properties of gases and liquids

THEPROPERTIESOF
GASESANDLIQUIDS
Bruce E. Poling
Professor of Chemical Engineering
University of Toledo
John M. Prausnitz
Professor of Chemical Engineering
University of California at Berkeley
John P. O’Connell
Professor of Chemical Engineering
University of Virginia
Fifth Edition
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iii
CONTENTS
Preface vii
Chapter 1 The Estimation of Physical Properties 1.1
1-1 Introduction / 1.1
1-2 Estimation of Properties / 1.3
1-3 Types of Estimation / 1.3
1-4 Organization of the Book / 1.6
Chapter 2 Pure Component Constants 2.1
2-1 Scope / 2.1
2-2 Vapor-Liquid Critical Properties / 2.2
2-3 Acentric Factor / 2.23
2-4 Boiling and Freezing Points / 2.26
2-5 Discussion of Estimation Methods for Pure Component Constants / 2.33
2-6 Dipole Moments / 2.34
2-7 Availability of Data and Computer Software / 2.35
Chapter 3 Thermodynamic Properties of Ideal Gases 3.1
3-1 Scope and Definitions / 3.1
3-2 Estimation Methods / 3.5
3-3 Method of Joback / 3.6
3-4 Method of Constantinou and Gani (CG) / 3.8
3-5 Method of Benson [1968; 1969] / 3.14
3-6 Discussion and Recommendations / 3.46
3-7 Heat of Combustion / 3.47
Chapter 4 Pressure-Volume-Temperature Relationships of Pure
Gases and Liquids 4.1
4-1 Scope / 4.1
4-2 Introduction to Volumetric Properties / 4.1

4-3 Corresponding States Principle / 4.5
4-4 Equations of State / 4.8
4-5 Virial Equation of State / 4.11
4-6 Analytical Equations of State / 4.17
4-7 Nonanalytic Equations of State / 4.25
4-8 Discussion of Equations of State / 4.31
4-9 PVT Properties of Liquids—General Considerations / 4.32
For more information about this title, click here
iv CONTENTS
4-10 Estimation of the Liquid Molar Volume at the Normal Boiling Point / 4.33
4-11 Saturated Liquid Densities as a Function of Temperature / 4.35
4-12 Compressed Liquid Densities / 4.43
Chapter 5 Pressure-Volume-Temperature Relationships of Mixtures 5.1
5-1 Scope / 5.1
5-2 Mixture Properties—General Discussion / 5.2
5-3 Corresponding States Principle (CSP): The Pseudocritical Method / 5.5
5-4 Virial Equations of State for Mixtures / 5.8
5-5 Analytical Equations of State for Mixtures / 5.12
5-6 Nonanalytic Equations of State for Mixtures / 5.18
5-7 Discussion of Mixture Equations of State / 5.22
5-8 Densities of Liquid Mixtures at Their Bubble Point / 5.23
5-9 Densities of Compressed Liquid Mixtures / 5.26
Chapter 6 Thermodynamic Properties of Pure Components
and Mixtures 6.1
6-1 Scope / 6.1
6-2 Fundamental Thermodynamic Relationships for Pure Components / 6.1
6-3 Departure Functions for Thermodynamic Properties / 6.4
6-4 Evaluation of Departure Functions for Equations of State / 6.6
6-5 Heat Capacities of Real Gases / 6.16
6-6 Heat Capacities of Liquids / 6.17

6-7 Partial Properties and Fugacities of Components in Mixtures / 6.26
6-8 True Critical Points of Mixtures / 6.30
Chapter 7 Vapor Pressures and Enthalpies of Vaporization of
Pure Fluids 7.1
7-1 Scope / 7.1
7-2 Theory / 7.1
7-3 Correlation and Extrapolation of Vapor-Pressure Data / 7.3
7-4 Ambrose-Walton Corresponding-States Method / 7.7
7-5 Riedel Corresponding-States Method / 7.9
7-6 Discussion and Recommendations for Vapor-Pressure Estimation and
Correlation / 7.11
7-7 Enthalpy of Vaporization of Pure Compounds / 7.13
7-8 Estimation of
⌬H
v
from Vapor-Pressure Equations / 7.14
7-9 Estimation of
⌬H
v
from the Law of Corresponding States / 7.16
7-10
⌬H
v
at the Normal Boiling Point / 7.19
7-11 Variation of
⌬H
v
with Temperature / 7.23
7-12 Discussion and Recommendations for Enthalpy of Vaporization / 7.24
7-13 Enthalpy of Fusion / 7.25

7-14 Enthalpy of Sublimation; Vapor Pressures of Solids / 7.28
Chapter 8 Fluid Phase Equilibria in Multicomponent Systems 8.1
8-1 Scope / 8.1
8-2 Thermodynamics of Vapor-Liquid Equilibria / 8.9
CONTENTS v
8-3 Fugacity of a Pure Liquid / 8.11
8-4 Simplifications in the Vapor-Liquid Equilibrium Relation / 8.12
8-5 Activity Coefficients; Gibbs-Duham Equation and Excess Gibbs Energy / 8.12
8-6 Calculation of Low-Pressure Binary Vapor-Liquid Equilibria with Activity
Coefficients / 8.19
8-7 Effect of Temperature on Low-Pressure Vapor-Liquid Equilibria / 8.22
8-8 Binary Vapor-Liquid Equilibria: Low-Pressure Examples / 8.23
8-9 Multicomponent Vapor-Liquid Equilibria at Low Pressure / 8.32
8-10 Determination of Activity Coefficients / 8.42
8-11 Phase Equilibrium with Henry’s Law / 8.111
8-12 Vapor-Liquid Equilibria with Equations of State / 8.120
8-13 Solubilities of Solids in High-Pressure Gases / 8.158
8-14 Liquid-Liquid Equilibria / 8.159
8-15 Phase Equilibria in Polymer Solutions / 8.177
8-16 Solubilities of Solids in Liquids / 8.180
8-17 Aqueous Solutions of Electrolytes / 8.191
8-18 Concluding Remarks / 8.193
Chapter 9 Viscosity 9.1
9-1 Scope / 9.1
9-2 Definitions of Units of Viscosity / 9.1
9-3 Theory of Gas Transport Properties / 9.2
9-4 Estimation of Low-Pressure Gas Viscosity / 9.4
9-5 Viscosities of Gas Mixtures at Low Pressures / 9.15
9-6 Effect of Pressure on the Viscosity of Pure Gases / 9.29
9-7 Viscosity of Gas Mixtures at High Pressures / 9.47

