47 —COO— 1 13.41 13.41 Total Zc = 0.274 Auxiliary quantities: ρc = 37.96 ρr = From Eqs. (2-66) and (2-85): µ∗r = 52.46 Tc = 304.21 K Pc = 7.383 MPa m = 0 D (nonpolar) x = (2173.4)(304.21)1/6 (44.01)−1/2(7.383)−2/3 = 224.1 Tr = (401.25 K)/(523.3 K) = 0.767 7.383 MPa kmol = 10.654 3 0.274 [0.008314 m 3 MPa/(K ⋅ kmol)](304.21 K) m 20 MPa ρ P = = = 1.295 ρc ZRT ρc 0.4983[0.008314m 3 ⋅ MPa/(K ⋅ kmol)](350 K) (10.654 m 3 ⋅ kmol) Calculation using Eq. (2-88) for nonpolar fluids: (1.78)2 (38.8) = 0.024 (523.3) 2 1/4   η− ηo   + 1  224.1   mPa ⋅ s    From Eq. (2-86): = 1.0230 + 0.23364(1.295) + 0.58533(1.295) 2 − 0.40758(1.295) 3 + 0.093324(1.295) 4 = 1.684 (88.1051)1/2 (523.3) A = 10 = 1.294 × 10 −5 37.96 −7 η= Calculation using Eq. (2-84): 1.684 4 − 1 mPa ⋅ s + 0.0174 mPa ⋅ s = 0.0489 mPa ⋅ s 224.1 This differs from the experimental value of 0.0473 mPa ⋅ s by 3.4 percent. (1.294 × 10 −5 ) (0.767) 2 1 + (270) (0.024) 4 ηo = = 1.003 × 10 −5 1/6 Pa ⋅ s [1 + (0.36) (0.767) (0.767 − 1)] 0.767 + (270) (0.024) 4 The estimated value is 1.5 percent lower than the DIPPR 801 recommended value of 1.018 × 10−5 Pa ⋅ s. The dependence of viscosity upon pressure is principally a density effect. Estimation of vapor viscosity at elevated pressures is commonly done by correlating density deviations from the low-pressure values estimated. Several methods are available, but the method developed by Jossi et al. and extended to polar fluids by Stiel and Thodos is relatively accurate and easy to apply. Recommended Method Jossi-Stiel-Thodos method. References: Stiel, L. I., and G. Thodos, AIChE J., 10 (1964): 26; Jossi, J. A., L. I. Stiel, and G. Thodos, AIChE J., 8 (1962): 59. Classification: Empirical correlation and corresponding states. Expected uncertainty: 9 percent—often less for nonpolar gases, larger for polar gases. Applicability: Nonassociating gases; rr < 2.6. Input data: M, Tc, Pc, Zc, m, ho (low-pressure viscosity at same T may be estimated by using methods given above), and r (may be calculated from T and P by using density methods given above). Description: Deviation of h from the low-pressure value ho is given by one of the following correlations depending upon its polarity and reduced density range: For nonpolar gases, 0.1 < rr < 3.0:   η− ηo    ξ + 1   mPa ⋅ s  1/6 1/4 = 1.0230 + 0.23364 ρr + 0.58533ρr2 − 0.40758ρ3r + 0.093324 ρr4 (2-88) Liquids Liquid viscosity can be correlated as a function of temperature for low pressures. Usually the correlation is based on the Andrade equation [Andrade, E. N. da C., Nature, 125 (1930): 309] ln ( η) = A + (2-94) or an extension of it. For example, the DIPPR 801 database uses the equation ln ( η) = A + B + C ln T + DT E T (2-95) which is analogous to the Riedel [Riedel, L., Chem. Ing. Tech., 26 (1954): 83] vapor pressure equation. Currently the most accurate method for predicting pure liquid viscosity is the GC method by Hsu et al. It has been found that most liquids have a viscosity between 0.15 mPa ⋅ s (or cP) and 0.55 mPa ⋅ s at the normal boiling point, and this “rule” can be used as a valuable criterion to validate estimated viscosities as a function of temperature. Recommended Method Hsu method. Reference: Hsu, H.-C., Y.-W. Sheu, and C.-H. Tu, Chem. Eng. J., 88 (2002): 27. Classification: Group contributions. Expected uncertainty: 20 percent. Applicability: Organic liquids; Tr < 0.75. Input data: Pc and molecular structure. Description: The temperature dependence of the liquid viscosity is given by N ∑ ci  N  N P η  N ln  = ∑ ai + T ∑ bi + i =1 2 +  ∑ di  ln  c    mPa ⋅ s  i =1 T  i =1   bar  i =1 For polar gases, rr ≤ 0.1:  η− η  1.111  mPa ⋅ s  ξ = 1.656ρr B T o (2-89) (2-96) where Pc is critical pressure and ai, bi, ci, and di are the group contributions obtained from Table 2-174. For polar gases, 0.1 < rr ≤ 0.9:  η− ηo  1.739  mPa ⋅ s  ξ = 0.0607 (9.045ρr + 0.63) (2-90) Example Estimate the liquid viscosity of benzotrifluoride at 303.15 K. Structural information: For polar gases, 0.9 < rr ≤ 2.2:  η− ηo     log  4 − log   ξ   = 0.6439 − 0.1005ρr  mPa ⋅ s     (2-91) For polar gases, 2.2 < rr ≤ 2.6:  η− ηo     3 2 log  4 − log   ξ   = 0.6439 − 0.1005ρr − 0.000475(ρr − 10.65)  mPa ⋅ s     (2-92) Group >C< (=CH})A (=C<)A (—F)3 Number 1 5 1 1 a 1.0031 −0.8570 0.7896 1.5394 Total −0.9529 100b 0.0001c d −0.3677 −0.0098 −0.0231 0.8465 0.4067 −6.0316 2.4376 −0.9222 17.8121 23.0463 1.1972 0.1311 0.1928 −2.9915 −0.9460 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-174 Group Contributions for the Hsu et al. Method* Table-specific nomenclature: R = in nonaromatic ring, A = in aromatic ring, RC = attached to nonaromatic ring, AC = attached to aromatic ring, X = halogen, (−X)n = n X atoms attached to same C atom Group a 100b 0.0001c d −1.0563 −0.2382 0.0060 0.4028 −0.3677 −0.2656 0.1612 0.4305 −0.1106 −0.0111 −0.1778 0.7637 −0.0120 1.7694 −0.0098 −0.0231 0.0444 0.0683 1.2165 −0.8665 0.8928 0.7556 1.4157 4.5094 −6.0316 0.9860 1.9408 3.1287 4.4245 0.3265 0.8437 7.2433 2.0143 19.0452 2.4376 −0.9222 8.1690 8.8426 34.2857 −14.7474 −0.0019 −0.1765 0.0751 0.6679 1.1972 −0.4417 0.2507 1.0465 −24.1836 25.0542 −1.5184 8.5951 −0.3677 13.3885 0.1311 0.1928 −0.4351 −0.1685 −11.6500 −2.7574 −0.5310 −1.0010 −0.3645 2.4275 0.8509 −0.3634 0.6362 −0.4377 0.0985 −0.2847 0.0872 −0.2612 0.1142 −0.2405 0.0413 −0.1841 −0.1693 −0.0113 −0.2162 0.0006 1.5834 0.0111 0.2848 1.0614 0.1801 0.1322 0.0427 0.0779 −0.0965 −0.3285 1.2621 0.5248 −1.2592 0.6232 9.5499 13.8366 29.8404 78.5417 77.1759 23.2329 50.0840 17.2243 2.9405 −4.3145 6.4296 3.7241 6.7008 3.8828 27.4079 12.6878 20.0309 9.4694 1.9325 5.4231 34.5474 7.2831 9.3746 49.1049 12.9392 15.8672 12.1837 4.4123 6.0066 1.9387 23.1473 14.2694 −23.9353 27.5184 −1.0300 0.3418 0.4246 0.9650 −6.9285 −0.0172 −1.0539 0.7139 0.1149 8.3131 0.5389 0.2386 0.7348 −12.4994 0.0002 1.1139 0.0279 0.6071 0.4686 0.8717 −0.4244 3.6587 2.1486 2.8583 2.8987 −0.0701 −0.0948 0.9549 0.3464 0.1148 1.3950 3.7646 0.8329 7.7525 −0.2126 −0.1723 0.4842 −0.0180 0.2208 0.5975 −0.2774 0.0432 26.4615 0.1316 1.5664 −4.5188 0.6712 0.1910 7.0544 5.7804 6.1893 23.2752 14.9707 14.0415 31.8007 20.9135 394.1670 45.5193 60.8742 −62.0987 37.9465 12.0578 0.1336 1.6467 0.4718 1.0653 0.1171 −0.0031 0.0001 1.8795 0.3530 1.2172 −4.6399 1.2353 1.9199 −0.0276 C, H Groups CH4 }CH3 }CH2} >CH} >C< =CH2 =CH} =C< ≡CH ≡C} (}CH2})R (>CH})R (=CH})R cycloalkene (>C<)R spirocyclane (=CH})A (=C<)A cycloalkene (=C<)A bi/terphenyl (=C<)A naphthalene (=C<)A turpentine (=C<)A tetralin −1.7296 0.0570 −0.1497 −2.2942 1.0031 0.9256 1.3365 −3.5020 87.6040 −91.6154 6.0416 −33.8745 1.2028 −56.2158 −0.8570 0.7896 2.0973 0.4392 27.3350 14.2586 }OH primary for C<3 }OH primary for C>2 }OH secondary }OH tertiary (}OH)RC }OH polyhydric (}OH)AC }OH alkoxyalcohol }O} (}O})R (}O})AC }CHO >CO (>CO)R HCOOH }COOH for C<7 }COOH for C>6 HCOO} }COO} for C<8 }COO} for C>7 >CHO} }(CO)}O}(CO)} anhydride }O}(CO)}O} carbonate (>NO)R }NO2 =CHNO2 (}NO2)AC }S} }SH primary }SH secondary }SH tertiary }CSO} for C<13 }CSO} for C>12 >SO 5.7852 1.4351 −2.6895 −18.5630 16.7808 −0.0125 −2.0856 −2.6991 −0.7185 −29.8045 −2.3454 −0.8288 −2.6622 45.9143 −2.7291 −4.0451 −0.6721 −3.3731 −0.0635 −2.5390 −5.4872 −11.8236 −8.0314 −16.9531 −13.0333 −1.9653 −1.2954 −3.2767 −2.1030 −0.2481 −12.3498 −15.2678 3.7475 −32.8607 O, S Groups N, X Groups }NH2 }NH} }N< (}NH2)AC (}NH})AC (}N<)AC HCONH2 HCONH} HCON< }CONH2 }CONH} }COONH2 }COONH} (>NH)R −1.1345 −6.9489 −2.1403 −6.3646 −1.7592 −1.2982 −1.5435 −8.1097 −122.3280 −6.7363 8.9977 17.8400 −10.1316 −0.1589 (Continued ) 2-353 2-354 PHYSICAL AnD CHEMICAL DATA TABLE 2-174 Group Contributions for the Hsu et al. Method* (Continued ) Table-specific nomenclature: R = in nonaromatic ring, A = in aromatic ring, RC = attached to nonaromatic ring, AC = attached to aromatic ring, X = halogen, (−X)n = n X atoms attached to same C atom Group a 100b 0.0001c d 0.1120 −0.1324 −0.0086 −0.3851 −0.1934 −1.0770 −0.3220 −0.4130 −0.0623 0.2607 −1.1189 0.8465 −0.2352 −0.3682 −0.5629 0.0109 0.1403 −0.6623 −0.3420 −0.1635 −0.2787 −0.0245 −0.0470 6.98437 7.7955 8.6310 3.0118 3.7798 0.1882 8.8683 13.3194 4.1382 11.3406 1.3134 17.8121 −0.1505 4.6451 3.6831 5.9474 10.3743 −2.4228 1.4253 3.0150 4.3362 7.2061 8.2815 0.9719 0.6293 −0.6443 0.5524 −0.4748 1.2223 0.1702 −1.1972 −0.2644 1.8461 2.6681 −2.9915 −0.2893 −0.0751 0.3613 −14.5771 −1.1972 0.7385 73.6293 0.0621 0.5635 −18.9106 0.4485 N, X Groups (=N})R }C≡N (}C≡N)AC }Cl primary =CHCl (}Cl)2 (}Cl)3 (}Cl)4 (}Cl)AC }F primary (}F)2 (}F)3 (}F)AC (}F)(}Cl) (}F)(}Cl)2 (}F)2(}Cl) (}F)2(}Cl)2 }Br primary }Br secondary (}Br)AC }I primary (}I)AC }(CO)}Cl −4.7601 −2.7194 0.9435 −1.7997 1.5851 −3.0561 −1.3357 4.2070 −0.3083 −9.4982 −10.3980 1.5394 0.4079 −0.8565 −3.4552 54.2824 −2.1710 −0.7586 −279.0030 −8.1919 −1.4672 70.9918 −2.3300 *Hsu, H.-C., Y.-W. Sheu, and C.-H. Tu, Chem. Eng. J., 88 (2002): 27 Supporting values: Pc = 32.1 MPa Calculation using Eq. (2-96): η   230,463 = exp  −0.9529 + (0.004067)(303.15) + − 0.9460 ln(32.1)  = 0.610 mPa ⋅ s (303.15) 2   The estimated value is 20 percent higher than the DIPPR 801 value of 0.509 mPa ⋅ s. Note that when the calculation is repeated at the normal boiling point (375.2 K), one obtains 0.343 mPa ⋅ s which is within the range of the aforementioned empirical rule. Liquid Mixtures Most methods for estimating liquid mixture viscosity interpolate between the pure-component values at the same temperature. The Grunberg-Nissan equation [Grunberg, L., and A. H. Nissan, Nature, 164 (1949): 799] C ln η = ∑ x i ln ηi + i C viscosity of organic mixtures without any mixture data. It can estimate mixture viscosity to a limited accuracy, but it is limited in scope by the small number of group contributions currently available. Recommended Method UNIFAC-VISCO method. Reference: Chevalier, J. L., P. Petrino, and Y. Gaston-Bonhomme, Chem. Eng. Sci., 43 (1988): 1303; Gaston-Bonhomme, Y., P. Petrino, and J. L. Chevalier, Chem. Eng. Sci., 49 (1994): 1799. Classification: Group contributions. Expected uncertainty: 20 percent. Applicability: Organic liquids. Input data: Molecular structure; pure-component molar volumes and viscosities at the mixture temperature. Description: Liquid mixture viscosity can be estimated in a manner similar to the UNIFAC method employed for mixture excess Gibbs energy and activity coefficients. The primary equation is  ηi V  gE gE η  C ⋅ i + c − r ln  = x i ln   mPa ⋅ s  ∑  mPa ⋅ s Vm  RT RT i =1 C 1 ∑ ∑ x i x j Gij 2 i =1 j =1 (2-97) is commonly used for nonaqueous mixtures. The parameter Gij generally must be regressed from an experimental mixture viscosity. However, Gij can be set to zero for hydrocarbon mixtures with expected errors in the mixture viscosity of about 15 percent. Estimation of liquid mixture viscosity without any mixture data is difficult because the viscosity is strongly affected by large molecular size differences and strong cross-interactions between different types of molecules. The UNIFAC-VISCO method described below can be used to predict liquid (2-98) where Vm is the mixture molar volume and Vi is the pure-component molar volume of component i. The combinatorial and residual excess Gibbs energies are calculated as in the standard UNIFAC method for activity coefficients (see [PGL5]) and for brevity is not shown here. However, the group interactions ymn are calculated using the interaction parameters αmn obtained from Table 2-175 in the equation α ψ mn = exp  − mn   298.15  TABLE 2-175 UnIFAC-VISCO* Group Interaction Parameters `mn m/n CH2 CH3 CH2cy CHar Cl CO COO OH CH3OH CH2 CH3 CH2cy CHar Cl CO COO OH CH3OH 0 −709.5 −538.1 −623.7 −710.3 586.2 541.6 −634.5 −526.1 66.53 0 187.3 237.2 375.3 −21.56 −44.25 1209.0 653.1 224.9 −130.7 0 50.89 −163.3 740.6 416.2 −138 751.3 406.7 −119.5 8.958 0 −139.8 −117.9 −36.17 197.7 51.31 60.30 82.41 251.4 177.2 0 −4.145 240.5 195.7 −140.9 859.5 11.86 −125.4 128.4 −404.3 0 22.92 664.1 −22.59 1172.0 −172.4 −165.7 −49.85 −525.4 29.20 0 68.35 −286.2 498.6 594.4 694.4 419.3 960.2 221.5 186.8 0 −23.91 −219.7 −228.7 −381.53 −88.81 −165.4 55.52 69.62 416.4 0 *Chevalier, J. L., P. Petrino, and Y. Gaston-Bonhomme, Chem. Eng. Sci., 43 (1988): 1303; Gaston-Bonhomme, Y., P. Petrino, and J. L. Chevalier, Chem. Eng. Sci., 49 (1994): 1799. (2-99) PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Example Estimate the viscosity of a mixture of 51.13 mol% ethanol(1) and 48.87 mol% benzene(2) at 298.15 K. Required input: Values from the DIPPR 801 database for the pure components at 298.15 K are h1 = 1.0774 mPa ⋅ s, h2 = 0.5997 mPa ⋅ s, V1 = 0.05862 m3/kmol, and V2 = 0.08948 m3/kmol. Groups, area fractions, and volume fractions: Group R Q N1 N2 CH3 0.9011 0.8480 1 0 CH2 0.6744 0.5400 1 0 CHar 0.5313 0.4000 0 6 OH 1.0000 1.2000 1 0 r2 q2 Group r1 q1 CH3 0.9011 0.848 0 0 CH2 0.6744 0.54 0 0 CHar 0 0 3.1878 2.4 OH 1 1.2 0 0 2.588 3.1878 2.4 Total 2.5755 2-355 Group fractions in pure components: Ethanol Group N X XQ Q lng CH3 CH2 CHar OH 1 1 0 1 0.3333 0.3333 0.0000 0.3333 0.283 0.180 0.000 0.400 0.3277 0.2087 0.0000 0.4637 0.5306 −0.9405 0.2095 0.6179 Sum 3 0.863 Benzene Group CH3 CH2 CHar OH N X XQ Q lng 0 0 6 0 0 0 1 0 0 0 0.4 0 0 0 1 0 0.257 −0.728 0.000 2.270 Sum 6 0.4 The pure-component Q and ln g equations are the same as shown above for the mixture groups. UNIFAC residual term: where in the above table N qi = ∑ N i ,k Qk and k =1 θ1 = 4 ∑x q i ri = ∑ N i ,k Rk k =1 (0.5113) (2.588) = = 0.53 (0.5113) (2.588) + (0.4887) (2.4) x 1 q1 2 g rE   4 = ∑ x i ∑ N m ,i (ln γ m − ln γ m ,i )  = 0.3425 RT i =1  m=1  N where Nm and ln gm refer to the mixture and Nm,i and ln gm,i refer to the pure-component values. Mixture volume: θ2 = 0.47 i 2  m3   m3  Vm = ∑ x iVi = 0.5113  0.05862 + 0.4887  0.08948   kmol  kmol  i =1 i =1 φ1 = x 1 r1 4 ∑x r (0.5113)(2.5755) = = 0.458 (0.5113)(2.5755) + (0.4887)(3.1878) φ2 = 0.542 = 0.07370 i i i =1 Using Eq. (2-98): UNIFAC combinatorial term: 2 2 E C m3 kmol η  0.05862    = 0.5113 ln 1.0774  ln   0.07370    mPa ⋅ s   g φ θ = ∑ x i ln i + 5∑ x i qi ln i = 0.124 RT i =1 xi φi i =1 0.08948    + 0.124 − 0.3425 = −0.4523 + 0.4887 ln  0.5997   0.07370    Group interactions: h = exp(−0.4523) mPa ⋅ s = 0.636 mPa ⋅ s αmn m/n group CH3 CH2 CHar OH CH3 CH2 CHar OH 0 66.53 237.2 1209 −709.5 0 −623.7 −634.5 −119.5 406.7 0 197.7 594.4 498.6 419.3 0 ymn m/n group CH3 CH2 CHar OH CH3 CH2 CHar OH 1.000 0.800 0.451 0.017 10.801 1.000 8.100 8.399 1.493 0.256 1.000 0.515 0.136 0.188 0.245 1.000 The αmn values were obtained from Table 2-175, and ymn values were calculated from Eq. (2-99). Group fractions in the mixture: Group N X XQ Q ln g CH3 0.5113 0.1145 0.097083 0.17370 0.293 CH2 0.5113 0.1145 0.061822 0.11061 −0.873 CHar 2.9322 0.6565 0.262618 0.46988 0.066 OH 0.5113 0.1145 0.137382 0.24581 1.077 Sum 4.4661 0.558905 The estimated value is 6.6 percent below the reported experimental value of 0.681 mPa ⋅ s [Kouris, S., and C. Panayiotou, J. Chem. Eng. Data, 34 (1989): 200]. THERMAL COnDUCTIVITY Thermal conductivity, k, is a measure of the rate at which heat conducts through the material and is defined as the proportionality constant in Fourier’s law of heat conduction that relates the gradient of temperature to the heat flux or flow per unit area. In SI, it has the units of W/(m ⋅ K). The conduction mechanism in gases is primarily via molecular collisions, and k increases with increasing temperature (increasing molecular velocity). The temperature dependence of low-pressure, gas-phase thermal conductivity is adequately correlated with k= AT B C 1+ T In dense media such as liquids, energy transfers more efficiently through the intermolecular force fields than through collisions. As a result, liquid thermal conductivity generally decreases with increasing temperature (except for water, aqueous solutions, and a few multihydroxy and multiamine compounds), corresponding to the decrease in density with increased temperature. The temperature dependence of liquid thermal conductivity at low to moderate pressures has been found to be well correlated by [Jamieson, D. T., J. Chem. Eng. Data 24 (1979): 244] k = A (1 + Bτ1/3 + C τ 2/3 + Dτ) Here Θ m = X mQm 4 ∑X Q i i =1 i 4    4  Θψ  and ln γ m = Qm 1 − ln  ∑ Θi ψ i ,m  − ∑ 4 i m ,i      1 i 1 i = =   ∑ Θ j ψ j ,i     i =1   (2-100) (2-101) where t = 1 – T/TC. For nonassociating liquids, this equation can be simplified to two parameters by setting C = 1 − 3B and D = 3B, generally without much loss in accuracy. Below or near the normal boiling point, the 2-356 PHYSICAL AnD CHEMICAL DATA temperature dependence of liquid thermal conductivity is nearly linear for modest temperature ranges and can be represented by (2-102) k = A − BT where B is generally in the range of 1 × 10−4 to 3 × 10−4 W/(m ⋅ K2). Gases Methods for estimating low-pressure gas thermal conductivities are based on kinetic theory and generally correlate the dimensionless group kM/hCu (M = molecular weight, h = viscosity, Cu = isochoric heat capacity), known as the Eucken factor. The method of Stiel and Thodos is recommended for pure nonpolar compounds, and the method of Chung is recommended for pure polar compounds. Recommended Method Stiel-Thodos method. Reference: Stiel, L. I., and G. Thodos, AIChE J., 10 (1964): 26. Classification: Empirical extension of theory. Expected uncertainty: 15 percent. Applicability: Pure nonpolar gases at low pressure. Input data: M, Tc, h, and Cu. Description: The following equations may be used depending upon the molecular shape: kM = 2.5 ηC υ monatomic  R  0.3523  kM = 1.30 +    1.7614 − Tr  ηC υ  Cυ    R kM = 1.15 + 2.033   ηC υ  Cυ  linear molecules nonlinear molecules (2-103) (2-104) (2-105) where h = viscosity at same conditions as desired for k. Because this method is only applicable at low pressures, Cu may usually be calculated as C op − R, where C op is the ideal gas isobaric heat capacity. Example Estimate the low-pressure thermal conductivity of toluene vapor at 500 K. Required properties from the DIPPR 801 database: M = 92.138 g/mol h(500 K) = 1.1408 × 10−5 Pa ⋅ s Tc = 591.75 K Cu = Cpo − R = (170.78 − 8.314) J/(mol ⋅ K) = 162.47 J/(mol ⋅ K) Auxiliary quantities: Example Estimate the low-pressure thermal conductivity of naphthalene vapor at 500 K. Required properties from the DIPPR 801 database: M = 128.17 g/mol Tc = 748.4 K h(500 K) = 1.0173 × 10−5 Pa ⋅ s w = 0.30203 Cu = Cpo − R = (219.82 − 8.314) J/(mol ⋅ K) = 211.51 J/(mol ⋅ K) Auxiliary quantities [Eqs. (2-107) and (2-108)]: Tr = 500/748.4 = 0.6681 R/Cu = (8.314)/(211.51) = 0.0393 g = 2.0 + (10.5)(0.6681)2 = 6.6866 α = (0.0393)−1 − 1.5 = 23.9388 b = 0.7862 − (0.7109)(0.30203) + (1.3168)(0.30203)2 = 0.6916  0.215 + 0.28288 (23.9388) − 1.061(0.6916) + 0.26665(6.6866)  Ψ = 1 + (23.9388)   0.6366 + 0.6916 (6.6866) + 1.061(23.9388) (0.6916)   = 9.4273 From Eq. (2-106): J    −5  (1.1408 × 10 Pa ⋅ s)  8.314 mol ⋅ K   mW k = (3.75) (9.4273)   = 23.33 g m⋅K   128.17 mol   The estimated value is 1.0 percent above the DIPPR 801 value of 23.09 mW/(m⋅K). Liquids For hydrocarbons at low to moderate pressures, a modification of the Pachaiyappan method should be used. For nonhydrocarbons, the Baroncini method provides accurate liquid thermal conductivity estimates for compounds clearly belonging to one of the chemical families specified below. Otherwise, the Missenard method is recommended as a general method for estimating thermal conductivity of pure liquids at ambient pressure. Recommended Method Modified Pachaiyappan. Reference: Pachaiyappan, V., S. H. Ibrahim, and N. R. Kuloor, Chem. Eng. 74(4) (1967): 140; API Technical Databook, 10th ed., chap. 12, 2017. Classification: Empirical correlation. Expected uncertainty: 10 percent. Applicability: Hydrocarbons only; low to moderate pressures. Input data: M, Tb, and Tc. Description: m  M  C  g ⋅ mol −1  k = −1 −1 V293   W ⋅m K  cm3 ⋅ mol −1  Tr = 500/591.75 = 0.845 R/Cu = (8.314)/(162.47) = 0.0512 From Eq. (2-105): J    −5  (1.1408 × 10 Pa ⋅ s)  162.47 mol ⋅ K   mW k = [1.15 + (2.033) (0.0512)]   = 25.2 g m⋅K   92.138 mol    3 + 20(1 − Tr )2/3   2/3   3 + 20(1 − Tr ,293 )  where M is molecular weight, V293 is the molar volume at 293.15 K, Tr is the reduced temperature, Tr,293 = (293.15 K)/(Tc) and the correlation parameters C and m are obtained from the table below: Classification The estimated value is 18 percent below the DIPPR 801 value of 30.76 mW/(m ⋅ K). Recommended Method Chung-Lee-Starling method. Reference: Chung, T.-H., L. L. Lee, and K. E. Starling, Ind. Eng. Chem. Fundam., 23 (1984): 8. Classification: Corresponding states. Expected uncertainty: 15 percent. Applicability: Pure organic gases at low pressure. Input data: Cv, w, Tc, M, and h. Description: The following equations apply: C m Unbranched, straight-chain hydrocarbon 0.1811 1.001 All branched, cyclic and aromatic hydrocarbons 0.4407 0.7717 Example Estimate the thermal conductivity of liquid n-butylbenzene at low pressure and 333.15 K. Required properties from DIPPR 801 database: M = 134.218 g/mol Tc = 660.5 K (2-106) V293 = 162.01 cm3/mol Auxiliary properties: Tr = (333.15 K)/(660.5 K) = 0.5044  R kM = 3.75 Ψ   ηC υ  Cυ  (2-109) Tr,293 = (293.15 K)/(660.5 K) = 0.4438 Since this is an aromatic hydrocarbon, C = 0.4407 and m = 0.7717 ( from the above table) From Eq. (2-109):  0.215 + 0.28288α − 1.061β + 0.26665 γ  Ψ = 1+ α   0.6366 + βγ + 1.061αβ  C α = υ − 1.5 β = 0.7862 − 0.7109ω + 1.3168ω 2 R (2-107) γ = 2.0 + 10.5 Tr2 (2-108) k (0.4407) (134.218 ) = (W ⋅ m -1 K -1 ) 162.01 0.7717  3 + 20(1 − 0.5044)2/3   3 + 20(1 − 0.4438)2/3  = 0.112   The estimated value is 5 percent below the experimental value of 0.118 W/(m ∙ K) reported by Rastorguev and Pugach [Rastorguev, Yu. L., and V. V. Pugach, Izv. Vyssh. Uchebn. Zaved., Neft Gaz, 13 (1970): 69]. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES Recommended Method 1 Baroncini method. Reference: Baroncini, C., F. DiFilippo, G. Latini, and M. Pacetti, Int. J. Thermophys., 2 (1981): 21. Classification: Empirical correlation. Expected uncertainty: 10 percent. Applicability: Particularly accurate for the following families: acetates, aliphatic ethers, halogenated compounds, dicarboxylic acids, ketones, aliphatic alcohols, aliphatic acids, propionates and butyrates, and unsaturated aliphatic esters. Input data: M, Tb, and Tc. Description: −β α −γ k T  M   Tc  (1 − Tr )0.38 = A  b        W/(m ⋅ K) K  g/mol  K Tr1/6 (2-110) Required properties from DIPPR 801 database: Tb = 475.133 K Tr = T/Tc = (400 K)/(704.65 K) = 0.5677 From Table 2-176 for alcohols: α = 1.2 β= 1 2 γ = 0.167 From Eq. (2-110): k (1 − 0.5677) 0.38 = (0.00339)(475.13)1.2 (108.1378) − 1/2 (704.65) −0.167 = 0.142 W/(m ⋅ K) 0.56771/6 The estimated value is 7.6 percent higher than the DIPPR 801 value of 0.132 W/(m ⋅ K). Recommended Method 2 Missenard method. Reference: Missenard, A., Comptes Rendus, 260 (1965): 5521. Classification: Corresponding states. Expected uncertainty: 20 percent. Applicability: Organic compounds; nonassociating. Input data: Tc, nA (number of atoms in molecule), r273 (liquid density at 273.15 K), Tb, M, Cp,273 (liquid heat capacity at 273.15 K). Description:  8.4  T 1/2  ρ  k273 =  1/4   b   273 3  mW/(m ⋅ K)  N A   K   g/m  k= 1/2  M   g/mol  −1/2 nA = 18 Tb = 412.27 K M = 106.165 kg/kmol Cp,273 = 200.64 kJ/(kmol ⋅ K) Auxiliary properties: Tr = 350/617 = 0.5673 Tr,273 = 273/617 = 0.4425 Tbr = 412.27/617 = 0.6682 From Eq. (2-111): k273 = (8.4)(412.27)1/2 (0.007681)1/2 (106.165) −1/2 (200.64)(18) −0.25 = 141.3 mW/(m ⋅ K) The estimated value is 4.5 percent above the DIPPR 801 value of 118.0 mW/(m⋅K). Auxiliary properties: A = 0.00339 ρ273 = 7.6812 kmol/m3 Tc = 617 K  141.3 mW  [3 + 20(1 − 0.5673)2/3 ]  k273 [3 + 20(1 − Tr )2/3 ]  mW m⋅K  k= = 123.3 = 3 + 20(1 − Tr ,273 )2/3 3 + 20(1 − 0.4425)2/3 m⋅K Example Estimate the thermal conductivity of liquid p-cresol at 400 K. Tc = 704.65 K Example Estimate the thermal conductivity of m-xylene at 350 K. Required properties from DIPPR 801 database: From Eq. (2-112): where A, α, β, and γ are obtained from Table 2-176. M = 108.1378 g/mol 2-357  C p ,273   J/(mol ⋅ K)    (2-111) k273 [3 + 20(1 − Tr )2/3 ] 3 + 20(1 − Tr ,273 )2/3 (2-112) where Tr,273 = (273 K)/Tc. Liquid Mixtures The thermal conductivity of liquid mixtures generally shows a modest negative deviation from a linear mass-fraction average of the pure-component values. Although more complex methods with some improved accuracy are available, two simple methods are recommended here that require very little additional information. The first method applies only to binary mixtures while the second can be used for multiple components. Recommended Method Filippov correlation. References: Filippov, L. P., Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk, 10 (1955): 67; Filippov, L. P., and N. S. Novoselova, Sugden, Vest. Mosk. Univ., Ser. Fiz. Mat. Estestv. Nauk, 10 (1955): 37. Classification: Empirical correlation. Expected uncertainty: 4 to 8 percent. Applicability: Binary liquid mixtures. Input data: Pure-component thermal conductivities ki at mixture conditions; wi. Description: The mixture thermal conductivity is calculated from the pure-component values using k = w1 k1 + w2 k2 − 0.72w1w2 k2 − k1 (2-113) where wi is the mass fraction of pure fluid i and ki is the thermal conductivity of pure component i at the mixture temperature. Recommended Method Li correlation. References: Li, C. C., AIChE J., 22 (1976): 927. Classification: Empirical correlation. Expected uncertainty: 4 to 8 percent. Applicability: Liquid mixtures. Input data: Pure-component thermal conductivities ki at mixture conditions; rL,i Description: The mixture thermal conductivity is correlated as a function of the mixture volume fractions fi: C C 2 ki k j j =1 ki + k j k = ∑ ∑ φi φ j i =1 (2-114) TABLE 2-176 Correlation Parameters for Baroncini et al. Method* for Estimation of Thermal Conductivity Family A a Saturated hydrocarbons 0.00350 1.2 Olefins 0.0361 1.2 Cycloparaffins 0.0310 1.2 Aromatics 0.0346 1.2 Alcohols 0.00339 1.2 Organic acids 0.00319 1.2 Ketones 0.00383 1.2 Esters 0.0415 1.2 Ethers 0.0385 1.2 Refrigerants R20, R21, R22, R23 0.562 0 Others 0.494 0 *Baroncini, C., et al., Int. J. Thermophys., 2 (1981): 21. b g 0.5 1 1 1 0.5 0.5 0.5 1 1 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.167 0.5 0.5 −0.167 −0.167 where φi = x i ρ−L1,i C ∑x j ρ−L1, j j =1 Example Estimate the thermal conductivity of a mixture containing 30.2 mol% diethyl ether(1) and 69.8 mol% methanol(2) at 273.15 K and 0.1 MPa, using the Filippov and Li correlations. Auxiliary data: The pure-component thermal conductivities and molar densities at 273.15 K recommended in the DIPPR 801 database are k1 = 0.1383 W/(m ⋅ K) r1 = 9.9335 kmol/m3 M1 = 74.1216 kg/kmol k2 = 0.2069 W/(m ⋅ K) r2 = 25.371 kmol/m3 M2 = 32.0419 kg/kmol The mass fractions corresponding to the mole fractions given above are w1 = 0.5 w2 = 0.5 2-358 PHYSICAL AnD CHEMICAL DATA The volume fractions are Example Estimate the surface tension of ethylacetylene at 237.45 K. Structure: -1 φ1 = (0.302)(9.9335) = 0.525 (0.302)(9.9335) -1 + (0.698)(25.371) -1 φ2 = 0.475 Calculation using Eq. (2-113): k = [(0.5)(0.1383) + (0.5)(0.2069) − (0.72)(0.5)(0.5) 0.2069 − 0.1383 ] W m⋅K = 0.160 W/(m ⋅ K) Group ni DPi ni DPi ≡CH ≡C— >CH2 (n = 1–11) CH3 1 1 1 1 43.64 28.64 39.92 55.25 43.64 28.64 39.92 55.25 Total 167.45 Calculation using Eq. (2-114): (0.525) (0.475) (2) (0.1383) (0.2069)  W  k = (0.525)2 (0.1383) + 2 ⋅ + (0.475)2 (0.2069)  0.1383 + 0.2069  m⋅K  = 0.167 W/(m ⋅ K) The Filippov value is 7.5 percent lower than the experimental value of 0.173 W/(m ⋅ K) [Jamieson, D. T., and B. K. Hastings, Thermal Conductivity, Proceedings of the Eighth Conference, C. Y. Ho and R. E. Taylor, eds., Plenum Press, New York, 1969]; the Li value is 3.5 percent lower than the experimental value. SURFACE TEnSIOn The surface at a vapor-liquid interface is in tension due to the difference in attractive forces experienced by molecules at the interface between the dense liquid phase and the low-density gas phase. This causes the liquid to contract to minimize the surface area. Surface tension is defined as the force in the surface plane per unit length. Jasper [Jasper, J. J., J. Phys. Chem. Ref. Data, 1 (1972): 841] has made a critical evaluation of experimental surface tension data for approximately 2200 pure chemicals and correlated surface tension s (mN/m = dyn/cm) with temperature as 4 13.2573   mN N  = 0.02429 σ = (167.45)   1000   m m  The estimated value is 0.9 percent above the DIPPR 801 recommended value of 0.02407 N/m. Recommended Method 2 Brock-Bird method. Reference: Brock, J. R., and R. B. Bird, AIChE J., 1 (1955): 174; Miller, D. G., Ind. Eng. Chem. Fundam., 2 (1963): 78. Classification: Corresponding states. Expected uncertainty: 5 percent. Applicability: Nonpolar and moderately polar organic compounds. Input data: Tc, Pc, and Tb. Description: σ P = (5.553 × 10 −5 )  c   Pa  mN/m Jasper’s evaluation also includes values of A and B for most of the tabulated chemicals. Surface tension decreases with increasing temperature and increasing pressure. Pure Liquids An approach suggested by Macleod [Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38] and modified by Sugden [Sugden, S. J., Chem. Soc., 125 (1924): 32] relates s to the liquid and vapor molar densities and a temperature-independent parameter called the Parachor P 4 (2-116) 2/3  Tc    K 1/3 F (1 − Tr )11/9 (2-118) where (2-115) s = A − BT σ   ρL − ρv   = P ⋅  mN/m   10 3 kmol/m3   Required properties: The DIPPR 801 database gives rL = 13.2573 kmol/m3 at 237.45 K. Calculation using Eq. (2-116): F= Tbr [ln(Pc /Pa) − 11.5261] − 1.3281 1 − Tbr (2-119) Example Estimate the surface tension for ethyl mercaptan at 303.15 K. Required properties from DIPPR 801: Tc = 499.15 K Pc = 5.49 × 106 Pa Tb = 308.15 K Supporting quantities: Tr = (303.15 K)/(499.15 K) = 0.6073 Tbr = (308.15 K)/(499.15 K) = 0.6173 F = {0.6173[ln (5.49 × 106) − 11.5261]/(1 − 0.6173)} − 1.3281 = 5.113 [ from Eq. (2-119)] From Eq. (2-118): where rL and rV are the saturated molar liquid and vapor densities, respectively. At low temperatures, where rL >> rV, the vapor density can be neglected, but at higher temperatures the density of both phases must be calculated. The surface tension is zero at the critical point where rL = rV. Quayle [Quayle, O. R., Chem. Rev., 53 (1953): 439] proposed a group contribution method for estimating P that has been improved in recent years by Knotts et al. [Knotts, T. A., et. al., J. Chem. Eng. Data, 46 (2001): 1007]. This method using P is recommended when groups are available; otherwise, the Brock-Bird [Brock, J. R., and R. B. Bird, AIChE J., 1 (1955): 174] corresponding-states method as modified by Miller [Miller, D. G., Ind. Eng. Chem. Fundam., 2 (1963): 78] may be used to estimate surface tension for compounds that are not strongly polar or associating. Recommended Method 1 Parachor method. References: Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden, S. J., Chem. Soc., 125 (1924): 32; Knotts, T. A., W. V. Wilding, J. L. Oscarson, and R. L. Rowley, J. Chem. Eng. Data, 46 (2001): 1007. Classification: Group contributions and QSPR. Expected uncertainty: 4 percent. Applicability: Organic compounds for which group values are available. Input data: rL, molecular structure, and Table 2-177. Description: Equation (2-116) is used with P calculated from N P = ∑ ni ∆Pi i =1 Group values for the Parachor are given in Table 2-177. (2-117) s = (5.553 × 10−5) (5.49 × 106)2/3(499.15)1/3(5.113) (1 − 0.6073)11/9 mN/m = 22.36 mN/m The estimated value is 1.4 percent lower than the DIPPR 801 value of 22.68 mN/m. Liquid Mixtures Compositions at the liquid-vapor interface are not the same as in the bulk liquid, and so simple (bulk) compositionweighted averages of the pure-fluid values do not provide quantitative estimates of the surface tension at the vapor-liquid interface of a mixture. The behavior of aqueous mixtures is more difficult to correlate and estimate than that of nonpolar mixtures because small amounts of organic material can have a pronounced effect upon the surface concentrations and the resultant surface tension. These effects are usually modeled with thermodynamic methods that account for the activity coefficients. For example, a UNIFAC method [Suarez, J. T., C. Torres-Marchal, and P. Rasmussen, Chem. Eng. Sci., 44 (1989): 782] is recommended and illustrated in [PGL5]. For nonaqueous systems the extension of the Parachor method, used above for pure fluids, is a simple and reasonably effective method for estimating s for mixtures. Recommended Method Parachor correlation. Reference: Hugill, J. A., and A. J. van Welsenes, Fluid Phase Equilib., 29 (1986): 383; Macleod, D. B., Trans. Faraday Soc., 19 (1923): 38; Sugden, S. J., Chem. Soc., 125 (1924). Classification: Corresponding states. Expected uncertainty: 3 to 10 percent. Applicability: Nonaqueous mixtures. PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES TABLE 2-177 Knotts* Group Contributions for the Parachor in Estimating Surface Tension Group Group DPi (a) Nonring C }CH3 55.25 >CH2 (n = 1–11) 39.92 >CH2 (n = 12–20) 40.11 >CH2 (n > 20) 40.51 >CH} 28.90 >C< 15.76 =CH2 49.76 =CH} 34.57 =C< 24.50 =C= 24.76 ≡CH 43.64 ≡C} 28.64 Branch corrections Per branch −6.02 sec-sec adjacency −2.73 sec-tert adjacency −3.61 tert-tert adjacency −6.10 (b) Nonaromatic ring C }CH2} 39.21 >CH} 23.94 >C< 7.19 =CH} 34.07 =C< 18.85 >CH} ( fused ring) 22.05 Ring corrections Three-member ring 12.67 Four-member ring 15.76 Five-member ring 7.04 Six-member ring 5.19 Seven-member ring 3.00 (c) Aromatic ring C >CH 34.36 >C} 16.07 }C} ( fused arom/arom) 19.73 }C} ( fused arom/aliph) 14.41 Arom ring corr ortho −0.60 para 3.40 meta 2.24 subst. naphthalene corr −7.07 (d) Oxygen groups }OH (alc, primary) 31.42 }OH (alc, sec) 22.68 }OH (alc, tertiary) 20.66 }OH (phenol) 30.32 }O} (nonring) 20.61 }O} (ring) 21.67 }O} (aromatic) 23.54 >C=O (nonring) 47.02 >C=O (ring) 50.04 O=CH} (aldehyde) 66.06 CHOOH ( formic) 94.01 }COOH (acid) 74.57 }OCHO ( formate) 82.29 }COO} (ester) 64.97 }COOCO} (acid anhyd) 115.07 }OC(=O)O} (ring) 84.05 *Knotts, T. A., et al., J. Chem. Eng. Data, 46 (2001): 1007. Input data: Liquid and vapor r at mixture T; Parachors of pure components; xi. Description: ρ ρ σm   =  PL ,m 3 L ,m 3 − Pv ,m 3 V ,m 3  mN/m  10 kmol/m 10 kmol/m  4 (2-120) where sm = surface tension of the mixture PL,m, PV,m = Parachor of liquid and vapor mixtures, respectively rL,m, rV,m = mixture molar density of liquid and vapor, respectively PL ,m = C 1 ∑ ∑ x i x j (Pi + Pj ) 2 i =1 j=1 C PV ,m = 44.98 44.63 46.44 46.53 29.04 31.97 33.92 10.77 15.71 23.24 26.49 80.94 65.23 67.54 93.43 73.64 57.05 91.69 77.12 64.32 73.86 75.05 66.89 63.34 65.33 68.30 51.37 51.75 51.47 72.21 93.20 90.13 21.81 26.24 51.16 54.56 66.30 70.39 90.84 92.04 105.11 54.50 44.93 28.64 115.59 48.84 22.65 25.06 106.03 Note that rV is generally very small compared to rL at temperatures substantially lower than Tc and can often be neglected. Example Estimate the surface tension for a 16.06 mol% n-pentane(1) + 83.94 mol% dichloromethane(2) mixture at 298.15 K. Required properties from DIPPR 801: P C 1 ∑ ∑ y i y j (Pi + Pj ) 2 i =1 j=1 DPi (e) Nitrogen groups R}NH2 (primary R) R}NH2 (sec R) R}NH2 (tert R) A}NH2 (attached to arom ring) >NH (nonring) >NH (ring) >NH (in arom ring) >N- (nonring) >N- (ring) }N= (nonring) >N (aromatic) HC≡N (hyd cyanide) }C≡N }C≡N (aromatic) ( f) Nitrogen and oxygen groups }C=ONH2 (amides) }C=ONH- (amides) }C=ON< (amides) }NHCHO >NCHO }N=O }NO2 }NO2 (aromatic) (g) Sulfur groups R-SH (primary R) R-SH (sec R) R-SH (tert R) }SH (aromatic) }S} (nonring) }S} (ring) }S} (aromatic) >S=O (nonring) >SO2 (nonring) >SO2 (ring) (h) Halogen groups }F }Cl }Br }I }F (aromatic) }Cl (aromatic) }Br (aromatic) }I (aromatic) (i) Si groups SiH4 >SiH} >Si< >Si< (ring) (j) Other inorganic groups }PO4 >P} >B} >Al} }ClO3 n-Pentane Dichloromethane The following definitions are used for the liquid and vapor mixture Parachors: C 2-359 (2-121) 8.6173 15.5211 Mixture Parachor from Eq. (2-121) and mixture density: PL,m = (0.1606)2(231.1) + (0.1606)(0.8394)(231.1 + 146.6) + (0.8394)2(146.6) = 160.17 −1 where xi is the mole fraction of component i in the liquid and yi is the mole fraction of component i in the vapor. rL/(kmol ⋅ m−3) at 298.15 K 231.1 146.6 −1  C x  0.1606 0.8394  kmol kmol ρL ,m =  ∑ i  =  = 13.752 3 +   8.6173 15.5211 m3 m  i =1 ρi  2-360 PHYSICAL AnD CHEMICAL DATA Calculation using Eq. (2-120): Because the temperature is low, the density of the vapor can be neglected, and mN σm = [(160.17) (0.013752)]4 = 23.54 mN/m m The estimated value is 2.9 percent below the experimental value of 24.24 mN/m reported by De Soria [De Soria, M. L. G., et al., J. Colloid Interface Sci., 103 (1985): 354]. FLAMMABILITY PROPERTIES Flash Point The flash point is the lowest temperature at which a liquid gives off sufficient vapor to form an ignitable mixture with air near the surface of the liquid or within the vessel used. ASTM test methods include procedures using a closed-cup apparatus (ASTM D 56, ASTM D 93, and ASTM D 3828), which is preferred, and an open-cup apparatus (ASTM D 92 and ASTM D 1310). Closed-cup values are typically lower than open-cup values. Estimation methods cannot take into account the apparatus and procedural influences on the observed flash point. Recommended Method Leslie-Geniesse method. Reference: Leslie, E. H., and J. C. Geniesse, International Critical Tables, vol. 2, McGraw-Hill, New York, 1927, p. 161. Classification: GC (element contributions). Expected uncertainty: ∼4 K or about 1.5 percent. Applicability: Organic compounds. Input data: Chemical structure and vapor pressure correlation. Description: The flash point TFP is obtained from the moles of oxygen required for stoichiometric combustion β, by back-solving from the vapor pressure correlation using P ∗ (TFP ) 1 = atm 8β (2-122) Recommended Method Rowley method. Reference: Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard. Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points, and Their Consanguinity: Critical Analysis, Experimental Exploration, and Prediction,” Ph.D. Dissertation, Brigham Young University, 2010. Classification: GC and extended theory. Expected uncertainty: 10 percent for the lower limit; 25 percent for the upper limit. Applicability: Organic compounds. Input data: Group contributions from Tables 2-178, ∆Hfo, and the thermal properties (ideal gas heat of formation and average isobaric heat capacity) of the combustion products. These latter quantities are given in Table 2-179. A vapor pressure correlation is also required to obtain the corresponding flammability limit temperature. Description: A GC method is used to obtain the adiabatic flame temperature (Tad) of a lower-limit fuel-air mixture using the ΔTad, j contributions shown in Table 2-178: ∑n ⋅∆T j o C p ,i H i (Tad ) ∆H f ,i (Tad − 298)K = + kJ/mol kJ/mol (kJ/mol ⋅ K) NC, NSi, NS, NH, NX, NO = number of carbon, silicon, sulfur, hydrogen, halogen, and oxygen atoms in the molecule, respectively Example Estimate the flash point of phenol. (2-125) The lower flammability limit in volume percent is then calculated from where P = vapor pressure at the flash point (2-123) (2-124) N where N is the total number of groups in the molecule. The ideal gas enthalpies Hi of the combustion products and oxygen at Tad are then calculated from the ideal gas enthalpies of formation at 298 K and the average isobaric heat capacities (given in Table 2-179) with Eq. (2-125): * N - N X - 2NO β = N C + N Si + N S + H 4 ad,j j Tad = 100% LFL = ν= 1+ ν ∆H of ,fuel − ∑ products ni H i (Tad ) + βH O2 (Tad ) C p ,air (Tad − 298) K (2-126) where β is defined in Eq. (2-123). The upper flammability limit in volume percent is obtained from the UFL group values given in Table 2-178 and Structure:  ∑n j ⋅ UFL j  UFL  j =  4.30C st0.72 +  % N     (2-127) where Cst is the fuel concentration required for stoichiometric combustion given by Atomic contributions: Atom type Number C H O 6 6 1 β = 6 + (6 − 2∙1)/4 = 7 From Eq. (2-123), The DIPPR 801 correlation for the vapor pressure of phenol is C st = 100 1 + 4.773β (2-128) Example Estimate the lower and upper flammability limits of toluene. Structure: 6  10,113 K P∗ T T  = exp  95.444 − − 10.09 In   + 6.7603 × 10 −18        T Pa K K   When this expression is used in Eq. (2-122) and solved for temperature, one obtains TFP = 350.84 K, which is 0.4 percent below the DIPRR recommended value of 352.15 K. Flammability Limits The lower flammability limit (LFL) is the equilibrium-mixture boundary-line volume percent of vapor or gas in air which if ignited will just propagate a flame away from the ignition source. Similarly, the upper flammability limit (UFL) is the upper volume percent boundary at which a flame can propagate in an ignited fuel/air equilibrium mixture. Each of these limits has a temperature at which the corresponding volumetric percent is reached. The lower flammability limit temperature corresponds approximately to the flash point, but since the flash point is determined with downward flame propagation and nonuniform mixtures and the lower flammability temperature is determined with upward flame propagation and uniform vapor mixtures, the measured lower flammability temperature is generally slightly lower than the flash point. Group contributions: Group CH3—c c— c—H nj ∆Tad 1 1 5 1862.04 1719.69 1731.92 UFLj −4.49 5.50 −1.25 Auxiliary calculations: Tad = [1862.04 + 1719.69 + (5)(1731.92)]/7 = 1748.8 β = 7 + 8/4 = 9 PREDICTIOn AnD CORRELATIOn OF PHYSICAL PROPERTIES 2-361 TABLE 2-178 Group Contributions for Quantities Used to Estimate Flammability Limits by Rowley et al.* Method for Organic Compounds (special notation: lower case indicates aromatic atom; # = triple bond; R = ring) Example DTad,i UFLi #C} vinyl acetate 991.44 −8.65 n pyridine 2622.13 4.46 #CH acetylene 1237.85 61.25 n piperazine 2124.88 13.32 =C< isobutene 1834.42 −7.15 >NH n-pentylamine 1566.76 −0.78 =CH trans-2-butene 1751.82 0.30 >N}(c) N-ethylaniline 2695.31 −7.25 =CH2 1-hexene 1558.49 3.06 N#C benzonitrile 939.73 −9.72 =CH}(c) styrene −76.72 −11.24 N=C=O methyl isocyanate 1147.48 4.95 =C}(c) α-methylstyrene 2091.10 −5.13 }NO2 nitroethane 1777.58 −11.46 >C< neopentane 1957.78 −0.23 }S} thiophene 1056.05 23.55 }CH isopropanol 1558.73 0.62 }SH ethyl mercaptan 1727.5 }CH2 propane 1705.21 −0.30 S= carbon disulfide Group Group Example DTad,i 272.36 UFLi 12.67 53.67 }CH3 butane 1856.30 −1.12 Si trimethylsilane −55.66 78.90 CH3}c toluene 1862.04 −4.49 Si(O3) tetraethoxysilane 2095.22 120.24 c} toluene 1719.69 5.50 (Si)}O} octamethyltrisiloxane 2347.17 −67.75 cH benzene 1731.92 −1.25 Si-(Cl) monochlorosilane 1062.27 −13.93 OH}(C) 1-methylcyclohexanol 786.14 4.90 Si}(Cl2) dichlorosilane 554.54 62.48 OH}(CH) isopropanol 1508.33 0.12 Si}(Cl3) methyl trichlorosilane −34.35 −18.52 −4.95 OH}(CH2) butanol 1397.73 5.32 F2}(C) 1,1-difluoroethane 2556.15 OH}(c) phenol 1337.25 9.15 F2}(C=C) 1,1-difluoroethylene 2088.23 3.43 OH}(CC#C) propargyl alcohol 2209.35 15.57 F3}(C) 3,3,3-trifluoropropene 2451.95 −12.81 O=C 3-pentanone 1532.45 2.50 O=CR cyclohexanone 954.03 −11.84 F}(C) methyl fluoride 1841.54 0.80 F}(C=C) vinyl fluoride 1477.04 15.38 −22.73 O=C}C=C methacrolein 1761.66 6.00 Cl2}(C) dichloromethane 2882.45 O=COC hexyl formate 1492.23 0.47 Cl2}(C=C) 1,1-dichloroethylene 2956.55 −15.50 (C)}O}(C) diethyl ether 1325.57 13.38 Cl3}(C) 1,1,1-trichloroethane 3046.39 −26.31 }COOH formic acid 1252.38 −5.12 Cl}(C) isopropyl chloride 1948.51 −5.20 }OR} furan 1402.11 26.05 Cl}(C=C) chloropropene 2294.79 0.16 }O}O} ethyl peroxide −728.23 0.76 Cl}(cc}Cl) o-dichlorobenzene 3257.79 −13.14 triethylamine 1442.71 8.85 Br} methylbromide 3389.83 >N} −24.38 *Rowley, J. R., R. L. Rowley, and W. V. Wilding, J. Hazard. Materials, 186 (2011): 551; Rowley, J. R., “Flammability Limits, Flash Points, and Their Consanguinity: Critical Analysis, Experimental Exploration, and Prediction,” Ph.D. Dissertation, Brigham Young University, 2010. Calculation of H(Tad ) from Eq. (2-125) and Table 2-179: Species H°(298 K)/(kJ/mol) Toluene CO2 H2O O2 Air Cp/[kJ/(mol ⋅ K)] 50.17 −393.51 −241.81 0 0 — 0.0372433 0.0335780 0.0293468 0.0289937 LFL = H(Tad)/(kJ/mol) — −339.48 −193.10 42.58 — From Eq. (2-126) and the stoichiometry of the combustion reaction, C7H8 + 9O2 = 7CO2 + 4H2O:  50.17 − [(7)(−339.48) + (4)(−193.10)] + (9)(42.58)  ν=  = 85.148 (0.0289937)(1749 − 298)   TABLE 2-179 Ideal Gas Enthalpies of Formation and Average Heat Capacities of Combustion Gases for Use in Eq. (2-125) Species Air O2 N2 CO2 H2O SO2 SiO2 HF HCl HBr HI H°/(kJ/mol) 0 0 0 −393.51 −241.81 −296.84 −305.43 −273.30 −92.31 −36.29 −26.50 100% = 1.16% 1 + 85.148 The UFL is found from Eqs. (2-127) and (2-128):   100 UFL = (4.30)    1 + (4.773)(9)  0.72 + −4.49 + 5.50 + (5)(−1.25) = 7.02% 7 These values agree well with the DIPPR 801 recommended values of 1.2 and 7.1 percent, respectively. Flammability limit temperatures are found by determining the temperature at which the vapor pressure equals the partial pressure corresponding to the LFL or UFL. The vapor pressure correlation for toluene from DIPPR 801 is 2  6729.8 K P∗ T T  = exp 76.945 − − 8.179ln   + 5.3017 × 10 −6        T Pa K K   Cp/[J/(mol ⋅ K)] 28.9937 29.3468 29.1260 37.2433 33.5780 39.8980 44.0254 29.1361 29.1436 29.1327 29.1583 Back-solving for T using the partial pressures of 0.0116 atm for LFL and 0.0702 atm for UFL gives TLFL = 277 K and TUFL = 311 K Autoignition Temperature The autoignition temperature (AIT) is the minimum temperature for a substance to initiate self-combustion in air in the absence of an ignition source. Methods to estimate AIT are in general rather approximate. The method illustrated here may provide reasonable estimates, but significant errors can also result. Estimated values should not be assumed to be reliable for design and safety purposes. 2-362 PHYSICAL AnD CHEMICAL DATA TABLE 2-180 Group Contributions for Pintar* Autoignition Temperature Method for Organic Compounds Group bi Group bi Group bi }CH3 301.91 }Cl3 1073.47 }SO3} — >CH2 −10.86 }F 360.60 }SO4} −31.71 >CH} −275.17 }F2 755.54 }CO3} 442.26 >C< −570.43 }F3 1082.00 }P= −334.91 }H 391.48 }Br 420.96 }PO} −549.59 }OH 324.10 }Br2 607.69 }OPO2} — }O} −18.60 }Br3 1260.00 }PO4= −329.45 † }O}O} −397.61 }I 310.53 Si}C −147.69 =C=O 57.65 }I2 — Si}O† −136.99 † }CHO 195.20 }I3 — Si}H −310.52 }COOH 370.75 }NH2 354.11 Si}Cl† −200.88 }COO} 43.90 >NH 9.88 Si}N† — }CO}O}CO} 46.11 }N= −249.91 Si}Si — }C6H5 380.27 }CN 469.67 Al — m}C6H4 153.15 =C=N} −273.70 B — o}C6H4 77.48 =N}NH2 378.27 Cr — p}C6H4 99.87 >N}NH2 −215.02 Na 534.29 Aromatic ring −1339.65 }NO2 292.57 cis −29.19 = 578.72 }SH 273.84 trans −38.31 ≡ 1116.50 }S} −60.75 Nonarom.ring 605.97 }Cl 347.39 }SO} −91.10 Add’l.ring 565.11 }Cl2 726.03 }SO2} — Zn 349.02 *Pintar, A. J., Estimation of Autoignition Temperature, Technical Support Document DIPPR Project 912, Michigan Technological University, Houghton, 1996. † Does not include contribution of atoms attached to silicon. Recommended Method Pintar method. Reference: Pintar, A. J., Estimation of Autoignition Temperature, Technical Support Document DIPPR Project 912, Michigan Technological University, Houghton, 1996. Classification: Group contributions. Expected uncertainty: 25 percent. Applicability: Organic compounds. Input data: Group contributions from Table 2-180. Description: A simple GC method with first-order contributions is given by N AIT = ∑ ni bi (2-129) Example Estimate the autoignition temperature of 2,3-dimethylpentane. Structure and group information: Group ni bi }CH3 >CH2 >CH} 4 1 2 301.91 −10.86 −275.17 i =1 where ni is the number of groups of type i in the molecule and bi is the contribution of group i to the autoignition temperature. A more accurate but somewhat more complicated logarithmic GC method was also developed by Pintar in the same reference cited here. Calculation using Eq. (2-129): AIT = 4(301.91) − 10.86 + 2(−275.17) = 646.4 K The estimated value is 6.3 percent above the DIPPR 801 recommended value of 608.15 K. Section 3 Mathematics Bruce A. Finlayson, Ph.D. Rehnberg Professor Emeritus, Department of Chemical Engineering, University of Washington; Member, National Academy of Engineering (Section Editor, numerical methods and all general material) Lorenz T. Biegler, Ph.D. Bayer Professor of Chemical Engineering, Carnegie Mellon University; Member, National Academy of Engineering (Optimization) GEnERAL REFEREnCES MATHEMATICS General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Mathematical Constants and Formulas . . . . . . . . . . . . . . . . . . . . . . . Integral Exponents (Powers and Roots) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algebraic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arithmetic-Geometric Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Carleman’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cauchy-Schwarz Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minkowski’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hölder’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lagrange’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4 3-5 3-5 3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-6 MEnSURATIOn FORMULAS Plane Geometric Figures with Straight Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parallelogram (opposite sides parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhombus (equilateral parallelogram). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trapezoid ( four sides, two parallel) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quadrilateral ( four-sided) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regular Polygon of n Sides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane Geometric Figures with Curved Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parabola . