The Properties of Gases
`and Liquids
`
`Robert C. Reid
`
`Professor of Chemical Engineering
`Massachusetts Institute of Technoiogy
`
`John M. Prausnitz
`
`Professor of Chemical Engineering
`University of California at Berkeley
`
`Bruce E. Poling
`Professor of Chemical Engineering
`
`University of Missouri at Fiolla
`
`Fourth Edition
`
`MoGraw-Hill Book Company
`
`New York St. Louis San Francisco Auckland Bogota
`Hamburg London Madrid Mexico
`Milan Montreal New Delhi Panama
`
`Paris Sao Paulo Singapore
`Sydney Tokyo Toronto
`1 of 7
`
`Arke
`
`Arkema Exhibit 1137
`
`1 of 7
`
`

`
`Library of Congress Cataloging—in—Publication Data
`
`Reid, Robert C.
`The properties of gases and liquids.
`
`Includes bibliographies and index.
`1. Gases
`2. Liquids.
`I. Prausnitz, J. M.
`II. Poling, Bruce E.
`III. Title.
`TP2-42.R4
`1987
`660’.042
`
`86~21358
`
`ISBN 0—07—051799-1
`
`Copyright © 1987, 1977, 1966, 1958 by McGraw—Hill, Inc. Printed in the
`United States of America. 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 data base or retrieval system, without the prior written
`permission of the publisher.
`
`Copyright renewed 1986 by Robert C. Reid and Virginia Sherwood.
`
`234567890 DOC/DOC 89321098
`
`ISBN D-D?-iJ5]i'?‘=I“i-1.
`
`The editors for this book were Betty Sun and Galen H. Fleck,
`the designer was Naomi Auerbach, and the
`production supervisor was Thomas G. Kowalczyk.
`It was set in Century Schoolbook by University Graphics, Inc.
`
`Printed and bound by R. R. Donnelley & Sons Company.
`
`2of7
`
`2 of 7
`
`

`
`
`
`Contents
`
`Preface
`
`ix
`
`1. The Estimation of Physical Properties
`1-1
`Introduction
`1
`1-2
`Estimation of Properties
`1-3
`Types of Estimation
`4
`1-4 Organization of the Book
`References
`10
`
`8
`
`3
`
`2. Pure Component Constants
`2-1
`Scope
`11
`2-2
`Critical Properties
`2-3 Acentric Factor
`
`23
`
`12
`
`2-4
`2-5
`
`Boiling and Freezing Points
`Dipole Moments
`26
`Notation
`26
`References
`
`2?
`
`25
`
`3. Pressure-Volume-Temperature Relations of Pure Gases
`and Liquids
`29
`3-1
`Scope
`3-2
`Two-Parameter Correlations
`3-3
`Three-Parameter Correlations
`
`29
`33
`
`11
`
`29
`
`35
`
`Analytical Equations of State
`3-4
`Virial Equation
`35
`3-5
`-12
`Cubic Equations of State
`3-6
`3-7 Generalized Benedict-Webb-Rubin Equations
`3-8 Discussion of Equations of State
`50
`52
`3-9
`PVT Properties of Liquids—~—Genera| Considerations
`3-10 Estimation of the Liquid Molar Volume at the Normal Boiling
`Point
`52
`
`47
`
`3-11 Estimation of Liquid Densities
`Notation
`69
`References
`
`69
`
`55
`
`3of7
`
`3 of 7
`
`