9-8 Liquid Viscosity / 9.51
9-9 Effect of High Pressure on Liquid Viscosity / 9.55
9-10 Effect of Temperature on Liquid Viscosity / 9.56
9-11 Estimation of Low-Temperature Liquid Viscosity / 9.59
9-12 Estimation of Liquid Viscosity at High Temperatures / 9.75
9-13 Liquid Mixture Viscosity / 9.77
Chapter 10 Thermal Conductivity 10.1
10-1 Scope / 10.1
10-2 Theory of Thermal Conductivity / 10.1
10-3 Thermal Conductivities of Polyatomic Gases / 10.2
10-4 Effect of Temperature on the Low-Pressure Thermal Conductivities of Gases / 10.18
10-5 Effect of Pressure on the Thermal Conductivities of Gases / 10.18
10-6 Thermal Conductivities of Low-Pressure Gas Mixtures / 10.29
10-7 Thermal Conductivities of Gas Mixtures at High Pressures / 10.35
10-8 Thermal Conductivities of Liquids / 10.42
10-9 Estimation of the Thermal Conductivities of Pure Liquids / 10.44
10-10 Effect of Temperature on the Thermal Conductivities of Liquids / 10.51
10-11 Effect of Pressure on the Thermal Conductivities of Liquids / 10.52
10-12 Thermal Conductivities of Liquid Mixtures / 10.56
Chapter 11 Diffusion Coefficients 11.1
11-1 Scope / 11.1
vi CONTENTS
11-2 Basic Concepts and Definitions / 11.1
11-3 Diffusion Coefficients for Binary Gas Systems at Low Pressures: Prediction from
Theory / 11.5
11-4 Diffusion Coefficients for Binary Gas Systems at Low Pressures: Empirical
Correlations / 11.9
11-5 The Effect of Pressure on the Binary Diffusion Coefficients of Gases / 11.12
11-6 The Effect of Temperature on Diffusion in Gases / 11.19
11-7 Diffusion in Multicomponent Gas Mixtures / 11.19

11-8 Diffusion in Liquids: Theory / 11.20
11-9 Estimation of Binary Liquid Diffusion Coefficients at Infinite Dilution / 11.21
11-10 Concentration Dependence of Binary Liquid Diffusion Coefficients / 11.33
11-11 The Effects of Temperature and Pressure on Diffusion in Liquids / 11.38
11-12 Diffusion in Multicomponent Liquid Mixtures / 11.41
11-13 Diffusion in Electrolyte Solutions / 11.43
Chapter 12 Surface Tension 12.1
12-1 Scope / 12.1
12-2 Introduction / 12.1
12-3 Estimation of Pure-Liquid Surface Tension / 12.2
12-4 Variation of Pure-Liquid Surface Tension with Temperature / 12.11
12-5 Surface Tensions of Mixtures / 12.12
Appendix A Property Data Bank A.1
Appendix B Lennard-Jones Potentials as Determined from Viscosity Data B.1
Appendix C Group Contributions for Multiproperty Methods C.1
Index follows Appendix C
vii
PREFACE
Reliable values of the properties of materials are necessary for the design of in-
dustrial processes. An enormous amount of data has been collected and correlated
over the years, but the rapid advance of technology into new fields seems always
to maintain a significant gap between demand and availability. The engineer is still
required to rely primarily on common sense, experience, and a variety of methods
for estimating physical properties.
This book presents a critical review of various estimation procedures for a lim-
ited number of properties of gases and liquids: critical and other pure component
properties; PVT and thermodynamic properties of pure components and mixtures;
vapor pressures and phase-change enthalpies; standard enthalpies of formation;
standard Gibbs energies of formation; heat capacities; surface tensions; viscosities;
thermal conductivities; diffusion coefficients; and phase equilibria. For most cases,