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catenary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Geometric Figures with Plane Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rectangular Parallelepiped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frustum of Pyramid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume and Surface Area of Regular Polyhedra with Edge l. . . . . . . . . . . . . . . . . Solids Bounded by Curved Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Torus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prolate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-6 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-7 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 Oblate Spheroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hemisphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ellipsoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miscellaneous Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume of a Solid Revolution (the solid generated by rotating a plane area about the x axis) . . . . . . . . . . . . Area of a Surface of Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area Bounded by f (x), the x Axis, and the Lines x = a, x = b . . . . . . . . . . . . . . . . . Length of Arc of a Plane Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Areas and Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irregular Volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-8 3-9 ELEMEnTARY ALGEBRA Operations on Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operations with Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractional Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laws of Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permutations, Combinations, and Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quartic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Polynomials of the nth Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-9 3-10 3-10 3-10 3-10 3-10 3-10 3-10 3-10 AnALYTIC GEOMETRY Plane Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Straight Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymptotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conic Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parametric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solid Analytic Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lines and Planes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11 3-11 3-11 3-11 3-11 3-12 3-12 3-12 3-12 3-1 3-2 MATHEMATICS Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13 3-13 PLAnE TRIGOnOMETRY Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of Circular Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Values of the Trigonometric Functions for Common Angles . . . . . . . . . . . . . . . . Relations between Functions of a Single Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of Negative Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relations between Angles and Sides of Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solutions of Triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Right Triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamental Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnitude of the Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approximations for Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 3-14 3-14 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-15 3-16 3-16 3-16 3-16 3-16 DIFFEREnTIAL AnD InTEGRAL CALCULUS Differential Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indeterminate Forms: L’Hôpital’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multivariable Calculus Applied to Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . State Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamic State Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Derivatives of Intensive Thermodynamic Functions . . . . . . . . . . . . . . . . Integral Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Indefinite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definite Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16 3-16 3-16 3-16 3-17 3-17 3-18 3-18 3-18 3-19 3-20 3-20 3-20 3-21 3-21 3-21 3-21 InFInITE SERIES Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operations with Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tests for Convergence and Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Series Summation and Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sums for the First n Numbers to Integer Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . Arithmetic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometric Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harmonic Progression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Series (See Also Elementary Algebra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taylor’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maclaurin’s Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithmic Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Sums of Infinite Series, and How They Grow. . . . . . . . . . . . . . . . . . . . . . . . 3-22 3-22 3-22 3-22 3-22 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 3-23 COMPLEX VARIABLES Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Powers and Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elementary Complex Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Complex Functions (Analytic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functions of a Complex Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harmonic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conformal Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 3-23 3-23 3-23 3-23 3-23 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-24 3-25 3-25 3-25 3-25 DIFFEREnTIAL EQUATIOnS Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations of the First Order. . . . . . . . . . . . . . . . . . . . . . . . . . . . Equations with Separable Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations of Higher Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Differential Equations with Constant Coefficients and Right-Hand Member of Zero (Homogeneous) . . . . . . . . . . . . . . . . . . . . . . . . Linear Nonhomogeneous Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Euler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bessel’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Legendre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laguerre’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hermite’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chebyshev’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Differential Equations of Second and Higher Order . . . . . . . . . . . . . . . . . Group Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separation of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integral-Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matched-Asymptotic Expansions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-25 3-26 3-26 3-26 3-26 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-27 3-28 3-28 3-29 3-29 3-30 DIFFEREnCE EQUATIOnS Nonlinear Difference Equations: Riccati Difference Equation . . . . . . . . . . . . . . 3-30 InTEGRAL EQUATIOnS Classification of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31 InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sufficient Conditions for the Existence of the Laplace Transform . . . . . . . . . . Properties of the Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convolution Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of the Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Cosine Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-32 3-32 3-32 3-33 3-33 3-33 3-33 MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS Matrix Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vector and Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LU Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution of Ax = b by Using LU Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . QR Factorization of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular-Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Principal Component Analysis (PCA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33 3-33 3-34 3-34 3-34 3-34 3-34 3-35 3-35 3-36 nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS Approximation Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36 nUMERICAL AnALYSIS AnD APPROXIMATE METHODS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Nonlinear Equations in One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods for Nonlinear Equations in One Variable . . . . . . . . . . . . . . . . . . . . . . . . . Methods for Multiple Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method of Successive Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton-Raphson Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lagrange Interpolation Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equally Spaced Forward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equally Spaced Backward Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Central Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spline Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Interpolation Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Smoothing Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton-Cotes Integration Formulas (Equally Spaced Ordinates) for Functions of One Variable. . . . . . . . . . . . . . . . . Gaussian Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Romberg’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36 3-37 3-37 3-37 3-37 3-37 3-37 3-37 3-37 3-38 3-38 3-38 3-38 3-38 3-39 3-39 3-39 3-39 3-39 3-39 3-39 3-39 3-40 3-40 3-40 3-40 MATHEMATICS Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Dimensional Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaussian Quadrature Points and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-40 3-40 3-40 nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS Implicit Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential-Algebraic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stability, Bifurcations, and Limit Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinary Differential Equations—Boundary-Value Problems . . . . . . . . . . . . . . . . . Finite Difference Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Difference Methods Solved with Spreadsheets. . . . . . . . . . . . . . . . . . . . . . . Orthogonal Collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galerkin Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adaptive Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Singular Problems and Infinite Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Numerical Solution of Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . Parabolic Equations in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elliptic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hyperbolic Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finite Volume Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parabolic Equations in Two or Three Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42 3-42 3-42 3-42 3-42 3-43 3-43 3-43 3-43 3-44 3-45 3-45 3-45 3-45 3-46 3-46 3-46 3-46 3-47 3-48 3-49 3-49 3-49 3-49 OPTIMIZATIOn Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gradient-Based Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Local Optimality Conditions: A Kinematic Interpretation . . . . . . . . . . . . . . . . . . Convex Cases of NLP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solving the General NLP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Gradient-Based NLP Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algorithmic Details for NLP Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimization Methods without Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classical Direct Search Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Derivative-Free Optimization (DFO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Global Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed Integer Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of Optimization Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-50 3-51 3-51 3-52 3-52 3-53 3-54 3-54 3-54 3-54 3-54 3-55 3-55 3-55 3-55 3-56 3-57 STATISTICS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Type of Data Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-58 3-58 3-58 3-58 3-58 Sample Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characterization of Chance Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enumeration Data and Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binomial Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Geometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Poisson Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hypergeometric Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement Data and Sampling Densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution of Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution for the Difference in Two Sample Means with Equal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t Distribution for the Difference in Two Sample Means with Unequal Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chi-Square Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for a Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for the Difference in Two Population Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Confidence Interval for a Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tests of Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Nature of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Mean Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Population Test of Hypothesis for Means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Paired Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Matched Pairs: Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for a Proportion: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Two Proportions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Test of Hypothesis for Two Proportions: Procedure . . . . . . . . . . . . . . . . . . . . . . . . Goodness-of-Fit Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Goodness-of-Fit Test: Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Way Test for Independence for Count Data . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Way Test for Independence for Count Data: Procedure. . . . . . . . . . . . . . . . Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynomial Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Nonlinear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Variance (ANOVA) and Factorial Design of Experiments . . . . . . . . . . ANOVA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Variance: Estimating the Variance of Four Treatments . . . . . . . . . . Factorial Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Level Factorial Design with Three Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3 3-59 3-59 3-59 3-59 3-59 3-59 3-60 3-60 3-60 3-61 3-61 3-62 3-62 3-62 3-63 3-63 3-63 3-63 3-64 3-64 3-64 3-64 3-65 3-65 3-66 3-66 3-67 3-67 3-67 3-68 3-68 3-69 3-69 3-69 3-70 3-70 3-70 3-70 3-70 3-71 3-71 3-71 3-72 3-72 DIMEnSIOnAL AnALYSIS PROCESS SIMULATIOn Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Modules or Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commercial Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-73 3-74 3-74 3-74 3-75 GEnERAL REFEREnCES Courant, R., and D. Hilbert, Methods of Mathematical Physics, vol. I, Interscience, New York, 1953; Finlayson, B. A., Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York, 1980; Finlayson, B. A., L. T. Biegler, and I. E. Grossmann, Mathematics in Chemical Engineering, Ullmann’s Encyclopedia of Industrial Chemistry, Published Online: 15 DEC 2006, DOI: 10.1002/14356007.b01_01.pub2, Wiley, New York, 2006; Jeffrey, A., Mathematics for Engineers and Scientists, 6th ed., Chapman & Hall/CRC, New York, 2004; Kaplan, W., Advanced Calculus, 5th ed., Addison-Wesley, Redwood City, Calif., 2003; Lipschultz, S., M. Spiegel, and J. Liu, Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 4th ed., McGraw-Hill Education, New York, 2012; Logan, J. D., and W. R. Wolesensky, Mathematical Methods in Biology, Wiley, New York, 2009; Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions, Cambridge University Press, London, 2010; see also http://dlmf.nist.gov; Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Plannery, Numerical Recipes, 3d ed., Cambridge University Press, London, 2007; Rice, R. G., and D. D. Do, Applied Mathematics and Modeling for Chemical Engineers, 2d ed., Wiley, New York, 2012; Stroud, K. A., and D. J. Booth, Engineering Mathematics, 7th ed., Industrial Press, South Norwick, Conn., 2013; Thompson, W. J., Atlas for Computing Mathematical Functions, Wiley, New York, 1997; Varma, A., and M. Morbidelli, Mathematical Methods in Chemical Engineering, Oxford Press, New York, 1997; Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, 3d ed., CRC Press, New York, 2009; Wrede, R. C., and M. R. Spiegel, Schaum’s Outline of Theory and Problems of Advanced Calculus, 3d ed., McGraw-Hill, New York, 2010. MATHEMATICS GEnERAL The basic problems of the sciences and engineering fall broadly into three categories: 1. Steady-state problems. In such problems the configuration of the system is to be determined. This solution does not change with time but continues indefinitely in the same pattern, hence the name steady state. Typical chemical engineering examples include steady temperature distributions in heat conduction, equilibrium in chemical reactions, and steady diffusion problems. 2. Eigenvalue problems. These are extensions of equilibrium problems in which critical values of certain parameters are to be determined in addition to the corresponding steady-state configurations. The determination of eigenvalues may also arise in propagation problems and stability problems. Typical chemical engineering problems include those in heat transfer and resonance in which certain boundary conditions are prescribed. 3. Propagation problems. These problems are concerned with predicting the subsequent behavior of a system from a knowledge of the initial state. For this reason they are often called the transient (time-varying) or unsteady-state phenomena. Chemical engineering examples include the transient state of chemical reactions (kinetics), the propagation of pressure waves in a fluid, transient behavior of an adsorption column, and the rate of approach to equilibrium of a packed distillation column. The mathematical treatment of engineering problems involves four basic steps: 1. Formulation. This involves the expression of the problem in mathematical language. That translation is based on the appropriate physical laws governing the process. 2. Solution. Appropriate mathematical and numerical operations are carried out so that logical deductions may be drawn from the mathematical model. 3. Interpretation. This process develops relations between the mathematical results and their meaning in the physical world. 4. Refinement. The procedure is recycled to obtain better predictions, as indicated by experimental checks. Steps 1 and 2 are of primary interest here. The actual details are left to the various subsections, and only general approaches will be discussed. The formulation step may result in algebraic equations, difference equations, differential equations, integral equations, or combinations of these. In any event these mathematical models usually arise from statements of physical laws such as the laws of mass and energy conservation in the form Input of x - output of x + production of x = accumulation of x Many general laws of the physical universe are expressible by differential equations. Specific phenomena are then singled out from the infinity of solutions of these equations by assigning the individual initial or boundary conditions which characterize the given problem. For steady-state or boundary-value problems (Fig. 3-1), the solution must satisfy the differential equation inside the region and the prescribed conditions on the boundary. FIG. 3-1 Boundary conditions. In mathematical language, the propagation problem is known as an initialvalue problem (Fig. 3-2). Schematically, the problem is characterized by a differential equation plus an open region in which the equation holds. The solution of the differential equation must satisfy the initial conditions plus any “side” boundary conditions. FIG. 3-2 Propagation problem. The description of phenomena in a continuous medium such as a gas or a fluid often leads to partial differential equations. In particular, phenomena of “wave” propagation are described by a class of partial differential equations called hyperbolic, and these are essentially different in their properties from other classes such as those that describe equilibrium (elliptic) or diffusion and heat transfer (parabolic). Prototypes are as follows: 1. Elliptic. Laplace’s equation ∂2 u ∂2 u + =0 ∂x 2 ∂ y 2 or Rate of input of x - rate of output of x + rate of production of x = rate of accumulation of x where x = mass, energy, etc. These statements may be abbreviated by the statement Input - output + production = accumulation 3-4 Poisson’s equation ∂2 u ∂2 u + = g (x , y ) ∂x 2 ∂ y 2 These do not contain the variable t (time) explicitly; accordingly, their solutions represent equilibrium configurations. Laplace’s equation corresponds to a “natural” equilibrium, while Poisson’s equation corresponds to an MATHEMATICS equilibrium under the influence of g(x, y). Steady heat-transfer and masstransfer problems are elliptic. 2. Parabolic. The heat equation ∂u ∂2 u ∂2 u = + ∂t ∂ x 2 ∂ y 2 describes unsteady or propagation states of diffusion as well as heat transfer. 3. Hyperbolic. The wave equation ∂2 u ∂2 u ∂2 u = + ∂t 2 ∂ x 2 ∂ y 2 describes wave propagation of all types when the assumption is made that the wave amplitude is small and that interactions are linear. The solution phase has been characterized in the past by a concentration on methods to obtain analytic solutions to the mathematical equations. These efforts have been most fruitful in the area of linear equations such as those just given. However, many natural phenomena are nonlinear. While there are a few nonlinear problems that can be solved analytically, most cannot. In those cases, numerical methods are used. Due to the widespread availability of software for computers, the engineer has quite good tools available. Numerical methods almost never fail to provide an answer to any particular situation, but they can never furnish a general solution of any problem. The mathematical details outlined here include both analytic and numeric techniques useful in obtaining solutions to problems. Our discussion to this point has been confined to those areas in which the governing laws are well known. However, in many areas, information on the governing laws is lacking and statistical methods are used. Broadly speaking, statistical methods may be of use whenever conclusions are to be drawn or decisions made on the basis of experimental evidence. Since statistics could be defined as the technology of the scientific method, it is primarily concerned with the first two aspects of the method, namely, the performance of experiments and the drawing of conclusions from experiments. Traditionally the field is divided into two areas: 1. Design of experiments. When conclusions are to be drawn or decisions made on the basis of experimental evidence, statistical techniques are most useful when experimental data are subject to errors. First, the design of experiments may be carried out in such a fashion as to avoid some of the sources of experimental error and make the necessary allowances for that portion which is unavoidable. Second, the results can be presented in terms of probability statements which express the reliability of the results. Third, a statistical approach frequently forces a more thorough evaluation of the experimental aims and leads to a more definitive experiment than would otherwise have been performed. 2. Statistical inference. The broad problem of statistical inference is to provide measures of the uncertainty of conclusions drawn from experimental data. This area uses the theory of probability, enabling scientists to assess the reliability of their conclusions in terms of probability statements. Both of these areas, the mathematical and the statistical, are intimately intertwined when applied to any given situation. The methods of one are often combined with those of the other. And both, in order to be successfully used, must result in the numerical answer to a problem, that is, they constitute the means to an end. Increasingly the numerical answer is being obtained from the mathematics with the aid of computers. The mathematical notation is given in Table 3-1. MISCELLAnEOUS MATHEMATICAL COnSTAnTS AnD FORMULAS Numerical values of the constants that follow are approximate to the number of significant digits given. π = 3.1415926536 e = 2.7182818285 γ = 0.5772156649 Radian = 57.2957795131° Pi Napierian (natural) logarithm base Euler’s constant Integral Exponents (Powers and Roots) If m and n are positive integers and a and b are numbers or functions, then the following properties hold: a −n = 1/a n a≠0 (ab)n = a n b n a n a m = a n+m (a n )m = a nm n a = a 1/n if a 0 = 1 (a ≠ 0) 0 a = 0 (a ≠ 0) a>0 3-5 TABLE 3-1 Mathematical Signs, Symbols, and Abbreviations ∓ (±) plus or minus (minus or plus) ∶ divided by, ratio sign ∷ proportional sign < less than ≮ not less than > greater than ≯ not greater than ≅ approximately equals, congruent to ∼ similar to ≎ ≠ equivalent to ≐ not equal to approaches, is approximately equal to ∝ varies as ∞ infinity ∴ therefore ∩ intersection square root cube root 3 n nth root ∠ angle ⊥ perpendicular to ∙ x log (or log10) ln (or loge) e a° a′ a″ sin cos tan cot (or ctn) sec csc sin–1 sinh cosh tanh sinh–1 f (x) or f(x) Δx Σ dx dy/dx or y ′ d 2y/dx 2 or y″ d ny/dx n ∂y/∂x ∂ny/∂xn ∂n z ∂x ∂ y parallel to ∫ ∫ numerical value of x common logarithm or Briggsian logarithm natural logarithm or hyperbolic logarithm or Napierian logarithm base (2.718) of natural system of logarithms an angle a degrees a prime, an angle a minutes a double prime, an angle a seconds, a second sine cosine tangent cotangent secant cosecant inverse sin, anti-sine, or angle whose sine is hyperbolic sine hyperbolic cosine hyperbolic tangent anti-hyperbolic sine or angle whose hyperbolic sine is function of x increment of x, delta x summation of differential of x derivative of y with respect to x second derivative of y with respect to x nth derivative of y with respect to x partial derivative of y with respect to x nth partial derivative of y with respect to x nth partial derivative with respect to x and y integral of b a . y ÿ Δ or ∇2 d ∮ integral between the limits a and b first derivative of y with respect to time second derivative of y with respect to time  ∂2 ∂2 ∂2  laplacian  2 + 2 + 2   ∂x ∂ y ∂z  sign of a variation sign for integration around a closed path 3-6 MATHEMATICS The equality holds if, and only if, the sequences |a1|p, |a2|p, …, |an|p and |b1|q, |b2|q, …, |bn|q are proportional and the argument (angle) of the complex numbers ak bk is independent of k. This last condition is of course automatically satisfied if a1, …, an and b1, …, bn are positive numbers. Lagrange’s Inequality Let a1, a2, …, an and b1, b2, …, bn be real numbers. Then Logarithms log ab = log a + log b , a > 0, b > 0 log a n = n log a log (a /b) = log a − log b 2 log n a = (1/n ) log a The common logarithm (base 10) is denoted log a (or log10 a in some texts). The natural logarithm (base e) is denoted ln a (or in some texts loge a). If the text is ambiguous (perhaps using log x for ln x), test the formula by evaluating it. ALGEBRAIC InEQUALITIES Arithmetic-Geometric Inequality Let An and Gn denote, respectively, the arithmetic and the geometric means of a set of positive numbers a1, a2, …, an. Then An ≥ Gn, that is,   n  n  n  ∑ ak bk  =  ∑ a k2  ∑ bk2  − ∑ (a k b j − a j bk )2        k =1   k =1  1 ≤ k ≤ j ≤ n  k =1 Example Two chemical engineers, Mary and John, purchase stock in the same company at times t1, t2, …, tn, when the price per share is, respectively, p1, p2, …, pn. Their methods of investment are different, however: John purchases x shares each time, whereas Mary invests P dollars each time ( fractional shares can be purchased). Who is doing better? While one can argue intuitively that the average cost per share for Mary does not exceed that for John, we illustrate a mathematical proof using inequalities. The average cost per share for John is equal to n a1 + a2 +  + an ≥ (a1a2  an )1/n n x ∑ pi The equality holds only if all the numbers ai are equal. Carleman’s Inequality The arithmetic and geometric means just defined satisfy the inequality Total money invested i =1 = Number of shares purchased nx 1 2 nP n = n 1 P ∑p ∑p i =1 i i =1 i  ar )1/r ≤ neAn n r =1 where e is the best possible constant in this inequality. Cauchy-Schwarz Inequality Let a = (a1, a2, …, an) and b = (b1, b2, …, bn), where the ai and bi are real or complex numbers. Then 2 n ∑ (a b ) k k k =1   n n ≤  ∑| a k |2  ∑| bk |2     k =1  k =1 The equality holds if, and only if, the vectors a and b are linearly dependent (i.e., one vector is a scalar times the other vector). Minkowski’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets of complex numbers. Then for any real number p > 1,  n  ∑| ak + bk | p      k =1 1/p  n ≤ ∑| a k | p    k =1 1/p  n + ∑| bk | p    k =1  n ∑ akbk ≤ ∑| ak | p  k =1   k =1 1/ p  n ∑| bk |q      k =1 Thus the average cost per share for John is the arithmetic mean of p1, p2, …, pn, whereas that for Mary is the harmonic mean of these n numbers. Since the harmonic mean is less than or equal to the arithmetic mean for any set of positive numbers and the two means are equal only if p1 = p2 = … = pn, we conclude that the average cost per share for Mary is less than that for John if two of the prices pi are distinct. One can also give a proof based on the Cauchy-Schwarz inequality. To this end, define the vectors a = ( p1−1/2 , p2−1/2 ,  , pn−1/2 ) b = ( p11/2 , p21/2 ,  , pn1/2 ) Then a · b = 1 + … + 1 = n, and so by the Cauchy-Schwarz inequality 1/p Hölder’s Inequality Let a1, a2, …, an and b1, b2, …, bn be any two sets of complex numbers, and let p and q be positive numbers with 1/p + 1/q = 1. Then n 1 n ∑ pi n i =1 The average cost per share for Mary is n ∑(a a = n n 1 pi (a ⋅ b ) 2 = n 2 ≤ ∑ i =1 ∑p j j =1 with the equality holding only if p1 = p2 = … = pn. Therefore n ∑p i n 1/q n ∑ i =1 1 pi ≤ i =1 n MEnSURATIOn FORMULAS Reference: http://mathworld.wolfram.com/SphericalSector.html, etc. PLAnE GEOMETRIC FIGURES WITH STRAIGHT BOUnDARIES Let A denote area and V volume in the following. Triangles (see also “Plane Trigonometry”) A = ½bh where b = base, h = altitude. Rectangle A = ab where a and b are the lengths of the sides. Parallelogram (opposite sides parallel) A = ah = ab sin α where a and b are the lengths of the sides, h is the height, and α is the angle between the sides. See Fig. 3-3. Rhombus (equilateral parallelogram) A = ½ab where a and b are the lengths of the diagonals. Trapezoid (four sides, two parallel) A = ½(a + b)h where the lengths of the parallel sides are a and b and h = height. Quadrilateral (four-sided) A = ½ab sin q where a and b are the lengths of the diagonals and the acute angle between them is q. Regular Polygon of n Sides See Fig. 3-4. 1 180° A = nl 2 cot where l = length of each side 4 n FIG. 3-3 Parallelogram. FIG. 3-4 Regular polygon. MEnSURATIOn FORMULAS l 180° R = csc 2 n where R is the radius of the circumscribed circle l 180° r = cot 2 n where r is the radius of the inscribed circle 3-7 Radius r of Circle Inscribed in Triangle with Sides a, b, c r= ( s − a )( s − b)( s − c ) where s = 1 2 (a + b + c ) s FIG. 3-7 Parabola . FIG. 3-6 Ellipse . Radius R of Circumscribed Circle R= abc 4 s ( s − a )( s − b)( s − c ) Ellipse (Fig. 3-6) Let the semiaxes of the ellipse be a and b. A = πab Area of Regular Polygon of n Sides Inscribed in a Circle of Radius r A = (nr /2) sin (360°/n) 2 C = 4aE(e) where e2 = 1 - b2/a2 and E(e) is the complete elliptic integral of the second kind Perimeter of Inscribed Regular Polygon 2  π  1 E (e ) = 1 −   e 2 +  2  2  P = 2nr sin (180°/n) Area of Regular Polygon Circumscribed about a Circle of Radius r A = nr2 tan (180°/n) Perimeter of Circumscribed Regular Polygon P = 2nr tan 180° n PLAnE GEOMETRIC FIGURES WITH CURVED BOUnDARIES Circle (see Fig. 3-5). Let C = circumference r = radius D = diameter A = area S = arc length subtended by q l = chord length subtended by q H = maximum rise of arc above chord, r - H = d q = central angle (rad) subtended by arc S C = 2πr = πD (π = 3.14159 …) S = rq = ½ Dq l = 2 r 2 − d 2 = 2 r sin (θ/2) = 2 d tan (θ/2) 1 1 θ 4 r 2 − l 2 = l cot 2 2 2 S d l θ = = 2 cos−1 = 2 sin −1 r r D d= A (circle) = πr2 = ¼πD2 A (sector) = ½rS = ½r2q A (segment) = A (sector) - A (triangle) = ½r2(q - sin q) Ring (area between two circles of radii r1 and r 2) The circles need not be concentric, but one of the circles must enclose the other. A = π(r1 + r2)(r1 - r2) FIG. 3-5 Circle . r1 > r2 [an approximation for the circumference C = 2 π (a 2 + b 2 )/ 2)]. Parabola (Fig. 3-7) Length of arc EFG = 4x2 + y 2 + Area of section EFG = 4 xy 3 y 2 2x + 4x 2 + y 2 ln 2x y Catenary (the curve formed by a cord of uniform weight suspended freely between two points A and B; Fig. 3-8) y = a cosh (x/a) The length of arc between points A and B is equal to 2a sinh (L/a). The sag of the cord is D = a cosh (L/a) - a. SOLID GEOMETRIC FIGURES WITH PLAnE BOUnDARIES Cube Volume = a3; total surface area = 6a2; diagonal = a 3 , where a = length of one side of the cube. Rectangular Parallelepiped Volume = abc; surface area = 2(ab + ac + bc); diagonal = a 2 + b 2 + c 2 , where a, b, and c are the lengths of the sides. Prism Volume = (area of base) × (altitude); lateral surface area = (perimeter of right section) × (lateral edge). Pyramid Volume = ⅓ (area of base) × (altitude); lateral area of regular pyramid = ½ (perimeter of base) × (slant height) = ½ (number of sides) (length of one side) (slant height) . Frustum of Pyramid It is formed from the pyramid by cutting off the top with a plane V = 1 3 ( A1 + A2 + A1 ⋅ A2 )h where h = altitude and A1 and A2 are the areas of the base; lateral area of a regular figure = ½ (sum of the perimeters of base) × (slant height) . FIG. 3-8 Catenary . 3-8 MATHEMATICS Volume and Surface Area of Regular Polyhedra with Edge l Type of surface 4 equilateral triangles 6 squares 8 equilateral triangles 12 pentagons 20 equilateral triangles Name Tetrahedron Hexahedron (cube) Octahedron Dodecahedron Icosahedron Volume 0.1179l3 1.0000l3 0.4714l3 7.6631l3 2.1817l3 Surface area 1.7321l2 6.0000l2 3.4641l2 20.6458l2 8.6603l2 SOLIDS BOUnDED BY CURVED SURFACES Cylinders (Fig. 3-9) V = (area of base) × (altitude); lateral surface area = (perimeter of right section) × (lateral edge). Right Circular Cylinder V = π (radius)2 × (altitude); lateral surface area = 2π (radius) × (altitude). Truncated Right Circular Cylinder V = πr2h lateral area = 2πrh h = ½ (h1 + h2) Hollow Cylinders Volume = πh(R2 - r2), where r and R are the internal and external radii, respectively, and h is the height of the cylinder. Sphere See Fig. 3-10. V (sphere) = 4∕3πR3 = 1∕6πD3 V (spherical sector) = ⅔πR2h1 V (spherical segment of one base) = 1∕6πh1(3 r 22 + h 21) V (spherical segment of two bases) = 1∕6πh2(3 r 21+ 3 r 22 + h 22 ) A (sphere) = 4πR2 = πD2 A (zone) = 2πRh = πDh A (lune on surface included between two great circles, with inclination of q radians) = 2R2q . Cone V = ⅓ (area of base) × (altitude) . Right Circular Cone V = (π/3)r2h, where h is the altitude and r is the radius of the base; curved surface area = πr r 2 + h 2 , curved surface of the frustum of a right cone = π(r1 + r2 ) h 2 + (r1 − r2 )2 , where r1 and r2 are the radii of the base and top, respectively, and h is the altitude; volume of the the frustum of a right cone = π(h/3) (r 21 + r1r2 + r 22) = h/3 ( A1 + A2 + A1 A2 ), where A1 = area of base and A2 = area of top . Ellipsoid V = (4∕3)πabc, where a, b, and c are the lengths of the semiaxes . Torus (obtained by rotating a circle of radius r about a line whose distance is R > r from the center of the circle) V = 2π2Rr2 Surface area = 4π2Rr Prolate Spheroid ( formed by rotating an ellipse about its major axis 2a) Surface area = 2πb2 + 2π(ab/e) sin-1 e b2 1 + e ln 1−e e Hemisphere V = V = 4∕3πa2b π 3 D 12 π A = D2 2 For a hemisphere (concave up) partially filled to a depth h1, use the formulas for spherical segment with one base, which simplify to V = πh 21(R - h1/3) = πh 21 (D/2 - h1/3) A = 2πRh1 = πDh1 For a hemisphere (concave down) partially filled from the bottom, use the formulas for a spherical segment of two bases, one of which is a plane through the center, where h = distance from the center plane to the surface of the partially filled hemisphere . V = πh(R2 - h2/3) = πh(D2/4 - h2/3) A = 2πRh = πDh Cone For a cone partially filled, use the same formulas as for right circular cones, but use r and h for the region filled . Ellipsoid If the base of a vessel is one-half of an oblate spheroid (the cross section fitting to a cylinder is a circle with radius of D/2 and the minor axis is smaller), then use the formulas for one-half of an oblate spheroid . V = 0 .1745D3 V = 0 .1309D3 S = 1 .236D2 S = 1 .084D2 minor axis = D/3 minor axis = D/4 MISCELLAnEOUS FORMULAS See also “Differential and Integral Calculus .” Volume of a Solid Revolution (the solid generated by rotating a plane area about the x axis) V = π ∫ [ f ( x )]2 dx b a where y = f (x) is the equation of the plane curve and a ≤ x ≤ b. Area of a Surface of Revolution S = 2 π ∫ y ds b a where ds = 1 + (dy /dx )2 dx and y = f ( x ) is the equation of the plane curve rotated about the x axis to generate the surface . Area Bounded by f (x), the x Axis, and the Lines x = a, x = b A= ∫ b a f ( x ) dx [ f ( x ) ≥ 0] Length of Arc of a Plane Curve If y = f (x), Length of arc s = V = 4∕3πab2 where a and b are the major and minor axes and e = eccentricity (e < 1) . Oblate Spheroid ( formed by the rotation of an ellipse about its minor axis 2b) Surface area = 2 πa 2 + π For process vessels, the formulas reduce to the following: ∫ b a 2  dy  1 +   dx  dx  If x = f (t), y = g(t), Length of arc s = ∫ t1 t0 2 2  dx   dy    +   dt  dt   dt  In general, (ds)2 = (dx)2 + (dy)2 . IRREGULAR AREAS AnD VOLUMES Irregular Areas Let y0, y1, …, yn be the lengths of a series of equally spaced parallel chords and h be their distance apart (Fig . 3-11) . The area of the figure is given approximately by any of the following: FIG. 3-9 Cylinder . FIG. 3-10 Sphere . FIG. 3-11 Irregular area . ELEMEnTARY ALGEBRA AT = (h/2)[(y0 + yn) + 2(y1 + y2 +  + yn-1)] As = (h/3)[(y0 + yn) + 4(y1 + y3 + y5 +  + yn-1) + 2(y2 + y4 +  + yn-2)] (trapezoidal rule) (n even, Simpson’s rule) 3-9 The greater the value of n, the greater the accuracy of the approximation. Irregular Volumes To find the volume, replace the y’s by cross-sectional areas Aj and use the results in the preceding equations. ELEMEnTARY ALGEBRA References: Stillwell, J., Elements of Algebra, Springer-Verlag, New York, 2010; Rich, B., and P. Schmidt, Schaum’s Outline of Elementary Algebra, 3d ed., McGraw-Hill Education, New York, 2009. OPERATIOnS On ALGEBRAIC EXPRESSIOnS An algebraic expression will be denoted here as a combination of letters and numbers such as 3ax - 3xy + 7x2 + 7x3/2 - 2.8xy Addition and Subtraction Only like terms can be added or subtracted in two algebraic expressions. Example (3x + 4xy - x2) + (3x2 + 2x - 8xy) = 5x - 4xy + 2x2. Multiplication Multiplication of algebraic expressions is term by term, and corresponding terms are combined. Example (2x + 3y - 2xy)(3 + 3y) = 6x + 9y + 9y2 - 6xy2. Division This operation is analogous to that in arithmetic. Example Divide 3e2x + ex + 1 by ex + 1. Divisor e x + 1 Dividend | 3e 2x + e x + 1 n n! where   = = number of combination of n things taken j at a time  j  j !(n − j )! and n! = 1 ⋅ 2 ⋅ 3 ⋅ 4 … n, 0! = 1. Example ( x + y ) 4 = x 4 + 4 x 3 y + 6 x 2 y 2 + 4 xy 3 + y 4. If n is not a positive integer, the sum formula no longer applies and an infinite series results for (a + b)n. Example (1 + x)1/2 = 1 + ½x - ½ ⋅ ¼x2 + ½ ⋅ ¼ ⋅ 3∕6 x3 … (convergent for x2 < 1) . Additional discussion can be found under “Infinite Series .” PROGRESSIOnS An arithmetic progression is a succession of terms such that each term, except the first, is derivable from the preceding by the addition of a quantity d, called the common difference . All arithmetic progressions have the form a, a + d, a + 2d, a + 3d, … . With a = first term, l = last term, d = common difference, n = number of terms, and s = sum of the terms, the following relations hold: s n −1 l = a + (n − 1)d = + d n 2 n n n s = [2 a + (n − 1)d ] = (a + l ) = [2 l − (n − 1)d ] 2 2 2 s (n − 1)d 2 s = −l a = l − (n − 1)d = − 2 n n l − a 2( s − an ) 2(nl − s ) = = d= n − 1 n (n − 1) n (n − 1) l −a 2s +1= n= d l +a 3e x − 2 quotient 3e 2x + 3e x − 2e x + 1 −2 e x − 2 + 3 (remainder) Therefore, 3e2x + ex + 1 = (ex + 1)(3ex - 2) + 3. Operations with Zero All numerical computations (except division) can be done with zero. Both a/0 and 0/0 have no meaning. Fractional Operations  −x  x −x x x −x x ax if a ≠ 0 − = −  = = = = y y −y y ay −y  −y y  x   z  xz x z x±z x /y  x   t  xt ± = =   =    =   y y y y t yt z /t  y   z  yz   Factoring It is that process of analysis consisting of reducing a given expression to the product of two or more simpler expressions, called factors. Some of the more common expressions are factored here: (1) x2 - y2 = (x - y)(x + y) (2) x2 + 2xy + y2 = (x + y)2 (3) x3 - y3 = (x - y)(x2 + xy + y2) (4) x3 + y3 = (x + y)(x2 - xy + y2) (5) x4 - y4 = (x - y)(x + y)(x2 + y2) (6) x5 + y5 = (x + y)(x4 - x3y + x2y2 - xy3 + y4) (7) xn - yn = (x - y)(xn -1 + xn -2y + xn -3y2 + … + yn -1) Laws of Exponents (a n )m = a nm ; a n + m = a n ⋅ a m ; a n/m = (a n )1/m ; a n − m = a n /a m ; a 1/m = m a ; a 1/2 = a ; x 2 = | x | (absolute value of x ). For x > 0, y > 0, xy = x y ; The arithmetic mean or average of two numbers a and b is (a + b)/2 and of n numbers a1, …, an is (a1 + a2 + … + an)/n. A geometric progression is a succession of terms such that each term, except the first, is derivable from the preceding by the multiplication of a quantity r called the common ratio . All such progressions have the form a, ar, ar2, …, ar n-1 . With a = first term, l = last term, r = ratio, n = number of terms, and s = sum of the terms, the following relations hold: l = ar n −1 = s= a (r n − 1) a (1 − r n ) rl − a lr n − l = = = r −1 r − 1 r n − r n −1 1− r a= s−a (r − 1) s log l − log a l = ,r = , log r = n −1 rn−l rn −1 s−l n= log[ a + (r − 1) s ] − log a log l − log a +1 = log r log r The geometric mean of two nonnegative numbers a and b is ab ; of n numbers is (a1a2 … an)1/n . The geometric mean of a set of positive numbers is less than or equal to the arithmetic mean . Example Find the sum of 1 + ½ + ¼ + … + 1∕64 . Here a = 1, r = ½, n = 7 . Thus for x > 0 n x m = x m/n ; n 1/x = 1/ n x s= BInOMIAL THEOREM + 1 2 ( 1 64 ) − 1 = 127/64 1 −1 2 s = a + ar + ar 2 +  + ar n −1 = If n is a positive integer, then (a + b)n = a n + na n−1b + a + (r − 1) s (r − 1) sr n − 1 = r rn −1 n (n − 1) n−2 2 a b 2! n  n  n− j j n (n − 1) (n − 2) n−3 3 a b a b +  + b n = ∑  j  3! j = 0 If | r | < 1, then lim s = n →∞ a ar n − 1− r 1− r a 1−r which is called the sum of the infinite geometric progression . 3-10 MATHEMATICS Example The present worth (PW) of a series of cash flows Ck at the end of year k is n PW = ∑ k =1 Ck (1 + i ) k where i is an assumed interest rate. (Thus the present worth always requires specification of an interest rate.) If all the payments are the same, Ck = R, then the present worth is n PW = R ∑ k =1 1 (1 + i ) k This can be rewritten as PW = R 1+ i n 1 ∑ (1 + i ) k =1 k -1 = R 1+ i n -1 1 ∑ (1 + i ) j =0 j This is a geometric series with r = 1/(1 + i) and a = R/(1 + i). The formulas above give PW (= s ) = R (1 + i )n − 1 i (1 + i )n The same formula applies to the value of an annuity (PW) now, to provide for equal payments R at the end of each of n years, with interest rate i. A progression of the form a, (a + d)r, (a + 2d)r2, (a + 3d)r3, etc., is a combined arithmetic and geometric progression. The sum of n such terms is s= a − [ a + (n − 1)d ]r n rd (1 − r n − 1 ) + 2 1− r (1 − r ) a + rd /(1 − r )2 . 1− r The nonzero numbers a, b, c, etc., form a harmonic progression if their reciprocals 1/a, 1/b, 1/c, etc., form an arithmetic progression. Example The progression 1, ⅓, 1∕5, 1∕7, …, 1∕31 is harmonic since 1, 3, 5, 7, …, 31 form an arithmetic progression . The harmonic mean of two numbers a and b is 2ab/(a + b) . Quadratic Equations Every quadratic equation in one variable is expressible in the form ax2 + bx + c = 0, a ≠ 0 . This equation has two solutions, say, x1 and x2, given by x 1  −b ± b 2 − 4 ac = x 2  2a If a, b, and c are real, the discriminant b2 - 4ac gives the character of the roots . If b2 - 4ac > 0, the roots are real and unequal . If b2 - 4ac < 0, the roots are complex conjugates . If b2 - 4ac = 0, the roots are real and equal. Two quadratic equations in two variables in general can be solved only by numerical methods (see Numerical Analysis and Approximate Methods) . Cubic Equations A cubic equation in one variable has the form x3 + bx2 + cx + d = 0 . Every cubic equation having complex coefficients has three complex roots . If the coefficients are real numbers, then at least one of the roots must be real . The cubic equation x3 + bx2 + cx + d = 0 may be reduced by the substitution x = y - b/3 to the form y3 + py + q = 0, where p = ⅓(3c - b2) and q = 1∕27(27d - 9bc + 2b3) . This reduced equation has the solutions y 1 = A + B , y 2 = − 1 2 ( A + B ) + (i 3/2) ( A − B ), y 3 = − 1 2 ( A + B ) − (i 3/2) ( A − B ), where i 2 = − 1, A = 3 − q /2 + R , B = 3 − q /2 − R , and R = ( p /3)3 + (q /2)2 . If b, c, and d are all real and if R > 0, there are one real root and two conjugate complex roots; if R = 0, there are three real roots, of which at least two are equal; if R < 0, there are three real unequal roots . If R < 0, which requires p < 0, these formulas are impractical . In this case, the roots are given by y k =  2 − p /3 cos[(ϕ/3) + 120 k ], k = 0, 1, 2 , where If | r | < 1, lim s = n →∞ PERMUTATIOnS, COMBInATIOnS, AnD PROBABILITY Each separate arrangement of all or a part of a set of things is called a permutation . The number of permutations of n things taken r at a time is written P (n , r ) = n! = n (n − 1) (n − 2)  (n − r + 1) (n − r )! Each separate selection of objects that is possible irrespective of the order in which they are arranged is called a combination . The number of combinations of n things taken r at a time is written C(n, r) = n!/[r!(n - r)!] . An important relation is r!C(n, r) = P(n, r) . If an event can occur in p ways and can fail to occur in q ways, with all ways being equally likely, the probability of its occurrence is p/(p + q), and that of its failure is q/(p + q) . Example Two dice may be thrown in 36 separate ways . What is the probability of throwing such that their sum is 7? The number 7 may arise in 6 ways: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1 . The probability of shooting a 7 is 1⁄6 . THEORY OF EQUATIOnS Linear Equations A linear equation is one of the first degree (i .e ., only the first powers of the variables are involved), and the process of obtaining definite values for the unknown is called solving the equation . Every linear equation in one variable is written Ax + B = 0 or x = -B/A. Linear equations in n variables have the form a11x1 + a12x2 +  + a1nxn = b1 a21x1 + a22x2 +  + a2nxn = b2  am1x1 + am2x2 +  + amnxn = bm The solution of the system may then be found by elimination or matrix methods if a solution exists (see Matrix Algebra and Matrix Computations) . φ = cos−1 q 2 /4 − p 3 /27 and the negative sign applies if q > 0, and the positive sign applies if q < 0 . Example Many equations of state involve solving cubic equations for the compressibility factor Z . For example, the Soave-Redlich-Kwong equation of state requires solving Z3 - Z2 + cZ + d = 0 d<0 where c and d depend on critical constants of the chemical species and temperature and pressure . In this case, only positive solutions, Z > 0, are desired . Quartic Equations See Olver et al . (2010) in General References . General Polynomials of the nth Degree If n > 4, there is no formula that gives the roots of the general equation . The roots can be found numerically (see “Numerical Analysis and Approximate Methods”) . Fundamental Theorem of Algebra Every polynomial of degree n has exactly n real or complex roots, counting multiplicities . Determinants Consider the system of two linear equations a11x1 + a12x2 = b1 a21x1 + a22x2 = b2 If the first equation is multiplied by a22 and the second by -a12 and the results are added, we obtain (a11a22 - a21a12)x1 = b1a22 - b2a12 The expression a11a22 - a21a12 may be represented by the symbol a11 a21 a12 = a11a22 − a21a12 a22 This symbol is called a determinant of second order . The value of the square array of n2 quantities aij, where i = 1, …, n, is the row index, j = 1, …, n. The column index, written in the form a11 a12 a13 ⋯ a1n a | A | = 21 ⋮ an 1 a22 ⋯⋯a2 n an 2 an 3 ⋯ ann AnALYTIC GEOMETRY is called a determinant. The n2 quantities aij are called the elements of the determinant. In the determinant |A|, let the ith row and jth column be deleted and a new determinant be formed having n - 1 rows and columns. This new determinant is called the minor of aij, denoted Mij. Example a11 a21 a31 a12 a22 a32 a13 a11 a23 The minor of a23 is M 23 = a31 a33 The cofactor Aij of the element aij is the signed minor of aij determined by the rule Aij = (-1)i+ jMij. The value of |A| is obtained by forming any of the n n equivalent expressions ∑ j = 1 aij Aij, ∑ i = 1 aijAij, where the elements aij must be taken from a single row or a single column of A. Example a11 a21 a31 a12 a22 a32 a13 a23 = a31 A31 + a32 A32 + a33 A33 a33 = a31 a12 a22 a13 a11 − a32 a23 a21 In general, Aij will be determinants of order n - 1, but they may in turn be expanded by the rule. Also, n ∑a j =1 a12 a32 a13 a11 + a33 a23 a21 a12 a22 3-11 ji  | A | i = k n A jk = ∑ aij A jk =   0 i ≠ k j =1 Fundamental Properties of Determinants 1. The value of a determinant |A| is not changed if the rows and columns are interchanged. 2. If the elements of one row (or one column) of a determinant are all zero, the value of |A| is zero. 3. If the elements of one row (or column) of a determinant are multiplied by the same constant factor, the value of the determinant is multiplied by this factor. 4. If one determinant is obtained from another by interchanging any two rows (or columns), the value of either is the negative of the value of the other. 5. If two rows (or columns) of a determinant are identical, the value of the determinant is zero. 6. If two determinants are identical except for one row (or column), the sum of their values is given by a single determinant obtained by adding corresponding elements of dissimilar rows (or columns) and leaving unchanged the remaining elements. 7. The value of a determinant is not changed if one row (or column) is multiplied by a constant and added to another row (or column). AnALYTIC GEOMETRY References: Gersting, J. L., Technical Calculus with Analytic Geometry, Dover, Mineola, N.Y., 2010. Analytic geometry uses algebraic equations and methods to study geometric problems. It also permits one to visualize algebraic equations in terms of geometric curves, which frequently clarifies abstract concepts. PLAnE AnALYTIC GEOMETRY Coordinate Systems The basic concept of analytic geometry is the establishment of a one-to-one correspondence between the points of the plane and number pairs (x, y). This correspondence may be done in a number of ways. The rectangular or cartesian coordinate system consists of two straight lines intersecting at right angles (Fig. 3-12). A point is designated by (x, y). Another common coordinate system is the polar coordinate system (Fig. 3-13). In this system the position of a point is designated by the pair (r, q), with r = x 2 + y 2 being the distance to the origin O(0, 0) and q being the angle the line r makes with the positive x axis (polar axis). To change from polar to rectangular coordinates, use x = r cos q and y = r sin q. To change from rectangular to polar coordinates, use r = x 2 + y 2 and q = tan-1 (y/x) if x ≠ 0; q = π/2 if x = 0. The distance between two points (x1, y1) and (x2, y2) is defined by d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 in rectangular coordinates or by d = r 21 + r 22 − 2 r1r2 cos (θ1 − θ2 ) in polar coordinates. Other coordinate systems are sometimes used. For example, on the surface of a sphere, latitude and longitude prove useful. Straight Line See Fig. 3-14. The slope m of a straight line is the tangent of the inclination angle q made with the positive x axis. If (x1, y1) and (x2, y2) are any two points on the line, then slope = m = (y2 - y1)/(x2 - x1). The slope of a line parallel to the x axis is zero; the slope of a line parallel to the y axis is undefined. Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if the product of their slopes is -1 (the exception being that case when the lines are parallel to the coordinate axes). Every equation of the type Ax + By + C = 0 represents a straight line, and every straight line has an equation of this form. A straight line is determined by a variety of conditions: FIG. 3-14 Straight line. Given conditions Equation of line 1. Parallel to x axis 2. Parallel to y axis 3. Point (x1, y1) and slope m 4. Intercept on y axis (0, b), m 5. Intercept on x axis (a, 0), m 6. Two points (x1, y1), (x2, y2) 7. Two intercepts (a, 0), (0, b) y = constant x = constant y - y1 = m(x - x1) y = mx + b y = m(x - a) y −y y − y 1 = 2 1 ( x − x1 ) x 2 − x1 x/a + y/b = 1 The angle b that a line with slope m1 makes with a line having slope m2 is given by tan b = (m2 - m1)/(m1m2 + 1). The distance from a point (x1, y1) to a line with equation Ax + By + C = 0 is d= | Ax 1 + By 1 + C | A2 + B 2 Occasionally some nonlinear algebraic equations can be reduced to linear equations under suitable substitutions or changes of variables. Example Consider y = bxn and B = log b. Taking logarithms gives log y = n log x + log b. Let Y = log y, X = log x, and B = log b. The equation then has the form Y = nX + B, which is a linear equation. Consider k = k0 exp (-E/RT); taking logarithms gives ln k = ln k0 - E/(RT). Let Y = ln k, B = ln k0, m = -E/R, and X = 1/T, and the result is Y = mX + B. II I III IV FIG. 3-12 Rectangular coordinates. FIG. 3-13 Polar coordinates. Asymptotes The limiting position of the tangent to a curve, as the point of contact tends to an infinite distance from the origin, is called an asymptote. Conic Sections The curves included in this group are obtained from plane sections of the cone. They include the circle, ellipse, parabola, hyperbola, and degeneratively the point and straight line. A conic is the locus of a point whose distance from a fixed point called the focus is in a constant 3-12 MATHEMATICS ratio to its distance from a fixed line, called the directrix. This ratio is the eccentricity e. If e = 0, the conic is a circle; if 0 < e < 1, the conic is an ellipse; if e = 1, the conic is a parabola; if e > 1, the conic is a hyperbola. Every conic section is representable by an equation of second degree. Conversely, every equation of second degree in two variables represents a conic. The general equation of the second degree is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. Let Δ be defined as the determinant 2A B ∆ = B 2C D E Δ≠0 Δ=0 AΔ < 0, A ≠ C, an ellipse AΔ < 0, A = C, a circle AΔ > 0, no locus 4 3 4 −4 −2 3 −2 = −596 ≠ 0, B 2 − 4 AC = 40 > 0 14 Polar equation B2 - 4AC = 0 B2 - 4AC > 0 Parabola Hyperbola Two parallel lines if Q = D2 + E2 - 4(A + C)F > 0 One straight line if Q = 0 no locus if Q < 0 Point 6 ∆= The curve is therefore a hyperbola. D E 2F The table characterizes the curve represented by the equation. B2 - 4AC < 0 Example 3x2 + 4xy - 2y2 + 3x - 2y + 7 = 0. Two intersecting straight lines Type of curve (1) r = a (2) r = 2a cos q (3) r = 2a sin q (4) r2 - 2br cos (q - b) + b2 - a2 = 0 (5) r = ke 1 − e cos θ Circle, Fig. 3-20 Circle, Fig. 3-21 Circle, Fig. 3-22 Circle at (b, b), radius a e = 1 parabola, Fig. 3-17 0 < e <1 ellipse, Fig. 3-16 e > 1 hyperbola, Fig. 3-18 Parametric Equations It is frequently useful to write the equations of a curve in terms of a parameter. For example, a circle of radius a, center at (0, 0), can be written in the equivalent form x = a cos f, y = a sin f, where f is the parameter. Similarly, x = a cos f and y = b sin f are the parametric equations of the ellipse x2/a2 + y2/b2 = 1 with parameter f. SOLID AnALYTIC GEOMETRY (1) ( x − h)2 + ( y − k )2 − a 2 x = h + acos θ y = k + asin θ (2) ( x − h)2 ( y − k )2 + =1 a2 b2 x = h + a cos φ y = k + a sin φ  −at  x = 2 t +1  y = a  t 2 +1 (3) x 2 + y 2 = a 2 Circle (Fig. 3-15) parameter is angle q Ellipse (Fig. 3-16) parameter is angle q dy = dx slope of tangent at (x, y) Circle parameter is t = (4) x 2 = y + k Parabola (Fig. 3-17) x2 y2 (5) 2 − 2 = 1 a b x (6) y = a cosh a Hyperbola with the origin at the center (Fig. 3-18)  s  x = a sinh−1 a  2 2  2 y =a +s  x = a (φ − sin φ)   y = a (1 − cos φ) (7) Cycloid FIG. 3-15 Catenary (such as hanging cable under gravity) Parameter s = arc length from (0, a) to (x, y) (Fig. 3-19) FIG. 3-16 Ellipse, 0 < e < 1. Circle. FIG. 3-19 Cycloid. Coordinate Systems There are three commonly used coordinate systems. Others may be used in specific problems (see Morse, P. M., and H. Feshbach, Methods of Theoretical Physics, vols. 1 and I2, McGraw-Hill, New York, 1953). The rectangular (cartesian) system (Fig. 3-23) consists of mutually orthogonal axes x, y, and z. A triple of numbers (x, y, z) is used to represent each point. The cylindrical coordinate system (r, q, z; Fig. 3-24) is frequently used to locate a point in space. These are essentially the polar coordinates (r, q) coupled with the z coordinate. As before, x = r cos q, y = r sin q, z = z and r2 = x2 + y2, y/x = tan q. If r is held constant and q and z are allowed to vary, the locus of (r, q, z) is a right circular cylinder of radius r along the z axis. The locus of r = C is a circle, and q = constant is a plane containing the z axis and making an angle q with the xz plane. Cylindrical coordinates are convenient to use when the problem has an axis of symmetry. The spherical coordinate system is convenient if there is a point of symmetry in the system. This point is taken as the origin and the coordinates (r, f, q) are illustrated in Fig. 3-25. The relations are x = r sin f cos q, y = r sin f sin q, z = r cos f, and r = r sin f. Also q = constant is a plane containing the z axis and making an angle q with the xz plane; f = constant is a cone with vertex at 0; r = constant is the surface of a sphere of radius r, center at the origin 0. Every point in the space may be given spherical coordinates restricted to the ranges 0 ≤ f ≤ π, r ≥ 0, 0 ≤ q < 2π. Lines and Planes The distance between two points ( x 1 , y 1 , z1 ), (x2, y2, z2) is d = ( x 1 − x 2 )2 + ( y 1 − y 2 )2 + ( z1 − z 2 )2 . There is nothing in the geometry of three dimensions quite analogous to the slope of a line in FIG. 3-17 Parabola, e = 1. FIG. 3-20 Circle center (0, 0), r = a. FIG. 3-18 Hyperbola, e > 1. FIG. 3-21 Circle center (a, 0), r = 2a cos q. AnALYTIC GEOMETRY FIG. 3-22 Circle center (0, a), r = 2a sin θ. 3-13 Space Curves Space curves are usually specified as the set of points whose coordinates are given parametrically by a system of equations x = f (t), y = g(t), z = h(t) in the parameter t. Example The equation of a straight line in space is (x - x1)/a = (y - y1)/b = (z - z1)/c. Since all these quantities must be equal (say, to t), we may write x = x1 + at, y = y1 + bt, and z = z1 + ct, which represent the parametric equations of the line. Example The equations z = a cos βt, y = a sin βt, and z = bt, with a, β, and b positive constants, represent a circular helix. Surfaces The locus of points (x, y, z) satisfying f (x, y, z) = 0, broadly speaking, may be interpreted as a surface. The simplest surface is the plane. The next simplest is a cylinder. Example The parabolic cylinder y = x2 (Fig. 3-26) is generated by a straight line parallel to the z axis passing through y = x2 in the plane z = 0. A surface whose equation is a quadratic in the variables x, y, and z is called a quadric surface. Some of the more common such surfaces are tabulated and pictured in Figs. 3-26 to 3-34. FIG. 3-23 Cartesian coordinates. FIG. 3-27 Ellipsoid. FIG. 3-24 Cylindrical coordinates. FIG. 3-25 FIG. 3-26 Parabolic cylinder. FIG. 3-28 Hyperboloid of one sheet. x 2 y 2 z2 + + = 1 (sphere if a = b = c ) a 2 b2 c 2 Spherical coordinates. the plane. Instead of specifying the direction of a line by a trigonometric function evaluated for one angle, a trigonometric function evaluated for three angles is used. The angles α, β, and γ that a line segment makes with the positive x, y, and z axes, respectively, are called the direction angles of the line, and cos α, cos β, and cos γ are called the direction cosines. Let (x1, y1, z1) and (x2, y2, z2) be on the line. Then cos α = (x2 - x1)/d, cos β = (y2 - y1)/d, and cos γ = (z2 - z1)/d, where d = the distance between the two points. Clearly cos2 α + cos2 β + cos2 γ = 1. If two lines are specified by the direction cosines (cos α1, cos β1, cos γ1) and (cos α2, cos β2, cos γ2), then the angle θ between the lines is cos θ = cos α1 cos α2 + cos β1 cos β2 + cos γ1 cos γ2. Thus the lines are perpendicular if and only if θ = 90° or cos α1 cos α2 + cos β1 cos β2 + cos γ1 cos γ2 = 0. The equation of a line with direction cosines (cos α, cos β, cos γ) passing through (x1, y1, z1) is (x - x1)/cos α = (y - y1)/cos β = (z - z1)/cos γ. The equation of every plane is of the form Ax + By + Cz + D = 0. The numbers A B C , , A2 + B 2 + C 2 A2 + B 2 + C 2 A2 + B 2 +C 2 x 2 y 2 z2 + − =1 a2 b2 c 2 FIG. 3-29 Hyperboloid of two sheets. x 2 y 2 z2 + − = −1 a 2 b2 c 2 are direction cosines of the normal lines to the plane. The plane through the point (x1, y1, z1) whose normals have these as direction cosines is A(x - x1) + B(y - y1) + C(z - z1) = 0. Example Find the equation of the plane through (1, 5, -2) perpendicular to the line (x + 9)/7 = (y - 3)/(-1) = z/8. The numbers (7, -1, 8) are called direction numbers. They are a constant multiple of the direction cosines cos α = 7/114, cos β = -1/114, and cos γ = 8/114. The plane has the equation 7(x - 1) - 1(y - 5) + 8(z + 2) = 0 or 7x - y + 8z + 14 = 0. The distance from the point (x1, y1, z1) to the plane Ax + By + Cz + D = 0 is d= | Ax 1 + By 1 + Cz1 + D | A2 + B 2 + C 2 FIG. 3-31 Elliptic paraboloid. x 2 y 2 z2 FIG. 3-30 Cone. 2 + 2 + 2 = 0 a b c x2 y2 + + cz = 0 a2 b2 3-14 MATHEMATICS FIG. 3-32 Hyperbolic paraboloid . x2 y2 − + cz = 0 a 2 b2 FIG. 3-33 Elliptic cylinder . x2 y2 + =1 a 2 b2 PLAnE TRIGOnOMETRY References: Gelfand, I. M., and M. Saul, Trigonometry, Birkhäuser, Boston, 2001; Heineman, E. Richard, and J. Dalton Tarwater, Plane Trigonometry, 7th ed., McGraw-Hill, New York, 1993. AnGLES An angle is generated by the rotation of a line about a fixed center from some initial position to some terminal position. If the rotation is clockwise, the angle is negative; if it is counterclockwise, the angle is positive. Angle size is unlimited. If α and b are two angles such that α + b = 90°, they are complementary; they are supplementary if α + b = 180°. Angles are most commonly measured in the sexagesimal system or by radian measure. In the first system there are 360° in 1 complete revolution (1 r); 1° = 1∕90 of a right angle . The degree is subdivided into 60 minutes; the minute is subdivided into 60 seconds . In the radian system, 1 radian (1 rad) is the angle at the center of a circle subtended by an arc whose length is equal to the radius of the circle . Thus 2π rad = 360°; 1 rad = 57 .29578°; 1° = 0 .01745 rad; 1 min = 0 .00029089 rad . The advantage of radian measure is that it is dimensionless. The quadrants are conventionally labeled, as Fig . 3-35 shows . FIG. 3-36 Triangles . FUnCTIOnS OF CIRCULAR TRIGOnOMETRY The trigonometric functions of angles are the ratios between the various sides of the reference triangles shown in Fig . 3-36 for the various quadrants . Clearly r = x 2 + y 2 ≥ 0. The fundamental functions (see Figs . 3-37, 3-38, 3-39) are as follows: Plane Trigonometry Sine of q = sin q = y/r Cosine of q = cos q = x/r Tangent of q = tan q = y/x FIG. 3-37 Graph of y = sin x. Secant of q = sec q = r/x Cosecant of q = csc q = r/y Cotangent of q = cot q = x/y FIG. 3-38 Graph of y = cos x. II I III IV FIG. 3-35 Quadrants . FIG. 3-39 Graph of y = tan x. FIG. 3-34 Hyperbolic cylinder . x2 y2 − =1 a 2 b2 PLAnE TRIGOnOMETRY Values of the Trigonometric Functions for Common Angles 1− x2 x = cot −1 2 x 1− x sin −1 x = cos−1 1 − x 2 = tan −1 q° q, rad sin q 0 30 0 π/6 45 π/4 2/2 60 π/3 3/2 90 π/2 0 1/2 1 cos q tan q 1 0 3/2 = sec−1 3/3 0 Given a > 0 Required angles are sin q0 = a cos q0 = a tan q0 = a sin q0 = a cos q0 = a tan q0 = a q0 and 180° - q0 q0 and 360° - q0 q0 and 180° + q0 180° + q0 and 360° - q0 180° - q0 and 180° + q0 180° - q0 and 360° - q0 x = cot −1 x 1 = sec−1 x 1− x2 = csc−1 π 1 = − sin −1 x 1− x 2 2 tan −1 x = sin −1 = cot −1 Find an acute angle q0 such that 1− x2 cos−1 x = sin −1 1 − x 2 = tan −1 3 +∞ If 90° ≤ q ≤ 180°, sin q = sin (180° - q); cos q = -cos (180° - q); tan q = -tan (180° - q). If 180° ≤ q ≤ 270°, sin q = -sin (270° - q); cos q = -cos (270° - q); tan q = tan (270° - q). If 270° ≤ q ≤ 360°, sin q = -sin (360° - q); cos q = cos (360° - q); tan q = -tan (360° - q). The reciprocal properties may be used to find the values of the other functions. If it is desired to find the angle when a function of it is given, the procedure is as follows: There will in general be two angles between 0° and 360° corresponding to the given value of the function. sin q = +a cos q = +a tan q = +a sin q = -a cos q = -a tan q = -a 1 π 1 = csc−1 = − cos−1 x x 2 1− x2 1 2/2 1/2 3-15 x 1 = cos−1 1+ x 2 1− x2 1+ x 2 1 = sec−1 1 + x 2 = csc−1 x x RELATIOnS BETWEEn AnGLES AnD SIDES OF TRIAnGLES Relations between Functions of a Single Angle sec q = 1/cos q; csc q = 1/sin q, tan q = sin q/cos q = sec q/csc q = 1/cot q; sin2 q + cos2 q = 1; 1 + tan2 q = sec2 q; 1 + cot2 q = csc2 q. For 0 ≤ q ≤ 90° the following results hold: Solutions of Triangles (Fig. 3-40) Let a, b, and c denote the sides and α, b, and γ the angles opposite the sides in the triangle. Let 2s = a + b + c, A = area, r = radius of the inscribed circle, R = radius of the circumscribed circle, and h = altitude. In any triangle α + b + γ = 180°. Law of Sines sin α/a = sin b/b = sin γ/c = 1/(2R). Law of Tangents θ θ sin θ = 2 sin   cos   2 2 a + b tan 1 2 (α + β) b + c tan 1 2 (β + γ) a + c tan 1 2 (α + γ) = = = ; ; a − b tan 1 2 (α − β) b − c tan 1 2 (β − γ) a − c tan 1 2 (α − γ) and θ θ cos θ = cos 2   − sin 2   2 2 The cofunction property is very important. cos q = sin (90° - q), sin q = cos (90° - q), tan q = cot (90° - q), cot q = tan (90° - q), etc. Functions of Negative Angles sin (-q) = -sin q, cos (-q) = cos q, tan (-q) = -tan q, sec (-q) = sec q, csc (-q) = -csc q, cot (-q) = -cot q. Identities Sum and Difference Formulas Let x, y be two angles. sin (x ± y) = sin x cos y ± cos x sin y; cos (x ± y) = cos x cos y ∓ sin x sin y ; tan (x ± y) = (tan x ± tan y)/(1 ∓ tan x tan y); sin x ± sin y = 2 sin ½(x ± y) cos ½(x ∓ y); cos x + cos y = 2 cos ½(x + y) cos ½(x - y); cos x - cos y = -2 sin ½(x + y) sin ½(x - y); tan x ± tan y = [sin (x ± y)]/(cos x cos y); sin2 x - sin2 y = cos2 y - cos2 x = sin (x + y) sin (x - y); cos2 x - sin2 y = cos2 y - sin2 x = cos (x + y) × cos (x - y); sin (45° + x) = cos (45° - x); sin (45° - x) = cos (45° + x); tan (45° ± x) = cot (45° ∓ x). Multiple and Half-Angle Identities Let x = angle, sin 2x = 2 sin x cos x; sin x = 2 sin ½x × cos ½x; cos 2x = cos2 x - sin2x = 1 - 2 sin2 x = 2 cos2 x - 1. tan 2x = (2 tan x)/(1 - tan2 x); sin 3x = 3 sin x - 4 sin3x; cos 3x = 4 cos3 x - 3 cos x. tan 3x = (3 tan x - tan3 x)/(1 - 3 tan2 x); sin 4x = 4 sin x cos x - 8 sin3 x cos x; cos 4x = 8 cos4 x - 8 cos2 x + 1. x sin   = 2 x cos   = 2 1 2 1 2 (1 − cos x ) (1 + cos x ) 1 − cos x sin x 1 − cos x x tan   = = = 2 1 + cos x 1 + cos x sin x Law of Cosines a2 = b2 + c2 - 2bc cos α; b2 = a2 + c2 - 2ac cos b; c2 = a2 + b2 - 2ab cos γ. More formulas can be generated by replacing a by b, b by c, c by a, α by b, b by γ, and γ by α. 1 1 A = bh = ab sin γ = s ( s − a ) ( s − b) ( s − c ) = rs 2 2 where r= ( s − a ) ( s − b) ( s − c ) s R = a/(2 sin α) = abc/4A h = c sin α = a sin γ = 2rs/b Right Triangle (Fig. 3-41) Given one side and any acute angle α or any two sides, the remaining parts can be obtained from the following formulas: a = (c + b) (c − b) = c sin α = b tan α b = (c + a ) (c − a ) = c cos α = a cot α c = a 2 + b2 sin α = a c cos α = b c tan α = a b β = 90° − α b 2 tan α c 2 sin 2α 1 a2 = = A = ab = 2 2 tan α 2 4 InVERSE TRIGOnOMETRIC FUnCTIOnS Note that y = sin -1 x = arcsin x is the angle y whose sine is x. Example y = sin-1 (½), y is 30°. The complete solution of the equation x = sin y is y = (-1)n sin-1 x + n(180°), -π/2 ≤ sin-1 x ≤ π/2 where sin-1 x is the principal value of the angle whose sine is x. The range of principal values of cos-1 x is 0 ≤ cos-1 x ≤ π and -π/2 ≤ tan-1 x ≤ π/2. If these restrictions are allowed to hold, the following formulas result: FIG. 3-40 Triangle. FIG. 3-41 Right triangle. 3-16 MATHEMATICS HYPERBOLIC TRIGOnOMETRY The hyperbolic functions are certain combinations of exponentials ex and e-x. Inverse Hyperbolic Functions If x = sinh y, then y is the inverse hyperbolic sine of x, written as y = sinh-1 x or arcsinh x. sinh-1 x = ln e ( x + x 2 + 1) cosh x = e x + e−x e x − e−x sinh x e x − e − x = ; sinh x = ; tanh x = cosh x e x + e − x 2 2 1+ x 1 cosh −1 x = ln e ( x + x 2 − 1); tanh −1 x = ln e ; 2 1− x coth x = cosh x ex + ex 1 1 2 = = = ; sech x = ; cosh x e x + e − x e x − e − x tanh x sinh x  1+ 1− x2  x +1 1 coth −1 x = ln e ; sech −1 x = ln e  ; x x −1 2   csch x = 1 2 = sinh x e x − e − x Fundamental Relationships sinh x + cosh x = ex; cosh x - sinh x = e-x; cosh2 x - sinh2 x = 1; sech2 x + tanh2 x = 1; coth2 x - csch2 x = 1; sinh 2x = 2 sinh x cosh x; cosh 2x = cosh2 x + sinh2 x = 1 + 2 sinh2 x = 2 cosh2 x - 1. tanh 2x = (2 tanh x)/(1 + tanh2 x); sinh (x ± y) = sinh x cosh y ± cosh x sinh y ; cosh (x ± y) = cosh x cosh y ± sinh x sinh y; 2 sinh2 x/2 = cosh x - 1; 2 cosh2 x/2 = cosh x + 1; sinh (-x) = -sinh x; cosh (-x) = cosh x; tanh (-x) = -tanh x. When u = a cosh x and u = a sinh x, then u2 - u2 = a2, which is the equation for a hyperbola. In other words, the hyperbolic functions in the parametric equations u = a cosh x and u = a sinh x have the same relation to the hyperbola u2 - u2 = a2 that the equations u = a cos q and u = a sin q have to the circle u2 + u2 = a2.  1+ 1+ x2  csch −1 = ln e   x   Magnitude of the Hyperbolic Functions cosh x ≥ 1 with equality only for x = 0; -∞ < sinh x < ∞; -1 < tanh x < 1. cosh x ~ ex/2 as x → ∞; sinh x → ex/2 as x → ∞. APPROXIMATIOnS FOR TRIGOnOMETRIC FUnCTIOnS For small values of q (q measured in radians) sin q ≈ q, tan q ≈ q; cos q ≈ 1 - q2/2. DIFFEREnTIAL AnD InTEGRAL CALCULUS References: Larson, R., and B. H. Edwards, Calculus, 10th ed., Brooks/Cole, Pacific Grove, Calif., 2013. exists. This implies continuity at x = a. However, a function may be continuous but not have a derivative. The derivative function is DIFFEREnTIAL CALCULUS f ′( x ) = Limits The limit of function f (x) as x approaches a (a is finite or else x is said to increase without bound) is the number N. Differentiation Define Δy = f (x + Δx) - f (x). Then dividing by Δx gives ∆y f ( x + ∆x ) − f ( x ) = ∆x ∆x lim f ( x ) = N x →a This states that f (x) can be calculated as close to N as desirable by making x sufficiently close to a. This does not put any restriction on f (x) when x = a. Alternatively, for any given positive number e, a number d can be found such that 0 < |a - x| < d implies that |N - f (x)| < e. The following operations with limits (when they exist) are valid: lim bf ( x ) = b lim f ( x ) x →a x →a lim[ f ( x ) + g ( x )] = lim f ( x ) + lim g ( x ) x →a x →a x →a lim[ f ( x ) g ( x )] = lim f ( x ) ⋅ lim g ( x ) x →a x →a x →a f (x ) f ( x ) lim if lim g ( x ) ≠ 0 lim = x →a x →a x →a g ( x ) lim g ( x ) x →a See “Indeterminant Forms” below when g(a) = 0. Continuity A function f (x) is continuous at the point x = a if lim [ f (a + h) − f (a )] = 0 h→0 Rigorously, it is stated that f (x) is continuous at x = a if for any positive e there exists a d > 0 such that | f (a + h) - f (a)| < e for all x with |x - a| < d. For example, the function (sin x)/x is not continuous at x = 0 and therefore is said to be discontinuous. Discontinuities are classified into three types: 1. Removable y = (sin x)/x at x = 0 2. Infinite y = 1/x at x = 0 1/x 3. Jump y = 10/(1 + e ) at x = 0+ y = 0+ x=0y=0 x = 0- y = 10 Derivative The function f (x) has a derivative at x = a, denoted as f ′(a), if lim h→0 f (a + h ) − f (a ) h f ( x + h) − f ( x ) df = lim dx h → 0 h Call Then lim ∆x → 0 ∆y dy = ∆ x dx f ( x + ∆x ) − f ( x ) dy = lim dx ∆x → 0 ∆x Differential Operations The following differential operations are valid: f, g, … are differentiable functions of x; c and n are constants; e is the base of the natural logarithms. dc =0 dx (3-1) dx =1 dx (3-2) df dg d ( f + g) = + dx dx dx (3-3) df dg d ( f × g) = f +g dx dx dx (3-4) dy 1 = dx dx /dy if dx ≠0 dy (3-5) d n df f = nf n−1 dx dx (3-6) d  f  g (df /dx ) − f (dg /dx ) = dx  g  g2 (3-7) df df d υ = × (chain rule) dx d υ dx (3-8) DIFFEREnTIAL AnD InTEGRAL CALCULUS df g =gf dx g −1 df dg + f g ln f dx dx (3-10) d d d 2 d 3 d A xy + x+ y = x + dx dx dx dx dx dy dy 2x + 3 y 2 =1+ y + x +0 dx dx u = sin x y = tan x Then, d tan x dy dy dx = = d sin x d υ dx d υ by the rules in Eqs. (3-6), (3-6), (3-2), (3-4), and (3-1), respectively. Thus dy 2 x − 1 − y = dx x − 3y2 d tan x 1 dx d sin x dx = sec2 x /cos x dex = ex dx (3-11) d(a ) = a lna dx (3-12) d ln x = (1/x) dx (3-13) x d log x = (log e/x) dx (3-14) d sin x = cos x dx (3-15) d cos x = -sin x dx (3-16) d tan x = sec x dx (3-17) d cot x = -csc2 x dx (3-18) d sec x = tan x sec x dx (3-19) d csc x = -cot x csc x dx (3-20) 2 d sin x = (1 - x ) 2 –1/2 -1 (3-21) dx d cos-1 x = -(1 - x2)–1/2 dx (3-22) d tan-1 x = (1 + x2)–1 dx (3-23) d cot-1 x = -(1 + x2)–1 dx (3-24) d sec-1 x = x–1(x2 - 1)–1/2 dx (3-25) d csc x = -x (x - 1) (3-26) –1 -1 2 –1/2 dx d sinh x = cosh x dx (3-27) d cosh x = sinh x dx (3-28) d tanh x = sech x dx (3-29) d coth x = -csch2 x dx (3-30) d sech x = -sech x tanh x dx (3-31) d csch x = -csch x coth x dx (3-32) 2 d sinh-1 x = (x2 + 1)–1/2 dx d cosh = (x - 1) -1 2 –1/2 (3-33) d coth x = -(x - 1) dx 2 -1 d sech x = -(1/x)(1 - x ) 2 –1/2 -1 d csch x = -x (x + 1) -1 –1 (3-8) 2 –1/2 dx If f ′( x ) > 0 on (a, b), then f is increasing on (a, b). If f ′( x ) < 0 on (a, b), then f is decreasing on (a, b). The graph of a function y = f (x) is concave up if f ′ is increasing on (a, b); it is concave down if f ′ is decreasing on (a, b). If f ′′( x ) exists on (a, b) and if f ′′( x ) > 0, then f is concave up on (a, b). If f ′′( x ) < 0, then f is concave down on (a, b). An inflection point is a point at which a function changes the direction of its concavity. Indeterminate Forms: L’Hôpital’s Theorem Forms of the type 0/0, ∞/∞, 0 × ∞, etc., are called indeterminates. To find the limiting values that the corresponding functions approach, L’Hôpital’s theorem is useful: If two functions f (x) and g(x) both become zero at x = a, then the limit of their quotient is equal to the limit of the quotient of their separate derivatives, if the limit exists, or is +∞ or -∞. Example Find lim n→0 lim Here x →0 Example Find dy/dx for y = x cos (1 − x ) . dy d d cos (1 − x 2 ) + cos (1 − x 2 ) = x dx dx dx d d cos (1 − x 2 ) = − sin (1 − x 2 ) (1 − x 2 ) dx dx x →∞ Example Find lim (1 − x )1/ x . x →0 = − sin (1 − x 2 ) (0 − 2 x ) y = (1 − x )1/ x (3-36) Then (3-37) lim (ln y ) = lim (3-16) (3-1), (3-6) x3 6 = lim x = 0 x →∞ ex x →∞ e lim x 3e − x = lim Let (3-4) d sin x cos x sin x dx /lim = lim = lim =1 x →0 x → 0 dx x →0 x dx 1 x →∞ x →0 x →0 Using x sin x . x Example Find lim x 3e − x . = 2 (3-17), (3-15) d 3 f (x ) d n f (x ) d 2 f (x ) df ( x ) = 0 for n ≥ 4 = 9 x 2 + 2, = 18 x , = 18, 2 3 dx dx n dx dx (3-35) (3-38) dx (3-5) If the functions and derivatives are known only numerically at some point, the same formulas may be used. Higher Differentials The first derivative of f (x) with respect to x is denoted by f ′ or df/dx. The derivative of the first derivative is called the second derivative of f (x) with respect to x and is denoted by f ′′, f (2), or d 2f/dx2; and similarly for the higher-order derivatives. Example Given f (x) = 3x3 + 2x + 1, calculate all derivative values. (3-34) dx d tanh-1 x = (1 - x2)–1 dx -1 Using = Differentials x (3-6) Example Find the derivative of tan x with respect to sin x. Let Example Derive dy/dx for x2 + y3 = x + xy + A. Here d x 1 −1/2 = x dx 2 dy 1 = 2 x 3/2 sin (1 − x 2 ) + x −1/2 cos (1 − x 2 ) dx 2 (3-9) da x = (ln a ) a x dx 3-17 Therefore, ln y = (1/x) ln (1 - x) ln (1 − x ) lim x →0 ln (1 − x ) = lim x →0 x x d [ln(1 − x )]/dx dx /dx x =0 x =0 = 1 (−1) 1− x = −1 x =0 lim y = e −1 x →0 Partial Derivative The abbreviation z = f (x, y) means that z is a function of the two variables x and y. The derivative of z with respect to x, treating y as a constant, is called the partial derivative with respect to x and is usually denoted as ∂z/∂x or ∂f (x, y)/∂x or simply fx . Partial differentiation, 3-18 MATHEMATICS like full differentiation, is quite simple to apply. Conversely, the solution of partial differential equations is appreciably more difficult than that of differential equations. 2 Example Find ∂z/∂x and ∂z/∂y for z = ye x + xe y . 2 2 ∂x ∂e x ∂z + ey =y = 2 xye x + e y ∂x ∂x ∂x 2 ∂y 2 ∂e y ∂z = e x + xe y +x = ex ∂y ∂y ∂y Order of Differentiation It is generally true that the order of differentiation is immaterial for any number of differentiations or variables, provided the function and the appropriate derivatives are continuous . For z = f (x, y) it follows that ∂3 f ∂3 f ∂3 f = = 2 ∂ y ∂x ∂ y ∂x ∂ y ∂x ∂ y 2 MULTIVARIABLE CALCULUS APPLIED TO THERMODYnAMICS Many of the functional relationships needed in thermodynamics are direct applications of the rules of multivariable calculus . This section reviews those rules in the context of the needs of thermodynamics . These ideas were expounded in one of the classic books on chemical engineering thermodynamics (see Hougen, O . A ., et al ., Part II, “Thermodynamics,” in Chemical Process Principles, 2d ed ., Wiley, New York, 1959) . State Functions State functions depend only on the state of the system, not on history or how one got there . If z is a function of two variables x and y, then z(x, y) is a state function, since z is known once x and y are specified . The differential of z is dz = M dx + N dy The line integral ∫ ( M dx + N dy ) c is independent of the path in xy space if and only if General Form for Partial Differentiation 1 . Given f (x, y) = 0 and x = g(t), y = h(t) . Then ∂M ∂N = ∂ y ∂x df ∂ f dx ∂ f dy = + dt ∂x dt ∂y dt and dz is called an exact differential . The total differential can be written as 2  ∂z   ∂z  dz =   dx +   dy  ∂x  y  ∂y  x 2 ∂ 2 f dx dy ∂ 2 f  dy  ∂ f d 2 x ∂ f d 2 y d 2 f ∂2 f  dx  + + =   +   +2 ∂ x dt 2 ∂ y dt 2 ∂ x ∂ y dt dt ∂ y 2  dt  dt 2 ∂ x 2  dt  Example Find df/dt for f = xy, x = r sin t, and y = r cos t. ∂  ∂z  ∂  ∂z    = ∂ y  ∂ x  y ∂ x  ∂ y  x = y (r cos t) + x(-r sin t) or = r2 cos2 t - r2 sin2 t 2 . Given f (x, y) = 0 and x = g(t, s), y = h(t, s) . Rearrangement gives the triple product rule (∂ y / ∂ x ) z  ∂ y   ∂z   ∂z   ∂z   ∂x   ∂ y  or       = − 1 (3-42)   = −     = −  ∂x  y  ∂ y  z  ∂z  x ∂x z  ∂ y  x (∂ y / ∂ z ) x ∂x y Differentiation of Composite Function ∂ f /∂x dy =− dx ∂ f /∂y Rule 2. Given f (u) = 0 where u = g(x), then ∂ f   ≠ 0 . y ∂   du df = f ′(u ) dx dx 2 d 2u du d2 f = f ′′ (u )   + f ′(u ) 2  dx  dx dx 2 Rule 3. Given f (u) = 0 where u = g(x, y), then 2 ∂2 f ∂2 u  ∂u  = f ′′   + f ′ 2 2  ∂x  ∂x ∂x 2 (3-41)    ∂z   ∂z   0 =   dx +   dy   ∂ y  x  z   ∂ x  y ∂ f ∂ f ∂x ∂ f ∂y = + ∂s ∂x ∂s ∂y ∂s Given f (x, y) = 0, then ∂2 z ∂2 z = ∂ y ∂x ∂x ∂ y Example Suppose z is constant and apply Eq . (3-40) . ∂ f ∂ f ∂x ∂ f ∂y = + ∂t ∂x ∂t ∂y ∂t Rule 1. (3-40) and thus the following application of Eq . (3-39) guarantees path independence . df ∂( xy )  d ρ sin t  ∂( xy )  d ρ cos t  =    + ∂ y  dt  ∂ x  dt  dt Then (3-39) 2 ∂ f ∂ u ∂u ∂ u = f ′′ + f′ ∂x ∂ y ∂x ∂ y ∂x ∂ y Alternatively, divide Eq . (3-40) by dy when holding some other variable w constant to obtain  ∂z   ∂z   ∂x   ∂z   ∂ y  =  ∂ x   ∂ y  +  ∂ y  y w w x (3-43) Also divide both numerator and denominator of a partial derivative by dw while holding a variable y constant to get the chain rule . (∂ z / ∂w ) y  ∂ z   ∂w   ∂z  = =  ∂ x  y (∂ x / ∂w ) y  ∂w  y  ∂ x  y (3-44) Thermodynamic State Functions In thermodynamics, the state functions include the internal energy U, enthalpy H, and Helmholtz and Gibbs free energies A and G, respectively, defined as follows: H = U + PV A = U - TS G = H - TS = U + PV - TS = A + PV 2  ∂u  ∂2 f ∂2 u = f ′′   + f ′ 2 2 ∂y ∂y  ∂y  where S is the entropy, T the absolute temperature, P the pressure, and V the volume . These are also state functions, in that the entropy is specified DIFFEREnTIAL AnD InTEGRAL CALCULUS once two variables (such as T and P) are specified, for example. Likewise, V is specified once T and P are specified; it is therefore a state function. In an open system, extensive properties, such as the total internal energy, are functions of two thermodynamic variables plus the mass or moles of each component. The mathematical derivations below are for a single-component system of constant mass. They are applicable when the mass stays constant, i.e., in an intensive system (or else an additional variable for moles N must be added). However, the relations between the thermodynamic variables can be regarded as internal energy per moles in a closed system, or at a point in an open system. The formulas illustrate the use of calculus in thermodynamics. If a process is reversible and only P-V work is done, the first law and differentials can be expressed as follows: dU = T dS - P dV (3-45) dH = T dS + V dP (3-46) dA = -S dT - P dV (3-47) dG = -S dT + V dP (3-48) Alternatively, if the internal energy is considered a function of S and V, then the differential is  ∂U   ∂U  dV dS +  dU =   ∂V  S  ∂S  V This is the equivalent of Eq. (3-43) and gives the following definitions:  ∂U   ∂U  , P = − T =  ∂V  S  ∂S  V Since the internal energy is a state function, Eq. (3-44) must be satisfied. 2 2 ∂U ∂U = ∂V ∂S ∂S ∂V  ∂P   ∂T     = −  ∂S  V ∂V  S This is This is one of the Maxwell relations, and the other Maxwell relations can be derived in a similar fashion by applying Eq. (3-41). See Sec. 4, Thermodynamics, “Constant-Composition Systems.” Partial Derivatives of Intensive Thermodynamic Functions The various partial derivatives of the thermodynamic functions can be classified into six groups. In the general formulas below, the variables U, H, A, G, and S are denoted by Greek letters (these can be extensive properties), while the variables V, T, and P are denoted by Latin letters (T and P can only be intensive properties). Type I (3 possibilities plus reciprocals)  ∂a  General:    ∂b  c  ∂P  specific:    ∂T  V Equation (3-42) gives 3-19 First evaluate the derivative, using Eq. (3-45). (∂S / ∂T )V  ∂S   ∂V   ∂V   =−   = −    ∂T V ∂S  T (∂S / ∂V )T ∂T  S Then evaluate the numerator and denominator as type II derivatives. Use Eq. (3-45) and Eq. (3-41) to get (∂S / ∂T )V = C v /T . Use Eqs. (3-47) and (3-41) to get the Maxwell relation (∂ P / ∂T )V = (∂S / ∂V )T . Finally use Eq. (3-42).  ∂V  Cv   Cv  ∂ P  T  ∂V  T =   = − ∂ ∂ ∂ V P V      ∂T S T  −    ∂T  P  ∂V  T ∂T  P These derivatives are of importance for reversible, adiabatic processes (such as in an ideal turbine or compressor), since then the entropy is constant. An example is the Joule-Thomson coefficient for constant H. 1   ∂V    ∂T  −V + T    =  ∂T  P  ∂ P  H C p  Type IV (30 possibilities plus reciprocals)  ∂α  General:    ∂β  c  ∂G  specific:   ∂A  p Use Eq. (3-47) to introduce a new variable T. (∂G / ∂T ) P  ∂G   ∂G   ∂T   =   =   ∂ A  P  ∂T  P  ∂ A  P (∂ A / ∂T ) P This operation has created two type II derivatives; using the differential Eqs. (3-47) and (3-48), we obtain S  ∂G  =  ∂ A  P S + P (∂V / ∂T ) P Type V (60 possibilities plus reciprocals)  ∂α  General:    ∂b  β  ∂G  specific:    ∂P  A Start from the differential for dG. Then we get  ∂T   ∂G   +V   = − S  ∂P  A ∂P  A The derivative is type III and can be evaluated by using Eq. (3-42). (∂ A / ∂ P )T  ∂G  +V =S  ∂ P  A (∂ A / ∂T ) P The two type II derivatives are then evaluated using the differential Eq. (3-47). (∂V / ∂T ) P  ∂V   ∂ P   ∂P     =−   = −  ∂T  P  ∂V  T (∂V / ∂ P )T ∂T  V Type II (30 possibilities plus reciprocals)  ∂α  General:    ∂b  c  ∂G  specific:    ∂T  V The differential for G is from Eq. (3-48) or Eq. (3-43) with x → P :  ∂P   ∂G     = − S + V  ∂T  V ∂T V Using the other equations for U, H, A, or S gives the other possibilities. Type III (15 possibilities plus reciprocals)  ∂a  General:    ∂b  α  ∂V  specific:    ∂T  S SP (∂V / ∂ P )T  ∂G  +V =  ∂ P  A S + P (∂V / ∂T ) P These derivatives are also of interest for free expansions or isentropic changes. Type VI (30 possibilities plus reciprocals)  ∂α  General:    ∂β  γ  ∂G  specific:   ∂A H We use Eq. (3-44) to obtain two type V derivatives. (∂G / ∂T ) H  ∂G    = ∂ A  H (∂ A / ∂T ) H These can then be evaluated using the procedures for type V derivatives. 3-20 MATHEMATICS InTEGRAL CALCULUS 2 2 2 ⌠ 4 − 9x dx . Let x = sin θ; then dx = cos θ d θ. Example Find  2 3 3 x ⌡ Indefinite Integral If f ′( x ) is the derivative of f (x), an antiderivative of f ′( x ) is f (x). Symbolically, the indefinite integral of f ′(x) is 2 2 ⌠ 2/3 1 − sin 2 θ  2 ⌠ (2/3) − x  dx = 3 3  cos θ d θ 2 2 2 x ⌡ ⌡ (2/3) sin θ  3 ∫ f ′( x ) dx = f ( x ) + c where c is an arbitrary constant to be determined by the problem. By virtue of the known formulas for differentiation, the following relationships hold (a is a constant): ∫ (du + d υ + dw ) = ∫ du + ∫ d υ + ∫ dw (3-49) = −3 cot θ − 3θ + c by trigonometric transform ∫a dυ = a ∫dυ (3-50) =− ∫υ n d υ= ∫ υ n +1 +c n +1 (n ≠ − 1) dυ = ln | υ | + c υ ∫a υ ∫e dυ = υ aυ +c ln a υ dυ = e + c (3-51) ∫ cos υ d υ = sin υ + c (3-56) 2 + e x − 10) dx = 3 ∫ x 2 dx + ∫ e x dx − 10 ∫ dx = x 3 + e x − 10 x + c Example: Constant of Integration By definition the derivative of x3 is 3x2, and x3 is therefore the integral of 3x2. However, if f = x3 + 10, it follows that f ′ = 3x2, and x3 + 10 is therefore also the integral of 3x2. For this reason the constant c in ∫3x2 dx = x3 + c must be determined by the problem conditions, i.e., the value of f for a specified x. Methods of Integration In practice it is rare when generally encountered functions can be directly integrated. For example, the integrand in ∫ sin x dx which appears quite simple has no elementary function whose derivative is sin x . In general, there is no explicit way of determining whether a particular function can be integrated into an elementary form. When they do not exist or cannot be found either from tabled integration formulas or directly, the only recourse is series expansion, as illustrated later. Indefinite integrals cannot be solved numerically unless they are redefined as definite integrals (see “Definite Integral”), that is, F (x) = ∫ f (x) dx is x indefinite, whereas F ( x ) = ∫ f (t ) dt is definite. Partial Fractions Rational functions are of the type f (x)/g(x) where f (x) and g(x) are polynomial expressions of degrees m and n, respectively. If the degree of f is higher than the degree of g, perform the algebraic division— the remainder will then be at least one degree less than the denominator. Consider the following types: Example Reducible denominator to linear unequal factors. 1 1 = x 3 − x 2 − 4 x + 4 ( x + 2) ( x − 2) ( x − 1) A = 1 12 3 x 3 +10 dx = ∫ (3 x 3 + 10)1/2 ( x 2 dx ) Trigonometric Substitution This technique is particularly well adapted to integrands in the form of radicals. For these the function is transformed to a trigonometric form. In the latter form they may be more easily recognizable relative to the identity formulas. These functions and their transformations are as follows: x 2 − a 2 Let x = a sec θ x 2 + a 2 Let x = a tan θ 2 a −x 2 Let x = a sin θ = A ( x − 2) ( x − 1) + B ( x + 2) ( x − 1) + C ( x + 2) ( x − 2) ( x + 2) ( x − 2) ( x − 1) = x 2 ( A + B + C ) + x (−3 A + B ) + (2 A − 2 B − 4C ) ( x + 2) ( x − 2) ( x − 1) -3A + B = 0 2A - 2B - 4C = 1 C = −13 1 1 1 1 = + − x 2 − x 2 − 4 x + 4 12( x + 2) 4( x − 2) 3( x − 1) Example Find ∫ x 2 3 x 3 +10 dx . Let υ = 3x3 + 10 for which dυ = 9x2 dx. Thus 1 1 = ∫ (3 x 3 + 10)1/2 (9 x 2 dx ) = ∫ υ1/2 d υ 9 9 1 υ3/2 [by Eq. (3 -51)] = + c 9 32 2 = (3 x 3 +10)3/2 + c 27 A B C + + x + 2 x − 2 x −1 A+B+C=0 a 2 = Equate coefficients and solve for A, B, and C. Direct Formula Many integrals can be solved by transformation in the integrand to one of the forms given previously. ∫x 3 − 3 sin −1 x + c in terms of x 2 y4 −3 3 ⌠ y dy 1 ⌠ x dx = 4 = ∫ y 2 ( y 4 − 3) dy  1/4 4 y  ⌡ (3 + 4 x ) ⌡ 7 3 1 1 y 3 y 1 = − + c = (3 + 4 x )7/4 − (3 + 4 x )3/4 + c 4 4 7 4 3 28 (3-54) (3-55) x x dx 4 3 Example Find ⌠ . Let 3 + 4x = y ; then 4 dx = 4y dy and  1/4 ⌡ (3 + 4 x ) (3-53) ∫ sin υ d υ = − cos υ + c 4 − 9x 2 Algebraic Substitution Functions containing elements of the type (a + bx)1/n are best handled by the algebraic transformation y n = a + bx. (3-52) Other integrals can be found at en.wikipedia.org/wiki/Lists_of_integrals. Example Find ∫ (3 x 2 + e x − 10) dx using Eq. (3-49). ∫ (3 x cos 2 θ 2 = 3⌠  2 d θ = 3 ∫ cot θ d θ ⌡ sin θ B = 14 Hence dx ⌠ dx + ⌠ dx - ⌠ dx ⌠ =  3   ⌡ x − x 2 − 4 x + 4 ⌡ 12( x + 2) ⌡ 4( x - 2) ⌡ 3( x - 1) Integration by Parts An extremely useful formula for integration is the relation d(uυ) = u dυ + υ du and uυ = ∫u dυ + ∫υ du or ∫u dυ = uυ - ∫u du It is particularly useful for trigonometric and exponential functions. Example Find ∫xex dx. Let u = x and dv = ex dx du = dx υ = ex DIFFEREnTIAL AnD InTEGRAL CALCULUS ∫xex dx = xex - ∫ex dx = xex - ex + c Therefore ∂ ∂b ∂ ∂b Example Find ∫e sin x dx. Let x u = ex du = ex dx du = sin x dx u = -cos x u = ex du = ex dx du = cos x dx u = sin x ∫ Series Expansion When an explicit function cannot be found, the integration can sometimes be carried out by a series expansion. 2 Example Find ∫e-x dx. Since ∫e −x2 dx d ∫ c ∫ When F ( x ) = 2 Example Find ∫ f ( x ) dx = − f (a ) b( x ) a(x ) if ∫ d c dα a and b are constant ∫ b a f ( x , y ) dy (3-57) f ( x , α ) dx the Leibniz rule gives ∫ b( x ) a(x ) ∂f dy ∂x the incorrect value 2 x3 x5 x7 + − +  for all x 3 5(2!) 7(3!) Definite Integral The value of a definite integral depends on the limits a and b and any selected variable coefficients in the function but not on the dummy variable of integration x. Symbolically indefinite integral where dF/dx = f (x) 2  1  ⌠ dx = −   = −2 ⌡0 ( x − 1)2  x − 1  0 Note that f (x) = 1/(x - 1)2 becomes unbounded as x → 1 and by rule 2 the integral diverges and hence is said not to exist. Methods of Integration All the methods of integration available for the indefinite integral can be used for definite integrals. In addition, several others are available for the latter integrals and are indicated below. Change of Variable This substitution is basically the same as previously indicated for indefinite integrals. However, for definite integrals, the limits of integration must also be changed: i.e., for x = f (t), ∫ b F (a , b) = ∫ f ( x ) dx b dx . Direct application of the formula would yield ( x − 1)2 x4 x6 dx = ∫ dx − ∫ x dx + ∫ dx − ∫ dx +  2! 3! F (x) = ∫ f (x) dx a f ( x ) dx = f (b) dF db da f [ x , b( x )] − f [ x , a ( x )] + = dx dx dx 2 =x− ∫ b f ( x , α) d α = 0 6 x x − + 2! 3! 2 e− x = 1 − x 2 + b a ∫ex sin x dx = -ex cos x + ex sin x - ∫ex sin x dx + c c = (e x /2) (sin x − cos x ) + 2 4 a b ∂ f ( x , α) dF (α ) =∫ dx a ∂α dα ∫ex sin x dx = -ex cos x + ∫ex cos x dx Again ∫ 3-21 definite integral b a t1 f ( x ) dx = ∫ f [φ(t )] ϕ′ (t ) dt t0 a t = t0 when x = a t = t1 when x = b where b F (α ) = ∫ f ( x , α ) dxF a There are certain restrictions of the integration definition: The function f (x) must be continuous in the finite interval (a, b) with at most a finite number of finite discontinuities. Relaxing two of these restrictions gives rise to so-called improper integrals and requires special handling. These occur when ∞ 1. The limits of integration are not both finite, i.e., ∫ e − x dx . 4 Example Find ∫ 16 − x 2 dx . Let 0 x = 4 sin q (x = 0, q = 0) dx = 4 cos q dq (x = 4, q = π/2) 0 2. The function becomes infinite within the interval of integration, i.e., ∫ 1 0 1 dx x Techniques for determining when integration is valid under these conditions are available in the references. Properties The fundamental theorem of calculus states ∫ b f ( x ) dx = F (b) − F (a ) a dF ( x )/dx = f ( x ) where Then ∫ 4 0 16 − x 2 dx = 16 ∫ π/2 cos 2 θ d θ = 16[ 1 2 θ + 1 4 sin 2θ]0π/2 = 4 π 0 Integration It is sometimes useful to generate a double integral to solve a problem. By this approach, the fundamental theorem indicated in Eq. (3-57) can be used. 1 xb − xa dx . Example Find ⌠  ⌡0 ln x ∫ Consider 1 0 Other properties of the definite integral are as follows: x α dx = 1 (α > − 1) α +1 Multiply both sides by dα and integrate between a and b. ∫ b a b c[ f ( x ) dx ] = c ∫ f ( x ) dx a b ∫ [ f ( x ) + f ( x )] dx = ∫ a ∫ b ∫ b ∫ b a a a 1 2 b a f1 ( x ) dx + ∫ b a f 2 ( x ) dx ∫ ∫ f ( x ) dx = − ∫ f ( x ) dx b f ( x ) dx = ∫ a b b a d α ∫ x α dx = 1 0 ∫ 1 0 c for some ξ in (a , b) 1 Therefore 1 ⌠ xb − xa b dx ∫ x α d α =  dx a ⌡0 ln x b f ( x ) dx + ∫ f ( x ) dx f ( x ) dx = (b − a ) f (ξ) 1 ⌠ dα b +1 d α ∫ x α dx =  = ln 0 ⌡a α + 1 a +1 But also a c b a b +1 ⌠ xb − xa  ln x dx = ln a + 1 ⌡0 3-22 MATHEMATICS InFInITE SERIES References: de Brujin, N. G., Asymptotic Methods in Analysis, Dover, New York, 2010; Zwillinger, D., Table of Integrals, Series, and Products, 8th ed., Academic, New York, 2014. where B1 = 1/b1 B2 = − b2 /b 31 B3 = (1/b 51 ) (2b 22 − b1b3 ) DEFInITIOnS B4 = (1/b 71) (5b1b2b3 − b 21b4 − 5b 32) A succession of numbers or terms formed according to some definite rule is called a sequence. The indicated sum of the terms of a sequence is called a series. A series of the form a0 + a1(x - c) + a2(x - c)2 + … + an(x - c)n + … is called a power series. Consider the sum of a finite number of terms in the geometric series (a special case of a power series). Sn = a + ar + ar2 + ar3 + … + ar n -1 (3-58) For any number of terms n, the sum equals ∫ 1− r 1− r n Sn = a S = a + ar + ar2 + … + arn + … (3-59) However, the defined sum of the terms [Eq. (3-59)] 1 − rn 1− r x2 x1 x2 f ( x ) dx = ∫ a0 dx + x1 ∫ x2 x1 x2 a1 x dx + ∫ a2 x 2 dx +  x1 6. A power series may be differentiated term by term and represents the function df (x)/dx within the same region of convergence as f (x). In this form, the geometric series is assumed finite. In the form of Eq. (3-58), it can further be defined that the terms in the series be nonending and therefore an infinite series. Sn = a Additional coefficients are available in the references. 3. Two series may be added or subtracted term by term provided each is a convergent series. The joint sum is equal to the sum (or difference) of the individuals. 4. The sum of two divergent series can be convergent. Similarly, the sum of a convergent series and a divergent series must be divergent. 5. A power series may be integrated term by term to represent the integral of the function within an interval of the region of convergence. If f (x) = a0 + a1x + a2x2 + …, then r ≠1 while valid for any finite value of r and n, now takes on a different interpretation. In this sense it is necessary to consider the limit of Sn as n increases indefinitely: S = lim Sn n→∞ 1 − rn n→∞ 1 − r = a lim The infinite series converges if the limit of Sn approaches a fixed finite value as n approaches infinity. Otherwise, the series is divergent. If r is less than 1 but greater than -1, the infinite series is convergent. For values outside of the range -1 < r < 1, the series is divergent because the sum is not defined. The range -1 < r < 1 is called the region of convergence. (We assume a ≠ 0.) There are also two types of convergent series. Consider the new series TESTS FOR COnVERGEnCE AnD DIVERGEnCE In general, the problem of determining whether a given series will converge can require a great deal of ingenuity and resourcefulness. It is necessary to apply one or more of the developed theorems in an attempt to ascertain the convergence or divergence of the series under study. The following defined tests are given in relative order of effectiveness. For examples, see references on advanced calculus. 1. Comparison test. A series will converge if the absolute value of each term (with or without a finite number of terms) is less than the corresponding term of a known convergent series. Similarly, a positive series is divergent if it is termwise larger than a known divergent series of positive terms. 2. nth-Term test. A series is divergent if the nth term of the series does not approach zero as n becomes increasingly large. 3. Ratio test. If the absolute ratio of the n + 1 term divided by the nth term as n becomes unbounded approaches a. A number less than 1, the series is absolutely convergent. b. A number greater than 1, the series is divergent. c. A number equal to 1, the test is inconclusive. Example For the power series a0 + a1 ( x − x 0 ) + a2 ( x − x 0 )2 +  the absolute ratio gives ε = lim n −>∞ 1 1 1 1 S = 1 − + − +  + (−1)n + 1 +  2 3 4 n 1 an+1 x − x0 = x − x0 an R In this case series (3-60) is defined as a conditionally convergent series. If the replacement series of absolute values also converges, the series is defined to converge absolutely. Series (3-60) is further defined as an alternating series, while series (3-61) is referred to as a positive series. where R is the inverse of the limit. For convergence e < 1; therefore the series converges for x − x 0 < R . 4. Alternating-series Leibniz test. If the terms of a series are alternately positive and negative and never increase in value, the absolute series will converge, provided that the terms tend to zero as a limit. 5. Cauchy’s root test. If the nth root of the absolute value of the nth term, as n becomes unbounded, approaches a. A number less than 1, the series is absolutely convergent. b. A number greater than 1, the series is divergent. c. A number equal to 1, the test is inconclusive. 6. Maclaurin’s integral test. Suppose ∑an is a series of positive terms and f is a continuous decreasing function such that f (x) ≥ 0 for 1 ≤ x < ∞ and ∞ f (n) = an. Then the series and the improper integral ∫ f ( x ) dx either both 1 converge or both diverge. OPERATIOnS WITH InFInITE SERIES SERIES SUMMATIOn AnD IDEnTITIES (3-60) It can be shown that series (3-60) does converge to the value S = ln 2. However, if each term is replaced by its absolute value, the series becomes unbounded and therefore divergent (unbounded divergent): 1 1 1 1 S = 1 + + + + + 2 3 4 5 (3-61) 1. The convergence or divergence of an infinite series is unaffected by the removal of a finite number of finite terms. This is a trivial theorem but useful to remember, especially when using the comparison test to be described in the subsection “Tests for Convergence and Divergence.” 2. A power series can be inverted, provided the first-degree term is not zero. Given y = b1x + b2x + b3x + b4x + b5x + b6x + b7x + … 2 then 3 4 5 6 7 x = B1y + B2y2 + B3y3 + B4y4 + B5y5 + B6y6 + B7y7 + … Sums for the First n Numbers to Integer Powers n ∑j= j =1 n ∑j n (n + 1) = 1 + 2 + 3 + 4 ++ n 2 2 = n (n + 1)(2n +1) 2 = 1 + 22 + 32 + 4 2 +  + n2 6 3 = n 2 (n + 1)2 3 = 1 + 23 + 33 +  + n3 4 j =1 n ∑j j =1 COMPLEX VARIABLES This is simply a special case of Taylor’s series when h is set to zero. Exponential Series Arithmetic Progression n ∑[a + (k − 1) d ] = a + (a + d ) + (a + 2d ) ex =1+ x + k =1 + (a + 3 d ) +  + [ a + (n − 1)]d 2 ln x = Geometric Progression ∑ar j -1 = a + ar + ar 2 + ar 3 +  + ar n - 1 = a j =1 1- r 1- r 1 1 1 r ≠1 1 1 1 x3 x5 x7 + − +  −∞ < x < ∞ 3! 5! 7! 2 x x4 x6 cos x = 1 − + − +  −∞ < x < ∞ 2! 4! 6! x3 1 3 x5 1 3 5 x7 −1 sin x = x + + ⋅ ⋅ + ⋅ ⋅ ⋅ +  ( x 2 < 1) 6 2 4 5 2 4 6 7 1 1 1 tan −1 x = x − x 3 + x 5 − x 7 +  ( x 2 < 1) 3 5 7 sin x = x − 1 k=0 The reciprocals of the terms of the arithmetic progression series are called a harmonic progression. No general summation formulas are available for this series. Binomial Series (See Also Elementary Algebra) n (n − 1) 2 n (n − 1)(n − 2) 3 x ± x + 2! 3! ( x 2 < 1) Taylor’s Series 2 or x x f (h + x ) = f (h) + xf ′(h) + f ′′(h) + f ′′′(h) +  2! 3! f ′′′( x 0 ) f ′′′( x 0 ) ( x - x 0 )2 ( x − x 0 )3 +  f ( x ) = f ( x 0 ) + f ′( x 0 ) ( x − x 0 ) + 3! 2! f ′( x ) = (1 + x )−1 , f ′′( x ) = − (1 + x )−2 , f ′′′( x ) = 2(1 + x )−3 , etc. f (0) = 0, f ′(0) = 1, f ′′(0) = −1, f ′′′(1) = 2, etc. ln ( x + 1) = x − x2 x3 x4 xn + − +  + (−1)n + 1 +  2 3 4 n which converges for -1 < x ≤ 1. Maclaurin’s Series f ( x ) = f (0) + xf ′(0) + Taylor Series The Taylor series for a function of two variables, expanded about the point (x0, y0), is f (x , y ) = f (x0 , y 0 ) + 3 Example Find a series expansion for f (x) = ln (1 + x) about x0 = 0. Thus 3 x − 1 1  x − 1 1  x − 1 +   +  ( x > 1 2)  +  x 2  x  3 x  Trigonometric Series* ∑ a + kd = a + a + d + a + 2d + a + 3d + a + 4 d +  + a + nd (1 ± x )n = 1 ± nx + −∞ < x < ∞  x − 1  1  x − 1  3  ln x = 2    +  ( x > 0) +   x + 1  3  x + 1   n Harmonic Progression n x2 x3 xn + ++ + 2! 3! n! Logarithmic Series 1 = na + n (n − 1)d 2 n 3-23 + 1  ∂2 f 2!  ∂ x 2 ∂f ∂x x0 , y0 ( x − x 0 )2 + 2 x0 , y0 (x − x0 )+ ∂2 f ∂x ∂ y ∂f ∂y ( y - y0 ) x0 , y0 ( x - x 0 )( y - y 0 ) + x0 , y0 ∂2 f ∂y 2  ( y - y 0 )2  +  x0 , y0 Partial Sums of Infinite Series, and How They Grow Calculus textbooks devote much space to tests for convergence and divergence of series that are of little practical value, since a convergent series either converges rapidly, in which case almost any test (among those presented in the preceding subsections) will do, or it converges slowly, in which case it is not going to be of much use unless there is some way to get at its sum without adding an unreasonable number of terms. To find out, as accurately as possible, how fast a convergent series converges and how fast a divergent series diverges, see Boas, R. P., Jr., Am. Math. Mon. 84: 237–258 (1977). *The tan x series has awkward coefficients and should be computed as (sign) sin x   1 − sin 2 x   x2 x3 f ′′(0) + f ′′′(0) +  2! 3! COMPLEX VARIABLES References: Ablowitz, M. J., and A. S. Fokas, Complex Variables: Introduction and Applications, 2d ed., Cambridge University Press, New York, 2012; Asmar, N., and G. C. Jones, Applied Complex Analysis with Partial Differential Equations, Prentice-Hall, Upper Saddle River, N.J., 2002; Brown, J. W., and R. V. Churchill, Complex Variables and Applications, 9th ed., McGraw-Hill, New York, 2013; Kwok, Y. K., Applied Complex Variables for Scientists and Engineers, 2d ed., Cambridge University Press, New York, 2010. Numbers of the form z = x + iy, where x and y are real, i2 = -1, are called complex numbers. The numbers z = x + iy are representable in the plane, as shown in Fig. 3-42. The following definitions and terminology are used: 1. Distance OP = r = modulus of z written | z |. | z | = x 2 + y 2 2. x is the real part of z. 3. y is the imaginary part of z. 4. The angle θ, 0 ≤ θ < 2π, measured counterclockwise from the positive x axis to OP, is the argument of z. θ = arctan y/x = arcsin y/r = arccos x/r if x ≠ 0, θ = π/2 if x = 0 and y > 0. 