`
`vi
`
`Contents
`
`4. Volumetric Properties of Mixtures
`4-1
`Scope
`74
`75
`4-2 Mixing Rules—General Discussion
`4-3
`Corresponding States: The Pseudocritical Method
`4-4
`Second Virial Coeflicients for Mixtures
`79
`
`75
`
`4-5 Mixing Rules for Redlich-Kwong-Type Equations of State
`4-6 Mixing Rules for the Lee-Kesler Equation
`34
`4-7
`Interaction Parameters—General Discussion
`
`85
`
`82
`
`Recent Developments in Mixing Rules
`4-8
`4-9 Densities of Liquid Mixtures
`89
`Notation
`92
`References
`
`93
`
`97
`
`5. Thermodynamic Properties
`5-1
`Scope
`95
`5-2
`Fundamental Thermodynamic Principles
`5-3 Departure Functions
`97
`5-4
`Evaluation of Departure Functions
`5-5
`Heat Capacities of Real Gases
`5-6
`True Critical Points of Mixtures
`
`121
`121
`
`101
`
`95
`
`136
`Heat Capacities of Liquids
`5-?
`5-8 Vapor Phase Fugacity of a Component in a Mixture
`Notation
`146
`References
`
`147
`
`143
`
`74
`
`95
`
`150
`
`6. Thermodynamic Properties of Ideal Gases
`6-1
`Scope and Definitions
`150
`6-2
`Estimation Methods
`152
`6-3 Method of Joback
`154
`6-4 Method of Yoneda
`157
`6-5 Method of Thinh et al.
`6-6 Method of Benson
`173
`6-7 Method of Cardozo
`190
`6-8 Discussion and Recommendations
`Notation
`201
`References
`
`167
`
`191
`
`203
`
`7. Vapor Pressures and Enthalpies of Vaporization of Pure
`Fluids
`
`205
`
`205
`Scope
`7-1
`Theory and Corresponding States Correlations
`7-2
`7-3 Antoine Vapor Pressure Equation
`209
`209
`7-4 Gomez-Thodos Vapor Pressure Equation
`212
`7-5
`Vapor Pressure Estimation with Two Reference Fluids
`214
`7-6
`Correlation and Extrapolation of Vapor Pressure Data
`7-7 Discussion of and Recommendations tor Vapor Pressure
`Estimation and Correlation
`216
`
`205
`
`218
`Enthalpy oi Vaporization of Pure Compounds
`7-8
`Estimation of AH, from the Law of Corresponding States
`7-9
`7-10 Estimation of AH, from Vapor Pressure Equations
`222
`7-11 AH, at the Normal Boiling Point
`225
`7-12 Variation of AH, with Temperature
`228
`
`219
`
`4of7
`
`4 of 7
`
`

`
`Contents
`
`V3;
`
`7-13 Discussion and Recommendations for Enthalpy of
`vaporization
`230
`
`231
`7-14 Enthalpy of Fusion
`7-15 Enthalpy of Sublimation; Vapor Pressures of Solids
`Notation
`236
`References
`
`238
`
`232
`
`3. Fluid Phase Equilibria in Multicomponent Systems
`8-1
`Scope
`241
`8-2
`Thermodynamics of Vapor-Liquid Equilibria
`8-3
`Fugacity of a Pure Liquid
`249
`250
`8-4
`Simplifications in the Vapor—Liquid Equilibrium Relation
`3-5
`Activity Coefficients; Gibbs-Duhem Equation and Excess Gibbs
`Energy
`251
`I
`259
`Calculation of Binary Vapor-Liquid Equilibria
`Effect of Temperature on Vapor-Liquid Equilibria
`Binary Vapor-Liquid Equilibria: Examples
`264
`Multicomponent Vapor-Liquid Equilibria
`273
`Estimation of Activity Coefficients
`283
`Solubilities of Gases in Liquids
`332
`Vapor-Liquid Equilibria at High Pressures
`Liquid-Liquid Equilibria
`357
`Phase Equilibria in Polymer Solutions
`Solubilities of Solids in Liquids
`372
`Aqueous Solutions of Electrolytes
`Concluding Remarks
`380
`Notation
`381
`References
`
`247
`
`262
`
`337
`
`368
`
`375
`
`"'4O'3U'l£hlJI\3-l8‘Dm-do‘
`..L_L.L.L...L_|._L
`
`241
`
`388
`
`
`
`384
`
`9. Viscosity
`398
`9-1
`Scope
`388
`9-2
`Definitions of Units of Viscosity
`389
`9-3
`Theory of Gas Transport Properties
`392
`9-4
`Estimation of Low-Pressure Gas Viscosity
`9-5 Viscosities of Gas Mixtures at Low Pressures
`
`404
`
`417
`
`Effect of Pressure on the Viscosity of Pure Gases
`9-6
`Viscosity of Gas Mixtures at High Pressures
`431
`9-7
`Liquid Viscosity
`433
`9-8
`436
`Effect of High Pressure on Liquid Viscosity
`9-9
`439
`9-10 Effect of Temperature on Liquid Viscosity
`456
`9-11 Estimation of Low-Temperature Liquid Viscosity
`9-12 Estimation of Liquid Viscosity at High Temperatures
`9-13 Liquid Mixture Viscosity
`473
`Notation
`433
`References
`
`485
`
`471
`
`10. Thermal Conductivity
`10-1
`Scope
`491
`492
`10-2
`Theory of Thermal Conductivity
`493
`10-3
`Thermal conductivities of Polyatomic Gases
`10-4
`Effect of Temperature on the Low-Pressure Thermal
`Conductivities of Gases
`514
`
`491
`
`5of7
`
`5 of 7
`
`