estimated properties are compared to experiment to indicate reliability. Most meth-
ods are illustrated by examples.
The procedures described are necessarily limited to those that appear to the
authors to have the greatest validity and practical use. Wherever possible, we have
included recommendations delineating the best methods for estimating each prop-
erty and the most reliable techniques for extrapolating or interpolating available
data.
Although the book is intended to serve primarily the practicing engineer, espe-
cially the process or chemical engineer, other engineers and scientists concerned
with gases and liquids may find it useful.
The first edition of this book was published in 1958, the second in 1966, the
third in 1977 and the fourth in 1987. In a sense, each edition is a new book because
numerous estimation methods are proposed each year; over a (roughly) 10-year
span, many earlier methods are modified or displaced by more accurate or more
general techniques. While most estimation methods rely heavily on empiricism, the
better ones—those that are most reliable—often have a theoretical basis. In some
cases, the theory is outlined to provide the user with the foundation of the proposed
estimation method.
There are some significant differences between the current edition and the pre-
ceding one:
1. Chapter 2 includes several extensive new group-contribution methods as well
as discussion and comparisons of methods based on descriptors calculated with
quantum-mechanical methods. Direct comparisons are given for more than 200
substances with data in Appendix A.
2. Chapter 3 includes several new methods as well as updated Benson-Method
tables for ideal-gas properties of formation and heat capacities. Direct com-
parisons are given for more than 100 substances with data in Appendix A.
3. Chapter 4 includes presentation of current equations of state for pure compo-
nents with complete formulae for many models, especially cubics. A new sec-
Copyright © 2001, 1987, 1977, 1966, 1958 by The McGraw-Hill Companies, Inc.

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viii PREFACE
tion discusses issues associated with near-critical and very high pressure sys-
tems. The Lee–Kesler corresponding-states tables, readily available elsewhere,
have been removed.
4. Chapter 5 includes presentation of current equations of state for mixtures with
complete formulae for many models, especially cubics. A new section discusses
current mixing and combining rules for equation-of-state parameters with at-
tention to inconsistencies.
5. Chapter 6 includes a revised introduction to thermodynamic properties from
equations of state with complete formulae for cubics. A new section discusses
real-gas and liquid heat capacities. Because they are readily available else-
where, the Lee–Kesler corresponding-states tables have been removed.
6. Chapter 7 gives attention to one form of the Wagner equation that appears to
be particularly successful for representing vapor pressures, and to the useful
tables of Majer and Svoboda for enthalpies of vaporization. Also included is a
new discussion of the entropy of fusion.
7. Chapter 8 has been extended to include discussion of systems containing solids,
a new correlation by Eckert et al. for activity coefficents at infinite dilution,
and some new methods for high-pressure vapor-liquid equilibria, including
those based on Wong–Sandler mixing rules.
8. In Chapters 9–12, most of the new methods for transport properties are based
on thermodynamic data or molecular-thermodynamic models. The successful
TRAPP method (from the National Institute of Science and Technology) is now
explained in more detail.
9. The property data bank in Appendix A has been completely revised. Most of
the properties are the same as in the last edition, but the format has been
changed to identify the sources of values. The introduction to Appendix A
describes the definitions and font usage of the data bank.
We selected only those substances for which we could readily obtain an

evaluated experimental critical temperature; the total number of compounds is
fewer than in the last edition. All of the entries in Appendix A were taken
from tabulations of the Thermodynamics Research Center (TRC), College Sta-
tion, TX, USA, or from other reliable sources as listed in the Appendix. We
also used experimentally-based results for other properties from the same
sources whenever available. Some estimated values are also included.
We tabulate the substances in alphabetical formula order. IUPAC names are
used, with some common names added, and Chemical Abstracts Registry num-
bers are given for each compound. We indicate origins of the properties by
using different fonts. We are grateful to TRC for permitting us to publish a
significant portion of their values.
10. Appendix C presents complete tables of parameters for the multi-property
group-contribution methods of Joback and of Constantinou and Gani.
The authors want to acknowledge with thanks significant contributions from
colleagues who provided assistance in preparing the current edition; their help has
been essential and we are grateful to them all: David Bush, Joe Downey, Charles
Eckert, Michael Frenkel, Rafiqui Gani and students of the CAPEC Center at the
Technical University of Denmark, Lucinda Garnes, Steven Garrison, Nathan Erb,
K. R. Hall, Keith Harrison, Marcia Huber, Kevin Joback, Kim Knuth, Claude Lei-
bovicci, Paul Mathias, Amy Nelson, Van Nguyen, Chorng Twu, Philippe Ungerer
and Randolph Wilhoit.
PREFACE ix
For her patient and devoted service in performing numerous editorial tasks, we
give special thanks to Nanci Poling. We are grateful to Nanci and also to Verna
O’Connell and Susan Prausnitz for their encouragement and support during this
project.
While we regret that the original author, Robert Reid, elected not to participate
in the preparation of this edition, we nevertheless want to record here our gratitude
to him for his pioneering leadership in establishing and collecting estimation meth-
ods for physical properties of fluids as required for chemical process and product

design.
B. E. Poling
J. M. Prausnitz
J. P. O’Connell
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1.1
CHAPTER ONE
THE ESTIMATION OF PHYSICAL
PROPERTIES
1-1 INTRODUCTION
The structural engineer cannot design a bridge without knowing the properties of
steel and concrete. Similarly, scientists and engineers often require the properties
of gases and liquids. The chemical or process engineer, in particular, finds knowl-
edge of physical properties of fluids essential to the design of many kinds of prod-
ucts, processes, and industrial equipment. Even the theoretical physicist must oc-
casionally compare theory with measured properties.
The physical properties of every substance depend directly on the nature of the
molecules of the substance. Therefore, the ultimate generalization of physical prop-
erties of fluids will require a complete understanding of molecular behavior, which
we do not yet have. Though its origins are ancient, the molecular theory was not
generally accepted until about the beginning of the nineteenth century, and even
then there were setbacks until experimental evidence vindicated the theory early in
the twentieth century. Many pieces of the puzzle of molecular behavior have now
fallen into place and computer simulation can now describe more and more complex
systems, but as yet it has not been possible to develop a complete generalization.
In the nineteenth century, the observations of Charles and Gay-Lussac were
combined with Avogadro’s hypothesis to form the gas ‘‘law,’’ PV
ϭ NRT, which
was perhaps the first important correlation of properties. Deviations from the ideal-
gas law, though often small, were finally tied to the fundamental nature of the