5. The numbers r, θ are the polar coordinates of z. 6. z = x - iy is the complex conjugate of z. ALGEBRA Let z1 = x1 + iy1 and z2 = x2 + iy2. Equality z1 = z2 if and only if x1 = x2 and y1 = y2. Addition z1 + z2 = (x1 + x2) + i(y1 + y2). Subtraction z1 - z2 = (x1 - x2) + i(y1 - y2). Multiplication z1z2 = (x1x2 - y1y2) + i(x1y2 + x2y1). Division FIG. 3-42 Complex plane. z1 /z 2 = x1 x 2 + y 1 y 2 x y − x1 y 2 , z 2 ≠ 0. + i 2 21 x 22 + y 22 x 2 + y 22 3-24 MATHEMATICS SPECIAL OPERATIOnS 2 2 2 zz = x + y = | z | ; z1 ± z 2 = z1 ± z 2 ; z1 = z1 ; z1 z 2 = z1 z 2 ;| z1 ⋅ z 2 | = | z1 | ⋅ | z 2 |; arg (z1 ⋅ z2) = arg z1 + arg z2; arg (z1/z2) = arg z1 - arg z2; i4n = 1 for n any integer; i2n = -1 where n is any odd integer; z + z = 2x; z - z = 2iy. Every complex quantity can be expressed in the form x + iy. General powers of z are defined by zα = eα log z. Since log z is infinitely many valued, so too is zα unless α is a rational number. DeMoivre’s formula can be derived from properties of ez. zn = rn (cos q + i sin q)n = rn (cos nq + i sin nq) TRIGOnOMETRIC REPRESEnTATIOn Thus By referring to Fig. 3-42, there results x = r cos θ and y = r sin θ so that z = x + iy = r (cos q + i sin q), which is called the polar form of the complex number. cos q + i sin q = eiq. Hence z = x + iy = reiq. z = x - iy = re-iq. Two important results from this are cos q = (eiq + e-iq)/2 and sin q = (eiq - e-iq)/2i. Let z1 = r1eiq1 and z2 = r2eiq2. This form is convenient for multiplication for z1 z 2 = r1 r2e i ( θ1 +θ2 ) and for division for z1 /z 2 = (r1 /r2 )e i ( θ1 −θ2 ) , z 2 ≠ 0. COMPLEX FUnCTIOnS (AnALYTIC) POWERS AnD ROOTS If n is a positive integer, zn = (reiq)n = rneinq = rn(cos nq + i sin nq). If n is a positive integer,   θ + 2 kπ    θ + 2 kπ  + i sin  z 1/n = r 1/n e i [( θ+ 2 kπ )/n ] = r 1/n cos   n    n   and selecting values of k = 0, 1, 2, 3, …, n - 1 gives the n distinct values of z1/n. The n roots of a complex quantity are uniformly spaced around a circle with radius r1/n in the complex plane in a symmetric fashion. Example Find the three cube roots of -8. Here r = 8, q = π. The roots are z0 = 2(cos π/3 + i sin π/3) = 1 + i 3 , z1 = 2(cos π + i sin π) = -2, and z2 = 2(cos 5π/3 + i sin 5π/3) = 1 - i 3 . (cos q + i sin q)n = cos nq + i sin nq In the real-number system a greater than b (a > b) and b less than c (b < c) define an order relation. These relations have no meaning for complex numbers. The absolute value is used for ordering. Some important relations follow: |z| ≥ x; |z| ≥ y ; |z1 ± z2| ≤ |z1| + |z2|; |z1 - z2| ≥ ||z1| - |z2||; |z| ≥ (|x| + |y|)/ 2 . Parts of the complex plane, commonly called regions or domains, are described by using inequalities. Example |z - 3| ≤ 5. This is equivalent to ( x − 3)2 + y 2 ≤ 5, which is the set of all points within and on the circle, centered at x = 3, y = 0 of radius 5. Example |z - 1| ≤ x represents the set of all points inside and on the parabola 2x = y2 + 1 or, equivalently, 2x ≥ y2 + 1. Functions of a Complex Variable If z = x + iy, w = u + iu and if for each value of z in some region of the complex plane one or more values of w are defined, then w is said to be a function of z, w = f (z). Some of these functions have already been discussed, such as sin z and log z. All functions are reducible to the form w = u(x, y) + iu(x, y), where u and u are real functions of the real variables x and y. Example z3 = (x + iy)3 = x3 + 3x2(iy) + 3x(iy)2 + (iy)3 = (x3 - 3xy2) + i(3x2y - y3). Differentiation The derivative of w = f (z) is ELEMEnTARY COMPLEX FUnCTIOnS Polynomials A polynomial in z, anzn + an -1zn -1 + … + a0, where n is a positive integer, is simply a sum of complex numbers times integral powers of z which have already been defined. Every polynomial of degree n has precisely n complex roots provided each multiple root of multiplicity m is counted m times. Exponential Functions The exponential function ez is defined by the equation ez = ex + iy = ex ⋅ eiy = ex(cos y + i sin y). Properties: e0 = 1; e z1 e z2 = e z1 + z2 ; e z1 / z2 = e z1 − z2 ; e z +2 kπi = e z , k an integer. Trigonometric Functions sin z = (eiz - e-iz)/2i; cos z = (eiz + e-iz)/2; tan z = sin z/cos z; cot z = cos z/sin z; sec z = 1/cos z; csc z = 1/sin z. Fundamental identities for these functions are the same as their real counterparts. Thus cos2 z + sin2 z = 1, cos (z1 ± z2) = cos z1 cos z2  sin z1 sin z2, sin (z1 ± z2) = sin z1 cos z2 ± cos z1 sin z2. The sine and cosine of z are periodic functions of period 2π; thus sin (z + 2π) = sin z. For computation purposes sin z = sin (x + iy) = sin x cosh y + i cos x sinh y, where sin x, cosh y, etc., are the real trigonometric and hyperbolic functions. Similarly, cos z = cos x cosh y - i sin x sinh y. If x = 0 in the results given, cos iy = cosh y and sin iy = i sinh y. Example Find all solutions of sin z = 3. From previous data sin z = sin x cosh y + i cos x sinh y = 3. Equating real and imaginary parts gives sin x cosh y = 3 and cos x sinh y = 0. The second equation can hold for y = 0 or for x = π/2, 3π/2, … . If y = 0, cosh 0 = 1 and sin x = 3 is impossible for real x. Therefore, x = ±π/2, ±3π/2, …, ±(2n + 1)π/2, n = 0, ±1, ±2, … . However, sin 3π/2 = -1 and cosh y ≥ 1. Hence x = π/2, 5π/2, … . The solution is z = [(4n + 1)π]/2 + i cosh-13, n = 0, 1, 2, 3, … . Example Find all solutions of ez = -i. ez = ex(cos y + i sin y) = -i. Equating real and imaginary parts gives ex cos y = 0, ex sin y = -1 from the first y = ±π/2, ±3π/2, … . But ex > 0. Therefore, y = 3π/2, 7π/2, -π/2, … . Then x = 0. The solution is z = i[(4n + 3)π]/2. Two important facets of these functions should be recognized. First, sin z is unbounded; second, ez takes all complex values except 0. Hyperbolic Functions sinh z = (ez - e-z)/2; cosh z = (ez + e-z)/2; tanh z = sinh z/cosh z; coth z = cosh z/sinh z; csch z = 1/sinh z; sech z = 1/cosh z. Identities are cosh2 z - sinh2 z = 1; sinh (z1 + z2) = sinh z1 cosh z2 + cosh z1 sinh z2; cosh (z1 + z2) = cosh z1 cosh z2 + sinh z1 sinh z2; cosh z + sinh z = ez; cosh z - sinh z = e-z. The hyperbolic sine and hyperbolic cosine are periodic functions with the imaginary period 2πi. That is, sinh (z + 2πi) = sinh z. Logarithms The logarithm of z, log z = log |z| + i(q + 2nπ), where log |z| is taken to the base e and q is the principal argument of z, that is, the particular argument lying in the interval 0 ≤ q < 2π. The logarithm of z is infinitely many valued. If n = 0, the resulting logarithm is called the principal value. The familiar laws log z1z2 = log z1 + log z2, log z1/z2 = log z1 - log z2, and log zn = n log z hold for the principal value. dw f ( z + ∆z ) − f ( z ) = lim dz ∆z → 0 ∆z and for the derivative to exist, the limit must be the same no matter how Δz approaches zero. If w1 and w2 are differentiable functions of z, the following rules apply: d (w1 ± w2 ) dw1 dw2 dw2 dw d (w1w2 ) = ± = w2 1 + w1 dz dz dz dz dz dz d (w1 /w2 ) w2 (dw1 /dz ) - w1 (dw2 /dz ) = dz w22 and dw dw1n = nw1n - 1 1 dz dz For w = f (z) to be differentiable, it is necessary that ∂u/∂x = ∂u/∂y and ∂u/∂x = -∂u/∂y. The last two equations are called the Cauchy-Riemann equations . The derivative ∂u ∂v ∂υ dw ∂u −i = +i = ∂y ∂x ∂ y dz ∂ x If f (z) possesses a derivative at z0 and at every point in some neighborhood of z0, then f (z) is said to be analytic or homomorphic at z0 . If the CauchyRiemann equations are satisfied and u , υ, ∂u ∂u ∂υ ∂υ , , , ∂x ∂ y ∂x ∂ y are continuous in a region of the complex plane, then f (z) is analytic in that region . Example w = z z = x2 + y2 . Here u = x2 + y2, u = 0 . ∂u/∂x = 2x, ∂u/∂y = 2y, ∂u/∂x = ∂u/∂y = 0 . These are continuous everywhere, but the CauchyRiemann equations hold only at the origin . Therefore, w is nowhere analytic, but it is differentiable at z = 0 only . Example w = ez = ex cos y + iex sin y. u = ex cos y and u = ex sin y. ∂u/∂x = ex cos y, ∂u/∂y = -ex sin y, ∂u/∂x = ex sin y, ∂u/∂y = ex cos y. The continuity and Cauchy-Riemann requirements are satisfied for all finite z. Hence ez is analytic (except at ∞) and dw/dz = ∂u/∂x + i(∂u/∂x) = ez. Example w = y 1 x − iy x = −i = z x2 + y2 x2 + y2 x2 + y2 It is easy to see that dw/dz exists except at z = 0 . Thus 1/z is analytic except at z = 0 . DIFFEREnTIAL EQUATIOnS Singular Points If f (z) is analytic in a region except at certain points, those points are called singular points. Example 1/z has a singular point at zero. Example tan z has singular points at z = ±(2n + 1)(π/2), n = 0, 1, 2, …. The derivatives of the common functions, given earlier, are the same as their real counterparts. Example (d/dz)(ln z) = 1/z, (d/dz)(sin z) = cos z. Harmonic Functions Both the real and the imaginary parts of any analytic function f = u + iu satisfy Laplace’s equation ∂2f/∂x2 + ∂2f/∂y2 = 0 . A function which possesses continuous second partial derivatives and satisfies Laplace’s equation is called a harmonic function. Example ez = ex cos y + iex sin y. u = ex cos y, ∂u/∂x = ex cos y, ∂2u/∂x2 = ex cos y, ∂u/∂y = -ex sin y, ∂2u/∂y2 = -ex cos y. Clearly ∂2u/∂x2 + ∂2u/∂y2 = 0 . Similarly, u = ex sin y is also harmonic . If w = u + iu is analytic, the curves u(x, y) = c and u(x, y) = k intersect at right angles, if w′(z) ≠ 0 . Integration In much of the work with complex variables a simple extension of integration called line or curvilinear integration is of fundamental importance . Since any complex line integral can be expressed in terms of real line integrals, we define only real line integrals . Let F (x, y) be a real, continuous function of x and y, and let c be any continuous curve of finite length joining points A and B (Fig . 3-43) . F(x, y) is not related to the curve c . Divide c into n segments, Δsi, whose projection on the x axis is Δxi and on the y axis is Δyi . Let (ei, hi) be the coordinates of an arbitrary point on Δsi . The limits of the sums 3-25 are known as line integrals . Much of the initial strangeness of these integrals b will vanish if it is observed that the ordinary definite integral ∫ f ( x ) dx is a just a line integral in which the curve c is a line segment on the x axis and F(x, y) is a function of x alone . The evaluation of line integrals can be reduced to evaluation of ordinary integrals . Example ∫c y (1 + x) dy, where c: y = 1 - x2 from (-1, 0) to (1, 0) . Clearly y = 1 - x2, dy = -2x dx. Thus ∫c y (1 + x) dy = -2 ∫1-1 (1 - x2)(1 + x)x dx = -8⁄15 . Let f (z) be any function of z, analytic or not, and c any curve as above . The complex integral is calculated as ∫c f (z) dz = ∫c (u dx - u dy) + i ∫c (u dx + u dy), where f (z) = u(x, y) + i u(x, y) . Properties of line integrals are the same as for ordinary integrals . That is, ∫c [ f (z) ± g(z)] dz = ∫c f (z) dz ± ∫c g(z) dz; ∫c kf (z) dz = k ∫c f (z) dz for any constant k, etc . Example ∫ c (x2 + iy) dz along c: y = x, 0 to 1 + i. This becomes ∫ (x c 2 + iy ) dz = ∫ ( x 2 dx - y dy ) c 1 1 1 0 0 0 + i ∫ ( y dx + x dy ) = ∫ x 2 dx − ∫ x dx + i ∫ x dx + i 2 c ∫ 1 0 x 2 dx = − 1 6 + 5i /6 lim ∑ F (ε i , ηi ) ∆y i = ∫ F ( x , y ) dy Conformal Mapping Every function of a complex variable w = f (z) = u(x, y) + iu(x, y) transforms the x, y plane into the u, u plane in some manner . A conformal transformation is one in which angles between curves are preserved in magnitude and sense . Every analytic function, except at those points where f ′(z) = 0, is a conformal transformation . See Fig . 3-44 . Example w = z2 . u + iu = (x2 - y2) + 2ixy or u = x2 - y2, u = 2xy. These are the transformation equations between the (x, y) and (u, u) planes . Lines parallel to the x axis, y = c1 map into curves in the u, u plane with parametric equations u = x2 - c12, u = 2c1x. Eliminating x, u = (u2/4c12) - c12, which represents a family of parabolas with the origin of the w plane as focus, the line u = 0 as axis and opening to the right . Similar arguments apply to x = c2 . The principles of complex variables are useful in the solution of a variety of applied problems, including Laplace transforms (see Integral Transforms) and process control (Sec . 8) . FIG. 3-43 Line integral . FIG. 3-44 Conformal transformation . n lim ∑ F (εi , ηi ) ∆si = ∫ F ( x , y ) ds ∆si → 0 i =1 c n lim ∑ F (ε i , ηi ) ∆x i = ∫ F ( x , y ) dx ∆si → 0 i =1 c n ∆si → 0 i =1 c DIFFEREnTIAL EQUATIOnS References: Ames, W . F ., Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, 1965; Aris, R ., and N . R . Amundson, Mathematical Methods in Chemical Engineering, vol . 2, First-Order Partial Differential Equations with Applications, Prentice-Hall, Englewood Cliffs, N .J ., 1973; Asmar, N . H ., Partial Differential Equations with Fourier Series and Boundary Value Problems, 3rd ed ., Pearson, New York, 2016 . Asmar, N ., Applied Complex Analysis with Partial Differential Equations, Prentice-Hall, Upper Saddle River, N .J ., 2002; Bronson, R ., and G . Costa, Schaum’s Outline of Differential Equations, 4th ed ., McGraw-Hill, New York, 2014; Brown, J . W ., and R . V . Churchill, Fourier Series and Boundary Value Problems, 8th ed ., McGraw-Hill Education, New York, 2011; Duffy, D ., Green’s Functions with Applications, 2d ed ., Chapman and Hall/CRC, New York, 2015; Kreyszig, E ., Advanced Engineering Mathematics, 10th ed ., Wiley, New York, 2011; Ramkrishna, D ., and N . R . Amundson, Linear Operator Methods in Chemical Engineering with Applications to Transport and Chemical Reaction Systems, Prentice-Hall, Englewood Cliffs, N .J ., 1985 . The natural laws in any scientific or technological field are not regarded as precise and definitive until they have been expressed in mathematical form . Such a form, often an equation, is a relation between the quantity of interest, say, product yield, and independent variables such as time and temperature upon which yield depends . When it happens that this equation involves, besides the function itself, one or more of its derivatives it is called a differential equation . Example The rate of the homogeneous bimolecular reaction A + B k→ C is characterized by the differential equation dx/dt = k(a - x) (b - x), where a = initial concentration of A, b = initial concentration of B, and x = x(t) = concentration of C as a function of time t. Example The differential equation of heat conduction in a moving fluid with velocity components ux, uy is ∂T ∂T k  ∂2 T ∂2 T  ∂T = + +υy + υx ∂ y ρc p  ∂ x 2 ∂ y 2  ∂x ∂t where T = T(x, y, t) = temperature, k = thermal conductivity, r = density, and cp = specific heat at constant pressure . ORDInARY DIFFEREnTIAL EQUATIOnS When the function involved in the equation depends upon only one variable, its derivatives are ordinary derivatives and the differential equation is called an ordinary differential equation . When the function depends upon several independent variables, then the equation is called a partial differential equation . The theories of ordinary and partial differential equations are quite different . In almost every respect the latter is more difficult . 3-26 MATHEMATICS Whichever the type, a differential equation is said to be of nth order if it involves derivatives of order n but no higher. The equation in the first example is of first order and that in the second example of second order. The degree of a differential equation is the power to which the derivative of the highest order is raised after the equation has been cleared of fractions and radicals in the dependent variable and its derivatives. A relation between the variables, involving no derivatives, is called a solution of the differential equation if this relation, when substituted in the equation, satisfies the equation. A solution of an ordinary differential equation which includes the maximum possible number of “arbitrary” constants is called the general solution. The maximum number of “arbitrary” constants is exactly equal to the order of the differential equation. If any set of specific values of the constants is chosen, the result is called a particular solution. Example The general solution of (d2x/dt2) + k2x = 0 is x = A cos kt + B sin kt, where A and B are arbitrary constants. A particular solution is x = ½ cos kt + 3 sin kt. In the case of some equations still other solutions exist called singular solutions. A singular solution is any solution of the differential equation which is not included in the general solution. Example y = x(dy/dx) - ¼(dy/dx)2 has the general solution y = cx - ¼c2, where c is an arbitrary constant; y = x2 is a singular solution, as is easily verified. ORDInARY DIFFEREnTIAL EQUATIOnS OF THE FIRST ORDER Equations with Separable Variables Every differential equation of the first order and of the first degree can be written in the form M(x, y) dx + N(x, y)dy = 0. If the equation can be transformed so that M does not involve y and N does not involve x, then the variables are said to be separated. The solution can then be obtained by quadrature, which means that y = ∫ f (x)dx + c, which may or may not be expressible in simpler form. Exact Equations The equation M(x, y) dx + N(x, y) dy = 0 is exact if and only if ∂M/∂y = ∂N/∂x. In this case there exists a function w = f (x, y) such that ∂f/∂x = M, ∂f/∂y = N, and f (x, y) = C is the required solution . f (x, y) is found as follows: treat y as though it were constant and evaluate ∫M(x, y) dx. Then treat x as though it were constant and evaluate ∫N(x, y) dy. The sum of all unlike terms in these two integrals (including no repetitions) is f (x, y) . Example (2xy - cos x) dx + (x2 - 1) dy = 0 is exact for ∂M/∂y = 2x, ∂N/∂x = 2x. ∫M dx = ∫(2xy - cos x) dx = x2y - sin x, ∫N dy = ∫(x2 - 1) dy = x2y - y. The solution is x2y - sin x - y = C, as may easily be verified . Linear Equations A differential equation is said to be linear when it is of first degree in the dependent variable and its derivatives . The general linear first-order differential equation has the form dy/dx + P(x)y = Q(x) . Its general solution is − P dx P dx y = e ∫  ∫ Qe ∫ dx + C    Example A tank initially holds 200 gal of a salt solution in which 100 lb is dissolved . Six gallons of brine containing 4 lb of salt run into the tank per minute . If mixing is perfect and the output rate is 4 gal/min, what is the amount A of salt in the tank at time t ? The differential equation of A is dA/dt = 4 - 2A/[100 + t] . Its general solution is A = (4/3)(100 + t) + C/(100 + t)2 . At t = 0, A = 100; so the particular solution is A = (4/3)(100 + t) (1/3) ×106/(100 + t)2 . ORDInARY DIFFEREnTIAL EQUATIOnS OF HIGHER ORDER The higher-order differential equations, especially those of order 2, are of great importance because of physical situations describable by them . Equation y(n) = f (x). The superscript (n) means n derivatives . Such a differential equation can be solved by n integrations . The solution will contain n arbitrary constants . Linear Differential Equations with Constant Coefficients and Right-Hand Member of Zero (Homogeneous) The solution of y ′′ + ay ′ + by = 0 depends upon the nature of the roots of the characteristic equation m2 + am + b = 0 obtained by substituting the trial solution y = emx in the equation . Distinct Real Roots If the roots of the characteristic equation are distinct real roots, r1 and r2, say, the solution is y = Ae r1 x + Be r2 x , where A and B are arbitrary constants . Example y ′′ + 4 y ′ + 3 = 0 . The characteristic equation is m2 + 4m + 3 = 0 . The roots are -3 and -1, and the general solution is y = Ae–3x + Be–x. Multiple Real Roots If r1 = r2, the solution of the differential equation is y = e r1 x ( A + Bx ) . Example y ′′ + 4 y + 4 = 0 . The characteristic equation is m2 + 4m + 4 = 0 with roots -2 and -2 . The solution is y = e-2x(A + Bx) . Complex Roots If the characteristic roots are p ± iq, then the solution is y = e px × (A cos qx + B sin qx) . Example The differential equation My ′′ + Ay ′ + ky = 0 represents the vibration of a linear system of mass M, spring constant k, and damping constant A. If A < 2 kM , the roots of the characteristic equation Mm 2 + Am + k = 0 are complex: − A ±i 2M k  A  −  M  2M  2 and the solution is   k  A 2    k  A 2  t + ic2 sin  y = e − ( At /2 M ) c1 cos  − −   t    M  2 M     M  2M   This solution is oscillatory, representing undercritical damping . All these results generalize to homogeneous linear differential equations with constant coefficients of order higher than 2 . These equations (especially of order 2) have been much used because of the ease of solution . Oscillations, electric circuits, diffusion processes, and heat flow problems are a few examples for which such equations are useful . Second-Order Equations: Dependent Variable Missing Such an equation is of the form  dy d 2 y  F  x, , 2  = 0  dx dx  It can be reduced to a first-order equation by substituting p = dy/dx and dp/dx = d2y/dx2 . Second-Order Equations: Independent Variable Missing Such an equation is of the form  dy d 2 y  F  y, , 2  = 0  dx dx  dp d2y du = p, =p dy dx 2 dx Set The result is a first-order equation in p  dp  F  y , p, p  = 0 dy   Example The capillary curve for one vertical plate is given by d2y 4y = dx 2 c 2   dy  2  1 +    dx   3/2 Its solution by this technique is c c c x + c 2 − y 2 − c 2 − h02 =  cosh −1 − cosh −1  2 y h0  where c and h0 are physical constants . Example The equation governing chemical reaction in a porous catalyst in plane geometry of thickness L is D dc d 2c (0) = 0, c ( L) = cυ = k f (c ), dx dx 2 where D is a diffusion coefficient, k is a reaction rate parameter, c is the concentration, kf (c) is the rate of reaction, and c0 is the concentration at the dc gives (Finlayson, 1980, p . 92) boundary . Making the substitution p = ds p Integrating gives dp k = f (c ) dc D p2 k = 2 D ∫ c c (0) f (c ) dc DIFFEREnTIAL EQUATIOnS If the reaction is very fast, c(0) ≈ 0 and the average reaction rate is related to p(L). This variable is given by 2k p ( L) =  D ∫ c (0) 0 1/2 f (c ) dc   c0′ (0) + ac1′ (0) + a 2c2′ (0) +  = 0 Form of Particular Integral Then P(x) is a (constant) A (constant) axn Anxn + An-1 xn -1 + … + A1x + A0 aerx Berx c cos kx   d sin kx  A cos kx + B sin kx g x n e rx cos kx   h x n e rx sin kx  (Anx + … + A0)e cos kx + (Bnx + … + B0)e sin kx n rx The goal is to find equations governing the functions {ci(x)} and solve them . Substitution into the equations gives the following equations: c0′′ ( x ) + ac1′′( x ) + a 2c2′′ ( x ) +  = a[c0 ( x ) + ac1 ( x ) + a 2c2 ( x ) + ]2 Thus, the average reaction rate can be calculated without solving the complete problem. Linear Nonhomogeneous Differential Equations Linear Differential Equations Right-Hand Member f (x) ≠ 0 Again the specific remarks for y ′′ + ay ′ + by = f ( x ) apply to differential equations of similar type but higher order. We shall discuss two general methods. Method of Undetermined Coefficients Use of this method is limited to equations exhibiting both constant coefficients and particular forms of the function f (x). In most cases f (x) will be a sum or product of functions of the type constant, xn (n a positive integer), emx, cos kx, sin kx. When this is the case, the solution of the equation is y = H(x) + P(x), where H(x) is a solution of the homogeneous equations found by the method of the preceding subsection and P(x) is a particular integral found by using the following table subject to these conditions: (1) When f (x) consists of the sum of several terms, the appropriate form of P(x) is the sum of the particular integrals corresponding to these terms individually. (2) When a term in any of the trial integrals listed is already a part of the homogeneous solution, the indicated form of the particular integral is multiplied by x. If f (x) is 3-27 n rx c0 (1) + ac1 (1) + a 2c2 (1) +  = 1 Like terms in powers of a are collected to form the individual problems . c0′′= 0, c0′ (0) = 0, c0 (1) = 1 c1′′= c02 , c1′(0) = 0, c1 (1) = 0 c2′′= 2c0 c1 , c2′ (0) = 0, c 2 (1) = 0 The solution proceeds in turn . c0 ( x ) = 1, c1 ( x ) = ( x 2 − 1) 5 − 6x 2 + x 4 , c2 ( x ) = 2 12 SPECIAL DIFFEREnTIAL EQUATIOnS See Olver et al . (2010) in General References . Euler’s Equation The linear equation xny(n) + a1xn -1y n-1 + … + an-1xy′ + any = R(x) can be reduced to a linear equation with constant coefficients by the change of variable x = et . To solve the homogeneous equation substitute y = xr into it, cancel the powers of x, which are the same for all terms, and solve the resulting polynomial for r . In case of multiple or complex roots there results the form y = xr(log x)r and y = xα[cos (b log x) + i sin (b log x)] . Bessel’s Equation The linear equation x2(d2y/dx2) + x(dy/dx) + (x2 - p2) y = 0 is the Bessel equation of integer order . By series methods, not to be discussed here, this equation can be shown to have the solution x J p ( x ) =    2 p ∞ (−1) k ( x /2)2 k k = 0 k !( p + k )! ∑ (Bessel function of the first kind of order p) and Since the form of the particular integral is known, the constants may be evaluated by substitution in the differential equation. Example y ′′ + 2 y ′ + y = 3e2x - cos x + x3. The characteristic equation is (m + 1)2 = 0 so that the homogeneous solution is y = (c1 + c2x)e-x. To find a particular solution we use the trial solution from the table, y = a1e2x + a2 cos x + a3 sin x + a4x3 + a5x2 + a6x + a7. By substituting this in the differential equation and collecting and equating like terms, there results a1 = ⅓, a2 = 0, a3 = -½, a4 = 1, a5 = -6, a6 = 18, and a7 = -24 . The solution is y = (c1 + c2x)e-x + ⅓e2x - ½ sin x + x3 - 6x2 + 18x - 24 . Method of Variation of Parameters This method is applicable to any linear equation . The technique is developed for a second-order equation but immediately extends to higher order . Let the equation be y ′′ + a ( x ) y ′ + b( x ) y = R ( x ), and let the solution of the homogeneous equation, found by some method, be y = c1f1(x) + c2f2(x) . It is now assumed that a particular integral of the differential equation is of the form P(x) = uf1 + vf2, where u and v are functions of x to be determined by two equations . One equation results from the requirement that uf1 + vf2 satisfy the differential equation, and the other is a degree of freedom open to the analyst . The best choice proves to be u ′f1 + v ′f 2 = 0 and u ′f1′+ vf 2′ = 0 Then u′ = du f2 =− R(x ) dx f1 f 2′− f 2 f1′ v′ = dv f1 R(x ) = dx f1 f 2′ − f 2 f1′ and since f1, f2, and R are known, u, v may be found by direct integration . Perturbation Methods If the ordinary differential equation has a parameter that is small and is not multiplying the highest derivative, perturbation methods can give solutions for small values of the parameter . Example Consider the differential equation for reaction and diffusion in a catalyst; the reaction is second-order: c″ = ac2, c′(0) = 0, c(1) = 1 . The solution is expanded in the following Taylor series in a. c(x, a) = c0(x) + ac1(x) + a c2(x) + … 2 Y p (x ) = J p ( x ) cos ( pπ) − J − p ( x ) sin ( pπ) (Bessel function of the second kind) (replace right-hand side by limiting value if p is an integer or zero) . The series converges for all x. Much of the importance of Bessel’s equation and Bessel functions lies in the fact that the solutions of numerous linear differential equations can be expressed in terms of them . Legendre’s Equation The Legendre equation (1 - x2)y″ - 2xy′ + n(n + 1) y = 0, n ≥ 0, has the solution Pn for n an integer . The polynomials Pn are the so-called Legendre polynomials, P0(x) = 1, P1(x) = x, P2(x) = ½(3x2 - 1), P3(x) = ½(5x3 - 3x), … For n positive and not an integer, see Olver et al . (2010) in General References . Laguerre’s Equation The Laguerre equation x(d2y/dx2) + (c - x) (dy/dx) - ay = 0 is satisfied by the confluent hypergeometric function . See Olver et al . (2010) in General References . Hermite’s Equation The Hermite equation y ′′ − 2 xy ′ + 2ny = 0 is satisfied by the Hermite polynomial of degree n, y = AHn(x), if n is a positive integer or zero . H0(x) = 1, H1(x) = 2x, H2(x) = 4x2 - 2, H3(x) = 8x3 - 12x, H4(x) = 16x4 - 48x2 + 12, Hr+1(x) = 2xHr(x) - 2rHr-1(x) . Chebyshev’s Equation The equation (1 − x 2 ) y ′′ − xy ′ + n 2 y = 0 for n a positive integer or zero is satisfied by the nth Chebyshev polynomial y = ATn(x) . T0(x) = 1, T1(x) = x, T2(x) = 2x2 - 1, T3(x) = 4x3 - 3x, T4(x) = 8x4 8x2 + 1; Tr+1(x) = 2xTr(x) - Tr -1(x) . PARTIAL DIFFEREnTIAL EQUATIOnS The analysis of situations involving two or more independent variables frequently results in a partial differential equation . Example The equation ∂T/∂t = k(∂2T/∂x2) represents the unsteady onedimensional conduction of heat . Example The equation for the unsteady transverse motion of a uniform beam clamped at the ends is ∂ 4 y ρ ∂2 y =0 + ∂ x 4 EI ∂t 2 3-28 MATHEMATICS Example The expansion of a gas behind a piston is characterized by the simultaneous equations The equations for flow and adsorption in a packed bed or chromatography column give a quasilinear equation . ∂u ∂u ∂ρ ∂u c 2 ∂ρ ∂u +ρ = 0 +u = 0 and +u + ∂x ∂x ∂t ∂x ρ ∂x ∂t The partial differential equation ∂2f/(∂x ∂y) = 0 can be solved by two integrations yielding the solution f = g(x) + h(y), where g(x) and h(y) are arbitrary differentiable functions . This result is an example of the fact that the general solution of partial differential equations involves arbitrary functions in contrast to the solution of ordinary differential equations, which involve only arbitrary constants . A number of methods are available for finding the general solution of a partial differential equation . In most applications of partial differential equations, the general solution is of limited use . In such applications the solution of a partial differential equation must satisfy both the equation and certain auxiliary conditions called initial and/or boundary conditions, which are dictated by the problem . Examples of these include those in which the wall temperature is a fixed constant T(x0) = T0, there is no diffusion across a nonpermeable wall, and the like . In ordinary differential equations, these auxiliary conditions allow definite numbers to be assigned to the constants of integration . Partial Differential Equations of Second and Higher Order Many of the applications to scientific problems fall naturally into partial differential equations of second order, although there are important exceptions in elasticity, vibration theory, and elsewhere . A second-order differential equation can be written as a ∂2 u ∂2 u ∂2 u +c 2 = f +b 2 ∂y ∂x ∂ y ∂x where a, b, c, and f depend upon x, y, u, ∂u/∂x, and ∂u/∂y. This equation is hyperbolic, parabolic, or elliptic, depending on whether the discriminant b2 - 4ac > 0, = 0, or < 0, respectively . Since a, b, c, and f depend on the solution, the type of equation can be different at different x and y locations . If the equation is hyperbolic, discontinuities can be propagated . See Courant and Hilbert (1953, 1962) and LeVeque, R . J ., Numerical Methods for Conservation Laws, Birkhäuser, Basel, Switzerland, 1992 . Phenomena of propagation such as vibrations are characterized by equations of “hyperbolic” type which are essentially different in their properties from other classes such as those which describe equilibrium (elliptic) or unsteady diffusion and heat transfer (parabolic) . Prototypes are as follows: Elliptic Laplace’s equation ∂2u/∂x2 + ∂2u/∂y2 = 0 and Poisson’s equation ∂2u/∂x2 + ∂2u/∂y2 = g(x, y) do not contain the variable time explicitly and consequently represent equilibrium configurations . Laplace’s equation is satisfied by static electric or magnetic potential at points free from electric charges or magnetic poles . Other important functions satisfying Laplace’s equation are the velocity potential of the irrotational motion of an incompressible fluid, used in hydrodynamics; the steady temperature at points in a homogeneous solid; and the steady state of diffusion through a homogeneous body . Parabolic The heat equation ∂T/∂t = ∂2T/∂x2 + ∂2T/∂y2 represents nonequilibrium or unsteady states of heat conduction and diffusion . Hyperbolic The wave equation ∂2u/∂t2 = c2(∂2u/∂x2 + ∂2u/∂y2) represents wave propagation of many varied types . Quasilinear first-order differential equations are like a ∂u ∂u = f +b ∂y ∂x φ df ∂c ∂c ∂c =0 + (1 − φ) + φu dc ∂t ∂x ∂t Here n = f (c) is the relation between concentration on the adsorbent and fluid concentration . The solution of problems involving partial differential equations often revolves about an attempt to reduce the partial differential equation to one or more ordinary differential equations . The solutions of the ordinary differential equations are then combined (if possible) so that the boundary conditions and the original partial differential equation are simultaneously satisfied . Three of these techniques are illustrated . Similarity Variables The physical meaning of the term “similarity” relates to internal similitude, or self-similitude . Thus, similar solutions in boundary-layer flow over a horizontal flat plate are those for which the horizontal component of velocity u has the property that two velocity profiles located at different coordinates x differ only by a scale factor . The mathematical interpretation of the term similarity is a transformation of variables carried out so that a reduction in the number of independent variables is achieved . There are essentially two methods for finding similarity variables, “separation of variables” (not the classical concept) and the use of “continuous transformation groups .” The basic theory is available in Ames (1965) . Example The equation ∂q/∂x = (A/y)(∂2q/∂y2) with the boundary conditions q = 0 at x = 0, y > 0; q = 0 at y = ∞, x > 0; q = 1 at y = 0, x > 0 represents the nondimensional temperature q of a fluid moving past an infinitely wide flat plate immersed in the fluid . Turbulent transfer is neglected, as is molecular transport except in the y direction . It is now assumed that the equation and the boundary conditions can be satisfied by a solution of the form q = f (y/xn) = f (u), where q = 0 at u = ∞ and q = 1 at u = 0 . The purpose here is to replace the independent variables x and y by the single variable u when it is hoped that a value of n exists which will allow x and y to be completely eliminated in the equation . In this case since u = y/xn, there results after some calculation ∂q/∂x = -(nu/x)(dq/du), ∂2q/∂y2 = (1/x2n)(d2q/du2), and when these are substituted in the equation, -(1/x)nu (dq/du) = (1/x3n)(A/u) (d2q/du2) . For this to be a function of u only, choose n = ⅓ . There results (d2q/du2) + (u2/3A)(dq/du) = 0 . Two integrations and use of the boundary conditions for this ordinary differential equation give the solution ∞ ∞ u 0 θ = ∫ exp(-u 3 /9 A ) du / ∫ exp (-u 3 /9 A ) du Group Method The type of transformation can be deduced using group theory . For a complete exposition, see Ames (1965) and Hill, J . M ., Differential Equations and Group Methods for Scientists and Engineers, CRC Press, New York, 1992; a shortened version can be found in Finlayson (1980) . Basically, a similarity transformation should be considered when one of the independent variables has no physical scale (perhaps it goes to infinity) . The boundary conditions must also simplify (and combine) since each transformation leads to a differential equation with one fewer independent variable . Example A similarity variable is found for the problem ∂c ∂  D (c ) ∂c  = , c (0, t ) = 1, c (∞ , t ) = 0, c ( x , 0) = 0 ∂t ∂ x  D0 ∂ x  where a, b, and f depend on x, y, and u, with a2 + b2 ≠ 0 . This equation can be solved using the method of characteristics, which writes the solution in terms of a parameter s, which defines a path for the characteristic . Note that the length dimension goes to infinity, so there is no length scale in the problem statement; this is a clue to try a similarity transformation . The transformation examined here is du dy dx = a, = b, = f ds ds ds t = a αt , x = a β x , c = a γ c These equations are integrated from some initial conditions . For a specified value of s, the value of x and y shows the location where the solution is u. The equation is semilinear if a and b depend just on x and y (and not u), and the equation is linear if a, b, and f all depend on x and y, but not u. Such equations give rise to shock propagation, and conditions have been derived to deduce the presence of shocks . Courant and Hilbert (1953, 1962); Rhee, H . K ., R . Aris, and N . R . Amundson, First-Order Partial Differential Equations, vol . 1, Theory and Applications of Single Equations, Prentice-Hall, Englewood Cliffs, N .J ., 1986; and LeVeque (1992), ibid . An example of a linear hyperbolic equation is the advection equation for flow of contaminants when the x and y velocity components are u and v, respectively . ∂c ∂c ∂c =0 +v +u ∂y ∂x ∂t With this substitution, the equation becomes a α−γ ∂  D ( a − γ c ) ∂c  ∂c = a 2β − γ   ∂ x  D0 ∂x  ∂t Group theory says a system is conformally invariant if it has the same form in the new variables; here, that is γ=0 α - γ = 2b - γ The invariants are η= β x , δ= α tδ or α = 2b DIFFEREnTIAL EQUATIOnS and the solution is Then u(x, t) satisfies c(x, t) = f (h)t γ/α We can take γ = 0 and d = b/α = ½. Note that the boundary conditions combine because the point x = ∞ and t = 0 gives the same value of h and the conditions on c at x = ∞ and t = 0 are the same. We thus make the transformation η= x ∂2 u ∂u = D 2 , u ( x , 0) = − 1, u (0, t ) = 0, u ( L , t ) = 0 L ∂x ∂t Assume a solution of the form u(x, t) = X(x)T(t), which gives 1 dT 1 d 2 X = DT dt X dx 2 x , c ( x , t ) = f ( η) 4 D0t The use of the 4 and D0 makes the analysis below simpler. The result is Since both sides are constant, this gives the following ordinary differential equations to solve: d  D (c ) df  df = 0, f (0) = 1, f (∞) = 0   + 2η d η  D0 d η  dη Thus, we solve a two-point boundary-value problem instead of a partial differential equation. When the diffusivity is constant, the solution is the error function, a tabulated function. c ( x , t ) = 1 − erf η = erfc η η 2 ∞ 1 dT 1 d2X = −λ , = −λ DT dt X dx 2 The solution of these is T = Ae − λDt 0 The combined solution for u(x, t) is 0 Separation of Variables This powerful, well-utilized method is applicable in certain circumstances. It consists of assuming that the solution for a partial differential equation has the form U = f (x)g(y). If it is then possible to obtain an ordinary differential equation on one side of the equation depending on only x and on the other side on only y, the partial differential equation is said to be separable in the variables x and y. If this is the case, one side of the equation is a function of x alone and the other of y alone. The two can be equal only if each is a constant, say, l. Thus the problem has again been reduced to the solution of ordinary differential equations. Example Laplace’s equation ∂2V/∂x2 + ∂2V/∂y2 = 0 plus the boundary conditions V(0, y) = 0, V(l, y) = 0, V(x, ∞) = 0, V(x, 0) = f (x) represents the steady-state potential in a thin plate (in the z direction) of infinite extent in the y direction and of width l in the x direction . A potential f (x) is impressed (at y = 0) from x = 0 to x = 1, and the sides are grounded . To obtain a solution of this boundary-value problem, assume V(x, y) = f (x)g(y) . Substitution in the differential equation yields f ′′( x ) g ( y ) + f ( x ) g ′′( y ) = 0 or g ′′( y )/g ( y ) = − f ′′( x )/f ( x ) = λ 2 (say) . This system becomes g ′′( y ) − λ 2 g ( y ) = 0 and f ′′( y ) + λ 2 f ( y ) = 0 . The solutions of these ordinary differential equations are, respectively, g(y) = Aely + Be–ly and f (x) = C sin lx + D cos lx. Then f (x)g(y) = (Aely + Be–ly) (C sin lx + D cos lx) . Now V(0, y) = 0 so that f (0)g(y) = (Aely + Be-ly) D ≡ 0 for all y. Hence D = 0 . The solution then has the form sin lx (Aely + Be-ly) where the multiplicative constant C has been eliminated . Since V(l, y) = 0, sin ll(Aely + Be-ly) ≡ 0 . Clearly the bracketed function of y is not zero, for the solution would then be the identically zero solution . Hence sin ll = 0 or ln = nπ/l, n = 1, 2, …, where ln = nth eigenvalue . The solution now has the form sin (nπx/l)(Aenπy/l + Be-nπy/l) . Since V(x, ∞) = 0, A must be taken to be zero because ey becomes arbitrarily large as y → ∞ . The solution then reads Bn sin (nπx/l)e-nπy/l, where Bn is the multiplicative constant . The differential equation is linear and homogeneous ∞ so that ∑ n=1 Bn e − nπy /l sin (nπx/l) is also a solution . Satisfaction of the last boundary condition is ensured by taking 2 l f ( x ) sin (nπx/l) dx = Fourier sine coefficients of f (x) l ∫0 Further, convergence and differentiability of this series are established quite easily . Thus the solution is ∞ V ( x , y ) = ∑ Bn e − nπy /l sin n =1 nπx l Example The diffusion problem in a slab of thickness L ∂2 c ∂c = D 2 , c (0, t ) = 1, c ( L , t ) = 0, c ( x , 0) = 0 ∂x ∂t can be solved by separation of variables . First transform the problem so that the boundary conditions are homogeneous (having zeros on the right-hand side) . Let c(x , t ) = 1 − X = B cos λ x + E sin λ x 2 erf η = ∫ e − ξ d ξ / ∫ e − ξ d ξ Bn = 3-29 x + u( x , t ) L u = A ( B cos λ x + E sin λ x ) e − λDt Apply the boundary condition that u(0, t) = 0 to give B = 0 . Then the solution is u = A (sin λ x )e − λDt where the multiplicative constant E has been eliminated . Apply the boundary condition at x = L. 0 = A (sin λ L)e − λDt This can be satisfied by choosing A = 0, which gives no solution . However, it can also be satisfied by choosing l such that sin λ L = 0, λ L = n π Thus λ= n 2π2 L2 The combined solution can now be written as  sin nπx  − n 2 π 2 Dt / L2 e u= A  L  Since the initial condition must be satisfied, we use an infinite series of these functions . ∞  sin nπx  − n 2 π 2 Dt / L2 e u = ∑ An   L  n =1 At t = 0, we satisfy the initial condition . ∞ x  sin nπ x  − 1 = ∑ An    L L  n =1 This is done by multiplying the equation by sin mπx L and integrating over x: 0 → L. (This is the same as minimizing the mean square error of the initial condition .) This gives L x Am L mπx = ∫  − 1 sin dx 0  L  2 L which completes the solution . Integral-Transform Method A number of integral transforms are used in the solution of differential equations . Only one, the Laplace transform, is discussed here [ for others, see Integral Transforms (Operational Methods)] . 3-30 MATHEMATICS The one-sided Laplace transform indicated by L[ f (t)] is defined by the equation ∞ L[ f (t)] ∫ f (t )e − st dt . It has numerous important properties. The ones of 0 interest here are L[ f ′(t )] = sL[ f (t )] − f (0) L[ f ′′(t )] = s 2 L[ f (t )] − sf (0) − f ′(0); L[ f (n)(t)] = snL[ f (t)] - sn -1f (0) - sn -2 f ′(0) - … - f (n -1)(0) for ordinary derivatives. For partial derivatives an indication of which variable is being transformed avoids confusion. Thus, if ∫ 0 or e − st 1 ∞ ∂c ∂2 c dt = ∫ e − st dt ∂t D 0 ∂x 2 sF d 2F = (1/D ) sF − c ( x ,0) = D dx 2 where F(x, s) = Lt[c(x, t)] . Hence ∂y  y = y ( x , t ), Lt   = sL[ y ( x , t )] − y ( x , 0)  ∂t  d 2F  s  −   F =0 dx 2  D   ∂ y  dL [ y ( x , t )] Lt   = t dx  ∂x  whereas ∞ since L[ y(x, t)] is “really” only a function of x. Otherwise the results are similar. These facts coupled with the linearity of the transform, i.e., L[af (t) + bg(t)] = aL[ f (t)] + bL[g(t)], make it a useful device in solving some linear differential equations. Its use reduces the solution of ordinary differential equations to the solution of algebraic equations for L[y]. the inverse transform must be obtained either from tables or by use of complex inversion methods. Example The equation ∂c/∂t = D(∂2c/∂x2) represents the diffusion in a semi-infinite medium, x ≥ 0 . Under the boundary conditions c(0, t) = c0 and c(x, 0) = 0, find a solution of the diffusion equation . By taking the Laplace transform of both sides with respect to t, The other boundary condition transforms into F(0, s) = c0/s. Finally the solution of the ordinary differential equation for F subject to F(0, s) = c0/s and F remains finite as x → ∞ is F ( x , s ) = (c0 /s )e − s/ D x . Reference to a table shows that the function having this as its Laplace transform is 2  c ( x , t ) = c0 1 − π  ∫ π/2 Dt 0 2  x   e − u du  = C 0 erfc   4 Dt   This is the same solution obtained above by the group method . Matched-Asymptotic Expansions Sometimes the coefficient in front of the highest derivative is a small number . Special perturbation techniques can then be used, provided the proper scaling laws are found . See Holmes, M . H ., Introduction to Perturbation Methods, 2d ed ., Springer, New York, 2013 . DIFFEREnCE EQUATIOnS References: Elaydi, Saber, An Introduction to Difference Equations, 3d ed ., Springer-Verlag, New York, 2005; Kelley, W . G ., and A . C . Peterson, Difference Equations: An Introduction with Applications, 2d ed ., Harcourt/Academic, San Diego, Calif ., 2001 . Some models have independent variables that do not vary continuously, but have meaning only for discrete values . Stagewise processes such as distillation, staged extraction systems, absorption columns, and continuous stirred tank reactors (CSTRs) are such processes . The dependent variable varies between stages, and the independent variable is the integral number of the stage . Difference equations arise in discrete models of environmental problems (see Logan and Wolesensky) . Difference equations also arise in the solution of partial differential equations using the finite difference method, and those are treated below (Numerical Analysis and Approximate Methods) . Examined here are solution methods applicable to the chemical engineering problems; for more detailed information see the references . The methods for difference equations mirror those for differential equations . In particular, find complementary solution and then a particular solution . The order of the difference equation is the difference between the largest and smallest arguments . Consider the countercurrent cascade shown in Fig . 3-45 . We let yi be the ratio of the mass of solute to mass of solvent in the ith cell; xi is the ratio of mass of solute to mass of carrier solvent in the ith cell . For illustration we take the equilibrium relation as linear yi = Kxi A material balance on the ith stage gives Lxi -1 + Vyi+1 - Lxi - Vyi = 0 Using the equilibrium relation transforms this equation to the form (L/K) yi-1 + Vyi+1 - (L/K)yi - Vyi = 0 or yi+1 - [(L/VK) + 1] yi + (L/VK)yi-1 = 0 With α = L/VK the final form of the difference equation is yi+1 - (α + 1)yi + αyi-1 = 0 . The solution is obtained by trying the general form yi = r i . This gives the characteristic equation r2 - (α + 1)r + α = 0 . One root is r = 1, and call the other root b . The solution is then yi = A + B bi . This completes the complementary solution . The number of units is taken as N . The particular solution is found by choosing A and B to fit boundary conditions . Here they are taken as the inlet feed composition x0 and the inlet solvent composition yN+1 . Using y0 = Kx0, we obtain two equations for A and B . The solutions are A = Kx0 - B and B = (Kx0 - yN+1)/(1 - bN+1) . The exit concentration is y1 = A + B b . Nonlinear Difference Equations: Riccati Difference Equation The Riccati equation yi+1 yi + ayi+1 + byi + c = 0 is a nonlinear difference equation which can be solved by reduction to linear form . Set y = z + h. The equation becomes zi+1zi + (h + a)zi+1 + (h + b)zi + h2 + (a + b)h + c = 0 . If h is selected as a root of h2 + (a + b)h + c = 0 and the equation is divided by zi+1zi, there results (h + b)/zi+1 + (h + a)/zi + 1 = 0 . This is a linear equation with constant coefficients for wi = 1/zi. The solution is i a+h 1 1 = K  − − yi − h  b + h  (a + h) + (b + h) y1 y2 L x0 FIG. 3-45 cell 1 y3 y2 = K2x2 y1 = K1x1 x1 cell 2 y4 V y3 = K3x3 x2 cell 3 x3 Countercurrent cascade . where K is a constant chosen to fit conditions at one point . This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required . If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation . InTEGRAL EQUATIOnS References: Davis, H . T ., Introduction to Nonlinear Differential and Integral Equations, Dover, New York, 2010; Statgold, I ., and M . J . Holst, Green’s Functions and Boundary Value Problems, 3d ed ., Interscience, New York, 2011 . An integral equation is any equation in which the unknown function appears under the sign of integration and possibly outside the sign of integration . If derivatives of the dependent variable appear elsewhere in the equation, the equation is said to be integrodifferential . InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) CLASSIFICATIOn OF InTEGRAL EQUATIOnS Volterra’s integral equations have an integral with a variable limit, whereas Fredholm’s integral equations have a fixed limit. The Volterra equation of the second kind is Integral equations can arise from the formulation of a problem by using Green’s function. The equation governing heat conduction with a variable heat generation rate is represented in differential form as d 2T Q ( x ) = dx 2 k x u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt a 3-31 T (0) = T (1) = 0 In integral form the same problem is whereas a Volterra equation of the first kind is 1 T (x ) = x u ( x ) = λ ∫ K ( x , t )u (t ) dt a Equations of the first kind are very sensitive to solution errors so that they present severe numerical problems. Volterra equations are similar to initialvalue problems. A Fredholm equation of the second kind is b u ( x ) = f ( x ) + λ ∫ K ( x , t )u (t ) dt 1 G ( x , y )Q ( y ) dy k ∫0 − x (1 − y ) G(x , y ) =  − y (1 − x ) x≤y y ≤x The Poisson equation governs electric charges a ∇ 2 Ψ = −4 πρ whereas a Fredholm equation of the first kind is b u ( x ) = ∫ K ( x , t )u (t ) dt and the formulation as an integral equation is a The limits of integration are fixed, and these problems are analogous to boundary value problems. An eigenvalue problem is a homogeneous equation of the second kind, and solutions exist only for certain l. Ψ (r) = ∫ ρ(r0 )G (r , r0 ) dV0 V where Green’s function in three dimensions is 1 G (r , r0 ) = , r = ( x − x 0 )2 + ( y − y 0 )2 + ( z − z 0 )2 r b u ( x ) = λ ∫ K ( x , t )u (t ) dt a An example of a Volterra equation is the heat conduction problem in a semi-infinite domain. ρC p ∂2 T ∂T =k 2 ∂x ∂t T ( x , 0) = 0 limT ( x , t ) = 0 x →0 G (r , r0 ) = −2 ln r , r = ( x − x 0 )2 + ( y − y 0 )2 0 ≤ x < ∞, t > 0 ∂T (0, t ) = − g (t ) ∂x ∂T lim (x , t ) = 0 x →∞ ∂ x If this is solved by using Fourier transforms [see Integral Transforms (Operational Methods)], the solution is 1 T (x ) = 1 G ( x , y )Q ( y ) dy k ∫0 1 T (x , t ) = and in two dimensions is 2 1 1 e − x /4( t − s ) ds g (s ) π ∫0 t−s See the references for other examples. Integral equations can be solved numerically, too. The methods are analogous to the usual methods for integrating differential equations (Runge-Kutta, predictor-corrector, Adams methods, etc.). Explicit methods are fast and efficient until the time step is very small, to meet the stability requirements. Then implicit methods are used, even though sets of simultaneous algebraic equations must be solved. The major part of the calculation is the evaluation of integrals, however, so that the added time to solve the algebraic equations is not excessive. Thus, implicit methods tend to be preferred. Volterra equations of the first kind are not well posed, and small errors in the solution can have disastrous consequences. The boundary element method uses Green’s functions and integral equations to solve differential equations. See Brebbia, C. A., and J. Dominguez, Boundary Elements—An Introductory Course, 2d ed., Computational Mechanics Publications, Southhampton, UK, 1992; and Mackerle, J., and C. A. Brebbia, eds., Boundary Element Reference Book, Springer Verlag, Berlin, 1988. InTEGRAL TRAnSFORMS (OPERATIOnAL METHODS) References: Davies, B., Integral Transforms and Their Applications, 3d ed., Springer, New York, 2002; Debnath, L., and D. Bhatta, Integral Transforms and Their Applications, 3d ed., Chapman and Hall/CRC, New York, 2014; Duffy, D. G., Transform Methods for Solving Partial Differential Equations, Chapman & Hall/CRC, New York, 2nd ed., 2004; see also references for Differential Equations. The term operational method implies a procedure of solving differential and difference equations by which the boundary or initial conditions are automatically satisfied in the course of the solution. The technique offers a very powerful tool in the applications of mathematics, but it is limited to linear problems. Most integral transforms are special cases of the equation g (s) = ∫ b a f (t ) K ( s , t )dt in which g(s) is said to be the transform of f (t) and K(s, t) is called the kernel of the transform. A tabulation of the more important kernels and the interval (a, b) of applicability follows. Name of transform (a, b) K(s, t) e-st Laplace (0, ∞) Fourier (–∞, ∞) 1 − ist e 2π Fourier cosine (0, ∞) 2 cos st π Fourier sine (0, ∞) 2 sin st π 3-32 MATHEMATICS LAPLACE TRAnSFORM The Laplace transform of a function f (t) is defined by F(s) = ∞ L{ f (t )} = ∫ e − st f (t ) dt , where s is a complex variable. Note that the trans0 form is an improper integral and therefore may not exist for all continuous functions and all values of s. We restrict consideration to those values of s and those functions f for which this improper integral converges. The Laplace transform is used in process control (see Sec. 8). The function L[ f (t)] = g(s) is called the direct transform, and L-1[g(s)] = f (t) is called the inverse transform. Both the direct and the inverse transforms are tabulated for many often recurring functions. In general, L-1[ g ( s )] = 6. Transform of a derivative. Let f be a differentiable function such that both f and f ¢ belong to the class L. Then L{ f ¢ (t)} = sF(s) - f (0). 