`
`Pure Component Constants
`
`23
`
`2-3 Acentric Factor
`one of the more common pure component constants is the acentric factor
`[38 39], which is defined as
`
`{-01 -—log Pup, (at T, = 0.7) — 1.000
`
`(2—3.1)
`
`To obtain values of co, the reduced vapor pressure (P, = P/PC) at T, =
`77/1‘, = 0.7 is required.
`As originally proposed, an represented the acentricity or nonsphericity
`of a molecule. For monatomic gases, to is, therefore, essentially zero. For
`methane,
`it is still very small. However, for higher—molecular—weight
`hydrocarbons, to increases. It also rises with polarity. At present, no is very
`widely used as a parameter which in some manner is supposed to measure
`the complexity of a molecule with respect to both the geometry and polar-
`ity, but the large values of to for some polar compounds (co > 0.4) are not
`meaningful in the context of the original meaning of this property.
`We show in Appendix A the acentric factor for many materials. The
`values were obtained, in most cases, from experimental data on T,, P,.,
`
`and vapor pressures.
`If acentric factors are needed for a material not shown in Appendix A,
`the usual technique is to locate (or estimate) the critical constants T, and
`P, and then determine the vapor pressure at T, = 0.7. This latter esti-
`mation would normally be made by using one of the reduced vapor pres-
`sure correlations given later in Chap. 7. As an example, if the vapor pres-
`sure correlation chosen were
`
`log Pup = A + 51
`
`(2-32)
`
`with A and B found, say, from the sets (T,,, P,; Tb, P = 1 atm), then
`
`(or:
`
`--CJIICA-.'J
`
`G
`
`1-8
`
`log P, — 1
`
`(2—3.3)
`
`where P,_., in this case, must be expressed in atmospheres and 8 = Tb/Tc.
`Similarly, if the Lee—Kesler vapor pressure relations (7-26) to (7-28)
`were used,
`
`or = —ln P, — 5.97214 + 6.096488“ + 1.28862 ln e - 0.1693-4795
`H
`
`"Cb
`
`15.2518 — 15.68759“ — 13.4721 ln 9 + 0.4357795
`
`where
`
`6of7
`
`(2-3.4)
`
`6 of 7
`
`

`
`24
`
`Properties of Gases and Liquids
`
`(2—3.4)
`and P, is in atmospheres. Lee and Kesler [23] report that Eq.
`yields values of to very close to those selected by Passut and Danner [36]
`and Henry and Danner [16] in their critical reviews.
`
`Example 2-4 Estimate the acentric factor of isopropylbenzene by using Eqs.
`(2-3.3) and (2-3.4). The accepted value is 0.326.
`
`solution From Appendix A, 7",. = 631.1 K, Tb = 425.6 K, P, = 32.1 bar = 31.7
`atm. Thus, 0 = (425.6/631.1) —- 0.674. With Eq. (2—3.3),
`
`0.674
`3
`w= 73:1 _0'674l0g3l.7 -- 1
`= 0.330
`
`Using Eq. (23.4),
`
`or = —ln (31.7) — 5.92714 -+ (6.09648)(0.674]'
`
`I + (1.28-862) ln (0.674)
`
`~(0.169347)(O.6’?4)5
`
`= —o.ss59
`
`B = 15.2518 ** {l5.6875)(0.674}"' — (13.4/721) ln (0.674) + (0.4357'?}(0.674)6
`= -2.662
`
`to = 5 = _0'8669 = 0.326
`5
`-2.662
`
`In many instances in the literature, one finds to related to Z, by
`
`P V
`Z, = RCT: = 0.291 - 0.08009
`
`(2-3.5)
`
`This equation results from applying a PVT correlation that employs 0.: at
`the critical point, where Z = Zc. Equation (23.5) is only very approxi-
`mate, as the reader can readily show from the values in Appendix A.
`In other recent papers dealing with the acentric factor, Nath [32]
`relates a: to the enthalpy of vaporization and to the reduced temperature;
`Hoshino et al. [17] propose a group contribution method to estimate to
`that is applicable to saturated hydrocarbons.
`the
`the years,
`Chappelear
`[9] makes an observation that, over
`“accepted” values of the acentric factor may change due to new vapor
`pressure data or critical constants. However, if one is using a correlation
`that was developed from earlier values of cu, then these acentric factors
`should be employed and not the newer, updated values. She notes the
`problem of carbon dioxide in particular. In Appendix A, we show co =
`0.225; others have quoted a value of 0.267 [35]. The differences result from
`the extrapolation technique used to extend the liquid region past the
`freezing point to a reduced temperature of 0.7. Neither co = 0.225 nor 0:
`= 0.267 can be considered a firm value, but if one were to use a correlation
`such as the Peng-Robinson equation of state [37], the acentric factor
`value of CO2 should be 0.225, since that was the value used by Peng and
`Robinson to develop their correlation.
`
`7of7
`
`7 of 7