molecules. The equation of van der Waals, the virial equation, and other equations
of state express these quantitatively. Such extensions of the ideal-gas law have not
only facilitated progress in the development of a molecular theory but, more im-
portant for our purposes here, have provided a framework for correlating physical
properties of fluids.
The original ‘‘hard-sphere’’ kinetic theory of gases was a significant contribution
to progress in understanding the statistical behavior of a system containing a large
number of molecules. Thermodynamic and transport properties were related quan-
titatively to molecular size and speed. Deviations from the hard-sphere kinetic the-
ory led to studies of the interactions of molecules based on the realization that
molecules attract at intermediate separations and repel when they come very close.
The semiempirical potential functions of Lennard-Jones and others describe attrac-
tion and repulsion in approximately quantitative fashion. More recent potential
functions allow for the shapes of molecules and for asymmetric charge distribution
in polar molecules.
Copyright © 2001, 1987, 1977, 1966, 1958 by The McGraw-Hill Companies, Inc.
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1.2 CHAPTER ONE
Although allowance for the forces of attraction and repulsion between molecules
is primarily a development of the twentieth century, the concept is not new. In
about 1750, Boscovich suggested that molecules (which he referred to as atoms)
are ‘‘endowed with potential force, that any two atoms attract or repel each other
with a force depending on their distance apart. At large distances the attraction
varies as the inverse square of the distance. The ultimate force is a repulsion which
increases without limit as the distance decreases without limit, so that the two atoms
can never coincide’’ (Maxwell 1875).
From the viewpoint of mathematical physics, the development of a comprehen-
sive molecular theory would appear to be complete. J. C. Slater (1955) observed
that, while we are still seeking the laws of nuclear physics, ‘‘in the physics of
atoms, molecules and solids, we have found the laws and are exploring the deduc-

tions from them.’’ However, the suggestion that, in principle (the Schro¨dinger equa-
tion of quantum mechanics), everything is known about molecules is of little com-
fort to the engineer who needs to know the properties of some new chemical to
design a commercial product or plant.
Paralleling the continuing refinement of the molecular theory has been the de-
velopment of thermodynamics and its application to properties. The two are inti-
mately related and interdependent. Carnot was an engineer interested in steam en-
gines, but the second law of thermodynamics was shown by Clausius, Kelvin,
Maxwell, and especially by Gibbs to have broad applications in all branches of
science.
Thermodynamics by itself cannot provide physical properties; only molecular
theory or experiment can do that. But thermodynamics reduces experimental or
theoretical efforts by relating one physical property to another. For example, the
Clausius-Clapeyron equation provides a useful method for obtaining enthalpies of
vaporization from more easily measured vapor pressures.
The second law led to the concept of chemical potential which is basic to an
understanding of chemical and phase equilibria, and the Maxwell relations provide
ways to obtain important thermodynamic properties of a substance from PVTx re-
lations where x stands for composition. Since derivatives are often required, the
PVTx function must be known accurately.
The Information Age is providing a ‘‘shifting paradigm in the art and practice
of physical properties data’’ (Dewan and Moore, 1999) where searching the World
Wide Web can retrieve property information from sources and at rates unheard of
a few years ago. Yet despite the many handbooks and journals devoted to compi-
lation and critical review of physical-property data, it is inconceivable that all de-
sired experimental data will ever be available for the thousands of compounds of
interest in science and industry, let alone all their mixtures. Thus, in spite of im-
pressive developments in molecular theory and information access, the engineer
frequently finds a need for physical properties for which no experimental data are
available and which cannot be calculated from existing theory.

While the need for accurate design data is increasing, the rate of accumulation
of new data is not increasing fast enough. Data on multicomponent mixtures are
particularly scarce. The process engineer who is frequently called upon to design
a plant to produce a new chemical (or a well-known chemical in a new way) often
finds that the required physical-property data are not available. It may be possible
to obtain the desired properties from new experimental measurements, but that is
often not practical because such measurements tend to be expensive and time-
consuming. To meet budgetary and deadline requirements, the process engineer
almost always must estimate at least some of the properties required for design.
THE ESTIMATION OF PHYSICAL PROPERTIES 1.3
1-2 ESTIMATION OF PROPERTIES
In the all-too-frequent situation where no experimental value of the needed property
is at hand, the value must be estimated or predicted. ‘‘Estimation’’ and ‘‘prediction’’
are often used as if they were synonymous, although the former properly carries
the frank implication that the result may be only approximate. Estimates may be
based on theory, on correlations of experimental values, or on a combination of
both. A theoretical relation, although not strictly valid, may nevertheless serve ad-
equately in specific cases.
For example, to relate mass and volumetric flow rates of air through an air-
conditioning unit, the engineer is justified in using PV
ϭ NRT. Similarly, he or she
may properly use Dalton’s law and the vapor pressure of water to calculate the
mass fraction of water in saturated air. However, the engineer must be able to judge
the operating pressure at which such simple calculations lead to unacceptable error.
Completely empirical correlations are often useful, but one must avoid the temp-
tation to use them outside the narrow range of conditions on which they are based.
In general, the stronger the theoretical basis, the more reliable the correlation.
Most of the better estimation methods use equations based on the form of an
incomplete theory with empirical correlations of the parameters that are not pro-
vided by that theory. Introduction of empiricism into parts of a theoretical relation