7. Transform of a higher-order derivative. Let f be a function which has continuous derivatives up to order n on (0, ∞), and suppose that f and its derivatives up to order n belong to the class L. Then L{ f (j)(t)} = s jF(s) - s j-1 f (0) - s j -2f ¢(0) - … - sf ( j -2)(0) - f (j -1)(0) for j = 1, 2, …, k. Example L{ f ″(t)} = s2L{ f (t)} - sf (0) - f¢ (0) Example Solve y ″ + y = 2et, y(0) = y¢(0) = 2. L[y ″] = -y¢(0) - sy(0) + s2L[y] = -2 - 2s + s2L[y]. Thus −2 − 2 s + s 2 L[ y ] + L[ y ] = 2 L[e t ] = 1 α+i∞ st e g ( s ) ds 2 πi ∫α−i∞ 0 Laplace transform of f exists for all complex numbers s with a sufficiently large real part. Note that condition 3 is automatically satisfied if f is assumed to be piecewise continuous on every finite interval 0 ≤ t < T. The function f (t) = t-1/2 is not piecewise continuous on 0 ≤ t < T but satisfies conditions 1 to 3. Let L denote the class of all functions on 0 < t < ∞ which satisfy conditions 1 to 3. Example Let f (t) be the Heaviside step function at t = t0; that is, f (t) = 0 for t ≤ t0 and f (t) = 1 for t > t0. Then Hence y = et + cos t + sin t. A short table (Table 3-2) of very common Laplace transforms and inverse transforms follows. The references and computer programs include more detailed tables. In Mathematica, the command∞ “Laplace Transform[cosh[a*t],t,s]” returns s/(s2−a2). note: Γ (n + 1) = x n e − x dx ∫ 0 (gamma function); Jn(t) = Bessel function of the first kind of order n. t 1 1 0 8. L  ∫a f (t ) dt  = L[ f (t )] + ∫a f (t ) dt s s TABLE 3-2 Laplace Transforms f (t) L{ f (t )} = ∫ e − st t0 ∫ ∞ 0 dt = lim ∫ e T →∞ − st t0 e − st0 1 dt = lim (e − st0 − e − sT ) = T →∞ s s provided s > 0 Example Let f (t) = eαt, t ≥ 0, where a is a real number. Then L{eαt} = e − ( s −a ) t dt = 1/( s − a ) provided Re s > a. Properties of the Laplace Transform 1. The Laplace transform is a linear operator: L{af (t) + bg(t)} = aL{ f (t)} + bL{g(t)} for any constants a and b and any two functions f and g whose Laplace transforms exist. 2. The Laplace transform of a real-valued function is real for real s. If f (t) is a complex-valued function f (t) = u(t) + iu(t), where u and u are real, then L{ f (t)} = L{u(t)} + iL{u(t)}. Thus L{u(t)} is the real part of L{ f (t)}, and L{u(t)} is the imaginary part of L{ f (t)}. 3. The Laplace transform of a function in the class L has derivatives of all orders, and L{t kf (t)} = (-1)k d kF(s)/dsk, k = 1, 2, 3, … , where F(s) is the Laplace transform of f (t). ∞ a st Example ∫0 e sin at dt = 2 2 , s > 0. s +a ∞ 2 as By property 3, L{t sin at } = ∫ e - st t sin at dt = 2 0 ( s + a 2 )2 Example By applying property 3 with f (t) = 1 and using the preceding results, we obtain dk 1 k! L{t k } = (−1) k k   = k+1 ds  s  s provided Re s > 0 for k = 1, 2, … . Similarly, we obtain L{t k e at } = (−1) k dk  1  k! =  ds k  s − a  ( s − a ) k +1 4. Frequency-shift property (or, equivalently, the transform of an exponentially modulated function). If F (s) is the Laplace transform of a function f (t) in class L, then for any constant a, L{eatf (t)} = F(s - a). Example L{te − at } = 1 ( s + a )2 ( s > 0). 5. Time-shift property. Let u(t - a) be the unit step function at t = a. Then L{ f (t - a)u(t - a)} = e-asF(s). f (t) g(s) 1 1/s e-at(1 - at) tn, (n = + integer) n! s n +1 Γ (n + 1) s n +1 s s2 + a2 t sin at 2a 1 sin at sinh at 2a 2 cos at cosh at tn, (n ≠ + integer) cos at T ∞ 2s 2 1 1 s = + + ( s − 1)( s 2 + 1) s − 1 s 2 + 1 s 2 + 1 L[ y ] = and to evaluate this integral requires a knowledge of complex variables, the theory of residues, and contour integration. A function is said to be piecewise continuous on an interval if it has only a finite number of finite (or jump) discontinuities. A function f on 0 < t < ∞ is said to be of exponential growth at infinity if there exist constants M and α such that | f (t)| ≤ Meat for sufficiently large t. Sufficient Conditions for the Existence of the Laplace Transform Suppose f is a function which is (1) piecewise continuous on every finite interval 0 < t < T, (2) of exponential growth at infinity, and δ (3) for which ∫ | f (t )| dt exists ( finite) for every finite d > 0. Then the 2 s −1 a s2 + a2 s s2 − a2 sin at cosh at e-at e sin at t J0(at) e-bt sin at 1 −k e s k 2 t s3 s 2 + 4a 4 s2 s4 − a4 s3 s4 − a4 a tan −1 s 1 s2 + a2 s +b ( s + b)2 + a 2 a ( s + b)2 + a 2 cos at erfc ½(cosh at + cos at) a s2 − a2 1 s+a sinh at -bt 1 (sinh at + sin at ) 2a g (s) s ( s + a )2 s ( s 2 + a 2 )2 s s 4 + 4a 4 na n J n (at ) t ( s 2 + a 2 − s )n (n > 0) 1 − a/s e s Γ (n) (n > 0) ( s − a )n J 0 (2 at ) t n −1e at s Example Find f (t) if L[ f (t )] = 1  1  1 1 . L sinh at  = 2 . s 2  s 2 − a 2   a  s − a2 t t1 1 sinh at  Therefore f (t ) = ∫  ∫ sinh at dt  dt = 2  − t .  0 a  a  0a  ∞  f (t )  = g ( s ) ds 9. L   t  ∫s ∞ ∞  f (t )  L  k  = ∫ ⋯∫ g ( s )(ds ) k s s  t      k integrals Example L   ∞ a ds sin at  ∞ s = L[sin at ] ds = ∫ 2 = cot −1 s s + a2 a t  ∫s 10. The unit step function 0 t < a u (t − a ) =  1 t > a L[u (t − a )] = e − as s MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS 11. The unit impulse function is ∞ at t = a δ(a ) = u ′(t − a ) =  0 elsewhere The Fourier transform is given by L[u ′(t − a )] = e − as 12. L-1[e-asg(s)] = f (t - a)u(t - a) (second shift theorem). 13. If f (t) is periodic of period b, that is, f (t + b) = f (t), then F [ f (t )] = F -1[ g ( s )] = Example The partial differential equations relating gas composition to position and time in a gas chromatograph are ∂y/∂n + ∂x/∂q = 0 and ∂y/∂n = x - y, where x = mx′, n = (kGaP/Gm)h, θ = (mkGaP/ρB)t and GM = molar velocity, y = mole fraction of the component in the gas phase, ρB = bulk density, h = distance from entrance, P = pressure, kG = mass-transfer coefficient, and m = slope of the equilibrium line . These equations are equivalent to ∂2y/∂n ∂θ + ∂y/∂n + ∂y/∂q = 0, where the boundary conditions considered here are y(0, θ) = 0 and x(n, 0) = y(n, 0) + (∂y/∂n) (n, 0) = δ(0) (see property 11) . The problem is conveniently solved by using the Laplace transform of y with ∞ - ns respect to n; write g ( s , θ) = ∫0 e y (n , θ) dn . Operating on the partial differential equation gives s(dg/dθ) - (∂y/∂q) (0, q) + sg - y(0, q) + dg/dq = 0 or (s + 1) (dg/dq) + sg = (∂y/∂θ) (0, θ) + y(0, q) = 0 . The second boundary condition gives g(s, 0) + sg(s, 0) - y(0, 0) = 1 or g(s, 0) + sg(s, 0) = 1 (L[δ(0)] = 1) . A solution of the ordinary differential equation for g consistent with this second condition is 1 − sθ/( s +1) g ( s , θ) = e s +1 Inversion of this transform gives the solution y (n , θ) = e − ( n+θ) I 0 (2 nθ ) where I0 = zero-order Bessel function of an imaginary argument . For large u, In(u) ∼ e u / 2 πu . For large n, exp[ −( θ − n )2 ] 2 π1/2 (nθ)1/4 or for sufficiently large n, the peak concentration occurs near θ = n. Other applications of Laplace transforms are given under Differential Equations . ∞ In brief, the condition for the Fourier transform to exist is that ∫ | f (t )| dt < ∞, although certain functions may have a Fourier transform −∞ even if this is violated . 1− a ≤ t ≤ a a Example The function f (t ) =  has F [ f (t )] = ∫ e − ist dt −a 0 elsewhere a a a 0 0 0 = ∫ e ist dt + ∫ e - ist dt = 2 ∫ cos st dt = 2 sin sa s Properties of the Fourier Transform Let F [ f (t)] = g(s); F -1[ g(s)] = f (t) . 1 . F [ f (n)(t)] = (is)nF [ f (t)] . 2 . F [a f (t) + bh(t)] = aF [ f (t)] + bF [h(t)] . 3 . F [ f (-t)] = g(-s) . 1  s 4 . F [ f (at )] = g   , a > 0 . a  a 5 . F [e-iwtf (t)] = g(s + w) . 6 . F [ f (t + t1)] = eist1g(s) . 7 . F [ f (t)] = G(is) + G(-is) if f (t) = f (-t) ( f even) F [ f (t)] = G(is) - G(-is) if f (t) = -f (-t) (f odd) where G(s) = L[ f (t)] . This result allows the use of the Laplace transform tables to obtain the Fourier transforms . Example Find F [e-a|t|] by property 7 . Now e-a|t| is even . So L[e-at] = 1/(s + a) . Therefore, F [e-a|t|] = 1/(is + a) + 1/(-is + a) = 2a/(s2 + a2) . FOURIER COSInE TRAnSFORM The convolution integral of two functions f (t) and r(t) is x(t) = f (t)∗r(t) = t ∫ f (τ)r (t − τ)d τ . Example 1 ∞ g ( s )e ist dt = f (t ) 2 π ∫−∞ The Fourier cosine transform is given by COnVOLUTIOn InTEGRAL 0 1 ∞ f (t )- ist dt = g ( s ) 2 π ∫−∞ and its inverse by 1  b − st L[ f (t )] =  e f (t )dt  1 − e − bs  ∫0 y (n , θ)  3-33 t t ∗ sin t = ∫ τ sin(t − τ) d τ = t − sin t . 0 Fc [ f (t )] = g ( s ) = 2 ∞ f (t )cos st dt π ∫0 Fc-1[ g ( s )] = f (t ) = 2 ∞ g ( s )cos st ds π ∫0 and its inverse by L[ f (t)]L[h(t)] = L[ f (t)∗h(t)] FOURIER TRAnSFORM References: https://en .wikipedia .org/wiki/Fourier_transform#Tables_ of_important_Fourier_transforms; Varma and Morbidelli (1997), see General References . The Fourier sine transform Fs is obtainable by replacing the cosine by the sine in these integrals . They can be used to solve linear differential equations; see the transform references . MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS References: Anton, H ., and C . Rorres, Elementary Linear Algebra with Applications, 9th ed ., Wiley, New York, 2004; Bernstein, D . S ., Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, 2d ed ., Princeton University Press, Princeton, N .J ., 2009 . MATRIX ALGEBRA Matrices n columns, A rectangular array of mn quantities, arranged in m rows and  a11 ⋯ a1n  a ⋯ a  21 2n  A = (aij ) =  ⋮    amn   am1 is called a matrix . The elements aij may be real or complex . The notation aij means the element in the ith row and jth column; i is called the row index and j the column index. If m = n, the matrix is said to be square and of order n. A matrix, even if it is square, does not have a numerical value, as a determinant does . However, if the matrix A is square, a determinant can be formed which has the same elements as matrix A. This is called the determinant of the matrix and is written det (A) or |A| . If A is square and det (A) ≠ 0, then A is said to be nonsingular; if det (A) = 0, then A is said to be singular . A matrix A has rank r if and only if it has a nonvanishing determinant of order r and no nonvanishing determinant of order > r. Equality of Matrices Let A = (aij), B = (bij) . Two matrices A and B are equal (=) if and only if they are identical; that is, they have the same number of rows and the same number of columns and equal corresponding elements (aij = bij for all i and j) . Addition and Subtraction The operations of addition (+) and subtraction (-) of two or more matrices are possible if and only if the matrices have the same number of rows and columns . Thus A ± B = (aij ± bij); i .e ., addition and subtraction are of corresponding elements . Transposition The matrix obtained from A by interchanging the rows and columns of A is called the transpose of A, written A¢ or AT . 1 2 1 3 4 AT =  3 1  Example A =     2 1 6   4 6  Note that (AT)T = A . 3-34 MATHEMATICS Multiplication Let A = (aij), i = 1, …, m1; j = 1, …, m2, and B = (bij), i = 1, …, n1, j = 1, …, n2. The product AB is defined if and only if the number of columns of A (m2) equals the number of rows of B (n1), that is, n1 = m2. For two such matrices the product P = AB is defined by summing the elementby-element products of a row of A by a column of B. This is the row-by-column rule. Thus n1 Pij = ∑ aik bkj k =1 The resulting matrix has m1 rows and n2 columns.  −4 3 17 24  3 2   1 1   0 1 5 6  =  −2 1 6 9  Example     −2 0 1 3    −8 5 29 42  5 4  It is helpful to remember that the element Pij is formed from the ith row of the first matrix and the jth column of the second matrix. The matrix product is not commutative. That is, AB ≠ BA in general. Inverse of a Matrix A square matrix A is said to have an inverse if there exists a matrix B such that AB = BA = I, where I is the identity matrix of order n.       The inverse B is a square matrix of the order of A, designated by A-1. Thus AA-1 = A-1A = I. A square matrix A has an inverse if and only if A is nonsingular. Certain relations are important: (1) (AB)-1 = B-1A-1 (2) (AB)T = BTAT (3) (A-1)T = (AT )-1 (4) (ABC)-1 = C-1B-1A-1 Scalar Multiplication Let c be any real or complex number. Then cA = (caij). Linear Equations in Matrix Form Every set of n nonhomogeneous linear equations in n unknowns a11 x 1 + a12 x 2 + ⋯ + a1n x n = b1 a21 x 1 + a22 x 2 + ⋯ + a2 n x n = b2 ⋮ an1 x1 + an 2 x 2 + ⋯ + ann x n = bn can be written in matrix form as AX = B, where A = (aij), XT = [x1 … xn], and BT = [b1 … bn]. The solution for the unknowns is X = A-1B. Special Square Matrices 1. A triangular matrix is a matrix all of whose elements above or below the main diagonal (set of elements a11, …, ann) are zero. If A is triangular, det (A) = a11a22 ann . 2. A diagonal matrix is one such that all elements both above and below the main diagonal are zero (that is, aij = 0 for all i ≠ j). If all diagonal elements are equal, the matrix is called scalar. If A is diagonal, A = (aij), A-1 = (1/aij). 3. If aij = aji for all i and j (that is, A = AT ), the matrix is symmetric. 4. If aij = -aji for i ≠ j but not all the aij are zero, the matrix is skew. 5. If aij = -aji for all i and j (that is, aii = 0), the matrix is skew symmetric. 6. If AT = A-1, the matrix A is orthogonal. 7. If the matrix A* = (aij )T and aij = complex conjugate of aij, then A* is the hermitian transpose of A. 8. If A = A-1, then A is involutory. 9. If A = A*, then A is hermitian. 10. If A = -A*, then A is skew hermitian. 11. If A-1 = A*, then A is unitary. If A is any matrix, then AAT and ATA are square symmetric matrices, usually of different order. By using a program such as MATLAB, these are easily calculated. Matrix Calculus Differentiation Let the elements of A = [aij(t)] be differentiable funcdA  daij (t )  tions of t. Then . = dt  dt  Example  sin t cos t  A=   − cos t sin t  t 2  A= 2 t t e  Example  t 2/2 2t  . 3 e t   ∫ Adt = t /3 The matrix B = A - lI is called the characteristic matrix or eigenmatrix of A. Here A is square of order n, l is a scalar parameter, and I is the n × n identity matrix. So det B = det (A - lI) = 0 is the characteristic equation (or eigenequation) for A. The characteristic equation is always of the same degree as the order of A. The roots of the characteristic equation are called the eigenvalues of A or characteristic values of A. 1 2  A=  3 8  Example 1 2   λ 0  1 − λ 2 . B=  = −  3 8  0 λ   3 8 − λ  Above is the characteristic matrix and f (l) = det (B) = det (A - lI) = (1 - l) (8 - l) - 6 = 2 − 9l + l2 = 0 is the characteristic equation. The eigenvalues of A are the roots of l2 - 9l + 2 = 0, which are (9 ± 73)/2 . A nonzero matrix Xi, which has one column and n rows, a column vector, satisfying the equation (A - lI)Xi = 0 1 0 ⋯⋅ 0   ⋅⋅ 0 1  ⋮ 1 0  0 ⋯⋅ 0 1  ⋮ Integration The integral ∫ A dt = [ ∫ aij (t ) dt ]. dA cos t − sin t  = dt sin t cos t  and associated with the ith characteristic root li is called an eigenvector. Vector and Matrix Norms To carry out error analysis for approximate and iterative methods for the solutions of linear systems, one needs notions for vectors in Rn and for matrices that are analogous to the notion of length of a geometric vector. Let Rn denote the set of all vectors with n components, x = (x1, …, xn). In dealing with matrices it is convenient to treat vectors in Rn as columns, and so x = (x1, …, xn)T; however, here we shall write them simply as row vectors. A norm on Rn is a real-valued function f defined on Rn with the following properties: 1. f (x) ≥ 0 for all x ∈ Rn. 2. f (x) = 0 if and only if x = (0, 0, …, 0). 3. f (ax) = |a| f (x) for all real numbers a and x ∈ Rn. 4. f (x + y) ≤ f (x) + f (y) for all x, y ∈ Rn. The usual notation for a norm is f (x) = x . The norm of a matrix is κ ( A ) ≡ A A −1 where A sup x ≠0 = n Ax = max k ∑ a jk x j =1 The norm is useful when doing numerical calculations. If the computer’s floating-point precision is 10-6, then k = 106 indicates an ill-conditioned matrix. If the floating-point precision is 10-12 (double precision), then a matrix with k = 1012 may be ill-conditioned. Two other measures are useful and are more easily calculated: Ratio = (k) max k a kk (k) min k a kk V= det A α 1α 2  α n α1 = (α i21 + α i22 + + α in2 )1/2 where akk(k) are the diagonal elements of the LU decomposition. MATRIX COMPUTATIOnS The principal topics in linear algebra involve systems of linear equations, matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, and least-squares problems. The calculations are routinely done on a computer. LU Factorization of a Matrix Let L be an n × n lower triangular matrix with unit diagonal elements. Let U be an n × n upper triangular matrix. If all the principal submatrices of an n × n matrix A are nonsingular, then it is possible to represent A = LU. The Gauss elimination method is in essence an algorithm to determine L and U. Solution of Ax = b by Using LU Factorization Suppose that the indicated system is compatible and that A = LU. Let z = Ux. Then Ax = LUx = b implies that Lz = b. Thus to solve Ax = b we first solve Lz = b for z and then solve Ux = z for x. This procedure does not require that A be invertible and can be used to determine all solutions of a compatible system Ax = b. Note that the systems Lz = b and Ux = z are both in triangular form and thus can be easily solved. The LU decomposition is essentially a gaussian elimination, arranged for maximum efficiency. The chief reason for doing an LU decomposition is that it takes fewer multiplications than would be needed to find an inverse. Also, once the LU decomposition has been found, it is possible to solve for MATRIX ALGEBRA AnD MATRIX COMPUTATIOnS multiple right-hand sides with little increase in work. The multiplication count for an n × n matrix and m right-hand sides is 1 1 Operation count = n 3 − n + mn 2 3 3 If an inverse is desired, it can be calculated by solving for the LU decomposition and then solving n problems with right-hand sides consisting of all zeros except one entry. Thus 4n2/3 - n/3 multiplications are required for the inverse. The determinant is given by n 3-35 An m × m unitary matrix U is formed from the eigenvectors ui of the first matrix. U = [u1, u2, …, um] An n × n unitary matrix V is formed from the eigenvectors vi of the second matrix. V = [v1, v2, …, vn] Then matrix A can be decomposed into Det A = ∏ aii( i ) i =1 where aii(i) are the diagonal elements obtained in the LU decomposition. A tridiagonal matrix is one in which the only nonzero entries lie on the main diagonal and on the diagonal just above and just below the main diagonal. The set of equations can be written as aixi-1 + bixi + cixi+1 = di The LU decomposition is b1 = b1 for k = 2, n do a a ak′ = k , bk′ = bk − k c k−1 bk′−1 bk′−1 enddo d1′ = d1 for k = 2, n do d k′ = d k − ak′ d k′−1 A = U∑V* where ∑ is a k × k diagonal matrix with diagonal elements dii = si > 0 for 1 ≤ i ≤ k. The eigenvalues of ∑*∑ are s2i. The vectors ui for k + 1 ≤ i ≤ m and vi for k + 1 ≤ i ≤ n are eigenvectors associated with the eigenvalue zero; the eigenvalues for 1 ≤ i ≤ k are s2i. The values of si are called the singular values of matrix A. If A is real, then U and V are real and hence orthogonal matrices. The value of the singular-value decomposition comes when a process is represented by a linear transformation and the elements of A and aij are the contribution to an output i for a particular variable as input variable j. The input may be the size of a disturbance, and the output is the gain (Seborg, D. E., T. F. Edgar, and D. A. Mellichamp, Process Dynamics and Control, 2d ed., Wiley, New York, 2004). If the rank is less than n, not all the variables are independent and they cannot all be controlled. Furthermore, if the singular values are widely separated, the process is sensitive to small changes in the elements of the matrix, and the process will be difficult to control. Example Consider the following example from Noble and Daniel (Applied Linear Algebra, Prentice-Hall, Upper Saddle River, N.J., 1987) with the MATLAB commands to do the analysis. Define the following real matrix with m = 3 and n = 2 (whose rank k = 1). >> a = [1 1 2 2 enddo x n = dn′/bn′ 2 2] for k = n - 1,1 do d′ − c x x k = k k k+1 d k′ The following MATLAB commands are used. a1 = a ∗ a enddo a 2 = a ∗ a′ The operation count for an n × n matrix with m right-hand sides is [ v , d 1] = eig (a1) 2(n - 1) + m(3n - 2) If |bi| > |ai| + |ci|, no pivoting is necessary, and this is true for many boundaryvalue problems and partial differential equations. Sparse matrices are ones in which the majority of the elements are zero. If the structure of the matrix is exploited, the solution time on a computer is greatly reduced. See Duff, I. S., A. M. Erisman, and J. K. Reid, Direct Methods for Sparse Matrices, Clarendon Press, Oxford, UK, 1986; Davis, T. A., Direct Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, Penn., 2006. The conjugate gradient method is one method for solving sparse matrix problems, since it only involves multiplication of a matrix times a vector. Thus the sparseness of the matrix is easy to exploit. The conjugate gradient method is an iterative method that converges for sure in n iterations where the matrix is an n × n matrix. Matrix methods, in particular finding the rank of the matrix, can be used to find the number of independent reactions in a reaction set. If the stoichiometric numbers for the reactions and molecules are put in the form of a matrix, the rank of the matrix gives the number of independent reactions. See Amundson, N. R., Mathematical Methods in Chemical Engineering, Prentice-Hall, Englewood Cliffs, N.J., 1966, p. 50. See also Dimensional Analysis. QR Factorization of a Matrix If A is an m × n matrix with m ≥ n, there exists an m × m unitary matrix Q = [q1, q2, …, qm] and an m × n right triangular matrix R such that A = QR. The QR factorization is frequently used in the actual computations when the other transformations are unstable. Singular-Value Decomposition If A is an m × n matrix with m ≥ n and rank k ≤ n, consider the two following matrices. AA* and A*A [u , d 2] = eig (a 2) The results are v = [ −0.7071 0.7071 0.7071 0.7071] d 1 = [0 0 0 18] u = [ 0.8944 0.2981 0.3333 − 0.4472 0.5963 0.6667 0 − 0.7454 0.6667] d2 = 0 0 0 0 0 0 0 0 18 2 Thus, σ1 = 18 and the eigenfunctions are the rows of v and u. The second column of v is associated with the eigenvalue σ12 = 18, and the third column of u is associated with the eigenvalue σ12 = 18. If A is square and nonsingular, the vector x that minimizes ||Ax - b|| is obtained by solving the linear equation x = A-1b (3-62) 3-36 MATHEMATICS When A is not square, the solution to mean by subtracting from each entry in the column the average of the column entries. Once this is done, the loadings are the vi and satisfy Ax = b cov(A) vi = σ i2 vi is and the score vector ui is given by x = Vy where yi = b′i/si for i = 1, …, k, b′ = UT b, and yk+1, yk+2, …, ym are arbitrary. The matrices U and V are those obtained in the singular-value decomposition. The solution which minimizes the norm, Eq. (3-62), is x with yk+1, yk+2, . . ., ym zero. These techniques can be used to monitor process variables. See Montgomery, D. C., Introduction to Statistical Quality Control, 6th ed., Wiley, New York, 2008; Piovos, M. J., and K. A. Hoo, “Multivariate Statistics for Process Control,” IEEE Control Systems 22(5):8 (2002). Principal Component Analysis (PCA) PCA is used to recognize patterns in data and reduce the dimensionality of the problem. Let the matrix A now represent data with the columns of A representing different samples and the rows representing different variables. The covariance matrix is defined as cov ( A ) = AT A m −1 This is just the same matrix discussed with singular-value decomposition. For data analysis, however, it is necessary to adjust the columns to have zero Avi = siui In process analysis, the columns of A represent different measurement techniques (temperatures, pressures, etc.), and the rows represent the measurement output at different times. In that case the columns of A are adjusted to have a zero mean and a variance of 1.0 (by dividing each entry in the column by the variance of the column). The goal is to represent the essential variation of the process with as few variables as possible. The ui, vi pairs are arranged in descending order according to the associated si. The si can be thought of as the variance, and the ui, vi pair captures the greatest amount of variation in the data. Instead of having to deal with n variables, one can capture most of the variation of the data by using only the first few pairs. An excellent example of this is given by Wise, B. M., and B. R. Kowalski, “Process Chemometrics,” Chap. 8 in Process Analytical Chemistry, eds. F. McLennan and B. Kowalski, Blackie Academic & Professional, London, 1995. When modeling a slurry-fed ceramic melter, they were able to capture 97 percent of the variation by using only four eigenvalues and eigenvectors, even though there were 16 variables (columns) measured. nUMERICAL APPROXIMATIOnS TO SOME EXPRESSIOnS APPROXIMATIOn IDEnTITIES Approximation For the following relationships the sign @ means approximately equal to, when X is small. These equations are derived by using a Taylor’s series (see Series Summation and Identities). Approximation 1 ≅1 X 1± X Approximation 1± X ≅1± X 2 Approximation (1 ± X)n @ 1 ± nX (1 ± X)-n @ 1  nX (a ± X)2 = a2 ± 2aX ex @ 1 + X sin X @ X(X rad) tan X @ X 2Y + X Y (Y + X ) ≅ 2 Stirling’s approximation X2  X   small  2Y  Y In N! @ N ln N - N Y 2 + X2 ≅Y + nUMERICAL AnALYSIS AnD APPROXIMATE METHODS References: Ascher, U. M., and C. Greif, A First Course in Numerical Methods, SIAM-Soc. Ind. Appl. Math., 2011; Atkinson, K., W. Han, and D. E. Stewart, Numerical Solution of Ordinary Differential Equations, Wiley, New York, 2009; Burden, R. L., J. D. Faires, A. C. Reynolds, and A. M. Burden, Numerical Analysis, 10th ed., Brookes/Cole, Pacific Grove, Calif., 2015; Chapra, S. C., and R. P. Canal, Numerical Methods for Engineers, 5th ed., McGraw-Hill, New York, 2006; Heys, Jeffrey, J., Chemical and Biomedical Engineering Calculations Using Python, Wiley, New York (2017); Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover, New York, 2009; Lau, H. T., A Numerical Library in C for Scientists and Engineers, CRC Press, Boca Raton, Fla., 3rd ed. 2007; LeVeque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge 2002; Morton, K. W., and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction, 2d ed., Cambridge University Press, Cambridge, 2005; Quarteroni, A., and A. Valli, Numerical Approximation of Partial Differential Equations, 2d ed., Springer, New York, 2008; Reddy, J. N., and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, 3d ed., CRC Press, Boca Raton, Fla., 2010; Zienkiewicz, O. C., R. L. Taylor, and J. Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann Elsevier, Oxford, UK, 2013. InTRODUCTIOn The goal of approximate and numerical methods is to provide convenient techniques for obtaining useful information from mathematical formulations of physical problems. Often this mathematical statement is not solvable by analytical means. Or perhaps analytic solutions are available but in a form that is inconvenient for direct interpretation. In the first case, it is necessary either to attempt to approximate the problem satisfactorily by one that will be amenable to analysis, to obtain an approximate solution to the original problem by numerical means, or to use the two techniques in combination. Numerical methods have been used to model polymerization, yeast fermentation, chemical vapor deposition, catalytic converters, pressure swing adsorption, insulin purification, ion exchange, and affinity chromatography, plus many other chemical engineering applications. Numerical techniques therefore do not yield exact results in the sense of the mathematician. Since most numerical calculations are inexact, the concept of error is an important feature. The four sources of error are as follows: 1. Gross errors. These result from unpredictable human, mechanical, or electrical mistakes. 2. Rounding errors. These are the consequence of using a number specified by m correct digits to approximate a number which requires more than m digits for its exact specification. For example, approximate the irrational number 2 by 1.414. Such errors are often present in experimental data, in which case they may be called inherent errors, due either to empiricism or to the fact that the computer dictates the number of digits. Such errors may be especially damaging in areas such as matrix inversion or the numerical solution of partial differential equations when the number of algebraic operations is extremely large. 3. Truncation errors. These errors arise from the substitution of a finite number of steps for an infinite sequence of steps which would yield the exact result. To illustrate this error, consider the infinite series for e-x: e-x = 1 - x + x2/2 - x3/6 + ET(x), where ET is the truncation error, ET = (1/24)e-ex4, for 0 < e < x. If x is positive, e is also positive. Hence e-e < 1. The approximation e-x ≈ 1 - x + x2/2 - x3/6 is in error by a positive amount smaller than (1/24)x4. A variety of general-purpose computer programs are available commercially. Mathematica (http://www.wolfram.com/), Maple (http://www .maplesoft.com/), and Mathcad (https://www.ptc.com/en/engineeringmath-software/mathcad) and MATLAB (http://www.mathworks.com/ nUMERICAL AnALYSIS AnD APPROXIMATE METHODS product/symbolic) all have the capability of doing symbolic manipulation so that algebraic solutions can be obtained. Different packages can solve some ordinary and partial differential equations analytically, solve nonlinear algebraic equations, make simple graphs and do linear algebra, and combine the symbolic manipulation with numerical techniques. In this section, examples are given for the use of MATLAB (http://www.mathworks.com/), a package of numerical analysis tools, some of which are accessed by simple commands and others of which are accessed by writing programs in C. Spreadsheets can also be used to solve certain problems, and these are described below too. A popular program used in chemical engineering education is Polymath (http://www.polymath-software.com/), which can numerically solve sets of linear or nonlinear equations, ordinary differential equations as initial-value problems, and perform data analysis and regression. The Wegstein method is a secant method applied to g(x) ≡ x - F(x). In Microsoft Excel, roots are found by using Goal Seek or Solver (an Add-In). Assign one cell to be x, put the equation for f (x) in another cell, and let Goal Seek or Solver find the value of x that makes the equation cell zero. In MATLAB, the process is similar except that a function (m-file) is defined and the command fzero (¢f ¢, x0) provides the solution x, starting from the initial guess x0. The Wegstein method is sometimes used to promote convergence when solving a mass and energy balance problem for a chemical process with recycle streams. METHODS FOR MULTIPLE nOnLInEAR EQUATIOnS Write a system of equations as Method of Successive Substitutions nUMERICAL SOLUTIOn OF LInEAR EQUATIOnS See the section Matrix Algebra and Matrix Computation. nUMERICAL SOLUTIOn OF nOnLInEAR EQUATIOnS In OnE VARIABLE Methods for Nonlinear Equations in One Variable Successive Substitutions Let f (x) = 0 be the nonlinear equation to be solved. If this is rewritten as x = F(x), then an iterative scheme can be set up in the form xk+1 = F(xk). To start the iteration, an initial guess must be obtained graphically or otherwise. The convergence or divergence of the procedure depends upon the method of writing x = F(x), of which there will usually be several forms. However, if a is a root of f (x) = 0, and if |F ′(a)| < 1, then for any initial approximation sufficiently close to a, the method converges to a. This process is called first-order because the error in xk+1 is proportional to the first power of the error in xk for large k. One way of writing the equation is xk+1 = xk + b f (xk). The choice of b is made such that |1 + b df/dx(a)| < 1. Convergence is guaranteed by the theorem given for simultaneous equations. Methods of Perturbation Let f (x) = 0 be the equation. In general, the iterative relation is αi = fi(`) x 2 = x1 − x1 − x 0 f ( x1 ) f ( x1 ) − f ( x 0 ) In each of the following steps αk is the slope of the line joining [xk, f (xk)] to the most recently determined point where f (xj) has the opposite sign from that of f (xk). This method is first-order. If one uses the most recently determined point (regardless of sign), the method is a secant method. Method of Wegstein This is a variant of the method of successive substitutions which forces and/or accelerates convergence. The iterative procedure xk+1 = F(xk) is revised by setting xˆk+1 = F ( x k ) and then taking x k+1 = qx k + (1 − q ) xˆk +1, where q is a suitably chosen number which may be taken as constant throughout or may be adjusted at each step. Wegstein found that suitable q’s are as follows: Behavior of successive substitution process Oscillatory divergence without Wegstein ½<q<1 without Wegstein 1<q q<0 Monotonic convergence Monotonic divergence Range of optimum q 0<q<½ Oscillatory convergence At each step q may be calculated to give a locally optimum value by setting q= xˆk+1 − xˆk xˆk+1 − 2 xˆk + xˆk−1 ` = f(`) or The following theorem guarantees convergence. Let ` be the solution to `i = fi(`). Assume that given h > 0, there exists a number 0 < m < 1 such that ∂ fi n ∑ ∂x j =1 x i − α i < h , i = 1,, n for ≤µ j x ik +1 = f i ( x ik ) Then x ik → α i as k increases [see Finlayson (1980)]. Newton-Raphson Method To solve the set of equations Fi(x1, x2, …, xn) = 0 Fi ({xj}) = 0 or or Fi(x) = 0 one uses a truncated Taylor series to get ∂ Fi ∂ j =1 x j n 0 = Fi ({ x k }) + ∑ xk+1 = xk - [ f (xk)/αk] where the iteration begins with x0 as an initial approximation and αk as some functional, derived below. Newton-Raphson Procedure This variant chooses αk = f ¢(xk) where f ¢ = df/dx and geometrically consists of replacing the graph of f (x) by the tangent line at x = xk in each successive step. If f ¢(x) and f ″ ≤(x) have the same sign throughout an interval a ≤ x ≤ b containing the solution, with f (a) and f (b) of opposite signs, then the process converges starting from any x0 in the interval a ≤ x ≤ b. The process is second-order. Method of False Position This variant is commenced by finding x0 and x1 such that f (x0) and f (x1) are of opposite sign. Then α1 = slope of secant line joining [x0, f (x0)] and [x1, f (x1)] so that 3-37 ( x kj +1 + x kj ) xk Thus one solves iteratively from one point to another. n ∑A ( x kj +1 − x kj ) = − Fi ({ x k }) Aijk = ∂ Fi ∂x j k ij j =1 where xk This method requires solution of sets of linear equations until either the functions are zero to some tolerance or the changes of the solution between iterations are small enough. Convergence is guaranteed provided the norm of matrix A is bounded, F(x) is bounded for the initial guess, and the second derivative of F(x) with respect to all variables is bounded. See Finlayson (1980) in General References. Homotopy methods are also possible; see Finlayson et al. (2006) in General References. InTERPOLATIOn When a function is known at several points, it is sometimes useful to have a means to interpolate and assign a value between those points. The interpolation can be a global approximation, i.e., a function defined using all the points, or piecewise approximation, i.e., a collection of functions, each defined over several different subsets of the points. Lagrange Interpolation Formulas A global polynomial is defined over the entire region of space m Pm ( x ) = ∑ c j x j j =0 This polynomial is of degree m (highest power is xm) and order m + 1 (m + 1 parameters {cj}). If we are given a set of m + 1 points y1 = f (x1), y2 = f (x2), …, ym+1 = f (xm+1) 3-38 MATHEMATICS then Lagrange’s formula gives a polynomial of degree m that goes through the m + 1 points: Pm ( x ) = is approximately independent of x0 and x1 in the range. The linear approximation to the function f (x), x0 < x < x1 then leads to the interpolation formula f ( x ) ≈ f ( x 0 ) + ( x − x 0 ) f [ x 0 − x1 ] ( x − x 2 )( x − x 3 )( x − x m +1 ) y1 ( x 1 − x 2 )( x 1 − x 3 )( x 1 − x m +1 ) ≈ f (x0 ) + ( x − x 1 )( x − x 3 )( x − x m +1 ) + y 2 + ( x 2 − x 1 )( x 2 − x 3 )( x 2 − x m +1 ) ( x − x 1 )( x − x 2 )( x − x m +1 ) + y m +1 ( x m +1 − x 1 )( x m +1 − x 2 )( x m +1 − x m ) Note that each coefficient of yj is a polynomial of degree m that vanishes at the points {xj} (except for one value of j) and takes the value of 1.0 at that point: Pm(xj) = yj m +1 x m +1 − x 1 (n + 2)! max x1 ≤ x ≤ x m+1 | f ( n + 2) ( x )| The evaluation of Pm(x) at a point other than at the defining points can be made with Neville’s algorithm [Press et al. (2007) in General References]. Orthogonal Polynomials Another form of polynomials is obtained by defining them so that they are orthogonal. It is required that Pm(x) be orthogonal to Pk(x) for k = 0, …, m − 1. 1 [( x 1 − x ) f ( x 0 ) − ( x 0 − x ) f ( x 1 )] x1 − x 0 Higher-order interpolation is also possible. Equally Spaced Forward Differences If the ordinates are equally spaced, that is, xj - xj -1 = Δx for all j, then the first differences are denoted by Δf (x0) = f (x1) - f (x0) or Δy0 = y1 - y0, where y = f (x). The differences of these first differences, called second differences, are denoted by Δ2y0, Δ2y1, …, Δ2yn. Thus Δ2y0 = Δy1 - Δy0 = y2 - y1 - y1 + y0 = y2 - 2y1 + y0 j = 1, 2, …, m + 1 If the function f (x) is known, the error in the approximation is [www .netliborg/lapack] |error (x )|≤ ≈ and in general j  j ∆ j y 0 = ∑ (-1)n   y j -n  n n=0  j j! where   = = binomial coefficients  n  n ! ( j − n )! If the ordinates are equally spaced, xn+1 - xn = Δx yn = y(xn) then the first and second differences are denoted by b ∫ W (x )P (x )P k m ( x )dx = 0 x − x0 [ f ( x 1 ) − f ( x 0 )] x1 − x 0 Δyn = yn+1 - yn k = 0,1,, m − 1 a Δ yn = Δyn+1 - Δyn = yn+2 - 2yn+1 + yn 2 The orthogonality includes a nonnegative weight function W(x) ≥ 0 for all a ≤ x ≤ b. This procedure specifies the set of polynomials to within multiplicative constants, which are set by requiring the leading coefficient to be 1.0 or by requiring the norm to be 1.0. b ∫W (x )P 2 m A new variable is defined α= xa − x0 ∆x and the finite interpolation formula through the points y0, y1, …, yn is written as follows: ( x )dx = 1 a The polynomial Pm(x) has m roots in the closed interval a to b. The polynomial p ( x ) = c 0 P0 ( x ) + c1 P1 ( x ) + c m P ( x ) minimizes b I = ∫ W ( x )[ f ( x ) − p ( x )]2 dx yα = y 0 + α ∆ y 0 + α (α − 1) 2 α (α + 1)(α − n + 1) n ∆ y 0 + + ∆ y0 2! n! (3-63) Keeping only the first two terms gives a straight line through (x0, y0) and (x1, y1); keeping the first three terms gives a quadratic function of position going through those points plus (x2, y2). The value α = 0 gives x = x0; α = 1 gives x = x1; and so on. Equally Spaced Backward Differences Backward differences are defined by ∇yn = yn - yn-1 a for a function f (x) when ∇2yn = ∇yn - ∇yn-1 = yn - 2yn-1 + yn-2 b c j = ∫ W ( x ) f ( x ) Pj ( x ) dx / W j a b W j = ∫ W ( x ) Pj2 ( x ) dx The interpolation polynomial of order n through the points y0, y-1, …, y-n is a Note that each cj is independent of m, the number of terms retained in the series. The minimum value of I is b n a j =0 I min = ∫ W ( x ) f 2 ( x ) dx − ∑W j c 2j Such functions are useful for continuous data, i.e., when f (x) is known for all x. The types of orthogonal polynomials include Chebyshev (a = –1, b = 1, W(x) = 1, used in spectral methods), Legendre (a = –1, b = 1, W(x) = 1/ 1 − x 2 ), shifted Legendre (a = 0, b = 1, W(x) = 1), used in the orthogonal colloca2 tion method), Jacobi, Hermite (a = -∞, b = ∞, W ( x ) = e − x ), and Laguerre polynomials. Linear Interpolation The simplest piecewise continuous interpolation is a straight line between the points. If a function f (x) is approximately linear in a certain range, then the ratio f ( x1 ) − f ( x 0 ) = f [ x 0 , x1 ] x1 − x 0 yα = y 0 + α ∇ y 0 + α (α + 1) 2 α (α + 1)(α + n − 1) n ∇ y 0 + + ∇ y0 2! n! The value of α = 0 gives x = x0; α = -1 gives x = x-1, and so on. Alternatively, the interpolation polynomial of order n through the points y1, y0, y-1, …, y−n is y α = y 1 + (α − 1)∇y 1 + (α − 1)α (α + 1)(α + n − 2) n α (α − 1) 2 ∇ y 1 + + ∇ y 1 (3-64) 2! n! Now α = 1 gives x = x1; α = 0 gives x = x0. Central Differences The central difference denoted by h δf ( x ) = f  x +  −  2 h f  x −   2 h h δ 2 f ( x ) = δf  x +  − δf  x −  = f ( x + h) − 2 f ( x ) + f ( x − h)   2 2 h h δ n f ( x ) = δ n −1 f  x +  − δ n −1 f  x −    2 2 is useful for calculating at the interior points of tabulated data. nUMERICAL AnALYSIS AnD APPROXIMATE METHODS Finite Element Method In the finite element method (see Ordinary Differential Equations—Boundary Value Problems) the independent variable x is divided into regions called elements . The simplest approximation is to use linear interpolation on each element, as described above. More useful is to use a quadratic interpolation between the two endpoints of the element and its midpoint. The points of an element are shown in Fig. 3-46. FIG. 3-46 xi – 1 xi xi + 1 u=0 12 1 Quadratic finite element. The derivatives at all the points are 1 f 0′ = f1′= f 2′ = h[ y 2 − y 1 ] 2 Second-Degree Least Squares with Five Points For five evenly spaced points x-2, x-1, x0, x1, and x2 (separated by distance h) and their ordinates f-2, f-1, f0, f1, and f2, assume a parabola is fit by least squares. Then the derivative at the center point is f0′ = 1/10h [-2f-2 - f-1 + f1 + 2f2] The derivatives at the other points are f −′2 = 1/ 70 h[ −54 f −2 + 13 f −1 + 40 f 0 + 27 f1 − 26 f 2 ] The element extends from xi-1 to xi+1. Define a new variable which takes the values u = 0, 0.5, and 1 at the three points, respectively. The interpolation is then f −′1 = 1/ 70 h[ −34 f −2 + 3 f −1 + 20 f 0 + 17 f1 − 6 f 2 ] 1 1 y = 2(u − 1)  u −  y i −1 + 4 u (1 − u ) y i + 2u  u −  y i +1   2 2 The interpolation clearly takes the correct values at u = 0, 0.5, and 1. Over the whole domain in x the interpolated function is continuous, but the first derivative is only piecewise continuous. Other types of finite elements include cubic functions, which are also continuous but the derivatives are only piecewise continuous. When Hermite cubic functions are used, however, the function and its first derivative are continuous throughout the domain in x. Spline Functions Splines are functions that match given values at the points x1, …, xNT and have continuous derivatives up to some order at the knots, or the points x2, …, xNT -1. Cubic splines are most common. The function is represented by a cubic polynomial within each interval (xi, xi+1) and has continuous first and second derivatives at the knots. Two more conditions can be specified arbitrarily. These are usually the second derivatives at the two endpoints, which are commonly taken as zero; this gives the natural cubic splines. Spline functions are useful because the interpolation error can be made small even with low-order polynomials. Some of the other methods may oscillate wildly between the quadrature points. See Schumaker, L. L., Spline Functions: Computational Methods, Soc. Ind. Appl. Math. (SIAM), 2015. nUMERICAL DIFFEREnTIATIOn Numerical differentiation should be avoided whenever possible, particularly when data are empirical and subject to appreciable observation errors. Errors in data can affect numerical derivatives quite strongly; i.e., differentiation is a roughening process. When such a calculation must be made, it is usually desirable first to smooth the data to a certain extent. Use of Interpolation Formula If the data are given over equidistant values of the independent variable x, an interpolation formula such as the Newton formula [Eq. (3-63) or (3-64)] may be used and the resulting formula differentiated analytically. If the independent variable is not at equidistant values, then Lagrange’s formulas must be used. By differentiating threepoint Lagrange interpolation formulas the following differentiation formulas result for equally spaced tabular points: Three-Point Formulas Let x0, x1, and x2 be the three points. 1 h2 f ′( x 0 ) = [ −3 f ( x 0 ) + 4 f ( x 1 ) − f ( x 2 )] + f ′′′(ε ) 2h 3 2 h 1 f ′( x1 ) = [ − f ( x 0 ) + f ( x 2 )] − f ′′′(ε ) 2h 6 h2 1 f ′( x 2 ) = [ f ( x 0 ) − 4 f ( x1 ) + 3 f ( x 2 )] + f ′′′(ε ) 2h 3 where the last term is an error term min j x j < ε < max j x j . Smoothing Techniques These techniques involve the approximation of the tabular data by a least-squares fit of the data by using some known functional form, usually a polynomial ( for the concept of least squares see Statistics). In place of approximating f (x) by a single least-squares polynomial of degree n over the entire range of the tabulation, it is often desirable to replace each tabulated value by the value taken on by a least-squares polynomial of degree n relevant to a subrange of 2M + 1 points centered, when possible, at the point for which the entry is to be modified. Thus each smoothed value replaces a tabulated value. Let fj = f (xj) be the tabular points and yj = smoothed values. First-Degree Least Squares with Three Points y 0 = 1 6[5 f 0 + 2 f1 − f 2 ] y 1 = 1 3[ f 0 + f 1 + f 2 ] y 2 = 1 6[ − f 0 + 2 f 1 + 5 f 2 ] 3-39 f1′= 1/ 70 h[6 f −2 − 17 f −1 + 20 f 0 − 3 f1 + 34 f 2 ] f 2′= 1/ 70 h[26 f −2 − 27 f −1 − 40 f 0 − 13 f1 + 54 f 2 ] Numerical Derivatives The results given above can be used to obtain numerical derivatives when solving problems on the computer, in particular for the Newton-Raphson method and homotopy methods. Suppose one has a program, subroutine, or other function evaluation device that will calculate f, given x . One can estimate the value of the first derivative at x0 using df f [ x 0 (1 + ε)] − f [ x 0 ] ≈ ε x0 dx x 0 (a first-order formula) or df f [ x 0 (1 + ε)] − f [ x 0 (1 − ε)] ≈ dx x 0 2 ε x0 (a second-order formula). The value of e is important; a value of 10-6 is typical, but smaller or larger values may be necessary depending on the computer precision and the application. One must also be sure that the value of x0 is not zero and use a different increment in that case. nUMERICAL InTEGRATIOn (QUADRATURE) A multitude of formulas have been developed to accomplish numerical integration, which consists of computing the value of a definite integral from a set of numerical values of the integrand. Newton-Cotes Integration Formulas (Equally Spaced Ordinates) b for Functions of One Variable The definite integral ∫ f ( x ) dx is to be a evaluated. Trapezoidal Rule This formula consists of subdividing the interval a ≤ x ≤ b into n subintervals a to a + h, a + h to a + 2h, … and replacing the graph of f (x) by the result of joining the ends of adjacent ordinates by line segments. If fj = f (xj) = f (a + jh), f0 = f (a), and fn = f (b), the integration formula is ∫ b a h f ( x ) dx = [ f 0 + 2 f1 + 2 f 2 + + 2 f n -1 + f n ] + En 2 where En = nh 3 (b − a )3 f ′′(ε) f ′′(ε) = 12 12n 2 a <ε<b This procedure is not of high accuracy. However, if f ″ ≤ (x) is continuous in a < x < b, the error goes to zero as 1/n2, n → ∞. When the finite element method is used with linear trial functions and equal-size elements, quadrature is the same as the trapezoid rule. Parabolic Rule (Simpson’s Rule) This procedure consists of subdividing the interval a < x < b into n/2 subintervals, each of length 2h, where n is an even integer. By using the notation as above the integration formula is b h ∫ f ( x ) dx = 3 [ f 0 + 4 f 1 + 2 f 2 + 4 f 3 + 2 f 4 +  + 4 f n - 3 + 2 f n - 2 + 4 f n -1 + f n ] + E n a where En = nh 5 (IV ) (b − a )5 (IV ) f (ε) = f (ε) 180n 4 180 a <ε<b 3-40 MATHEMATICS This method approximates f (x) by a parabola on each subinterval. This rule is generally more accurate than the trapezoidal rule. It is the most widely used integration formula. When the finite element method is used with quadratic trial functions and equal-size elements, quadrature is the same as Simpson’s rule. Gaussian Quadrature Gaussian quadrature provides a highly accurate formula based on irregularly spaced points, but the integral needs to be transformed onto the interval from 0 to 1. x = a + (b - a)u ∫ ∫ b a b a dx = (b - a)du Replacing the ≈ by an equality (an approximation) and solving for c and I0 give I0 = 2m I 2 − I1 2m − 1 To obtain the most accurate value, first calculate I1, I2, …, by halving h each time. Then calculate new estimates from each pair, calling them J1, J2, … ; that is, in the formula above, replace I0 with J1. The formulas are reapplied for each pair of J to obtain K1, K2, … . The process continues until the required tolerance is obtained. 1 f ( x ) dx = (b − a ) ∫ f (u ) du I1 I 2 I 3 I 4 0 J1 J 2 J 3 m f (u ) du = ∑Wi f (ui ) K1 K 2 L1 i =1 The quadrature is exact when f is a polynomial of degree 2m - 1 in x . Because there are m weights and m Gauss points, we have 2m parameters that are chosen to exactly represent a polynomial of degree 2m - 1, which has 2m parameters. The Gauss points and weights are given in the table. Romberg’s method is most useful for a low-order method (small m) because significant improvement is then possible. Example Evaluate the same integral by using the trapezoid rule and then apply the Romberg method. Use 11, 21, 41, and 81 points with m = 2. To achieve six-digit accuracy, any result from J2 through L1 is suitable, even though the base results (I1 through I4) are not that accurate. Gaussian Quadrature Points and Weights m ui Wi 2 0.21132 48654 0.50000 00000 0.78867 51346 0.50000 00000 0.11270 16654 0.27777 77778 0.50000 00000 0.44444 44445 3 4 5 0.88729 83346 0.27777 77778 0.06943 18442 0.17392 74226 0.33000 94783 0.32607 25774 0.66999 05218 0.32607 25774 0.93056 81558 0.17392 74226 0.04691 00771 0.11846 34425 0.23076 53450 0.23931 43353 0.50000 00000 0.28444 44444 0.76923 46551 0.23931 43353 0.95308 99230 0.11846 34425 I1 = 0.24491 14823 I2 = 0.24560 56002 J1 = 0.24583 69728 I = ∫ e sin x dx Using the gaussian quadrature formulas gives the following values for various values of m . Clearly, three internal points, requiring evaluation of the integrand at only three points, give excellent results. m I 2 0.24609 64306 3 0.24583 48774 4 0.24583 70044 5 0.24583 70070 Romberg’s Method Romberg’s method uses extrapolation techniques to improve the answer [Press et al. (2007)]. If we let I1 be the value of the integral obtained using interval size h = Δx, I2 be the value of I obtained when using interval size h/2, I3 be the value obtained when using an interval of size h/4, etc., and I0 is the true value of I, then the error in a method is approximately hm, or I ≈ I 0 + ch m h I 2 ≈ I 0 + c    2 m J2 = 0.24583 70049 J3 = 0.24583 70069 K1 = 0.24583 70156 K2 = 0.24583 70075 Orthogonal Polynomials The quadrature formulas for orthogonal polynomials are the same as for gaussian quadrature above, with different points and different weights. Cubic Splines The quadrature formula is x NT ∫ y ( x ) dx = x1 1 NT −1 3 1 NT −1 ∆x i ( y i + y i +1 ) − ∑ ∑ ∆x i ( y i′′+ y i′′+1 ) 24 i =1 2 i =1 with y 1′ = 0, y ′′NT = 0 for natural cubic splines. Computer Methods These methods are easily programmed in a spreadsheet program such as Microsoft Excel. In MATLAB, the trapezoid rule can be calculated by using the command trapz(x,y), where x is a vector of x values xi and y is a vector of values y(xi). Alternatively, use the commands F = @(x) exp(-x).