provides a powerful method for developing a reliable correlation. For example, the
van der Waals equation of state is a modification of the simple PV
ϭ NRT; setting
N
ϭ 1,
a
P ϩ (V Ϫ b) ϭ RT (1-2.1)
ͩͪ
2
V
Equation (1-2.1) is based on the idea that the pressure on a container wall, exerted
by the impinging molecules, is decreased because of the attraction by the mass of
molecules in the bulk gas; that attraction rises with density. Further, the available
space in which the molecules move is less than the total volume by the excluded
volume b due to the size of the molecules themselves. Therefore, the ‘‘constants’’
(or parameters) a and b have some theoretical basis though the best descriptions
require them to vary with conditions, that is, temperature and density. The corre-
lation of a and b in terms of other properties of a substance is an example of the
use of an empirically modified theoretical form.
Empirical extension of theory can often lead to a correlation useful for estimation
purposes. For example, several methods for estimating diffusion coefficients in low-
pressure binary gas systems are empirical modifications of the equation given by
the simple kinetic theory for non-attracting spheres. Almost all the better estimation
procedures are based on correlations developed in this way.
1-3 TYPES OF ESTIMATION
An ideal system for the estimation of a physical property would (1) provide reliable
physical and thermodynamic properties for pure substances and for mixtures at any
temperature, pressure, and composition, (2) indicate the phase (solid, liquid, or gas),
(3) require a minimum of input data, (4) choose the least-error route (i.e., the best
1.4 CHAPTER ONE

estimation method), (5) indicate the probable error, and (6) minimize computation
time. Few of the available methods approach this ideal, but some serve remarkably
well. Thanks to modern computers, computation time is usually of little concern.
In numerous practical cases, the most accurate method may not be the best for
the purpose. Many engineering applications properly require only approximate es-
timates, and a simple estimation method requiring little or no input data is often
preferred over a complex, possibly more accurate correlation. The simple gas law
is useful at low to modest pressures, although more accurate correlations are avail-
able. Unfortunately, it is often not easy to provide guidance on when to reject the
simpler in favor of the more complex (but more accurate) method; the decision
often depends on the problem, not the system.
Although a variety of molecular theories may be useful for data correlation,
there is one theory which is particularly helpful. This theory, called the law of
corresponding states or the corresponding-states principle, was originally based on
macroscopic arguments, but its modern form has a molecular basis.
The Law of Corresponding States
Proposed by van der Waals in 1873, the law of corresponding states expresses the
generalization that equilibrium properties that depend on certain intermolecular
forces are related to the critical properties in a universal way. Corresponding states
provides the single most important basis for the development of correlations and
estimation methods. In 1873, van der Waals showed it to be theoretically valid for
all pure substances whose PVT properties could be expressed by a two-constant
equation of state such as Eq. (1-2.1). As shown by Pitzer in 1939, it is similarly
valid if the intermolecular potential function requires only two characteristic pa-
rameters. Corresponding states holds well for fluids containing simple molecules
and, upon semiempirical extension with a single additional parameter, it also holds
for ‘‘normal’’ fluids where molecular orientation is not important, i.e., for molecules
that are not strongly polar or hydrogen-bonded.
The relation of pressure to volume at constant temperature is different for dif-
ferent substances; however, two-parameter corresponding states theory asserts that

if pressure, volume, and temperature are divided by the corresponding critical prop-
erties, the function relating reduced pressure to reduced volume and reduced tem-
perature becomes the same for all substances. The reduced property is commonly
expressed as a fraction of the critical property: P
r
ϭ P/ P
c
; V
r
ϭ V/V
c
; and T
r
ϭ
T/ T
c
.
To illustrate corresponding states, Fig. 1-1 shows reduced PVT data for methane
and nitrogen. In effect, the critical point is taken as the origin. The data for saturated
liquid and saturated vapor coincide well for the two substances. The isotherms
(constant T
r
), of which only one is shown, agree equally well.
Successful application of the law of corresponding states for correlation of PVT
data has encouraged similar correlations of other properties that depend primarily
on intermolecular forces. Many of these have proved valuable to the practicing
engineer. Modifications of the law are commonly made to improve accuracy or ease
of use. Good correlations of high-pressure gas viscosity have been obtained by
expressing
␩

/
␩
c
as a function of P
r
and T
r
. But since
␩
c
is seldom known and not
easily estimated, this quantity has been replaced in other correlations by other
characteristics such as or the group where is the viscosity
1/2 2/3 1/6
␩
Њ,
␩
Њ , MPT,
␩
Њ
cT c c c
at T
c
and low pressure, is the viscosity at the temperature of interest, again at
␩
Њ
T
THE ESTIMATION OF PHYSICAL PROPERTIES 1.5
FIGURE 1-1 The law of corresponding states applied to the PVT
properties of methane and nitrogen. Literature values (Din, 1961): ⅙

methane, ● nitrogen.
low pressure, and the group containing M, P
c
, and T
c
is suggested by dimensional
analysis. Other alternatives to the use of
␩
c
might be proposed, each modeled on
the law of corresponding states but essentially empirical as applied to transport
properties.
The two-parameter law of corresponding states can be derived from statistical
mechanics when severe simplifications are introduced into the partition function.
Sometimes other useful results can be obtained by introducing less severe simpli-
fications into statistical mechanics to provide a more general framework for the
development of estimation methods. Fundamental equations describing various
properties (including transport properties) can sometimes be derived, provided that
an expression is available for the potential-energy function for molecular interac-
tions. This function may be, at least in part, empirical; but the fundamental equa-
tions for properties are often insensitive to details in the potential function from
which they stem, and two-constant potential functions frequently serve remarkably
well. Statistical mechanics is not commonly linked to engineering practice, but there
is good reason to believe it will become increasingly useful, especially when com-
bined with computer simulations and with calculations of intermolecular forces by
computational chemistry. Indeed, anticipated advances in atomic and molecular
physics, coupled with ever-increasing computing power, are likely to augment sig-
nificantly our supply of useful physical-property information.
Nonpolar and Polar Molecules
Small, spherically-symmetric molecules (for example, CH