*sin(x) Q = quad(F,0,1) −x 0 I4 = 0.24582 25436 L1 = 0.24583 70049 Example Calculate the value of the following integral. 1 I3 = 0.24577 91537 Monte Carlo methods can be used, too (see Monte Carlo Simulations). Singularities When the integrand has singularities, a variety of techniques can be tried. The integral may be divided into one part that can be integrated analytically near the singularity and another part that is integrated numerically. Sometimes a change of argument allows analytical integration. Series expansion might be helpful, too. When the domain is infinite, it is possible to use Gauss-Legendre or Gauss-Hermite quadrature. Also a transformation can be made. For example, let u = 1/x and then ∫ b f ( x ) dx = ∫ 1/ a 1/b a 1  1 f   du u2  u  ab > 0 Two-Dimensional Formula Two-dimensional integrals can be calculated by breaking down the integral into one-dimensional integrals. b g2 ( x ) a g1 ( x ) ∫∫ G(x ) = ∫ b f ( x , y ) dx dy = ∫ G ( x ) dx a g2 ( x ) g1 ( x ) f ( x , y ) dy Gaussian quadrature can also be used in two dimensions, provided the integration is on a square or can be transformed to one. (Domain transformations might be used to convert the domain to a square.) 1 1 0 0 ∫∫ mx my i =1 i =1 f ( x , y )dx dy = ∑Wxi ∑W yi f ( x i , y j ) nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS 3-41 nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS A differential equation for a function that depends on only one variable, often the variable time, is called an ordinary differential equation. The general solution to the differential equation includes many possibilities; the boundary or initial conditions are needed to specify which of those are desired. If all conditions are at one point, then the problem is an initial-value problem and can be integrated from that point on. If some of the conditions are available at one point and others at another point, then the ordinary differential equations become two-point boundary-value problems, which are treated in the next section. Initial-value problems as ordinary differential equations arise in control of lumped-parameter models, transient models of stirred tank reactors, and in all models where there are no spatial gradients in the unknowns. Many computer packages exist to solve initial-value problems, but it is important to understand the choices one must make and how to interpret the output (and change the choices) when the results are anomalous. Furthermore, many problems can be solved using spreadsheets (universally available) provided one understands the methods. It is important to know, too, when simple methods in spreadsheets won’t work. A higher-order differential equation z (n ) + F ( z (n−1) , z (n−2) ,  , z ) = 0 with initial conditions for z, and its first n - 1 derivatives can be converted into a set of first-order equations using y i ≡ z (i −1) = ( i − 1) d z d (i − 2) dy i −1 = z = dt (i − 1) dt dt The higher-order equation can be written as a set of first-order equations. dy 1 dy dy dy = y 2 , 2 = y 3 , 3 = y 4 ,, n = − F ( y n − 1 , y n − 2 ,, y 2 , y 1 ) dt dt dt dt The set of equations is then written as dy = f ( y , t ), y (0) = y 0 dt The methods in this section are described for a single equation, but they all apply to multiple equations. The simplest method is Euler’s method, which is first-order. y n + 1 = y n + Δt f ( y n ) and errors are proportional to Δt . The second-order Adams-Bashforth method is y n+1 = y n + Δt [3 f ( y n ) - f ( y n−1 )] 2 Errors are proportional to Δt2, and high-order methods are available. Notice that the higher-order explicit methods require knowing the solution (or the right-hand side) evaluated at times in the past. Since these were calculated to get to the current time, this presents no problem except for starting the problem. Then it may be necessary to use Euler’s method with a very small step size for several steps in order to generate starting values at a succession of time points. The methods, error terms, order of the method, function evaluations per step, and stability limitations are listed in Finlayson (1980) in General References. The advantage of the high-order Adams-Bashforth method is that it uses only one function evaluation per step, yet achieves high-order accuracy. The disadvantage is the necessity of using another method to start. In MATLAB the function ode113 uses a version of the Adams-Bashforth method. These methods can be used for simple problems when all the variables change on the same time scale and precise results are not needed. Euler’s method is easily done in a spreadsheet. Figure 3-47 shows the commands in a spreadsheet for two differential equations, columns 1 to 3. dy 1 /dt = y 2 − y 1 , dy 2 /dt = − y 2 , y 1 (0) = 1, y 2 (0) = 1 Once columns 4 to 6 are created, the formulas for the additional time steps are created by copying down. The Richardson extrapolation (see below) can be used to improve the accuracy. Runge-Kutta methods are explicit methods that use several function evaluations for each time step. Runge-Kutta methods are traditionally written Equations Eq. time 0 =D3+$F$1 =D4+$F$1 =D5+$F$1 =D6+$F$1 =D7+$F$1 FIG. 3-47 Equations Eq. 1 1 =E3+$F$1*(F3–E3) =E4+$F$1*(F4–E4) =E5+$F$1*(F5–E5) =E6+$F$1*(F6–E6) =E7+$F$1*(F7–E7) Equations Eq. 2 1 =F3–$F$1*F3 =F4–$F$1*F4 =F5–$F$1*F5 =F6–$F$1*F6 =F7–$F$1*F7 time 0 0.1 0.2 0.3 0.4 0.5 delta t Results 1 1 1 0.99 0.972 0.9477 0.91854 0.1 Results 2 1 0.9 0.81 0.729 0.6561 0.59049 Spreadsheet for Euler’s method. for f (t, y). The first-order Runge-Kutta method is Euler’s method. A secondorder Runge-Kutta method is Δt n [ f + f (t n + ∆t , y n + ∆t f n )] 2 while the midpoint scheme is also a second-order Runge-Kutta method y n+1 = y n +  ∆t ∆t n  y n + 1 = y n + ∆t f  t n + , y n + f    2 2 A popular fourth-order Runge-Kutta method uses the Runge-Kutta-Fehlberg formulas, which have the property that the method is fourth-order but achieves fifth-order accuracy. The coefficients are available at en.wikipedia .org/wiki/Runge-Kutta-Fehlberg_method. An extension of this method is ode45 in MATLAB. Usually one would use a high-order method to achieve high accuracy. The Runge-Kutta-Fehlberg method is popular because it is high-order and does not require a starting method (as does an Adams-Bashforth method). However, it does require four function evaluations per time step, or four times as many as a fourth-order Adams-Bashforth method. For problems in which the function evaluations are a significant portion of the calculation time, this might be important. Given the speed and availability of desktop computers, the efficiency of the methods is most important only for very large problems that are going to be solved many times or for problems in which some variables change rapidly while others change slowly. For other problems, the most important criterion for choosing a method is probably the time the user spends setting up the problem. The stability limits for the explicit methods are based on the largest eigenvalue of the linearized system of equations δf dy i n = ∑ Aij y j , Aij = i δy j dt j = 1 y For linear problems, the eigenvalues do not change, so that the stability and oscillation limits must be satisfied for every eigenvalue of matrix A. In solving nonlinear problems, the equations are linearized about the solution at the local time, and the analysis applies for small changes in time, after which a new analysis about the new solution must be made. Thus, for nonlinear problems, the eigenvalues keep changing, and the largest stable time step changes, too. The stability limits are as follows: Euler method, l Δt ≤ 2 Runge-Kutta, second-order, l Δt < 2 Runge-Kutta-Fehlberg, l Δt < 3.0 Richardson extrapolation can be used to improve the accuracy of a method. Suppose we step forward one step Δt with a pth-order method. Then redo the problem, this time stepping forward from the same initial point, but in two steps of length Δt/2, thus ending at the same point. Call the solution of the one-step calculation y1 and the solution of the two-step calculation y2. Then an improved solution at the new time is given by y= 2 p y 2 − y1 2 p −1 This gives a good estimate provided Δt is small enough that the method is truly convergent with order p . This process can also be repeated in the same way Romberg’s method was used for quadrature. The error term in the various methods can be used to deduce a step size that will give a user-specified accuracy. Most packages today are based on a user-specified tolerance; the step size is changed during the calculation to 3-42 MATHEMATICS achieve that accuracy. The accuracy itself is not guaranteed, but it improves as the tolerance is decreased. Implicit Methods When some dependent variables change rapidly while others change slowly, we say the problem is stiff and implicit methods are needed. Implicit methods use different interpolation formulas involving y n+1 and result in nonlinear equations to be solved for y n+1. Then iterative methods must be used to solve the equations. The backward Euler method is a first-order method: y n+1 = y n + Δtf ( y n+1 ) Errors are proportional to Δt for small Δt . The trapezoid rule is a secondorder method. y n +1 = y n + Δt [ f ( y n ) + f ( y n + 1 )] 2 Errors are proportional to Δt2 for small Δt . When the trapezoid rule is used with the finite difference method for solving partial differential equations, it is called the Crank-Nicolson method. The implicit methods are stable for any step size but do require the solution of a set of nonlinear equations, which must be solved iteratively. The set of equations can be solved using the successive substitution method or Newton-Raphson method. See Bogacki, M. B., K. Alejski, and J. Szymanewski, Comp . Chem . Eng . 13: 1081–1085 (1989) for an application to dynamic distillation problems. The best packages for stiff equations (see below) use backward-difference formulas. Gear first developed these, and the first two orders are given below (Gear, G. W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1971). 1. y n+1 = y n + Δt f ( y n+1) where e is the porosity of the catalyst, R is the catalyst radius, and De is the effective diffusion coefficient inside the catalyst. 4. Time for heat transfer is t internal heat transfer = R 2 ρs C s R 2 = ke α where rs is the catalyst density, Cs is the catalyst heat capacity per unit mass, ke is the effective thermal conductivity of the catalyst, and α is the thermal diffusivity. For example, in the model of a catalytic converter for an automobile [Ferguson, N. B., and B. A. Finlayson, AIChE J. 20: 539–550 (1974)], the time constant for internal diffusion was 0.3 s; internal heat transfer, 21 s; and device flow-through, 0.003 s. The device flow-through is so fast that it might as well be instantaneous. The stiffness is approximately 7000, and implicit methods must be used to integrate the equations. Alternatively, a quasistatic model can be developed. In this case the time derivative is deleted for the variables that change rapidly on the grounds that those variables are essentially in steady state with respect to the rest of the problem, even if the steady state changes slowly. Differential-Algebraic Systems Sometimes models involve ordinary differential equations subject to some algebraic constraints. For example, the equations governing one equilibrium stage (as in a distillation column) are dx n = V n + 1 y n + 1 − Ln x n − V n y n + Ln − 1 x x − 1 dt x n − 1 − x n = E n ( x n −1 − x *,n ) M N ∑x i =1 i =1 4 1 2 2. y n + 1 = y n + y n − 1 + ∆t f ( y n + 1 ) 3 3 3 These methods require solving sets of nonlinear equations. By adroit manipulation and estimation, a package will change the order to achieve a required accuracy with a minimum number of time steps and iterations. The programs ode15s and ode23s in MATLAB use these techniques. Stiffness The concept of stiffness is described for a system of linear equations. dy = Ay dt where x and y are the mole fraction in the liquid and vapor, respectively; L and V are liquid and vapor flow rates, respectively; M is the holdup; and the superscript is the stage number. The efficiency is E, and the concentration in equilibrium with the vapor is x*. The first equation is an ordinary differential equation for the mass of one component on the stage, while the third equation represents a constraint that the mass fractions add to 1. This is a differential-algebraic system of equations. Differential-algebraic equations can be written in the general notation Let li be the eigenvalues of matrix A. The stiffness ratio SR is defined as To solve the general problem by using the backward Euler method, replace the nonlinear differential equation with the nonlinear algebraic equation for one step. max i | Re (λ i )| SR = max i | Re (λ i )| (3-65) SR = 20 is not stiff, SR = 103 is stiff, and SR = 106 is very stiff. If the problem is nonlinear, then the solution is expanded about the current state. n ∂f dy i = f i [ y (t n )] + ∑ i [ y j − y j (t n )] dt j =1 ∂ y j The question of stiffness then depends on the solution at the current time. Consequently nonlinear problems can be stiff during one time period and not stiff during another. While the chemical engineer may not actually calculate the eigenvalues, it is useful to know that they determine the stability and accuracy of the numerical scheme and the step size used. Problems are stiff when the time constants for different phenomena have very different magnitudes. Consider flow through a packed bed reactor. The time constants for different phenomena are as follows: 1. Time for device flow-through t flow = L φAL = u Q where Q is the volumetric flow rate, A is the cross-sectional area, L is the length of the packed bed, and f is the void fraction. 2. Time for reaction tr × n = 1 k where k is a rate constant (time-1). 3. Time for diffusion inside the catalyst t internal diffusion = εR 2 De  dy  F t , y ,  = 0  dt   y n +1 − y n  F t , y n + 1 ,  =0 ∆t   This equation must be solved for y n+1. The Newton-Raphson method can be used, and if convergence is not achieved within a few iterations, the time step can be reduced and the step repeated. In actuality, the higher-order backward-difference Gear methods are used in DASSL (Ascher, U. M., and L. R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, Philadelphia, Penn., 1998). The program ode15s in MATLAB can be used to solve differential-algebraic equations. Differential-algebraic systems are more complicated than differential systems because the solution may not always be defined. See Pontelides et al. [Comp . Chem . Eng. 12: 449–454 (1988)] for a model of a distillation column in which the column pressure strongly affects the possible solutions and initial conditions. Byrne and Ponzi [Comp . Chem . Eng. 12: 377–382 (1988)] and Chan, T. F. C., and H. B. Keller [SIAM J . Sci . Stat . Comput. 3: 173–194 (1982)] also list several chemical engineering examples of differential-algebraic systems and solve one involving two-phase flow. Computer Software Efficient computer packages are available for solving ordinary differential equations as initial-value problems. The packages are widely available and good enough that most chemical engineers use them and do not write their own. On the NIST web page http://gams .nist.gov/Problem.html insert “ordinary differential equations” to find packages that can be downloaded. On the Netlib website http://www.netlib.org/, search the Netlib repository, and choose “ode” to find packages that can be downloaded. Using Microsoft Excel to solve ordinary differential equations is cumbersome, except for the simplest problems. Stability, Bifurcations, and Limit Cycles Some aspects of this subject involve the solution of nonlinear equations; other aspects involve the integration of ordinary differential equations; applications include chaos and fractals as well as the unusual operation of some chemical engineering nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS equipment. Kubicek, M., and M. Marek, Computational Methods in Bifurcation Theory and Dissipative Structures, Springer-Verlag, Berlin (1983, 2012), give an excellent introduction to the subject and the details needed to apply the methods. A concise survey with some chemical engineering examples is given in Doherty, M. F., and J. M. Ottino, Chem . Eng . Sci. 43: 139–183 (1988). Bifurcation results are closely connected with the stability of the steady states, which is essentially a transient phenomenon. Sensitivity Analysis When one is solving differential equations, it is frequently necessary to know the solution as well as the sensitivity of the solution to the value of a parameter. Such information is useful when doing parameter estimation (to find the best set of parameters for a model) and for deciding if a parameter needs to be measured accurately. An added equation is created by differentiating the ordinary differential equation with respect to the parameter and solving that equation concurrently. See Finlayson et al. (2006) in General References. Molecular Dynamics Special integration methods have been developed for molecular dynamics calculations owing to the structure of the equations. A very large number of equations are to be integrated, with the following form based on molecular interactions between molecules. mi d 2 ri = Fi ({ r }) dt 2 Fi ({ r }) = − ∇V The symbol mi is the mass of the ith particle, ri is the position of the ith particle, Fi is the force acting on the ith particle, and V is the potential energy that depends upon the location of all the particles (but not their velocities). Since the major part of the calculation lies in the evaluation of the forces, or potentials, a method must be used that minimizes the number of times the forces are calculated to move from one time to another time. Rewrite this equation in the form of an acceleration as d 2 ri 1 = Fi ({ r }) ≡ a i dt 2 m In the Verlet method, this equation is written by using central finite differences (see Interpolation and Finite Differences). Note that the accelerations do not depend upon the velocities. ri(t + Δt) = 2ri (t) - ri (t - Δt) + ai(t)Δt2 The calculations are straightforward, and no explicit velocity is needed. The storage requirement is modest, and the precision is modest (it is a secondorder method). Note that one must start the calculation with values of {r} at times t and t - Δt. In the Verlet velocity method, an equation is written for the velocity, too. ORDInARY DIFFEREnTIAL EQUATIOnS—BOUnDARY-VALUE PROBLEMS Diffusion problems in one dimension lead to boundary-value problems. The boundary conditions are applied at two different spatial locations: at one side the concentration may be fixed and at the other side the flux may be fixed. Because the conditions are specified at two different locations, the problems are not initial-value in character. It is not possible to begin at one position and integrate directly because at least one of the conditions is specified somewhere else and there are not enough conditions to begin the calculation. Thus, methods have been developed especially for boundaryvalue problems. Boundary-value methods provide a description of the solution either by providing values at specific locations or by an expansion in a series of functions. Thus, the key issues are the method of representing the solution, the number of points (i.e., the mesh) or the number of terms in the series, and how the approximation converges to the exact answer, i.e., how the error changes with the number of points or number of terms in the series. In addition, boundary conditions and nonlinear transport coefficients are handled differently in the various methods. These issues are discussed for each of the methods: finite difference, orthogonal collocation, and Galerkin finite element methods. Sometimes the solution has singularities or the domain is semi-infinite, and these situations require special treatment. The first approach is to try to find an analytical solution. Flow in a pipe is governed by the equation 1 d  du  ∆P µr  = − r dr  dr  L where u is the velocity, r is the radial position, m is the viscosity, and ΔP/L is the pressure drop per length. The solution is finite at the origin, r = 0, and takes the value zero at the radius of the pipe R . For a newtonian fluid, the viscosity is constant. This equation can be integrated once to obtain r ΔP r 2 du =− + c1 µL 2 dr u=− 1 ri (t + ∆t ) = ri (t ) + v i ∆t + a i (t ) ∆t 2 2 Beginning with values of {r} and {v} at time 0, one calculates the new positions and then the new velocities. This method is second-order in Δt too. Molecular dynamics is used in chemical engineering for a variety of applications, including drug design, protein folding, nucleation and growth processes, and the phase behavior of polymeric, colloidal, and self-assembled systems [see Pamer, J. C., and P. G. Debenedettii, Recent Advances in Molecular Simulation: A Chemical Engineering Perspective, AIChE J . 61, 370–383 (2015)]. For additional details about the method, see Hinchliffe, A., Molecular Modelling for Beginners, 2d ed., Wiley, New York, 2008; Jensen, J. H., Molecular Modeling Basics, CRC Press, Boca Raton, Fla., 2010; Leach, A. R., Molecular Modelling: Principles and Applications, 2d ed., Prentice Hall, Upper Saddle River, N.J., 2001; Schlick, T., Molecular Modeling and Simulations, 2d ed., Springer, New York, 2010. See https://en.wikipedia. org/wiki/List_of_software_for_molecular_mechanics_modeling for computer packages, especially the free programs LAMMPS (lammps.sandia. gov) and GROMACS (www.gromacs.org, especially for biological molecules). See also Calvetti, D. E., and E. Somersalo, Computational Mathematical Modeling: An Integrated Approach Across Scales, SIAM, 2012, for methods to include phenomena that occur on different physical scales. ΔP r c1 du =− + µL 2 r dr ΔP r 2 + c1 ln r + c2 µL 4 Since the velocity is finite at the origin, c1 is taken as zero; c2 is taken as c2 = ∆P R 2 µL 4 so that the velocity is zero at r = R. The solution is then 1 v i (t + ∆t ) = v i (t ) + [a i (t ) + a i (t + ∆t )] ∆t 2 The position of the particles is expanded in a Taylor series. or and integrated again to get dv i = ai dt The trapezoid rule [see Numerical Integration (Quadrature)] is applied to obtain 3-43 u= ∆P 2 2 (R - r ) 4µL This problem requires no numerical methods. But if the viscosity were appropriate to a non-newtonian fluid and depended upon the shear rate, e.g., for a Bird-Carreau fluid µ= η0 2 (1−n )/2   du   1 + λ     dr    then numerical methods would be required, as described in this subsection. Finite Difference Method To apply the finite difference method, we first spread grid points through the domain. Figure 3-48 shows a uniform mesh of n points (nonuniform meshes are possible too). The unknown, here c(x), at a grid point xi is assigned the symbol ci = c(xi). The finite difference FIG. 3-48 Finite difference mesh; Δx uniform. 3-44 MATHEMATICS method can be derived easily by using a Taylor expansion of the solution about this point. Expressions for the derivatives are ci + 1 − ci d 2 c Δ x ci − ci − 1 d 2 c ∆ x dc dc = − 2 + , = + 2 + dx i dx i 2 dx i dx i 2 Δx ∆x ci + 1 − ci −1 d 3c ∆ x 2 dc = − 3 + dx i dx i 3! 2∆ x The truncation error in the first two expressions is proportional to Δx, and the methods are said to be first-order. The truncation error in the third expression is proportional to Δx2, and the method is said to be second-order. Usually the last equation is used to ensure the best accuracy. The finite difference representation of the second derivative is ci + 1 − 2 ci + ci − 1 d c 2 ∆ x d c = − 4 + dx 2 i dx i 4! ∆x2 2 2 4 The truncation error is proportional to Δx2. To solve a differential equation, it is evaluated at a point i and then these expressions are inserted for the derivatives. Example Consider the equation for convection, diffusion, and reaction in a tubular reactor. 1 d 2c dc − = Da R (c ) Pe dx 2 dx Pe is the Peclet number and Da is the Damköhler number. The finite difference representation is 1 ci + 1 − 2ci + ci − 1 ci + 1 − ci − 1 − = Da R (ci ) Pe 2 Δx Δx 2 This equation is written for i = 2 to n - 1, or the internal points. The equations would then be coupled but would also involve the values of c1 and cn as well. These are determined from the boundary conditions. If the boundary condition involves a derivative, it is important that the derivatives be evaluated using points that exist. Three possibilities exist; the first two are dc dx dc dx = c2 − c1 ∆x = −3c1 + 4 c2 − c3 2∆ x 1 1 The third alternative is to add a false point, outside the domain, as c0 = c(x = -Δx). c −c dc = 2 0 dx 1 2 Δ x Since this equation introduces a new variable c0, another equation is needed and is obtained by writing the finite difference equation for i = 1 too. The sets of equations can be solved by using the Newton-Raphson method. The first form of the derivative gives a tridiagonal system of equations, and the standard routines for solving tridiagonal equations suffice. For the other two options, some manipulation is necessary to put them into a tridiagonal form. Frequently, the transport coefficients, such as the diffusion coefficient or thermal conductivity, depend on the dependent variable, concentration, or temperature, respectively. Then the differential equation might look like d  dc   D (c )  = 0 dx  dx  This could be written as two equations. − dJ =0 dx J = − D (c ) dc dx Because the coefficient depends on c, the equations are more complicated. A finite difference method can be written in terms of the fluxes at the midpoints i + 1/2. J i + 1/2 − J i − 1/2 − =0 ∆x ci + 1 − ci J i + 1/2 = − D (ci + 1/2 ) ∆x These are combined to give the complete equation. D (ci + 1/2 ) (ci + 1 − ci ) − D (ci − 1/2 ) (ci − ci − 1 ) =0 ∆x2 This represents a set of nonlinear algebraic equations that can be solved with the Newton-Raphson method. However, in this case, a viable iterative strategy is to evaluate the transport coefficients at the last value and then solve D (cik+ 1/2 ) (cik++11 − cik + 1 ) − D (cik− 1/2 ) (cik + 1 − cik−+11 ) =0 ∆x 2 The advantage of this approach is that it is easier to program than a full Newton-Raphson method. If the transport coefficients do not vary radically, then the method converges. If the method does not converge, then it may be necessary to use the full Newton-Raphson method. There are two common ways to evaluate the transport coefficient at the midpoint: Use the average value of the solution on each side to evaluate the diffusivity, or use the average value of the diffusivity on each side. Both methods have truncation error Δx2. The spacing of the grid points need not be uniform. See Finlayson (1980) and Finlayson et al. (2006) in General References. Example A reaction diffusion problem is solved with the finite difference method. dc d 2c = φ2c , (0) = 0 c (1) = 1 dx dx 2 The solution is derived for f = 2. It is solved several times, first with two intervals and three points (at x = 0, 0.5, 1), then with four intervals, then with eight intervals. The reason is that when an exact solution is not known, one must use several Δx values and see that the solution converges as Δx approaches zero. With two intervals, the equations are as follows. The points are x1 = 0, x2 = 0.5, and x3 = 1.0; and the solutions at those points are c1, c2, and c3, respectively. A false boundary is used at x0 = -0.5. c0 − c2 c0 − 2c1 + c2 c1 − 2c2 + c3 = 0, − φ2c1 = 0, − φ2c2 = 0, c3 = 1 2∆ x ∆x2 ∆x2 The solution is c1 = 0.2857, c2 = 0.4286, and c3 = 1.0. The problem is solved again with four and then eight intervals. The value of concentration at x = 0 takes the following values for different Δx values . These values are extrapolated using the Richardson extrapolation technique to get c(0) = 0.265718. Using this value as the best estimate of the exact solution, the errors in the solution are tabulated versus Δx . Clearly the errors go as Δx2 (decreasing by a factor of 4 when Δx decreases by a factor of 2), thus validating the solution. The exact solution is 0.265802. n-1 Δx c(0) 2 4 8 0.5 0.25 0.125 0.285714 0.271043 0.267131 n-1 Δx Error in c(0) 2 4 8 0.5 0.25 0.125 0.02000 0.00532 0.00141 Finite Difference Methods Solved with Spreadsheets A convenient way to solve the finite difference equations for simple problems is to use a computer spreadsheet. The equations for the problem solved in the example can be cast into the following form: c1 = 2c 2 2 + φ 2 ∆x 2 ci + 1 + ci − 1 2 + φ 2 ∆x 2 cn + 1 = 1 ci = nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS 3-45 This is the process that makes the method a Galerkin method. The basis for the orthogonality condition is that any function that is orthogonal to each member of a complete set is zero. The residual is being made orthogonal; and if the basis functions are complete and you use infinitely many of them, then the residual is zero. Once the residual is zero, the problem is solved. This equation is integrated by parts to give the following equation: NT FIG. 3-49 −∑ ∫ i =1 Finite difference method using spreadsheets. Let us solve the problem using 6 nodes, or 5 intervals. Then the connection between the cell in the spreadsheet and the nodal value is shown in Fig. 3-49. The following equations are placed into the various cells. A1: = 2*B1/(2.+(phi*dx)**2) B1: = (A1 + C1)/(2.+(phi*dx)**2) F1: = 1. The equation in cell B1 is copied into cells C1 through E1. Then turn on the iteration scheme in the spreadsheet and watch the solution converge. Whether convergence is achieved can depend on how you write the equations, so some experimentation may be necessary. Theorems for convergence of the successive substitution method are useful in this regard. Orthogonal Collocation The orthogonal collocation method has found widespread application in chemical engineering, particularly for chemical reaction engineering. In the collocation method, the dependent variable is expanded in a series of orthogonal polynomials. See Interpolation: Lagrange Interpolation Formulas. 1 0 1 db j dbi   NT dxai = φ2 ∫ b j ( x ) R  ∑ ai bi ( x )  dx j = 1, , NT − 1 0 dx dx   i =1 (3-66) This equation defines the Galerkin method, and a solution that satisfies this equation ( for all j = 1, …, ∞) is called a weak solution. For an approximate solution, the equation is written once for each member of the trial function, j = 1, …, NT - 1, and the boundary condition is applied. NT ∑a b (1) = c i i B i =1 The Galerkin finite element method results when the Galerkin method is combined with a finite element trial function. The domain is divided into elements separated by nodes, as in the finite difference method. The solution is approximated by a linear (or sometimes quadratic) function to provide the Galerkin finite element equations. For example, with the grid shown in Fig. 3-48, a linear interpolation would be used between points xi and xi+1. c ( x ) = ci (1 − u ) + ci + 1u u≡ x − xi x i +1 − x i N c ( x ) = ∑ am Pm ( x ) m=0 The differential equation is evaluated at certain collocation points. The collocation points are the roots to an orthogonal polynomial, as first used by Lanczos [Lanczos, C., J . Math . Phys. 17:123-199 (1938); and Lanczos, C., Applied Analysis, Prentice Hall, Upper Saddle River, N.J., 1956]. A major improvement was proposed by Villadsen and Stewart [Villadsen, J. V., and W. E. Stewart, Chem . Eng . Sci. 22:1483-1501 (1967)], who proposed that the entire solution process be done in terms of the solution at the collocation points rather than the coefficients in the expansion. This method is especially useful for reaction diffusion problems that frequently arise when modeling chemical reactors. It is highly efficient when the solution is smooth, but the finite difference method is preferred when the solution changes steeply in some region of space. The error decreases very rapidly as N is increased since it is proportional to [1/(1 - N)]N -1. See Finlayson (1980) in General References. Galerkin Finite Element Method In the finite element method, the domain is divided into elements, and an expansion is made for the solution on each finite element (see Interpolation: Finite Element Method). In the Galerkin finite element method, an additional idea is introduced: the Galerkin method is used to solve the equation. The Galerkin method is explained using the equations for reaction and diffusion in a porous catalyst pellet. d 2c = φ2 R (c ) dx 2 dc (0) = 0, c (1) = 1 dx The unknown solution is expanded in a series of known functions {bi(x)} with unknown coefficients {ai}. NT c ( x ) = ∑ai bi ( x ) i =1 The trial solution is substituted into the differential equation to obtain the residual. NT Residual = ∑ ai i =1 d 2bi   NT − φ2 R  ∑ ai bi ( x )  2 dx 1 = i   The residual is then made orthogonal to the set of basis functions.  NT 1 ∫ b ( x ) ∑ a 0 j i =1 i    NT d 2bi − φ2 R  ∑ ai bi ( x )   dx = 0 2 dx    i = 1 j = 1, , NT A finite element method based on these functions would have an error proportional to Δ x2. The finite element representations for the first derivative and second derivative are the same as in the finite difference method, but this is not true for other functions or derivatives. With quadratic finite elements, take the region from xi-1 and xi+1 as one element with x = x i−1 at u = 0, x = x i at u = ½, and x = x i+1 at u = 1. Then the interpolation would be c ( x ) = ci − 1 N 1 (u ) + ci N 2 (u ) + ci +1 N 3 (u )  1 N 1 (u ) = 2(u − 1)u −  N 2 (u ) = 4 u (1 − u )  2  1 N 3 (u ) = 2u u −   2 A finite element method based on these functions would have an error proportional to Δ x3. Thus, it would converge faster than one based on linear interpolation. Adaptive Meshes In many two-point boundary-value problems, the difficulty in the problem lies in the formation of a boundary-layer region, or a region in which the solution changes very dramatically. In such cases, it is prudent to use small mesh spacing there, with either the finite difference method or the finite element method. If the region is known a priori, small mesh spacings can be assumed at the boundary layer. If the region is not known, however, other techniques must be used. These techniques are known as adaptive mesh techniques. The mesh size is made small where some property of the solution is large. For example, if the truncation error of the method is nth-order, then the nth-order derivative of the solution is evaluated and a small mesh is used where it is large. Alternatively, the residual (the differential equation with the numerical solution substituted into it) can be used as a criterion. It is also possible to define the error that is expected from a method one order higher and one order lower. Then a decision about whether to increase or decrease the order of the method can be made, taking into account the relative work of the different orders. This provides a method of adjusting both the mesh spacing (Δ x, or sometimes called h) and the degree of polynomial ( p). Such methods are called h-p methods. Many finite element programs have the capability to do this mesh refinement automatically. Singular Problems and Infinite Domains If the solution being sought has a singularity, it may be difficult to find a good numerical solution. Sometimes even the location of the singularity may not be known. One method of solving such problems is to refine the mesh near the singularity, relying on the better approximation due to a smaller Δx . Another approach is to incorporate the singular trial function into the approximation. Thus, if the solution approaches f (x) as x goes to zero and f (x) becomes infinite, one may define a new variable u(x) = y(x) - f (x) and derive an equation for u . The differential equation is more complicated, but the solution is better near the singularity. See Press et al. (2007) in General References. 3-46 MATHEMATICS Sometimes the domain is semi-infinite, as in boundary-layer flow. The domain can be transformed from the x domain (0 - ∞) to the h domain (1 - 0) using the transformation h = exp (-x). Another approach is to use a variable mesh, perhaps with the same transformation. For example, use h = exp (-bx) and a constant mesh size in h; the value of b is found experimentally. Still another approach is to solve on a finite mesh in which the last point is far enough away that its location does not influence the solution. A location that is far enough away must be found by trial and error. Packages to solve boundary-value problems are available on the Internet. On the NIST web page http://gams.nist.gov/Problem.html insert “ordinary differential equations” to find packages for boundary-value problems. On the Netlib website http://www.netlib.org/ search on “boundary-value problem.” Any spreadsheet that has an iteration capability can be used with the finite difference method. Some packages for partial differential equations also have a capability for solving one-dimensional boundary-value problems (e.g., Comsol Multiphysics). where the distribution function f (x) satisfies f ( x ) ≥ 0, b a (3-67) f ( x ) dx = 1 The quantity GN is an estimation of G, and the fundamental theorem of Monte Carlo guarantees that the expected value of GN is G, if G exists (Kalos, M. H., and P. A. Whitlock, Monte Carlo Methods, vol. 1, Wiley, New York, 1986). The error in the calculation is given by ε= This subsection considers a method of solving numerically the Fredholm integral equation of the second kind: Ω0 The distribution function f (x) can be taken as constant, for example, 1/W0. We choose variables x1, x2, …, xN randomly from f (x) and form the arithmetic mean 1 GN = ∑ g (xi ) N i nUMERICAL SOLUTIOn OF InTEGRAL EQUATIOnS u ( x ) = f ( x ) + λ ∫ k ( x , t ) u (t ) dt for u ( x ) ∫ σ1 N 1/2 where σ 12 is calculated from σ 12 = ∫ Ω0 g 2 ( x ) f ( x ) dx − G 2 The method discussed arises because a definite integral can be closely approximated by any of several numerical integration formulas (each of which arises by approximating the function by some polynomial over an interval). Thus the definite integral in Eq. (3-67) can be replaced by an integration formula, and Eq. (3-67) may be written Thus the number of terms needed to achieve a specified accuracy e can be calculated once an estimate of σ 12 is known. n  u ( x ) = f ( x ) + λ (b − a ) ∑ci k ( x , t i )u (ti )  i = 1  Various methods, such as influence sampling, can be used to reduce the number of calculations needed. See also Lapeyre, B., Introduction to MonteCarlo Methods for Transport and Diffusion Equations, Oxford University Press, London, 2003; Liu, J. S., Monte Carlo Strategies in Scientific Computing, Springer, New York, 2008; and Thomopoulos, N. T., Essentials of Monte Carlo Simulation: Statistical Methods for Building Simulation Models, Springer, New York, 2013. Some computer programs are available that perform simple Monte Carlo calculations using Microsoft Excel. Monte Carlo methods for molecular simulation lead to an equilibrium configuration of the molecules. Thus, the approach to that equilibrium is not modeled, and this is an advantage over molecular dynamics (see below) when the equilibrium configuration is the desired result, since the Monte Carlo method is faster. A good open-source Monte Carlo program is CASSANDRA at the University of Notre Dame. (3-68) where t1, …, tn are points of subdivision of the t axis, a ≤ t ≤ b, and the c’s are coefficients whose values depend upon the type of numerical integration formula used. Now Eq. (3-68) must hold for all values of x, a ≤ x ≤ b; so it must hold for x = t1, x = t2, …, x = tn. Substituting for x successively t1, t2, …, tn and setting u(ti) = ui and f (ti) = fi, we get n linear algebraic equations for the n unknowns u1, …, un. That is, ui = fi + l(b - a)[c1k(ti , t1)u1 + c2k(ti , t2)u2 + … + cnk(ti , tn)un] i = 1, 2, …, n These uj may be solved for by the methods under Numerical Solution of Linear Equations and Associated Problems and substituted into Eq. (3-68) to yield an approximate solution for Eq. (3-67). Because of the work involved in solving large systems of simultaneous linear equations it is desirable that only a small number of u values be computed. Thus the gaussian integration formulas are useful because of the economy they offer. Solutions for Volterra equations are done in a similar fashion, except that the solution can proceed point by point or in small groups of points depending on the quadrature scheme. See Linz, P., Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, Penn., 1985. There are methods that are analogous to the usual methods for integrating differential equations (Runge-Kutta, predictor-corrector, Adams methods, etc.). Explicit methods are fast and efficient until the time step is very small to meet the stability requirements. Then implicit methods are used, even though sets of simultaneous algebraic equations must be solved. The major part of the calculation is the evaluation of integrals, however, so that the added time to solve the algebraic equations is not excessive. Thus, implicit methods tend to be preferred. Volterra equations of the first kind are not well posed, and small errors in the solution can have disastrous consequences. The boundary element method uses Green’s functions and integral equations to solve differential equations. See Brebbia, C. A., and J. Dominguez, Boundary Elements— An Introductory Course, 2d ed., Computational Mechanics Publications, Southhampton, UK, 1992; Poljak, D., and C. A. Brebbia, Boundary Element Methods for Electrical Engineers, WIT Press, Ashurst, UK, 2005. MOnTE CARLO SIMULATIOnS Some physical problems, such as those involving the interaction of molecules, are usually formulated as integral equations. Monte Carlo methods are especially well suited to their solution. This section cannot give a comprehensive treatment of such methods, but their use in calculating the value of an integral will be illustrated. Suppose we wish to calculate the integral G= ∫ Ω0 g ( x ) f ( x ) dx N= σ 12 ε2 nUMERICAL SOLUTIOn OF PARTIAL DIFFEREnTIAL EQUATIOnS The numerical methods for partial differential equations can be classified according to the type of equation (see Partial Differential Equations): parabolic, elliptic, and hyperbolic. This section uses the finite difference method to illustrate the ideas, and these results can be programmed for simple problems. For more complicated problems, however, it is common to rely on computer packages. Thus, some discussion is given to the issues that arise in using computer packages. These methods are used in modeling microfluidics (with small Reynolds numbers) and turbulence (with large Reynolds numbers). Parabolic Equations in One Dimension By combining the techniques applied to initial-value problems and boundary-value problems, it is possible to easily solve parabolic equations in one dimension. The method is often called the method of lines. It is illustrated here using the finite difference method, but the Galerkin finite element method and the orthogonal collocation method can also be combined with initial-value methods in similar ways. The analysis is done by example. The finite volume method is described under Hyperbolic Equations. Example Consider the diffusion equation, with boundary- and initialvalue conditions. ∂c ∂2 c =D 2 ∂t ∂x c(x, 0) = 0, c(0, t) = 1, c(1, t) = 0 We denote by ci the value of c(xi , t) at any time. Thus, ci is a function of time, and differential equations in ci are ordinary differential equations. nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS 3-47 Write a finite difference form for the time derivative and average the right-hand sides, evaluated at the old and new times. cin++11 − 2cin + 1 + cin−+11 cin+ 1 − 2cin + cin− 1 cin + 1 − cin = D (1 − θ) + Dθ ∆x 2 ∆t ∆x 2 Now the equations are of the form − D ∆ tθ  n + 1 D ∆tθ n + 1 D ∆tθ n + 1  ci − 1 ci + 1 +  1 + 2  ci −  ∆x 2  ∆x 2 ∆x 2 D∆t (1 − θ) n (ci + 1 − 2cin + cin− 1 ) = cin + ∆x 2 and require solving a set of simultaneous equations, which have a tridiagonal structure. Using q = 0 gives the Euler method (as above), q = 0.5 gives the Crank-Nicolson method, and q = 1 gives the backward Euler method. The Crank-Nicolson method is also the same as applying the trapezoid rule to do the integration. The stability limit is given by ∆t FIG. 3-50 Computational molecules. h = Δx = Δy . By evaluating the diffusion equation at the ith node and replacing the derivative with a finite difference equation, the following working equation is derived for each node i, i = 2, …, n (see Fig. 3-50). ci + 1 − 2ci + ci − 1 dci =D dt ∆x2 This can be written in the general form of a set of ordinary differential equations by defining matrix AA. dc = AAc dt This set of ordinary differential equations can be solved using any of the standard methods, and the stability of the integration of these equations is governed by the largest eigenvalue of AA. When Euler’s method is used to integrate in time, the equations become cin+ 1 − 2cin +cin− 1 cin + 1 − cin =D ∆t ∆x 2 where cin = c(xi, tn). Notice that if the solution is known at every point at one time n, then it is a straightforward calculation to find the solution at every point at the new time n + 1. If Euler’s method is used for integration, the time step is limited by ∆t ≤ 2 | λ |max n ≤ max ∑ AA ji = max 2< j <n i =2 4D ∆x2 This gives the well-known stability limit ∆t The price of using implicit methods is that one now has a system of equations to solve at each time step, and the solution methods are more complicated (particularly for nonlinear problems) than the straightforward explicit methods. Phenomena that happen quickly can also be obliterated or smoothed over by using a large time step, so implicit methods are not suitable in all cases. The engineer must decide if she or he wants to track those fast phenomena, and choose an appropriate method that handles the time scales that are important in the problem. Other methods can be used in space, such as the finite element method, the orthogonal collocation method, or the method of orthogonal collocation on finite elements. One simply combines the methods for ordinary differential equations (see Ordinary Differential Equations—Boundary-Value Problems) with the methods for initial-value problems (see Numerical Solution of Ordinary Differential Equations as Initial-Value Problems). Fast Fourier transforms can also be used on regular grids (see Fast Fourier Transform). Elliptic Equations Elliptic equations can be solved with both finite difference and finite element methods. One-dimensional elliptic problems are two-point boundary-value problems. Two- and three-dimensional elliptic problems are often solved with iterative methods when the finite difference method is used and with direct methods when the finite element method is used. So there are two aspects to consider: how the equations are discretized to form sets of algebraic equations and how the algebraic equations are then solved. The prototype elliptic problem is steady-state heat conduction or diffusion  ∂2 T ∂2 T  k 2 + 2  = Q ∂y   ∂x possibly with a heat generation term per unit volume Q . The boundary conditions taken here are T = f (x, y) on the boundary (S) with f a known function. Illustrations are given for constant thermal conductivity k while Q is a known function of position. The finite difference formulation is given using the following nomenclature: Ti, j = T(i Δx, j Δy) whereas if the Runge-Kutta-Fehlberg method is used, the 2 in the numerator is replaced by 3.0. The largest eigenvalue of AA is bounded by Gerschgorin’s theorem. λ 0.25 D ≤ ∆x 2 1 − 2 θ 1 D ≤ ∆x2 2 The smallest eigenvalue is independent of Δx (it is Dπ2/L2) so that the ratio of largest to smallest eigenvalue is proportional to 1/Δx2. Thus, the problem becomes stiff as Δx approaches zero. See Eq. (3-65). The effect of the increased stiffness is that a smaller and smaller time step (Δt) must be taken as the mesh is refined (Δx2 → 0). At the same time, the number of points is increasing, so the computation becomes very lengthy. Implicit methods are used to overcome this problem. The finite difference formulation is then (see Fig. 3-50) Ti + 1, j − 2Ti , j + Ti − 1, j Ti , j + 1 − 2Ti , j + Ti , j − 1 + = Qi , j Δx 2 Δy 2 Ti , j = f ( x i , y j ) on S (3-69) If the boundary is parallel to a coordinate axis, any derivative is evaluated as in the section on boundary-value problems, using either a one-sided, centered difference or a false boundary. If the boundary is more irregular and not parallel to a coordinate line, then more complicated expressions are needed and the finite element method may be the better method. Equation (3-69) provides a set of linear equations that must be solved. These equations and their boundary conditions may be written in matrix form as At = f where t is the set of temperatures at all the points, f is the set of heat generation terms at all points, and A is formed from the coefficients of Tij in Eq. (3-69). 3-48 MATHEMATICS The solution can be obtained simply by solving the set of linear equations. For three-dimensional problems, the matrix A is sparse, and iterative methods are used. These include Gauss-Seidel, alternating direction, overrelaxation methods, conjugate gradient, and multigrid methods. In Gauss-Seidel methods, one writes the equation for Tij in terms of the other temperatures and cycles through all the points over and over. In the alternating direction method, one solves along one line (that is, x = constant), keeping the side values fixed, and then repeats this for all lines, and then repeats the process. Multigrid methods solve the problem on successively refined grids, which has advantages for both convergence and error estimation. Conjugate gradient methods frequently use a preconditioned matrix. The equation is multiplied by another matrix, which is chosen so that the resulting problem is easier to solve than the original one. Finding such matrices is an art, but it can speed convergence. The generalized minimal residual method is described in http://mathworld.wolfram.com/ GeneralizedMinimalResidualMethod.html. Additional resources can be found at http://www.netlib.org/linalg/html_templates/Templates. html. When the problem is nonlinear, the iterative methods may not converge, or the mesh may have to be refined before they converge, so some experimentation is sometimes necessary. Spreadsheets can be used to solve two-dimensional problems on rectangular grids. The equation for Tij is obtained by rearranging Eq. (3-69).  ∆x 2  Qi , j ∆x 2 2 1 + 2  Ti , j = Ti + 1, j + Ti − 1, j + 2 (Ti , j + 1 + T1, j − 1 ) − ∆x 2 k ∆y  ∆y  This equation is inserted into a cell and copied throughout the space represented by all the cells; when the iteration feature is turned on, the solution is obtained. The Galerkin finite element method (FEM) is useful for solving elliptic problems and is particularly effective when the domain or geometry is irregular. As an example, cover the domain with triangles and define a trial function on each triangle. The trial function takes the value 1.0 at one corner and the value 0.0 at the other corners and is linear in between. For a triangle with corners at (x, y) = (0, 0.58), (0.66, 0), and (1, 0.66) one of three trial functions is shown in Fig. 3-51. These trial functions on each triangle are pieced together to give a trial function on the whole domain. General treatments of the finite element method are available (see references). The steps in the solution method are similar to those described for boundary-value problems, except now the problems are much bigger so that the numerical analysis must be done very carefully to be efficient. Most engineers, however, just use a finite element program without generating it. There are three major caveats that must be addressed. First, the solution is dependent on the mesh laid down, and the only way to assess the accuracy of the solution is to solve the problem with a more refined mesh. Second, the solution obeys the shape of the trial function inside the element. Thus, if linear functions are used on triangles, a three-dimensional view of the solution, plotting the solution versus x and y, consists of a series of triangular planes joined together at the edges, as in a geodesic dome. Third, the Galerkin finite element method is applied to both the differential equations and the boundary conditions. Computer programs are usually quite general and may allow the user to specify boundary conditions that are not realistic. Also, natural boundary conditions are satisfied if no other boundary condition (ones involving derivatives) is set at a node. Thus, the user of finite element codes must be very clear what boundary conditions and differential equations are built into the computer code. When the problem is nonlinear, the Newton-Raphson method is used to iterate from an initial guess. Nonlinear problems lead to complicated integrals to evaluate, and they are usually evaluated using gaussian quadrature. One nice feature of the finite element method is the use of natural boundary conditions. It may be possible to solve the problem on a domain that is shorter than needed to reach some limiting condition (such as at an outflow boundary). The externally applied flux is still applied at the shorter domain, and the solution inside the truncated domain is still valid. Examples are given in Chang, M. W., and B. A. Finlayson, Int . J . Num . Methods Eng . 15, 935–942 (1980), and Finlayson, B. A., Numerical Methods for Problems with Moving Fronts, Ravenna Park Publishing, Seattle, Wash. (1992). The effect of this is to allow solutions in domains that are smaller, thus saving computation time and permitting the solution in semi-infinite domains. The trial functions in the finite element method are not limited to linear ones. Quadratic functions and even higher-order functions are frequently used. The same considerations hold as for boundary-value problems: The higher-order trial functions converge faster, but require more work. It is possible to refine both the mesh h and the power of polynomial in the trial function p in an h-p method. Some problems have constraints on some of the variables. For flow problems, the pressure must usually be approximated by using a trial function that is one order lower than the polynomial used to approximate the velocity. Hyperbolic Equations The most common situation yielding hyperbolic equations involves unsteady phenomena with convection. Two typical equations are the convective diffusive equation ∂c ∂c ∂2 c +u =D 2 ∂t ∂x ∂x and the chromatography equation. (See Partial Differential Equations.) If the diffusion coefficient is zero, the convective diffusion equation is hyperbolic. If D is small, the phenomenon may be essentially hyperbolic, even though the equations are parabolic. Thus the numerical methods for hyperbolic equations may be useful even for special parabolic equations. Equations for several methods are given here. If the convective term is treated with a centered difference expression, the solution exhibits oscillations from node to node, and these go away only if a very fine grid is used. The simplest way to avoid the oscillations with a hyperbolic equation is to use upstream derivatives. If the flow is from left to right, this would give ci − ci − 1 ci + 1 − 2c i + ci − 1 dci =D +u Δx 2 Δx dt The effect of using upstream derivatives is to add artificial or numerical diffusion to the model. This can be ascertained by rearranging the finite difference form of the convective diffusion equation ci +1 − ci − 1  dci uΔx  ci + 1 − 2c i + ci − 1 = D+ +u   Δx 2 2Δ x 2  dt Thus the diffusion coefficient has been changed from D to D + 1 u∆ x 2 Alternatively, the diffusion coefficient has been multiplied by the factor Pecell  u∆ x   D ′ = D  1 +  = D  1 +   2  2D  0.5 ∆x u∆x uL ∆x = = Pe is called the cell Peclet number. When D D L L the diffusion coefficient is very small (or diffusion is slow compared with convection), the Peclet number will be large. In that case, extraneous diffusion will be included in the solution unless the mesh size (denoted by Δx) is small compared with the characteristic length of the problem. To avoid this problem (by keeping the factor small), very fine meshes must be used, and the smaller the diffusion coefficient, the smaller the required mesh size. A variety of other methods are used to obtain a good solution without using extremely fine meshes. The flux correction methods keep track of the flux of material into and out of a cell ( from one node to another) and put limits on the flux to make sure that no more material leaves the cell than is there originally plus the input amount. See Finlayson, B. A., Numerical where Pecell = 0 0.7 0.6 0.5 1 0.8 0.4 0.6 0.3 0.2 0.4 0.1 0 FIG. 3-51 a triangle. 0.2 0 Trial functions for Galerkin finite element method: a linear polynomial on nUMERICAL SOLUTIOn OF ORDInARY DIFFEREnTIAL EQUATIOnS AS InITIAL-VALUE PROBLEMS i –1st cell ith cell i−1 i−1/2 i i+1/2 ∆x FIG. 3-52 Nomenclature for finite volume method. Methods for Problems with Moving Fronts, Ravenna Park Publishing, Seattle, Wash., 1992, for many examples. All the methods have a limit to the time step that is set by the convection term. Essentially, the time step should not be so big as to take the material farther than it can go at its velocity. This is usually expressed as a Courant number limitation. Co = u∆t ≤1 ∆x Some methods require a smaller limit, depending upon the amount of diffusion present (see Finlayson, 1992, Appendix). In the finite element method, Petrov-Galerkin methods are used to minimize the unphysical oscillations. The Petrov-Galerkin method essentially adds a small amount of diffusion in the flow direction to smooth the unphysical oscillations. The amount of diffusion is usually proportional to Δx so that it becomes negligible as the mesh size is reduced. The value of the Petrov-Galerkin method lies in being able to obtain a smooth solution when the mesh size is large, so that the computation is feasible. This is not so crucial in one-dimensional problems, but it is essential in two- and threedimensional problems and purely hyperbolic problems. Finite Volume Methods Finite volume methods are utilized extensively in computational fluid dynamics. An excellent presentation is by LeVeque (2002). In this method, a mass balance is made over a cell, accounting for the change in what is in the cell, and the flow in and out. Figure 3-52 illustrates the geometry of the ith cell. A mass balance made on this cell (with area A perpendicular to the paper) is A ∆x (cin + 1 − cin ) = ∆t A ( J i − 1/2 − J i + 1/2 ) where J is the flux due to convection and diffusion, positive in the +x direction. J = uc − D ci − ci − 1 ∂c , J i − 1/2 = ui − 1/2ci − 1/2 − D ∂x ∆x The concentration at the edge of the cell is taken as 1 ci − 1/2 = (ci + ci − 1 ) 2 Rearrangement for the case when the velocity u is the same for all nodes gives cin + 1 − c n i u (ci + 1 − ci − 1 ) D = 2 (ci + 1 − 2ci + ci + 1 ) + 2 ∆x ∆x ∆t This is the same equation obtained by using the finite difference method. This coincidence occurs only when the velocity is constant, which isn’t usually true. In two and three dimensions, the mesh need not be rectangular, as long as it is possible to compute the velocity normal to an edge of the cell. The finite volume method is useful for applications involving filling, such as injection molding, when only part of the cell is filled with fluid. Such applications do involve some approximations, since the interface is not tracked precisely, but they are useful engineering approximations. Parabolic Equations in Two or Three Dimensions Computations become much more lengthy when there are two or more spatial dimensions. For example, we may have the unsteady heat conduction equation ρC p  ∂2 T ∂2 T  ∂T =k 2 + 2 −Q ∂t ∂y   ∂x Most engineers use computer packages to solve such problems. If there is both convection and diffusion in the problem, the same considerations 3-49 apply: A fine mesh is needed when the Peclet number is large. The upstream weighting and Petrov-Galerkin methods can be used, but it is important to apply the smoothing only in the direction of flow, since smoothing in the direction transverse to the flow direction would be incorrect. Some transverse smoothing is unavoidable, but the engineer needs to be sure that the smoothing is just enough to allow a good solution without creating large errors. See Finlayson (1980) in General References; Kuzmin, D., and J. Hämäläinen, Finite Element Methods for Computational Fluid Dynamics: A Practical Guide, SIAM-Soc. Ind. Appl. Math., 2014; and Layton, W., Introduction to the Numerical Analysis of Incompressible Viscous Flows, SIAM, 2008. Computer Software When one is choosing computer software to solve a problem, there are a number of important considerations. The first decision is whether to use an approximate, engineering flow model, developed from correlations, or to solve the partial differential equations that govern the problem. Correlations are quick and easy to apply, but they may not be appropriate to the problem or give the needed detail. When one is using a computer package to solve partial differential equations, the first task is always to generate a mesh covering the problem domain. This is not a trivial task, and special methods have been developed to permit importation of a geometry from a computer-aided design (CAD) program. Then the mesh must be created automatically. If the boundary is irregular, the finite element method is especially well suited, although special embedding techniques can be used in finite difference methods (which are designed to be solved on rectangular meshes). Another capability to consider is the ability to track free surfaces that move during the computation. This phenomenon introduces the same complexity that occurs in problems with a large Peclet number, with the added difficulty that the free surface moves between mesh points and improper representation can lead to unphysical oscillations. The method used to solve the equations is important, and both explicit and implicit methods (as described above) can be used. Implicit methods may introduce unacceptable extra diffusion, so the engineer needs to examine the solution carefully. The methods used to smooth unphysical oscillations from node to node are also important, and the engineer needs to verify that the added diffusion or smoothing does not give inaccurate solutions. Since current-day problems are mostly nonlinear, convergence is always an issue since the problems are solved iteratively. Robust programs provide several methods for convergence, each of which is best in some circumstance or other. It is wise to have a program that includes many iterative methods. If the iterative solver is not very robust, the only recourse to solving a steady-state problem may be to integrate the time-dependent problem to steady state. The solution time may be long, and the final result may be further from convergence than would be the case if a robust iterative solver were used. A variety of computer programs are available on the Internet, some free. First consider general-purpose programs. The website http://www.netlib .org/pdes/index.html lists programs for 2D elliptic partial differential equations as well as Clawpack for hyperbolic systems of equations from LeVeque (2002). On the NIST website http://gams.nist.gov/ search on “partial differential equations.” Lau (2007) provides many programs in C++ (also see http://numerical.recipes /). The multiphysics program Comsol Multiphysics also solves many standard equations arising in mathematical physics. Computational fluid dynamics (CFD) programs are more specialized, and most have been designed to solve sets of equations that are appropriate to specific industries. They can then include approximations and correlations for some features that would be difficult to solve for directly. ANSYS (http://www.ansys.com) is a major program having incorporated both Fluent and CFX. Comsol Multiphysics (http://www.comsol.com) is particularly useful because it incorporates many different types of physics (and equations), has a convenient graphical-user interface, permits easy mesh generation and refinement (including adaptive mesh refinement), allows the user to add phenomena and equations easily, permits solution by continuation methods (thus enhancing convergence), and has extensive graphical output capabilities. Other packages are also available (see http:// cfd-online.com/), and these may contain features and correlations specific to the engineer’s industry. One important point to note is that for turbulent flow, all the programs contain approximations, using the k-epsilon models of turbulence, or large eddy simulations; the direct numerical simulation of turbulence is too slow to apply to very big problems, although it does give insight (independent of any approximations) that is useful for interpreting turbulent phenomena. Thus, the method used to include those turbulent correlations is important, and the method also may affect convergence or accuracy. FAST FOURIER TRAnSFORM The discrete Fourier transform can be used to differentiate a function, and this is used in the spectral method for solving differential equations as well as in modeling turbulent flow. Gottlieb, D., and S. A. Orszag, Numerical Analysis 3-50 MATHEMATICS of Spectral Methods: Theory and Applications, SIAM, Philadelphia, Penn., 1977, discusses why they work; Trefethen, L. N., Spectral Methods in Matlab, SIAM, Philadelphia, Penn., 2000, shows how to use them in MATLAB. Suppose we have a grid of equidistant points x n = n∆x , n = 0,1, 2,  , 2 N − 1, ∆x = L 2N Thus at the grid points N 2 πik 2 ik π xn / L dy e = ∑ Yk dx n k = −N L The process works as follows. From the solution at all grid points the Fourier transform is obtained by using the fast Fourier transform (FFT), {Yk}. Then this is multiplied by 2πik/L to obtain the Fourier transform of the derivative. The solution is known at each of these grid points {y(xn)}. First the discrete Fourier transform is taken: Yk = 1 2N 2 N −1 ∑ y ( x n )e −2 ik π xn / L k = − N , − N + 1,  , 0,  , N − 1, N n=0 Yk′ = Yk Then the inverse Fourier transform is taken using FFT, giving the value of the derivative at each of the grid points. 1 N dy = ∑ Yk′e 2 ik π xn / L dx n L k = − N The inverse transformation is y (x ) = 2 πik L 1 N ∑ Yke 2ik π x /L L k = −N The spectral method is used for direct numerical simulation (DNS) of turbulence. The Fourier transform is taken of the differential equation, and the resulting equation is solved. Then the inverse transformation gives the solution. When there are nonlinear terms, as in turbulent flow, they are calculated at each node in physical space, and the Fourier transform is taken of the result. This technique is especially suited to time-dependent problems, and the major computational effort is in the fast Fourier transform. Differentiate this to get 2 πik 2 ik π x / L dy 1 N e = ∑ Yk dx L k = −N L OPTIMIZATIOn References: General references include the following textbooks. For nonlinear programming, see Nocedal, J., and S. J. Wright, Numerical Optimization, Springer, New York, 2006; Conn, A. R., N. Gould, and P. Toint, Trust Region Methods, SIAM, Philadelphia, Penn., 2000; Biegler, L. T., Nonlinear Programming: Concepts, Algorithms and Applications to Chemical Engineering, SIAM, Philadelphia, Penn., 2010; Edgar, T. F., D. M. Himmelblau, and L. S. Lasdon, Optimization of Chemical Processes, McGraw-Hill, New York, 2002. For operations research and linear programming, Hillier, F. S., and G. J. Lieberman, Introduction to Operations Research, McGraw-Hill, New York, 2015. For mixed integer programming, Nemhauser, G. L., and L. A. Wolsey, Integer and Combinatorial Optimization, Wiley, New York, 1999. For global optimization and mixed integer nonlinear programming, Floudas, C. A., Deterministic Global Optimization: Theory, Algorithms and Applications, Kluwer, Norwell, Mass., 2000; Tawarmalani, M., and N. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Many useful resources including descriptions, trial software, and examples can be found on the NEOS server maintained at Argonne National Laboratory. Background material for this section includes the two previous sections on matrix algebra and numerical analysis. InTRODUCTIOn Optimization is a key enabling tool for decision making in chemical engineering. It has evolved from a methodology of academic interest into a technology that continues to have a significant impact on engineering research and practice. Optimization algorithms form the core tools for (1) experimental design, parameter estimation, model development, and statistical analysis; (2) process synthesis analysis, design, and retrofit; (3) model predictive control and real-time optimization; and (4) planning, scheduling, and the integration of process operations into the supply chain. As shown in Fig. 3-53, optimization problems that arise in chemical engineering can be classified in terms of continuous and discrete variables. For the former, nonlinear programming (NLP) problems form the most general case, and widely applied specializations include linear programming (LP) and quadratic programming (QP). An important distinction for NLP is whether the optimization problem is convex or nonconvex. The latter NLP problem may have multiple local optima, and an important question is whether a global solution is required for the NLP. Another important distinction is whether the problem is assumed to be differentiable or not. Mixed integer problems also include discrete variables. These can be written as mixed integer nonlinear programs (MINLPs), or as mixed integer linear programs (MILP), if all variables appear linearly in the constraint and objective functions. For the latter an important case occurs when all the variables are integer; this gives rise to an integer programming (IP) problem. IP problems can be further classified into many special problems (e.g., assignment, traveling salesperson, etc.), which are not shown in Fig. 3-53. Similarly, the MINLP problem also gives rise to special problem classes, although here the main distinction is whether its relaxation is convex or nonconvex. The ingredients of formulating optimization problems include a mathematical model of the system, an objective function that quantifies a criterion to be extremized, variables that can serve as decisions, and, optionally, inequality constraints on the system. When represented in algebraic form, the general formulation of discrete and continuous optimization problems can be written as the following mixed integer optimization problem: Min f (x, y) subject to h(x, y) = 0 g(x, y) ≤ 0 x ∈ n y ∈ {0, 1}t (3-70) where f (x, y) is the objective function (e.g., cost, energy consumption, etc.), h(x, y) = 0 are the equations that describe the performance of the system (e.g., material balances, production rates), and the inequality constraints g(x, y) ≤ 0 may define process specifications or constraints for feasible plans and schedules. Note that the operator max f (x, y) is equivalent to Min[-f (x, y)] . We define the real n vector x to represent the continuous variables while the t vector y represents the discrete variables, which, without loss of generality, are often restricted to take values of 0 or 1 to define logical or discrete decisions, such as assignment of equipment and sequencing of tasks. (These variables can also be formulated to take on other integer values as well.) Problem (3-70) corresponds to a mixed integer nonlinear program Optimization Mixed Integer (Discrete) NLP (Continuous) MINLP MILP Nondifferentiable Differentiable Convex Nonconvex IP LP QP Local Global FIG. 3-53 Classes of optimization problems and algorithms. Direct Search OPTIMIZATIOn For continuous variable optimization, we consider Eq. (3-70) without discrete variable y. The general NLP problem (3-71) is presented here: subject to h(x) = 0, g(x) ≤ 0 9 8 7 100 6 5 50 4 3 10 2 GRADIEnT-BASED nOnLInEAR PROGRAMMInG Min f (x) 10 x2 when any of the functions involved are nonlinear. If all functions are linear, it corresponds to a mixed integer linear program (3-89). If there are no 0–1 variables, then problem (3-70) reduces to a nonlinear program (3-71) or linear program (3-78) depending on whether the functions are linear. Following the road map in Fig. 3-53, we start with continuous variable optimization and consider in the next section the solution of NLP problems with differentiable objective and constraint functions. If only local solutions are required for the NLP problem, then very efficient large-scale methods can be considered. This is followed by methods that are not based on local optimality criteria; we consider direct search optimization methods that do not require derivatives as well as deterministic global optimization methods. Following this, we consider the solution of mixed integer problems and outline the main characteristics of algorithms for their solution. Finally, we conclude with a discussion of optimization modeling software and its implementation on engineering models. x* −2 2 0 1 1 (3-71) and we assume that the functions f (x), h(x), and g(x) have continuous first and second derivatives. A key characteristic of Eq. (3-71) is whether the problem is convex or not, i.e., whether it has a convex objective function and a convex feasible region. A function f(x) of x in some domain X is convex if and only if, for all points x1, x2 ∈ X, 3-51 3 2 4 5 x1 6 7 8 9 10 FIG. 3-54 Unconstrained minimum. 10 9 (3-72) holds for all α ∈ (0, 1). [Strict convexity requires that the inequality Eq. (3-72) be strict.] Convex feasible regions require g(x) to be a convex function and h(x) to be linear. Referring to Fig. 3-53, problem (3-71) is convex if and only if f (x) and g(x) are convex functions and h(x) is a linear function. Otherwise, the problem is nonconvex. If Eq. (3-71) is a convex problem, then any local solution is guaranteed to be a global solution to Eq. (3-71). Moreover, if the objective function is strictly convex, then this solution x* is unique. On the other hand, nonconvex problems may have multiple local solutions, i.e., feasible solutions x* only within some nonvanishing neighborhood. We first consider methods that find only local solutions to nonconvex problems, as more difficult (and expensive) search procedures are required to find a global solution. Local methods are currently very efficient and have been developed to deal with very large NLP problems. Moreover, by considering the structure of convex NLP problems (including LP and QP problems), even more powerful methods can be applied. To study these methods, we first consider conditions for local optimality. Local Optimality Conditions: A Kinematic Interpretation Instead of a formal development of conditions that define a local optimum, we present a more intuitive kinematic illustration. Consider the contour plot of the objective function f (x), given in Fig. 3-54, as a smooth valley in space of variables x1 and x2. For the contour plot of this unconstrained problem, Min f (x), consider a ball rolling in this valley to the lowest point of f (x), denoted by x*. This point is at least a local minimum and is defined by a point with a zero gradient and at least nonnegative curvature in all (nonzero) directions p. We use the first-derivative (gradient) vector ∇f (x) and second-derivative (hessian) matrix ∇xx f (x) to state the necessary first- and second-order conditions for unconstrained optimality: ∇x f (x*) = 0 p ∇xx f (x*)p ≥ 0 T for all p ≠ 0 (3-73) These necessary conditions for local optimality can be strengthened to sufficient conditions by making the inequality in Eq. (3-73) strict (i.e., positive curvature in all directions). Equivalently, the sufficient (necessary) curvature conditions can be stated as follows: ∇xx f (x*) has all positive (nonnegative) eigenvalues and is therefore defined as a positive (semidefinite) definite matrix. Now consider the imposition of inequality g(x) ≤ 0 and equality constraints h(x) = 0 in Fig. 3-55. Continuing the kinematic interpretation, the inequality constraints g(x) ≤ 0 act as “fences” in the valley, and equality constraints h(x) = 0 act as “rails.” Consider now a ball, constrained on a rail and within fences, to roll to its lowest point. This stationary point occurs when the normal forces exerted by the fences [-∇g(x*)] and rails [-∇h(x*)] on the ball are balanced by the force of gravity [-∇f (x*)]. This condition can be stated by the following Karush-Kuhn-Tucker (KKT) necessary conditions for constrained optimality. h(x*)=0 8 7 6 x2 f[αx1 + (1 - α)x2] ≤ αf[x1 + (1 - α)x2] + (1 - α)f(x2) f (x*) 5 4 100 3 x* 2 50 −2 g(x*) 0 h(x* ) 1 1 2 10 2 g(x)≤0 3 4 5 6 7 8 9 10 x1 FIG. 3-55 Constrained minimum. Balance of Forces It is convenient to define the Lagrange function L(x, l, n) = f (x) + g(x)Tl + h(x)Tn, along with “weights” or multipliers l and n for the constraints. The stationarity condition (balance of forces acting on the ball) is then given by ∇L(x, l, n) = ∇f (x) + ∇h(x) l + ∇g(x) n = 0 (3-74) Feasibility Both inequality and equality constraints must be satisfied (the ball must lie on the rail and within the fences): h(x) = 0 g(x) ≤ 0 (3-75) Complementarity Inequality constraints are either strictly satisfied (active) or inactive, in which case they are irrelevant to the solution. In the latter case the corresponding KKT multiplier must be zero. This is written as nTg(x) = 0 n≥0 (3-76) Constraint Qualification For a local optimum to satisfy the KKT conditions, an additional regularity condition is required on the constraints. This can be defined in several ways. A typical condition is 3-52 MATHEMATICS that the active constraints at x* be linearly independent; i.e., the matrix [∇h(x*)|∇gA(x*)] is full column rank, where gA is the vector of inequality constraints with elements that satisfy gA,I (x*) = 0. With this constraint qualification, the KKT multipliers (l, n) are guaranteed to be unique at the optimal solution. Second-Order Conditions As with unconstrained optimization, nonnegative (positive) curvature is necessary (sufficient) in all the allowable (i.e., constrained) nonzero directions p. The necessary second-order conditions can be stated as pT ∇xxL(x*)p ≥ 0 for all p ≠ 0 with ∇h(x*)Tp = 0, ∇gA (x*)Tp ≤ 0, ∇gA,i (x*)Tp = 0 for ni > 0 (3-77) and the corresponding sufficient conditions require the first inequality in Eq. (3-77) to be strict. Note that in Fig. 3-54, the allowable directions p span the entire space for x while in Fig. 3-55 there are no allowable directions p . Convex Cases of NLP Problems Linear programs and quadratic programs are special cases of Eq. (3-71) that allow for more efficient solution, based on application of KKT conditions Eq. (3-74) through Eq. (3-77). Because these are convex problems, any locally optimal solution is a global solution. In particular, if the objective and constraint functions in Eq. (3-71) are linear, then the following linear program (LP) Min cTx subject to Ax = b and Cx ≤ d (3-78) can be solved in a finite number of steps, and the optimal solution lies at a vertex of the polyhedron described by the linear constraints. This is shown in Fig. 3-56, and in so-called primal degenerate cases, multiple vertices can be alternate optimal solutions, with the same values of the Min objective function. The standard method to solve Eq. (3-78) is the simplex method, developed in the late 1940s, although since Karmarkar’s discovery in 1984 interior point methods have also become quite advanced and competitive for highly constrained problems. The simplex method proceeds by moving successively from vertex to vertex with improved objective function values. Methods to solve Eq. (3-78) are well implemented and widely used, especially in planning and logistical applications. They also form the basis for MILP methods discussed later. Currently, state-of-the-art LP solvers can handle millions of variables and constraints, and the application of further decomposition methods leads to the solution of problems that are two or three orders of magnitude larger than this. See the general references of Hillier and Lieberman (2015) and Nocedal and Wright (2006) for more details. Also, the interior point method is described below from the perspective of more general NLP problems. Quadratic programs (QPs) represent a slight modification of Eq. (3-78) and can be stated as Min cTx+1/2 xTQx subject to Ax = b Cx ≤ d If the matrix Q is positive semidefinite (positive definite) when projected into the null space of the active constraints, then Eq. (3-79) is (strictly) convex and the QP is a global (and unique) minimum. Otherwise, local solutions may exist for Eq. (3-79), and more extensive global optimization methods are needed to obtain the global solution. Like LPs, convex QPs can be solved in a finite number of steps. However, as seen in Fig. 3-57, these optimal solutions may lie on a vertex, on a constraint boundary, or in the interior. A number of active set strategies have been created that solve the KKT conditions of the QP and incorporate efficient updates of active constraints. Popular methods include null space algorithms, range space methods, and Schur complement methods. As with LPs, QP problems can also be solved with interior point methods. Solving the General NLP Problem Solution techniques for Eq. (3-71) deal with satisfaction of the KKT conditions, Eq. (3-74) through Eq. (3-77). Many NLP solvers are based on successive quadratic programming (SQP) as it allows the construction of a number of NLP algorithms based on the Newton-Raphson method for equation solving (see the Numerical Analysis section). SQP solvers have been shown to require the fewest function evaluations to solve NLP problems, and they can be tailored to a broad range of process engineering problems with different structure. Min Min Linear Program Min Min Linear Program (Alternate Optima) FIG. 3-56 Contour plots of linear programs. (3-79) Convex Objective Functions Linear Constraints FIG. 3-57 Contour plots of convex quadratic programs. OPTIMIZATIOn 3-53 where e = [1, 1, …, 1]T, S = diag{s}, and V = diag{n}. SQP methods find solutions that satisfy Eq. (3-80) by generating Newton-like search directions at iteration k. However, Eq. (3-80d) and active bounds Eq. (3-80e) are dependent at the solution and serve to make the KKT system ill conditioned near the solution. SQP algorithms treat these conditions in two ways. In the active set strategy, discrete decisions are made regarding the active constraint set i ∈ I = {i| gi(x*) = 0}, and Eq. (3-80d) is replaced by si = 0, i ∈ I, and ni = 0, i ∉ I. Determining the active set is a combinatorial problem, and a straightforward way to determine an estimate of the active set [and to satisfy Eq. (3-80e)] is to formulate and solve, at a point xk, the following QP at iteration k: for various values of m, while active set methods require the solution of the more expensive QP subproblem Eq. (3-81). Thus, if there are few inequality constraints or an active set is known (say from a good starting guess, or a known QP solution from a previous iteration), then solving Eq. (3-81) is not expensive and the active set method is favored. However, for problems with many inequality constraints, interior point methods are often faster, as they avoid the combinatorial problem of selecting the active set. This is especially true for large-scale problems where a large number of bounds are active. Examples that demonstrate the application of these approaches include the solution of model predictive control (MPC) problems and the solution of large optimal control problems using barrier NLP solvers. For instance, IPOPT allows the solution of problems with more than 1,000,000 variables and up to 50,000 degrees of freedom [see Biegler et al., Chem . Eng . Sci . 57(4): 575–593 (2002); Laird et al., ASCE J . Water Resource Management and Planning 131(2):125 (2005)]. Other Gradient-Based NLP Solvers In addition to SQP methods, a number of NLP solvers have been developed and adapted for large-scale problems. Generally these methods require more function evaluations than for SQP methods, but they perform very well when interfaced to optimization modeling platforms, where function evaluations are cheap. All these can be derived from the perspective of applying Newton steps to portions of the KKT conditions. LANCELOT (Conn et al., 2000) is based on the solution of boundconstrained subproblems. Here an augmented lagrangian is formed from Eq. (3-71), and the following subproblem is solved: Min ∇f (xk)Tp + 1/2 pT ∇xxL(xk, lk, nk)p Min f (x) + lTh(x) + nT[g(x) + s] + 1/2 r||h(x), g(x) + s||2 subject to s ≥ 0 (3-85) The SQP strategy applies the equivalent of a Newton step to the KKT conditions of the nonlinear programming problem, and this leads to a fast rate of convergence. By adding slack variables s, the first-order KKT conditions can be rewritten as ∇f (x) + ∇h(x) l + ∇g(x) n = 0 h(x) = 0 g(x) + s = 0 SVe = 0 (s, n) ≥ 0 subject to: h(x ) + ∇h(x ) p = 0 g(x ) + ∇g(x ) p + s = 0 k k T k k T (3-80a) (3-80b) (3-80c) (3-80d) (3-80e) s≥0 (3-81) The KKT conditions of Eq. (3-81) are given by ∇f (xk) + ∇2L(xk, lk, nk)p + ∇h(xk) l + ∇g(xk) n = 0 (3-82a) h(xk) + ∇h(xk) T p = 0 (3-82b) g(x ) + ∇g(x ) p + s = 0 (3-82c) SVe = 0 (3-82d) (s, n) ≥ 0 (3-82e) k k T where the hessian of the Lagrange function ∇xxL(x, l, n) = ∇xx[ f (x) + h(x)Tl + g(x)Tn] is calculated directly or through a quasi-Newton approximation (created by differences of gradient vectors). If Eq. (3-81) is strictly convex, it is easy to show that Eqs. (3-82a) through (3-82c) correspond to a Newton-Raphson step for Eqs. (3-80a) through (3-80c) applied at iteration k. Also, selection of the active set is now handled at the QP level by satisfying the conditions of Eqs. (3-82d) and (3-82e). To evaluate and change candidate active sets, QP algorithms apply inexpensive matrix updating strategies to the KKT matrix associated with Eq. (3-82). Details of this approach can be found in Nocedal and Wright (2006). As alternatives that avoid the combinatorial problem of selecting the active set, interior point (or barrier) methods modify the NLP problem Eq. (3-71) to form Min f (xk) - mΣI ln si subject to h(xk) = 0 g(xk) + s = 0 (3-83) where the solution to Eq. (3-84) has s > 0 for the penalty parameter m > 0. Decreasing m to 0 leads to solution of problem Eq. (3-71). The KKT conditions for this problem can be written as ∇f (x*) + ∇h(x*) l + ∇g(x*) n = 0 h(x*) = 0 g(x*) + s = 0 (3-84) SVe = me and for m > 0, s > 0, and n > 0, Newton steps generated to solve Eqs. (3-84) are well behaved and analogous to Eq. (3-82), with a modification on the righthand side of Eq. (3-82d). A detailed description of a particular interior point algorithm, called IPOPT, can be found in Wächter and Biegler [Math . Prog . 106(1): 25–57 (2006)]. Both active set and interior point methods possess clear trade-offs. Interior point methods may require more iterations to solve Eqs. (3-84) The above subproblem can be solved very efficiently for fixed values of the multipliers l and n and penalty parameter r. Here a gradient projection trust region method is applied. Once subproblem Eq. (3-85) is solved, the multipliers and penalty parameter are updated in an outer loop, and the cycle repeats until the KKT conditions for Eq. (3-71) are satisfied. LANCELOT works best when exact second derivatives are available. This promotes a fast convergence rate in solving each subproblem and allows a bound-constrained trust region method to exploit directions of negative curvature in the hessian matrix. Reduced gradient methods are active set strategies that rely on partitioning the variables and solving Eq. (3-80) in a nested manner. Without loss of generality, problem Eq. (3-71) can be rewritten as Min f (z) subject to c(z) = 0 and a ≤ z ≤ b . Variables are partitioned as nonbasic variables (those fixed to their bounds), basic variables (those that can be solved from the equality constraints), and superbasic variables (those remaining variables between bounds that serve to drive the optimization); this leads to zT = [zNT, zBT, zST]. This partition is derived from local information and may change over the course of the optimization iterations. The corresponding KKT conditions can be written as ∇N f (z) + ∇N c(z)γ = ba - bb (3-86a) ∇B f (z) + ∇Bc(z)γ = 0 (3-86b) ∇S f (z) + ∇Sc(z)γ = 0 (3-86c) c(z) = 0 zN,j = aj or bj ba,j ≥ 0 bb,j = 0 (3-86d) or bb,j ≥ 0 ba,j = 0 (3-86e) where γ and b are the KKT multipliers for the equality and bound constraints, respectively, and Eq. (3-86e) replaces the complementarity conditions in Eq. (3-76). Reduced gradient methods work by nesting equations Eqs. (3-86b and d) within Eqs. (3-86a and c). At iteration k, for fixed values of zNk and zSk, we can solve for zB by using Eq. (3-86d) and for γ by using Eq. (3-86b). Moreover, linearization of these equations leads to sensitivity information (i.e., constrained derivatives or reduced gradients) that indicates how zB changes with respect to zS and zN. The algorithm then proceeds by updating zS by using reduced gradients derived from Eq. (3-86b) and given by df (z)/dzS = ∇S f (z) + ∇Sc(z) γ = ∇S f (z) - ∇Sc(z) ∇Bc(z)-1 ∇B f (z) (3-87) Driving df/dzS to zero, with quasi-Newton or Newton iterations, solves Eq. (3-86c). Following this, bound multipliers b are calculated from Eq. (3-86a). Over the course of the iterations, if the variable zB or zS exceeds its bounds or if some bound multipliers b become negative, then the variable partition needs to be changed and Eqs. (3-86) are reconstructed. These reduced gradient methods are embodied in the popular GRG2, CONOPT, and SOLVER codes (Edgar et al., 2002). The SOLVER code has been incorporated into Microsoft Excel. 3-54 MATHEMATICS Algorithmic Details for NLP Methods All the above NLP methods incorporate concepts from the Newton-Raphson method for equation solving. Essential features of these methods are that they provide (1) accurate derivative information to solve for the KKT conditions, (2) stabilization strategies to promote convergence of the Newton-like method from poor starting points, and (3) regularization of the jacobian matrix in Newton’s method (the so-called KKT matrix) if it becomes singular or ill conditioned. 1. NLP methods that use first and second derivatives . The KKT conditions require first derivatives to define stationary points, so accurate first derivatives are essential to determine locally optimal solutions for differentiable NLPs. Moreover, Newton-Raphson methods that are applied to the KKT conditions, as well as the task of checking second-order KKT conditions, necessarily require second-derivative information. (Note that second-order conditions are not checked by methods that do not use second derivatives.) With the recent development of automatic differentiation tools, many modeling and simulation platforms can provide exact first and second derivatives for optimization. When second derivatives are available for the objective or constraint functions, they can be used directly in LANCELOT as well as SQP and reduced gradient methods. Otherwise, on problems with few superbasic variables, both reduced gradient methods and SQP methods [with reduced gradient methods applied to the QP subproblem Eq. (3-81)] can benefit from positive definite quasi-Newton approximations (Nocedal and Wright, 2006) applied to reduced second-derivative quantities (the socalled reduced hessian). Finally, for problems with least squares functions (see Statistics subsection), as in data reconciliation, parameter estimation, and model predictive control, one often assumes that the values of the objective function and its gradient at the solution are vanishingly small. Under these conditions, one can show that the multipliers (l, n) also vanish and ∇xxL(x, l, n) can be substituted by ∇xx f (x*). This Gauss-Newton approximation has been shown to be very efficient for the solution of least squares problems (see Nocedal and Wright, 2006). 2. Line search and trust region methods promote convergence from poor starting points. These are commonly used with the search directions calculated from NLP subproblems such as Eq. (3-81). In a trust region approach, the constraint ||p|| ≤ Δ is added, and the iteration step is taken if there is sufficient reduction of some merit function (e.g., the objective function weighted with some measure of the constraint violations). The size of the trust region Δ is adjusted based on the agreement of the reduction of the actual merit function compared to its predicted reduction from the subproblem (see Conn et al., 2000). Such methods have strong global convergence properties and are especially appropriate for ill-conditioned NLPs. This approach has been applied in the KNITRO code (see Nocedal and Wright, 2006). Line search methods can be more efficient on problems with reasonably good starting points and well-conditioned subproblems, as in real-time optimization. Typically, once a search direction is calculated from Eq. (3-81), or other related subproblem, a step size α ∈ (0, 1) is chosen so that xk + α p leads to a sufficient decrease of a merit function. As a recent alternative, a novel filter stabilization strategy ( for both line search and trust region approaches) has been developed based on a bicriterion minimization, with the objective function and constraint infeasibility as competing objectives [Fletcher et al., SIAM J . Optim . 13(3):635 (2002)]. This method often leads to better performance than that based on merit functions. 3. Regularization of the KKT matrix for the NLP subproblem is essential for good performance of general-purpose algorithms. For instance, to obtain a unique solution to Eq. (3-81), active constraint gradients must be full rank and the hessian matrix, when projected into the null space of the active constraint gradients, must be positive definite. These properties may not hold far from the solution, and corrections to the hessian in SQP may be necessary. Regularization methods ensure that subproblems such as Eq. (3-81) remain well conditioned; they include addition of positive constants to the diagonal of the hessian matrix to ensure its positive definiteness, judicious selection of active constraint gradients to ensure that they are linearly independent, and scaling the subproblem to reduce the propagation of numerical errors. Often these strategies are heuristics built into particular NLP codes. While quite effective, most of these heuristics do not provide convergence guarantees for general NLPs. From the conceptual descriptions as well as algorithmic details given above, it is clear that NLP solvers are complex algorithms that have required considerable research and development to turn them into reliable and efficient software tools. Practitioners who are confronted with engineering optimization problems should therefore leverage these efforts, rather than write their own codes. Table 3-3 presents a sampling of available NLP codes that represent the above classifications. OPTIMIZATIOn METHODS WITHOUT DERIVATIVES A broad class of optimization strategies does not require derivative information. These methods have the advantage of easy implementation and little prior knowledge of the optimization problem. In particular, such TABLE 3-3 Representative nLP Solvers Method Algorithm type Stabilization Second-order information CONOPT (Drud, 1994) Reduced gradient Line search Exact and quasi-Newton GRG2 (Edgar et al., 2002) Reduced gradient Line search Quasi-Newton IPOPT SQP, barrier Line search Exact KNITRO (Byrd et al., 1997) SQP, barrier Trust region Exact and quasi-Newton LANCELOT Augmented Lagrangian, bound constrained Trust region Exact and quasi-Newton LOQO SQP, barrier Line search Exact MINOS Reduced gradient, augmented Lagrangian Line search Quasi-Newton NPSOL SQP, active set Line search Quasi-Newton SNOPT Reduced space SQP, active set Line search Quasi-Newton SOCS SQP, active set Line search Exact SOLVER Reduced gradient Line search Quasi-Newton SRQP Reduced space SQP, active set Line search Quasi-Newton methods are well suited for “quick and dirty” optimization studies that explore the scope of optimization for new problems, prior to investing effort for more sophisticated modeling and solution strategies. Most of these methods are derived from heuristics that naturally spawn numerous variations. As a result, a very broad literature describes these methods. Here we discuss only a few important trends in this area. Classical Direct Search Methods Developed in the 1960s and 1970s, these methods include one-at-a-time search and methods based on experimental designs (EVOP). At that time, direct search methods were the most popular optimization methods in chemical engineering. Methods that fall into this class include the pattern search of Hooke and Jeeves [J . ACM 8: 212 (1961)], the conjugate direction method of Powell (1964), the simplex search of Nelder-Mead [Comput . J . 7: 308 (1965)], and the adaptive random search methods of Luus-Jaakola [AIChE J. 19: 760 (1973)], Goulcher and Cesares Long [Comp . Chem . Engr. 2: 23 (1978)], and Banga et al. [in State of the Art in Global Optimization, C. Floudas and P. Pardalos, eds., Kluwer, Dordrecht, 1996, p. 563]. All these methods require only objective function values for unconstrained minimization. Associated with these methods are numerous studies on a wide range of process problems. Moreover, many of these methods include heuristics that prevent premature termination (e.g., directional flexibility in the complex search as well as random restarts and direction generation). Simulated Annealing This strategy is related to random search methods and derives from a class of heuristics with analogies to the motion of molecules in the cooling and solidification of metals (Laarhoven and Aarts, Simulated Annealing: Theory and Applications, Reidel Publishing, Dordrecht, 1987). Here a temperature parameter q can be raised or lowered to influence the probability of accepting points that do not improve the objective function. The method starts with a base point x and objective value f (x) . The next point x′ is chosen at random from a distribution. If f (x′) < f (x), the move is accepted with x′ as the new point. Otherwise, x′ is accepted with probability p(q, x′, x) . Options include the Metropolis distribution p(q, x, x′) = exp{-[ f (x′) - f (x)]/q} and the Glauber distribution, p(q, x, x′) = exp{-[ f (x′) - f (x)]/q}/(1 + exp{-[ f (x′) f (x)]/q}) . The q parameter is then reduced, and the method continues until no further progress is made. Genetic Algorithms This approach, described in Holland, J. H., Adaptations in Natural and Artificial Systems (University of Michigan Press, Ann Arbor, 1975), is based on the analogy of improving a population of solutions through modifying their gene pool. It also has similar performance characteristics as random search methods and simulated annealing. Two forms of genetic modification, crossover or mutation, are used, and the elements of the optimization vector x are represented as binary strings. Crossover deals with random swapping of vector elements (among parents with highest objective function values or other rankings of population) or any linear combinations of two parents. Mutation deals OPTIMIZATIOn 3-55 with the addition of a random variable to elements of the vector. Genetic algorithms (GAs) have seen widespread use in process engineering, and a number of codes are available. Edgar et al. (2002) describe a related GA that is available in MS Excel. Derivative-Free Optimization (DFO) Over the past two decades, the availability of parallel computers and faster computing hardware and the need to incorporate complex simulation models within optimization studies have led a number of optimization researchers to reconsider classical direct search approaches. In particular, Dennis and Torczon [SIAM J . Optim . 1: 448 (1991)] developed a multidimensional search algorithm that extends the simplex approach of Nelder and Mead (1965). They note that the Nelder-Mead algorithm fails as the number of variables increases, even for very simple problems. To overcome this, their multidimensional pattern search approach combines reflection, expansion, and contraction steps that act as line search algorithms for a number of linearly independent search directions. This approach is easily adapted to parallel computation, and the method can be tailored to the number of processors available. Moreover, this approach converges to locally optimal solutions for unconstrained problems and observes an unexpected performance synergy when multiple processors are used. The work of Dennis and Torczon (1991) has spawned considerable research on the analysis and code development for DFO methods. In addition, Conn et al. (Introduction to Derivative Free Optimization, SIAM, Philadelphia, Penn., 2009) constructed a multivariable DFO algorithm that uses a surrogate model for the objective function within a trust region method. Here points are sampled to obtain a well-defined quadratic interpolation model, and descent conditions from trust region methods enforce convergence properties. A comprehensive overview and convergence analysis of pattern search, surrogate, and trust region DFO methods is presented in Conn, Scheinberg, and Vicente (2009). Moreover, several DFO codes have been developed that lead to black box optimization implementations for large, complex simulation models [see Audet and Dennis, SIAM J . Optim. 13: 889 (2003); Kolda et al., SIAM Rev . 