4
) are well fitted by a
two-constant law of corresponding states. However, nonspherical and weakly polar
molecules do not fit as well; deviations are often great enough to encourage de-
velopment of correlations using a third parameter, e.g., the acentric factor,
␻
. The
acentric factor is obtained from the deviation of the experimental vapor pressure–
temperature function from that which might be expected for a similar substance
1.6 CHAPTER ONE
consisting of small spherically-symmetric molecules. Typical corresponding-states
correlations express a desired dimensionless property as a function of P
r
, T
r
, and
the chosen third parameter.
Unfortunately, the properties of strongly polar molecules are often not satisfac-
torily represented by the two- or three-constant correlations which do so well for
nonpolar molecules. An additional parameter based on the dipole moment has often
been suggested but with limited success, since polar molecules are not easily char-
acterized by using only the dipole moment and critical constants. As a result, al-
though good correlations exist for properties of nonpolar fluids, similar correlations
for polar fluids are often not available or else show restricted reliability.
Structure and Bonding
All macroscopic properties are related to molecular structure and the bonds between
atoms, which determine the magnitude and predominant type of the intermolecular
forces. For example, structure and bonding determine the energy storage capacity
of a molecule and thus the molecule’s heat capacity.
This concept suggests that a macroscopic property can be calculated from group

contributions. The relevant characteristics of structure are related to the atoms,
atomic groups, bond type, etc.; to them we assign weighting factors and then de-
termine the property, usually by an algebraic operation that sums the contributions
from the molecule’s parts. Sometimes the calculated sum of the contributions is not
for the property itself but instead is for a correction to the property as calculated
by some simplified theory or empirical rule. For example, the methods of Lydersen
and of others for estimating T
c
start with the loose rule that the ratio of the normal
boiling temperature to the critical temperature is about 2:3. Additive structural in-
crements based on bond types are then used to obtain empirical corrections to that
ratio.
Some of the better correlations of ideal-gas heat capacities employ theoretical
values of (which are intimately related to structure) to obtain a polynomialC
Њ
p
expressing as a function of temperature; the constants in the polynomial areCЊ
p
determined by contributions from the constituent atoms, atomic groups, and types
of bonds.
1-4 ORGANIZATION OF THE BOOK
Reliable experimental data are always to be preferred over results obtained by
estimation methods. A variety of tabulated data banks is now available although
many of these banks are proprietary. A good example of a readily accessible data
bank is provided by DIPPR, published by the American Institute of Chemical En-
gineers. A limited data bank is given at the end of this book. But all too often
reliable data are not available.
The property data bank in Appendix A contains only substances with an eval-
uated experimental critical temperature. The contents of Appendix A were taken
either from the tabulations of the Thermodynamics Research Center (TRC), College

Station, TX, USA, or from other reliable sources as listed in Appendix A. Sub-
stances are tabulated in alphabetical-formula order. IUPAC names are listed, with
some common names added, and Chemical Abstracts Registry numbers are indi-
cated.
THE ESTIMATION OF PHYSICAL PROPERTIES 1.7
FIGURE 1-2 Mollier diagram for dichlorodifluoro-
methane. The solid lines represent measured data.
Dashed lines and points represent results obtained by es-
timation methods when only the chemical formula and
the normal boiling temperature are known.
In this book, the various estimation methods are correlations of experimental
data. The best are based on theory, with empirical corrections for the theory’s
defects. Others, including those stemming from the law of corresponding states, are
based on generalizations that are partly empirical but nevertheless have application
to a remarkably wide range of properties. Totally empirical correlations are useful
only when applied to situations very similar to those used to establish the corre-
lations.
The text includes many numerical examples to illustrate the estimation methods,
especially those that are recommended. Almost all of them are designed to explain
the calculation procedure for a single property. However, most engineering design
problems require estimation of several properties; the error in each contributes to
the overall result, but some individual errors are more important that others. For-
tunately, the result is often adequate for engineering purposes, in spite of the large
measure of empiricism incorporated in so many of the estimation procedures and
in spite of the potential for inconsistencies when different models are used for
different properties.
As an example, consider the case of a chemist who has synthesized a new
compound (chemical formula CCl
2
F

2
) that boils at Ϫ20.5ЊC at atmospheric pressure.
Using only this information, is it possible to obtain a useful prediction of whether
or not the substance has the thermodynamic properties that might make it a practical
refrigerant?
Figure 1-2 shows portions of a Mollier diagram developed by prediction methods
described in later chapters. The dashed curves and points are obtained from esti-
mates of liquid and vapor heat capacities, critical properties, vapor pressure, en-
1.8 CHAPTER ONE
thalpy of vaporization, and pressure corrections to ideal-gas enthalpies and entro-
pies. The substance is, of course, a well-known refrigerant, and its known properties
are shown by the solid curves. While environmental concerns no longer permit use
of CCl
2
F
2
, it nevertheless serves as a good example of building a full description
from very little information.
For a standard refrigeration cycle operating between 48.9 and
Ϫ6.7ЊC, the evap-
orator and condenser pressures are estimated to be 2.4 and 12.4 bar, vs. the known
values 2.4 and 11.9 bar. The estimate of the heat absorption in the evaporator checks
closely, and the estimated volumetric vapor rate to the compressor also shows good
agreement: 2.39 versus 2.45 m
3
/hr per kW of refrigeration. (This number indicates
the size of the compressor.) Constant-entropy lines are not shown in Fig. 1-2, but
it is found that the constant-entropy line through the point for the low-pressure
vapor essentially coincides with the saturated vapor curve. The estimated coefficient
of performance (ratio of refrigeration rate to isentropic compression power) is es-

timated to be 3.8; the value obtained from the data is 3.5. This is not a very good
check, but it is nevertheless remarkable because the only data used for the estimate
were the normal boiling point and the chemical formula.
Most estimation methods require parameters that are characteristic of single pure
components or of constituents of a mixture of interest. The more important of these
are considered in Chap. 2.
The thermodynamic properties of ideal gases, such as enthalpies and Gibbs en-
ergies of formation and heat capacities, are covered in Chap. 3. Chapter 4 describes
the PVT properties of pure fluids with the corresponding-states principle, equations
of state, and methods restricted to liquids. Chapter 5 extends the methods of Chap.
4 to mixtures with the introduction of mixing and combining rules as well as the
special effects of interactions between different components. Chapter 6 covers other
thermodynamic properties such as enthalpy, entropy, free energies and heat capac-
ities of real fluids from equations of state and correlations for liquids. It also intro-
duces partial properties and discusses the estimation of true vapor-liquid critical
points.
Chapter 7 discusses vapor pressures and enthalpies of vaporization of pure sub-
stances. Chapter 8 presents techniques for estimation and correlation of phase equi-
libria in mixtures. Chapters 9 to 11 describe estimation methods for viscosity, ther-
mal conductivity, and diffusion coefficients. Surface tension is considered briefly in
Chap. 12.
The literature searched was voluminous, and the lists of references following
each chapter represent but a fraction of the material examined. Of the many esti-
mation methods available, in most cases only a few were selected for detailed
discussion. These were selected on the basis of their generality, accuracy, and avail-
ability of required input data. Tests of all methods were often more extensive than
those suggested by the abbreviated tables comparing experimental with estimated
values. However, no comparison is adequate to indicate expected errors for new
compounds. The average errors given in the comparison tables represent but a crude
overall evaluation; the inapplicability of a method for a few compounds may so

increase the average error as to distort judgment of the method’s merit, although
efforts have been made to minimize such distortion.
Many estimation methods are of such complexity that a computer is required.
This is less of a handicap than it once was, since computers and efficient computer
programs have become widely available. Electronic desk computers, which have
become so popular in recent years, have made the more complex correlations prac-
tical. However, accuracy is not necessarily enhanced by greater complexity.
The scope of the book is inevitably limited. The properties discussed were se-
lected arbitrarily because they are believed to be of wide interest, especially to
THE ESTIMATION OF PHYSICAL PROPERTIES 1.9
chemical engineers. Electrical properties are not included, nor are the properties of
salts, metals, or alloys or chemical properties other than some thermodynamically
derived properties such as enthalpy and the Gibbs energy of formation.
This book is intended to provide estimation methods for a limited number of
physical properties of fluids. Hopefully, the need for such estimates, and for a book
of this kind, may diminish as more experimental values become available and as
the continually developing molecular theory advances beyond its present incomplete
state. In the meantime, estimation methods are essential for most process-design
calculations and for many other purposes in engineering and applied science.
REFERENCES
Dewan, A. K., and M. A. Moore: ‘‘Physical Property Data Resources for the Practicing
Engineer/ Scientist in Today’s Information Age,’’ Paper 89C, AIChE 1999 Spring National
Mtg., Houston, TX, March, 1999. Copyright Equilon Enterprise LLC.
Din, F., (ed.): Thermodynamic Functions of Gases, Vol. 3, Butterworth, London, 1961.
Maxwell, James Clerk: ‘‘Atoms,’’ Encyclopaedia Britannica, 9th ed., A. & C. Black, Edin-
burgh, 1875–1888.
Slater, J. C.: Modern Physics, McGraw-Hill, New York, 1955.
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2.1
CHAPTER TWO

PURE COMPONENT
CONST ANTS
2-1 SCOPE
Though chemical engineers normally deal with mixtures, pure component properties
underlie much of the observed behavior. For example, property models intended
for the whole range of composition must give pure component properties at the
pure component limits. In addition, pure component property constants are often
used as the basis for models such as corresponding states correlations for PVT
equations of state (Chap. 4). They are often used in composition-dependent mixing
rules for the parameters to describe mixtures (Chap. 5).
As a result, we first study methods for obtaining pure component constants of
the more commonly used properties and show how they can be estimated if no
experimental data are available. These include the vapor-liquid critical properties,
atmospheric boiling and freezing temperatures and dipole moments. Others such as
the liquid molar volume and heat capacities are discussed in later chapters. Values
for these properties for many substances are tabulated in Appendix A; we compare
as many of them as possible to the results from estimation methods. Though the
origins of current group contribution methods are over 50 years old, previous edi-
tions show that the number of techniques were limited until recently when com-
putational capability allowed more methods to appear. We examine most of the
current techniques and refer readers to earlier editions for the older methods.
In Secs. 2-2 (critical properties), 2-3 (acentric factor) and 2-4 (melting and boil-
ing points), we illustrate several methods and compare each with the data tabulated
in Appendix A and with each other. All of the calculations have been done with
spreadsheets to maximize accuracy and consistency among the methods. It was
found that setting up the template and comparing calculations with as many sub-
stances as possible in Appendix A demonstrated the level of complexity of the
methods. Finally, because many of the methods are for multiple properties and
recent developments are using alternative approaches to traditional group contri-
butions, Sec. 2-5 is a general discussion about choosing the best approach for pure