45(3): 385 (2003)]. Direct search methods are easy to apply to a wide variety of problem types and optimization models. Moreover, because their termination criteria are not based on gradient information and stationary points, they are more likely to favor the search for globally optimal rather than locally optimal solutions. These methods can also be adapted easily to include integer variables. However, no rigorous convergence properties to globally optimal solutions have yet been discovered. Also, these methods are best suited for unconstrained problems or for problems with simple bounds. Otherwise, they may have difficulties with constraints, as the only options open for handling constraints are equality constraint elimination and addition of penalty functions for inequality constraints. Both approaches can be unreliable and may lead to failure of the optimization algorithm. Finally, the performance of direct search methods scales poorly (and often exponentially) with the number of decision variables. While performance can be improved with the use of parallel computing, these methods are rarely applied to problems with more than a few dozen decision variables. For simplicity, consider the problem Min f (x) subject to g(x) ≤ 0 where each function can be defined by additive terms. Convex relaxations for f (x) and g(x) can be derived in the following ways: • Convex additive terms remain unmodified in these functions. • Concave additive unary terms are replaced by linear underestimating functions that match the terms at the boundaries of their subregions. • Nonconvex polynomial terms can be replaced by a set of scalar bilinear terms, with new variables introduced to define the higher-order polynomials. • The scalar bilinear terms can be relaxed by using the McCormick underestimator; e.g., the bilinear term xz is replaced by a new variable w and linear inequality constraints GLOBAL OPTIMIZATIOn MIXED InTEGER PROGRAMMInG Deterministic optimization methods are available for nonconvex nonlinear programming problems of the form of Eq. (3-71) that guarantee convergence to the global optimum. More specifically, one can show under mild conditions that they converge to an e distance to the global optimum in a finite number of steps. These methods are generally more expensive than local NLP methods, and they require the exploitation of the structure of the nonlinear program. Because global optima cannot be characterized by properties analogous to KKT conditions for local optima, global optimization methods work by partitioning the problem domain (i.e., containing the feasible region) into subregions. Upper bounds on the objective function are computed over all subregions of the problem. In addition, lower bounds can be derived from convex relaxations of the objective function and constraints for each subregion. The algorithm then proceeds to eliminate all subregions that have infeasible constraint relaxations or lower bounds that are greater than the least upper bound. After this, the remaining regions are further partitioned to create new subregions, and the cycle continues until the upper and lower bounds converge. This basic concept leads to a wide variety of global algorithms, with the following features that can exploit different problem classes. Bounding strategies relate to the calculation of upper and lower bounds. For the former, any feasible point or, preferably, a locally optimal point in the subregion can be used. For the lower bound, convex relaxations of the objective and constraint functions are derived. The refining step deals with the construction of partitions in the domain and further partitioning them during the search process. Finally, the selection step decides on the order of exploring the open subregions. Mixed integer programming deals with both discrete and continuous decision variables. For this presentation we consider discrete decisions as binary variables, that is, yi = 0 or 1, and we consider the mixed integer problem (3-70). Unlike in local optimization methods, there are no optimality conditions, such as the KKT conditions, that can be applied directly. Instead, as in global optimization methods, a systematic search of the solution space, coupled with upper and lower bounding information, is applied. As with global optimization problems, large mixed integer programs can be expensive to solve, and some care is needed in problem formulation. Mixed Integer Linear Programming If the objective and constraint functions are all linear, then Eq. (3-70) becomes a mixed integer linear programming problem given by w ≥ xlz + zlx - xlzl w ≥ xuz + zux - xuzu w ≤ xuz + zlx - xuzl w ≤ xlz + zux - xlzu (3-88) where the subregions are defined by xl ≤ x ≤ xu and zl ≤ z ≤ zu . Thus the feasible region and the objective function are replaced by convex envelopes to form relaxed problems. Solving these convex relaxed problems leads to global solutions that are lower bounds to the NLP in the particular subregion. Finally, we see that gradient-based NLP solvers play an important role in global optimization algorithms, as they often yield the lower and upper bounds for the subregions. The spatial branch and bound global optimization algorithm can therefore be given by the following steps: 0. Initialize algorithm. Calculate upper and lower bounds over the entire (relaxed) feasible region. For iteration k with a set of partitions Mkj and bounds in each subregion fLj and fUj : 1. Bound . Define the best upper bound fU = Minj fUj and delete ( fathom) all subregions j with lower bounds fLj ≥ fU. If the remaining subregions satisfy fLj ≥ fU - e, stop. 2. Refine . Divide the remaining active subregions into partitions Mk,j1 and Mk,j2. (Many branching rules are available for this step.) 3. Select . Solve the convex relaxed NLP in the new partitions to obtain fLj1 and fLj2. Delete the partition if there is no feasible solution. 4. Update . Obtain upper bounds fUj1 and fUj2 to new partitions, if present. Set k = k + 1, update partition sets, and go to step 1. Note that a number of improvements can be made to the bounding, refinement, and selection strategies in the algorithm that accelerate the convergence of this method. A comprehensive discussion of all these options can be found in Floudas (2000) and Tawarlamani and Sahinidis (2002). Also, a number of efficient global optimization codes have recently been developed, including αBB, BARON, LGO, and OQNLP . An interesting numerical comparison of these and other codes can be found in Neumaier et al., Math . Prog . B 103(2): 335 (2005). Min aTx + cTy subject to Ax + By ≤ b x ≥ 0 y ∈ {0, 1}t (3-89) Note that if we relax the t binary variables by the inequalities 0 ≤ y ≤ 1, then Eq. (3-89) becomes a linear program with a (global) solution that is a lower bound to the MILP Eq. (3-89). There are specific MILP classes where the LP relaxation of Eq. (3-89) has the same solution as the MILP. Among these problems is the well-known assignment problem. Other MILPs that can be solved with efficient special-purpose methods are the knapsack problem, the set covering and set partitioning problems, and the traveling salesperson problem. See Nemhauser and Wolsey (1999) for a detailed treatment of these problems. More generally, MILPs are solved with branch and bound algorithms, similar to the spatial branch and bound method of the previous section, that 3-56 MATHEMATICS explore the search space. As seen in Fig. 3-58, binary variables are used to define the search tree, and a number of bounding properties can be noted from the structure of Eq. (3-89). Upper bounds on the objective function can be found from any feasible solution to Eq. (3-89), with y set to integer values. These can be found at the bottom or “leaf ” nodes of a branch and bound tree (and sometimes at intermediate nodes as well). The top, or root, node in the tree is the solution to the linear programming relaxation of Eq. (3-89); this is a lower bound to Eq. (3-89). On the other hand, as one proceeds down the tree with a partial assignment of the binary variables, a lower bound for any leaf node in that branch can be found from solution of the linear program at this intermediate node with the remaining binary variables relaxed. This leads to the following properties: • Any intermediate node with an infeasible LP relaxation has infeasible leaf nodes and can be fathomed (i.e., all remaining children of this node can be eliminated). • If the LP solution at an intermediate node is not less than an existing integer solution, then the node can be fathomed. These properties lead to pruning of the search tree. Branching then continues in the tree until the upper and lower bounds converge. This basic concept leads to a wide variety of MILP algorithms with the following features. LP solutions at intermediate nodes are relatively easy to calculate with the simplex method. If the solution of the parent node is known, multiplier information from this solution can be used to calculate (via efficient pivoting operations) the LP solution at the child node. Branching strategies to navigate the tree take a number of forms. More common depth-first strategies expand the most recent node to a leaf node or infeasible node and then backtrack to other branches in the tree. These strategies are simple to program and require little storage of past nodes. On the other hand, breadth-first strategies expand all the nodes at each level of the tree, select the node with the lowest objective function, and then proceed until the leaf nodes are reached. Here more storage is required, but generally fewer nodes are evaluated than in depth-first search. In addition, selection of binary variable for branching is based on a number of criteria, including choosing the variable with the relaxed value closest to 0 or 1, or the one leading to the largest change in the objective. A number of improved branching rules can accelerate the convergence of this method, and a number of efficient, large-scale MILP codes are widely used, including CPLEX, OSL, XPRESS, and ZOOM. Additional description of these strategies can be found in Nemhauser and Wolsey (1999). Example To illustrate the branch and bound approach, we consider the MILP: Min Z = x + y 1 + 2 y 2 + 3 y 3 subject to − x + 3 y 1 + y 2 + 2 y 3 ≤ 0 − 4 y 1 − 8 y 2 − 3 y 3 ≤ −10 Min f (x) + cTy subject to g(x) + By ≤ b Min f (x) + cTy- subject to g(x) + By- ≤ b -7Inf. (0,1,0) -6Z=7.625 (0, 0.875, 1) x≥0 f(x) ≥ f(xk) + ∇f(xk)T(x - xk) (3-91) (3-92) Consequently, linearization of Eq. (3-90) at a point xk, to form the problem Min subject to f (xk) + ∇f (xk)T(x - xk) + cTy g(xk) + ∇g(xk)T(x - xk) + By ≤ b x≥0 y ∈ {0, 1}t (3-93) leads to overapproximation of the feasible region and underapproximation of the objective function in Eq. (3-90). Consequently, solution of Eq. (3-93) is a lower bound to the solution of Eq. (3-90). Adding more linearizations from other points does not change the bounding property, so for a set of points xl, l = 1, …, k, the problem -1Z=5 (0.5, 1, 0) y1 -node#Z (y1, y2, y3) (3-90) if feasible, leads to a solution that is an upper bound on the MINLP solution. In addition, linearizations of a convex function f(x) leads to underestimation of the function itself, i.e., The solution to this problem is given by x = 4, y1 = 1, y2 = 1, y3 = 0, and Z = 7. Here we use a depth-first strategy and branch on the variables closest to 0 or 1. Figure 3-58 shows the progress of the branch and bound algorithm as the binary variables are selected and the bounds are updated. The sequence numbers for each node in Fig. 3-58 show the order in which they are processed. The grayed partitions correspond to the deleted nodes, and at termination of the algorithm we see that Z = 7 and an integer solution is obtained at an intermediate node where coincidentally y3 = 0. y3 x ≥ 0 y ∈ {0, 1}t where the binary variables are kept as separate linear terms. MINLP strategies can be classified into two types. The first deals with nonlinear extensions of the branch and bound method discussed above for MILPs. The second deals with outer approximation decomposition strategies that provide lower and upper bounding information for convergence. Nonlinear Branch and Bound The MINLP Eq. (3-90) can be solved in a similar manner to Eq. (3-89). If the functions f (x) and g(x) in Eq. (3-90) are convex, then direct extensions to the branch and bound method can be made. A relaxed NLP can be solved at the root node, upper bounds to the solution of Eq. (3-90) can be found at the leaf nodes, and the bounding properties due to NLP solutions at intermediate nodes still hold. However, this approach is more expensive than the corresponding MILP method. First, NLPs are more expensive than LPs to solve. Second, unlike with relaxed LP solutions, NLP solutions at child nodes cannot be updated directly from solutions at parent nodes. Instead, the NLP needs to be solved again (but one hopes with a better starting guess). The NLP branch and bound method is used in the SBB code interfaced to GAMS. In addition, Leyffer [Comput . Optim . Appl . 18: 295 (2001)] proposed a hybrid MINLP strategy nested within an SQP algorithm. At each iteration, a mixed integer quadratic program is formed, and a branch and bound algorithm is executed to solve it. If f (x) and g(x) are nonconvex, additional difficulties can occur. In this case, nonunique, local solutions can be obtained at intermediate nodes, and consequently lower bounding properties would be lost. In addition, the nonconvexity in g(x) can lead to locally infeasible problems at intermediate nodes, even if feasible solutions can be found in the corresponding leaf node. To overcome problems with nonconvexities, global solutions to relaxed NLPs can be solved at the intermediate nodes. This preserves the lower bounding information and allows nonlinear branch and bound to inherit the convergence properties from the linear case. However, as noted above, this leads to much more expensive solution strategies. Outer Approximation Decomposition Methods Again, we consider the MINLP Eq. (3-90) with convex f (x) and g(x). Note that the NLP with binary variables fixed at y- x ≥ 0 , y 1 , y 2 , y 3 ∈{0,1} -5Z=6.33 (0,1,0.67) Without loss of generality, Mixed Integer Nonlinear Programming we can rewrite the MINLP in Eq. (3-71) as -2Z=6.25 (1, 0.75, 0) y2 -4Inf. (1,0,1) FIG. 3-58 Branch and bound sequence for MILP example. -3Z=7 (1,1,0) Min α subject to α ≥ f ( x l ) + ∇f ( x l )T ( x − x l ) + c T y   l = 1,k g ( x l ) + ∇g ( x l )T ( x − x l ) + By ≤ b  x ≥0 y ∈{0, 1}t (3-94) where α is a scalar variable, still has a solution that is a lower bound to Eq. (3-90). The outer approximation strategy is depicted in Fig. 3-59. OPTIMIZATIOn Initialize x 0, y 0 Upper bound with y fixed NLP (3-91) Update y Lower bound MILP (3-94) + integer cuts LB ≥ UB FIG. 3-59 Outer approximation MINLP algorithm. The outer approximation algorithm first initializes the process, either with a predetermined starting guess or by solving a relaxed NLP based on Eq. (3-90). An upper bound to the solution is then generated by fixing the binary variables to their current values yk and solving the NLP Eq. (3-91). This solution determines the continuous variable values xk for the MILP Eq. (3-94). [If Eq. (3-94) is an infeasible problem, any point may be chosen for xk, or the linearizations could be omitted.] Note that this MILP also contains linearizations from previous solutions of Eq. (3-91). Finally, the integer cut ∑| y i − y ik | ≥ 1 is added to Eq. (3-94) to avoid revisiting previously encountered values of binary variables. Solution of Eq. (3-94) yields new values of y and (without the integer cut) must lead to a lower bound to the solution of Eq. (3-90). Consequently, if the objective function of the lower bounding MILP is greater than the least upper bound determined in solutions of Eq. (3-91), then the algorithm terminates. Otherwise, the new values of y are used to solve the next NLP Eq. (3-91). Compared to nonlinear branch and bound, the outer approximation algorithm usually requires very few solutions of the MILP and NLP subproblems. This is especially advantageous on problems where the NLPs are large and expensive to solve. Moreover, there are three variations of outer approximation that may be suitable for particular problem types: In generalized benders decomposition (GBD) the lower bounding problem Eq. (3-94) is replaced by the MILP Min α subject to x ≥ 0, y ∈{0, 1}t α ≥ f ( x l ) + c T y + [ g ( x l ) + By ]T νl   ∑| y i − y il | ≥ 1  l = 1,, k i  (3-95) where nl is the vector of KKT multipliers from the solution of Eq. (3-91) at iteration l. This MILP can be derived through a reformulation of the MILP used in Fig. 3-59 with the inactive constraints from Eq. (3-91) dropped. Solution of Eq. (3-95) leads to a weaker lower bound than Eq. (3-94), and consequently, more solutions of the NLP and MILP subproblems are needed to converge to the solution. However, Eq. (3-95) contains only a single continuous variable and far fewer inequality constraints and is much less expensive to solve than Eq. (3-94). Thus, GBD is favored over outer approximation if Eq. (3-91) is relatively inexpensive to solve or solution of Eq. (3-94) is too expensive. The extended cutting plane (ECP) algorithm is complementary to GBD. While the lower bounding problem in Fig. 3-59 remains essentially the same, the continuous variables xk are chosen from the MILP solution and the NLP Eq. (3-91) is replaced by a simple evaluation of the objective and constraint functions. As a result, only MILP problems [Eq. (3-94) plus integer cuts] need to be solved. Consequently, the ECP approach has weaker upper bounds than outer approximation and requires more MILP solutions. It has advantages over outer approximation when the NLP Eq. (3-91) is expensive to solve. The third extension to the outer approximation approach is based on a branch-and-cut algorithm, which solves a continuous linear program at each node of the search tree, and therefore improves the lower bounds while branching on integer variables. BONMIN, a comprehensive MINLP code described in Bonami et al. [“An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs,” Discrete Optimization 5(2): 186–204 (2008)] 3-57 incorporates NLP branch and bound, branch and cut, and outer approximation as options, along with hybrids of these strategies. Additional difficulties arise for the outer approximation algorithm and its GBD, ECP, and branch and cut extensions when either f (x) or g(x) is nonconvex. Under these circumstances, the lower bounding properties resulting from the linearization and formulation of the MILP subproblem are lost, and the MILP solution may actually exclude the solution of Eq. (3-90). Hence, these algorithms need to be applied with care to nonconvex problems. To deal with nonconvexities, one can relax the linearizations in Eq. (3-94) through the introduction of additional deviation variables that can be penalized in the objective function. Alternately, the linearizations in Eq. (3-94) can be replaced by valid underestimating functions, such as those derived for global optimization [e.g., Eq. (3-86)]. However, this requires specific structural knowledge of Eq. (3-90) and may lead to weak lower bounds for the resulting MILP. Finally, the performance of both MILP and MINLP algorithms is strongly dependent on the problem formulations Eq. (3-89) and Eq. (3-90). In particular, the efficiency of the approach is impacted by the lower bounds produced by the relaxation of the binary variables and subsequent solution of the linear program in the branch and bound tree. A number of approaches have been proposed to improve the quality of the lower bounds, including these: • Logic-based methods such as generalized disjunctive programming (GDP) can be used to formulate MINLPs with fewer discrete variables that have tighter relaxations. The imposition of logic-based constraints prevents the generation of unsuitable alternatives, leading to less expensive searches. In addition, constrained logic programming (CLP) methods offer efficient alternatives to MILP solvers for highly combinatorial problems. See Jain and Grossmann, INFORMS Journal of Computing, 13: 258–276 (2001) for more details. • Convex hull formulations of MILPs and MINLPs lead to relaxed problems that have much tighter lower bounds. This leads to the examination of far fewer nodes in the branch and bound tree. See Grossmann and Lee, Comput . Optim . Applic . 26: 83 (2003) for more details. • Reformulation and preprocessing strategies including bound tightening of the variables, coefficient reduction, lifting facets, and special ordered set constraints frequently lead to improved lower bounds and significant performance improvements in mixed integer programming algorithms. See Bixby, R., and E. Rothberg, Annals of Operations Research, 49(1): 37–41 (2007) for more details. A number of efficient codes are available for the solution of MINLPs, including AlphaECP, BARON, BONMIN, DICOPT, MINLP, and SBB. All are available within the GAMS modeling platform. DEVELOPMEnT OF OPTIMIZATIOn MODELS The most important aspect to a successful optimization study is the formulation of the optimization model. These models must reflect the real-world problem so that meaningful optimization results are obtained; they also must satisfy the properties of the problem classes in Fig. 3-53. For instance, NLPs addressed by gradient-based methods need to have functions that are defined in the variable domain and have bounded and continuous first and second derivatives. In mixed integer problems, proper formulations are also needed to yield good lower bounds for efficient search. With increased understanding of optimization methods and the development of efficient and reliable optimization codes, optimization practitioners now focus on the formulation of optimization models that are realistic, well posed, and inexpensive to solve. Finally, convergence properties of NLP, MILP, and MINLP solvers require accurate first (and often second) derivatives from the optimization model. If these contain numerical errors (say, through finite difference approximations), then the performance of these solvers can deteriorate considerably. As a result of these characteristics, modeling platforms are essential for the formulation task. These are classified into two broad areas: optimization modeling platforms and simulation platforms with optimization. Optimization modeling platforms provide general-purpose interfaces for optimization algorithms and remove the need for the user to interface to the solver directly. These platforms allow the general formulation for all problem classes discussed above with direct interfaces to state-of-the-art optimization codes. Three representative platforms are GAMS (General Algebraic Modeling Systems), AMPL (A Mathematical Programming Language), and AIMMS (Advanced Integrated Multidimensional Modeling Software). All three require problem model input via a declarative modeling language and provide exact gradient and hessian information through automatic differentiation strategies. Although it is possible, these platforms were not designed to handle externally added procedural models. As a result, these platforms are best applied on optimization models that can be developed entirely within their modeling framework. Nevertheless, these platforms are 3-58 MATHEMATICS widely used for large-scale research and industrial applications. In addition, the MATLAB platform allows for flexible formulation of optimization models as well, although it currently has only limited capabilities for automatic differentiation and limited optimization solvers. Simulation platforms with optimization are often dedicated, applicationspecific modeling tools to which optimization solvers have been interfaced. These lead to very useful optimization studies, but because they were not originally designed for optimization models, they need to be used with some caution. In particular, most of these platforms do not provide exact derivatives to the optimization solver; often they are approximated through finite differences. In addition, the models themselves are constructed and calculated through numerical procedures, instead of through an open declarative language. Examples of these include widely used process simulators such as Aspen/Plus, PRO/II, and Hysys . Also note that more recent platforms such as Aspen Custom Modeler, GPROMS, and MOSAIC include declarative models and exact first derivatives . Finally, for optimization tools that must be linked to procedural models, reliable and efficient automatic differentiation (AD) tools that provide exact first (often second) derivatives are available that link to models written in C, C++, FORTRAN, Python, and other modeling platforms. Example AD tools include ADIC, ADOL-C, CasADi, CppAD, and TAPENADE. When used with care, these can be applied to existing procedural models and, when linked to modern NLP and MINLP algorithms, can lead to powerful optimization capabilities. STATISTICS References: Box, G. P., J. S. Hunter, and W. G. Hunter, Statistics for Experimenters: Design, Innovation, and Discovery, 2d ed., Wiley, New York, 2005; Cropley, J. B., “Heuristic Approach to Complex Kinetics,” pp. 292–302 in Chemical Reaction Engineering—Houston, ACS Symposium Series 65, American Chemical Society, Washington, D.C., 1978; Schiller, Jr., J. J., R. A. Srinivasan, and M. Spiegel, Schaum’s Outline of Probability and Statistics, 4th ed., McGraw-Hill, New York, 2012; Mendenhall, W., and T. Sincich, Statistics for Engineering and the Sciences, 5th ed., Pearson, Boston, 2006; Moore, D. S., G. P. McCabe, and B. Craig, Introduction to the Practice of Statistics, 8th ed., Freeman, San Francisco, 2014; Montgomery, D. C., and G. C. Runger, Applied Statistics and Probability for Engineers, 6th ed., Wiley, New York, 2013; see also Logan and Wolesensky (2009) in General References and https://cloud.r-project.org/ for Statistics in R. InTRODUCTIOn Statistics represents a body of knowledge that enables one to deal with quantitative data reflecting any degree of uncertainty. There are six basic aspects of applied statistics: 1. Type of data 2. Random variables 3. Models 4. Parameters 5. Sample statistics 6. Characterization of chance occurrences From these can be developed strategies and procedures for dealing with (1) estimation and (2) inferential statistics. The following has been directed more toward inferential statistics because of its broader utility. Detailed illustrations and examples are used throughout to develop basic statistical methodology for dealing with a broad area of applications. If you are new to statistics, look first at the examples and find one that is appropriate to your application. In addition to this material, there are many specialized topics as well as some very subtle areas that have not been discussed. The references should be used for more detailed information. Section 8 discusses the use of statistics in statistical process control (SPC). Type of Data In general, statistics deals with two types of data: counts and measurements. Counts represent the number of discrete outcomes, such as the number of defective parts in a shipment, the number of losttime accidents, and so forth. Measurement data are treated as a continuum. For example, the tensile strength of a synthetic yarn theoretically could be measured to any degree of precision. A subtle aspect associated with count and measurement data is that some types of count data can be dealt with through the application of techniques that have been developed for measurement data alone. This ability is due to the fact that some simplified measurement statistics serve as an excellent approximation for the more tedious count statistics. Random Variables Applied statistics deals with quantitative data. In tossing a fair coin the successive outcomes would tend to be different, with heads and tails occurring randomly over time. Given a long strand of synthetic fiber, the tensile strength of successive samples would tend to vary significantly from sample to sample. Counts and measurements are characterized as random variables, that is, observations which are susceptible to chance. Virtually all quantitative data are susceptible to chance in one way or another. Models Part of the foundation of statistics consists of the mathematical models that characterize an experiment. The models themselves are mathematical ways of describing the probability, or relative likelihood, of observing specified values of random variables. For example, in tossing a coin once, a random variable x could be defined by assigning to x the value 1 for a head and 0 for a tail. Given a fair coin, the probability of observing a head on a toss would be .5, and similarly for a tail. Therefore, the mathematical model governing this experiment can be written as x P(x) 0 1 .5 .5 where P(x) stands for what is called a probability function . This term is reserved for count data, in that probabilities can be defined for particular outcomes. The probability function that has been displayed is a very special case of the more general case, which is called the binomial probability distribution . For measurement data which are considered continuous, the term probability density is used. For example, consider a spinner wheel which conceptually can be thought of as being marked off on the circumference infinitely precisely from 0 up to, but not including, 1. In spinning the wheel, the probability of the wheel’s stopping at a specified marking point at any particular x value, where 0 ≤ x < 1, is 0, for example, stopping at the value x = .5 . For the spinning wheel, the probability density function would be defined by f (x .) = 1 for 0 ≤ x < 1. Graphically, this is shown in Fig. 3-60. The relative probability concept refers to the fact that density reflects the relative likelihood of occurrence; in this case, each number between 0 and 1 is equally likely. For measurement data, probability is defined by the area under the curve between specified limits. A density function always must have a total area of 1. Example For the density of Fig. 3-60 P[0 ≤ x ≤ .4] = .4 P[.2 ≤ x ≤ .9] = .7 P[.6 ≤ x < 1] = .4 and so forth. Since the probability associated with any particular point value is zero, it makes no difference whether the limit point is defined by a closed interval (≤ or ≥) or an open interval (< or >). Many different types of models are used as the foundation for statistical analysis. These models are also referred to as populations. Parameters As a way of characterizing probability functions and densities, certain types of quantities called parameters can be defined. For example, the center of gravity of the distribution is defined to be the population mean, which is designated as m. For the coin toss m = .5, which corresponds to the average value of x; i.e., for one-half of the time x will take on a value 0 and for the other half a value 1. The average would be .5. For the spinning wheel, the average value would also be .5. FIG. 3-60 Density function. STATISTICS Another parameter is called the standard deviation, which is designated as s. The square of the standard deviation is used frequently and is called the variance s2. Basically, the standard deviation is a quantity which measures the spread or dispersion of the distribution from its mean m. If the spread is broad, then the standard deviation will be larger than if it were more constrained. For specified probability and density functions, the respective mean, or expected value E(x), variance Var(x), and standard deviation s are defined by the following: Probability functions (discrete variables and counts) Probability density functions (continuous variables) E ( x ) = µ = ∑ x p( x ) E ( x ) = µ = ∫ x f ( x ) dx x x Var( x ) = σ = ∑ ( x − µ) P ( x ) 2 2 Var( x ) = σ = ∫ ( x − µ)2 f ( x ) dx 2 x x Sample Statistics Many types of sample statistics will be defined. Two very special types are the sample mean, designated as x, and the sample standard deviation, designated as s . These are, by definition, random variables. Parameters such as m and s are not random variables; they are fixed constants corresponding to a probability function or distribution. Example In an experiment, six random numbers (rounded to four decimal places) were observed from the uniform distribution f (x) = 1 for 0 ≤ x < 1: 0.1009, 0.3754, 0.0842, 0.9901, 0.1280, 0.6606 The sample mean corresponds to the arithmetic average of the observations, which will be designated as x1 through x6, where x= 1 n ∑ x i with n = 6 x = 0.3899 n i =1 (3-96) The sample standard deviation s is defined by the computation s= ∑( x i − x )2 n −1 = n ∑ x i2 − (∑ x i )2 n (n − 1) (3-97) In effect, this represents the root of a statistical average of the squares. The divisor quantity n - 1 will be referred to as the degrees of freedom. The sample value of the standard deviation for the data given is .3686. The value of n - 1 is used in the denominator because the deviations from the sample average must total zero, or ∑( x i − x)= 0 Thus knowing n - 1 values of xi - x permits calculation of the nth value of xi - x. The sample mean and sample standard deviation are obtained by using Microsoft Excel with the commands AVERAGE(B2:B7) and STDEV(B2:B7) when the observations are in cells B2 to B7. In effect, the standard deviation quantifies the relative magnitude of the deviation numbers, i.e., a special type of “average” of the distance of points from their center. In statistical theory, it turns out that the corresponding variance quantities s2 have remarkable properties which make possible broad generalities for sample statistics and therefore also their counterparts, the standard deviations. For the corresponding population, the parameter values are m = .50 and s = .2887, which are obtained by calculating the integrals defined above with f (x) = 1 and integrating x from 0 to 1. If, instead of using individual observations only, averages of 6 were reported, then the corresponding population parameter values would be m = .50 and σ x = σ / 6 = .1179. The corresponding variance for an average will be written occasionally as Var (x) = var (x)/n . In effect, the variance of an average is inversely proportional to the sample size n, which reflects the fact that sample averages will tend to cluster much more closely than individual observations. This is illustrated in greater detail under Measurement Data and Sampling Densities. Characterization of Chance Occurrences To deal with a broad area of statistical applications, it is necessary to characterize the way in which random variables will vary by chance alone. The basic foundation for this characteristic is laid through a density called the gaussian, or normal, distribution. 3-59 Determining the area under the normal curve is a very tedious procedure. However, by standardizing a random variable that is normally distributed, it is possible to relate all normally distributed random variables to one table. The standardization is defined by the identity z = (x - m)/s, where z is called the unit normal. Further, it is possible to standardize the sampling distribution of averages x by the identity z = ( x − µ)/(σ / n ). A remarkable property of the normal distribution is that, almost regardless of the distribution of x, sample averages x will approach the gaussian distribution as n gets large. Even for relatively small values of n, of about 10, the approximation in most cases is quite close. For example, sample averages of size 10 from the uniform distribution will have essentially a gaussian distribution. Also, in many applications involving count data, the normal distribution can be used as a close approximation. In particular, the approximation is quite close for the binomial distribution within certain guidelines. The normal probability distribution function can be obtained in Microsoft Excel by using the NORM.DIST function and supplying the desired mean and standard deviation. The cumulative value can also be determined. In the MATLAB Statistics Toolbox the corresponding command is normcdf(x, m, s). EnUMERATIOn DATA AnD PROBABILITY DISTRIBUTIOnS Introduction Many types of statistical applications are characterized by enumeration data in the form of counts. Examples are the number of losttime accidents in a plant, the number of defective items in a sample, and the number of items in a sample that fall within several specified categories. The sampling distribution of count data can be characterized through probability distributions. In many cases, count data are appropriately interpreted through their corresponding distributions. However, in other situations analysis is greatly facilitated through distributions which have been developed for measurement data. Examples of each will be illustrated in the following subsections. Binomial Probability Distribution Nature Consider an experiment in which each outcome is classified into one of two categories, one of which will be defined as a success and the other as a failure. Given that the probability of success p is constant from trial to trial, then the probability of observing a specified number of successes x in n trials is defined by the binomial distribution. The sequence of outcomes is called a Bernoulli process . Nomenclature Let p̂ = x/n be the proportion of successes in n trials. Probability Law n x p ( x ) = p   =   p x (1 − p )n− x x = 0,1, 2, , n  n   x n n! where   =  x  n !(n − x )! Properties E ( x ) = np E ( pˆ ) = p Var( x ) = np (1 − p ) Var( pˆ ) = p (1 − p )/n Example In three tosses of a coin, what is the probability of seeing three heads? This problem uses the binomial probability distribution because each toss is independent of the previous ones. Assuming the coins are “fair” and the probability of heads is ½, then the probability of 3 heads in 3 tosses is 3 P= 0 3!  1   1  1     = 3!0!  2   2  8 Likewise, the probability of 2 heads and 1 tail in 3 tosses is 2 P= 1 3!  1   1  3     = 2!1!  2   2  8 Geometric Probability Distribution Nature Consider an experiment in which each outcome is classified into one of two categories, one of which will be defined as a success and the other as a failure. Given that the probability of success p is constant from 3-60 MATHEMATICS trial to trial, then the probability of observing the first success on the xth trial is defined by the geometric distribution. Probability Law P(x) = p(1 - p)x -1 x = 1, 2, 3, … Properties Example A commercial item is sold in a retail outlet as a unit product. In the past, sales have averaged 10 units per month with no seasonal variation. The retail outlet must order replacement items 2 months in advance. If the outlet starts the next 2-month period with 25 items on hand, what is the probability that it will run out of stock before the end of the second month? Given a = 10/month, then l = 10 × 2 = 20 for the total period of 2 months: E(x) = 1/p Var (x) = (1 - p)/p2 If the event is described as y = x - 1, that is, y is the number of failures before the first success, then E( y) = (1 - p)/p Var (x) = (1 - p)/p2 Example Let y be the number of tosses of a die prior to the toss in which a 2 or 3 first appears. Since the probability of a 2 or 3 in a single toss is 1/3, the probability function of x and the expected value is E( y ) = 1 − p 1 − 1/3 = =2 1/3 p That is, you will (on average) do two tosses before you get a 2 or 3. Likewise, the expected value of getting your first 2 or 3 on the xth toss is E (x ) = λ x −λ e x! x = 0,1, 2,  Properties E(x) = l Var(x) = l Example The number of broken filaments in a thread line has been averaging .015 per yard. What is the probability of observing exactly two broken filaments in the next 100 yd? In this example, a = .015/yd and L = 100 yd; therefore l = (.015)(100) = 1.5: P ( x = 2) = 25 26 0 20 25  20 x  20 20 2 ∑ x ! e -20 = e -20 1 + 1 + 2! + + 25!  0 = 0.888 25 Therefore P(x ≥ 26) = .112 or roughly an 11 percent chance of a stockout. Hypergeometric Probability Distribution Nature In an experiment in which one samples from a relatively small group of items, each of which is classified in one of two categories, A or B, the hypergeometric distribution can be defined. One example is the probability of drawing two red and two black cards from a deck of cards. The hypergeometric distribution is the analog of the binomial distribution when successive trials are not independent, i.e., when the total group of items is not infinite. This happens when the drawn items are not replaced. 1 1 = =3 p 1/3 The difference between these is simply in the first case you are counting the tosses before the “success” and in the second case you are including the toss giving the “success.” Poisson Probability Distribution Nature The Poisson probability distribution is used to assess the number of events that will occur in a span of time, regardless of when the event occurred last, provided you know the average rate of events and the events are independent of the time since the last event. For example, in monitoring a moving thread line, one criterion of quality would be the frequency of broken filaments. These can be identified as they occur through the thread line by a broken filament detector mounted adjacent to the thread line. In this context, the random occurrences of broken filaments can be modeled by the Poisson distribution. This is called a Poisson process and corresponds to a probabilistic description of the frequency of defects or, in general, what are called arrivals at points on a continuous line or in time. Other examples include these: 1. The number of cars (arrivals) that pass a point on a high-speed highway between 10:00 and 11:00 a.m. on Wednesdays 2. The number of customers arriving at a bank between 10:00 and 10:10 a.m. 3. The number of telephone calls received through a switchboard between 9:00 and 10:00 a.m. 4. The number of insurance claims that are filed each week 5. The number of spinning machines that break down during 1 day at a large plant. Nomenclature x = total number of arrivals in a total length L or total period T a = average rate of arrivals for a unit length or unit time l = aL = expected or average number of arrivals for the total length L l = aT = expected or average number of arrivals for the total time T Probability Law Given that a is constant for the total length L or period T, the probability of observing x arrivals in some period L or T is given by P (x ) = ∞ P ( x ≥ 26) = ∑ p ( x ) = 1 − ∑ p ( x ) (1.5)2 −1.5 e = .2510 2! Population Sample Category A X x Category B N-X n-x N n Total Probability Law  N − X X  N / P (x ) =   n − x   x   n  nX N X N − X N −n var( x ) = n N N N −1 E (x ) = Example What is the probability that an appointed special committee of 4 has no female members when the members are randomly selected from a candidate group of 10 males and 7 females? Here N = 17, X = 7, n = 4, x = 0, and  10   7   4   0  P ( x = 0) = = .0882  17   4  This distribution can be used in Texas Hold’em poker. See http: en.wikipedia. org/wiki/Hypergeometric-distribution. To compute these probabilities in Microsoft Excel, put the value of x in cell B2, say, and use the functions Binomial distribution: = BINOM.DIST(B2, n, p, 0) Poisson distribution: = POISSON.DIST(B2, l, 0) Hypergeometric distribution: = HYPGEOM.DIST(B2, n, X, N, 1) The factorial function is FACT(n) in Microsoft Excel and factorial(n) in MATLAB. Be sure that x is an integer. Conditional Probability It is useful to predict the probability of one event, given that a second event has already occurred. For example, suppose you draw a card from a deck of 52 cards, half red and half black (event A). The probability of the first card being red is 26/52 = 1/2. But suppose the question is: What is the probability that the first two cards drawn are red (without replacing the first card)? In the second draw (event B) there are STATISTICS only 25 red cards of 51 total cards, so that the probability of drawing a red card is 25/51. Then the probability of drawing two red cards is 1 25 25 P(AB) =     =  2   51  102 3-61 may be described by the t distribution. The chi-square test allows us to find whether an observed frequency of observation differs significantly from those expected from a model. Finally, the F test is used to compare variances and their properties. While tables exist to compute the various functions, here the commands will be given to compute them using Microsoft Excel. Similar commands are available in MATLAB and Mathematica. This is sometimes written as P(A  B) i.e., the probability of both events A and B occurring. The P(B|A) is called the conditional probability of event B, given that event A has occurred. Conditional probabilities satisfy the general equation P (B|A) = P (AB) if P (A) ≠ 0 P (A) which is a restatement of the numerical equation in a different form, P(B|A) = 25/51, P(A) = 1/2, and P(AB) = 25/102. Likewise P (A|B) = P (AB) if P (B) ≠ 0 P (B) Microsoft Excel command Designated symbol Variable Sampling distribution of z NORM.DIST(X, m, s, 0) z x −µ σ n Averages TINV(α, df) t x −µ s n Averages when s is unknown* CHIINV(α, df) c2 (s2/s2)(df) Variances* FINV(α, df1, df2) 2 1 s /s F 2 2 Ratio of two independent sample variances* The probabilities satisfy Bayes’ theorem P (A|B) = *When sampling from a gaussian distribution. P (B|A) P (A) P (B|A) P (A) + P (B|A c ) P (A c ) where Ac is the complement of A, that is, A did not occur. Example The table below gives the numbers of Bachelor’s degrees in engineering in the United States in 2013–2014. Given that a graduate is a woman, what is the probability that she obtained a degree in chemical engineering, biological engineering, or biomedical engineering? Normal Distribution The most common probability density function is the gaussian or normal probability function. This function describes a bell-shaped curve that indicates the probability of a measurement deviating from the average of many measurements. The formula is f ( x , µ, σ) = Aerospace Biological/Biomedical Chemical Civil Civil/Environ. Electrical Mechanical Materials Industrial subtotal Other Total Observations* NORM.DIST(X, m, s, 0) x −µ σ Total Women 3695 510 13.8 6150 8110 12333 1893 14088 23675 1440 4877 76261 22912 99173 2573 2944 2393 573 1927 3196 379 1541 16036 3303 19339 41.8 36.3 19.4 30.3 13.7 13.5 26.3 31.6 21.0 14.4 19.5 1  ( x − µ)2  exp  − 2π σ 2 σ 2   % Women The curve is typically scaled so that the mean µ is 0; the symbol s is the standard deviation, see Fig. 3-61. The area under the curve is 1.0. The Microsoft Excel function NORM.DIST(x, m, s, 1) gives the probability that a sample measurement is less than x when the measurements have a mean of µ and a standard deviation of s, that is, the integral from negative infinity to x. For example, NORM.DIST(1, 0, 1, 1) (mean 0 and standard deviation of 1) gives the value .8413. Thus, the probability of a measurement x being less than 1 (i.e., the mean plus 1 standard deviation) is .8413. NORM.DIST(-1, 0, 1, 1) gives the value .1587 for the probability of a measurement being less than -1, or less than the mean minus 1 standard deviation. Thus, the probability that x is between +1 standard deviation and -1 standard deviation is .8413 .1587 = .6827. The probability of a measurement falling within 2 standard The data are from the American Society of Engineering Education, ASEE Report 11-47.pdf, Brian L. Yoder, accessed July 14, 2015. http://www.asee .org/papers-and-publications/publications/college-profiles/14Engineering bytheNumbersPart1.pdf Define event A as being a female graduate, B as graduating in chemical engineering (male or female), C as graduating in biological/biomedical engineering (male or female). We thus have P(A) = 19339/99173 = 0.1950, P (B) = 8110/99173 = 0.0818 P(C) = 6150/99173 = 0.0620 34.13% Also P (AB) = 2944/99173 = 0.02968. We want P(B|A) which is P(AB)/P(A) = 0.02968/0.19500 = 0.152. This should be the same as 2944/19339, which it is. Likewise P(C|A) = 0.133. Since events B and C are independent, the probability of a woman graduate being in one of these fields is the sum of these, or 0.285. This is considerably higher than the probability of a graduate being a woman, .195; or if one looks just at the other engineering fields, the probability of a woman graduate being in them is only .163. MEASUREMEnT DATA AnD SAMPLInG DEnSITIES This section describes the probability of measurement data. If the number of samples is large, the data often form a normal distribution, so that is discussed first. If the sample size is smaller (somewhat less than 30), the data 34.13% 13.60% z = –3 2.14% z = –2 x = µ – 3σ x = µ – 2σ FIG. 3-61 13.60% z = –1 z=0 z=1 2.14% z=2 z=3 x=µ–σ x=µ x=µ+σ x = µ + 2σ x = µ + 3σ Normal probability distribution. 3-62 MATHEMATICS deviations of the mean is .9545, and the probability of a measurement falling with 3 standard deviations of the mean is 0.9975. In the Excel formulas, the last 1 is a logical variable and can be replaced by TRUE ( for 1). The standard normal variable is defined as 0.3 x −µ σ t for df = 10 Then z is a normal random variable with a mean of 0 and a standard deviation of 1. Likewise, x = m + sz. Example Suppose one measures the concentration of some product coming off a production line. After 25 measurements one computes the average of 5.2 (in some units) with a variance of .15, using Eqs. (3-96) and (3-97). One believes the variation is randomly distributed so that it would be modeled by the normal distribution. What is the probability that a product will have the concentration between 5.0 and 5.4? The first method uses the data as they come. Calculate NORM.DIST(5.4, 5.2, .15, 1) = .90879 to get the probability that the concentration is below 5.4 and NORM.DIST(5.0, 5.2, .15, 1) = .09121 to get the probability that the concentration is below 5.0. The probability that the concentration is between 5.0 and 5.4 is then .90879 - .09121 = .81758, or 82 percent. An alternative solution is to calculate the standard normal variables. z= 5.4 − 5.2 = 1.33333 0.15 and z= 5.0 − 5.2 = −1.33333 0.15 Then NORM.DIST(1.33333, 0, 1, 1) - NORM.DIST(-1.33333, 0, 1, 1) = .90879 - .09121 = .81758. The central limit theorem says that a set of random variables approaches a normal distribution as n, the number of measurements, goes to infinity. In addition, averages turn out to vary less than individual measurements. Suppose one calculates the average of n concentrations this week, next week, etc. The corresponding relationship for the Z scale is z= x −µ n σ or x =µ+ σ z n The Microsoft Excel command CONFIDENCE(α, s, n) gives the confidence interval about the mean for a sample size n, where s is the standard deviation and α is the confidence level. Example Suppose one makes measurements of the concentration several times a week, and the average and variance of individual measurements are as given above. For a variance of 0.15, at a 95 percent confidence level what is the probable range of measurements? The formula CONFIDENCE(0.05, 0.15, 100) = 0.0293. Thus, with 95 percent confidence the weekly averages will be 5.2 ± 0.029 or between 4.91 and 5.49. t Distribution of Averages The normal curve relies on a knowledge of s, or in special cases, when it is unknown, s can be used with the normal curve as an approximation when n > 30. For example, with n > 30 the intervals ± s and ± 2s will include roughly 68 and 95 percent of the sample values, respectively, when the distribution is normal. In applications, sample sizes are usually small and s is unknown. In these cases, the t distribution can be used where t = ( x − µ)( s / n ) x = µ + ts n or See Fig. 3-62. The t distribution is also symmetric and centered at zero. It is said to be robust in the sense that even when the individual observations x are not normally distributed, sample averages of x have distributions that tend toward normality as n gets large. Even for small n of 5 through 10, the approximation is usually relatively accurate. It is sometimes called the Student’s t distribution. Since the t distribution relies on the sample standard deviation s, the resultant distribution will differ according to the sample size n . To designate this difference, the respective distributions are classified according to what are called the degrees of freedom and abbreviated as df. In simple problems, the df are just the sample size minus 1. In general, degrees of freedom are the number of quantities minus the number of constraints. The mathematical definition of the t distribution is t A (t , df ) = Standard normal  x2  1  1 +  ∫ df 1 df df 1/2 B  ,  − t 2 2  df +1 2 dx f(t) z= 0.4 0.2 t for df = 1 0.1 0.0 –4 FIG. 3-62 –3 –2 –1 0 t 1 2 3 4 The t distribution function. where B is the incomplete beta function. A(t, df) is the probability, for degrees of freedom df, that a certain statistic t (measuring the observed difference of means) would be smaller than the observed value if the means were in fact the same. Limiting values are A(0, df) = 0 and A(∞, df) = 1. The Microsoft Excel function TDIST(X, df,1) gives the right-tail probability, and TDIST(X, df, 2) gives twice that. The probability that t ≤ X is 1 - TDIST(X, df, 1) when X ≥ 0 and TDIST(abs(X), df, 1) when X < 0. The probability that -X ≤ t ≤ + X is 1 - TDIST(X, df, 2). To find the limits for a given confidence level, one uses the Microsoft Excel function TINV(α, df). For a two-tailed distribution, to achieve 95 percent confidence, the two tails represent 2.5 percent each, and one uses α = 0.05. Example For a sample size n = 5, what values of t define a midarea of 90 percent? For 4 df using Microsoft Excel, TINV(.1, 4) = 2.132. Thus, P[-2.132 ≤ t ≤ 2.132] = .90. Also, TDIST(2.132, 4, 2) = 0.10 and 1 - TDIST(2.1