component constants. Finally, dipole moments are treated in Sec. 2-6.
Most of the estimation methods presented in this chapter are of the group, bond,
or atom contribution type. That is, the properties of a molecule are usually estab-
lished from contributions from its elements. The conceptual basis is that the inter-
molecular forces that determine the constants of interest depend mostly on the
bonds between the atoms of the molecules. The elemental contributions are prin-
Copyright © 2001, 1987, 1977, 1966, 1958 by The McGraw-Hill Companies, Inc.
Click here for terms of use.
2.2 CHAPTER TWO
cipally determined by the nature of the atoms involved (atom contributions), the
bonds between pairs of atoms (bond contributions or equivalently group interaction
contributions), or the bonds within and among small groups of atoms (group con-
tributions). They all assume that the elements can be treated independently of their
arrangements or their neighbors. If this is not accurate enough, corrections for
specific multigroup, conformational or resonance effects can be included. Thus,
there can be levels of contributions. The identity of the elements to be considered
(group, bond,oratom) are normally assumed in advance and their contributions
obtained by fitting to data. Usually applications to wide varieties of species start
with saturated hydrocarbons and grow by sequentially adding different types of
bonds, rings, heteroatoms and resonance. The formulations for pure component
constants are quite similar to those of the ideal gas formation properties and heat
capacities of Chap. 3; several of the group formulations described in Appendix C
have been applied to both types of properties.
Alternatives to group /bond /atom contribution methods have recently appeared.
Most are based on adding weighted contributions of measured properties such as
molecular weight and normal boiling point, etc. (factor analysis) or from ‘‘quan-
titative structure-property relationships’’ (QSPR) based on contributions from mo-
lecular properties such as electron or local charge densities, molecular surface area,
etc. (molecular descriptors). Grigoras (1990), Horvath (1992), Katritzky, et al.
(1995; 1999), Jurs [Egolf, et al., 1994], Turner, et al. (1998), and St. Cholakov, et

al. (1999) all describe the concepts and procedures. The descriptor values are com-
puted from molecular mechanics or quantum mechanical descriptions of the sub-
stance of interest and then property values are calculated as a sum of contributions
from the descriptors. The significant descriptors and their weighting factors are
found by sophisticated regression techniques. This means, however, that there are
no tabulations of molecular descriptor properties for substances. Rather, a molecular
structure is posed, the descriptors for it are computed and these are combined in
the correlation. We have not been able to do any computations for these methods
ourselves. However, in addition to quoting the results from the literature, since some
tabulate their estimated pure component constants, we compare them with the val-
ues in Appendix A.
The methods given here are not suitable for pseudocomponent properties such
as for the poorly characterized mixtures often encountered with petroleum, coal and
natural products. These are usually based on measured properties such as average
molecular weight, boiling point, and the specific gravity (at 20
ЊC) rather than mo-
lecular structure. We do not treat such systems here, but the reader is referred to
the work of Tsonopoulos, et al. (1986), Twu (1984, Twu and Coon, 1996), and
Jianzhong, et al. (1998) for example. Older methods include those of Lin and Chao
(1984) and Brule, et al. (1982), Riazi and Daubert (1980) and Wilson, et al. (1981).
2-2 VAPOR-LIQUID CRITICAL PROPERTIES
Vapor-liquid critical temperature, T
c
, pressure, P
c
, and volume, V
c
, are the pure-
component constants of greatest interest. They are used in many corresponding
states correlations for volumetric (Chap. 4), thermodynamic (Chaps. 5–8), and

transport (Chaps. 9 to 11) properties of gases and liquids. Experimental determi-
nation of their values can be challenging [Ambrose and Young, 1995], especially
for larger components that can chemically degrade at their very high critical tem-
PURE COMPONENT CONSTANTS 2.3
peratures [Teja and Anselme, 1990]. Appendix A contains a data base of properties
for all the substances for which there is an evaluated critical temperature tabulated
by the Thermodynamics Research Center at Texas A&M University [TRC, 1999]
plus some evaluated values by Ambrose and colleagues and by Steele and col-
leagues under the sponsorship of the Design Institute for Physical Properties Re-
search (DIPPR) of the American Institute of Chemical Engineers (AIChE) in New
York and NIST (see Appendix A for references). There are fewer evaluated P
c
and
V
c
than T
c
. We use only evaluated results to compare with the various estimation
methods.
Estimation Techniques
One of the first successful group contribution methods to estimate critical properties
was developed by Lydersen (1955). Since that time, more experimental values have
been reported and efficient statistical techniques have been developed that allow
determination of alternative group contributions and optimized parameters. We ex-
amine in detail the methods of Joback (1984; 1987), Constantinou and Gani (1994),
Wilson and Jasperson (1996), and Marrero and Pardillo (1999). After each is de-
scribed and its accuracy discussed, comparisons are made among the methods,
including descriptor approaches, and recommendations are made. Earlier methods
such as those of Lyderson (1955), Ambrose (1978; 1979; 1980), and Fedors (1982)
are described in previous editions; they do not appear to be as accurate as those

evaluated here.
Method of Joback. Joback (1984; 1987) reevaluated Lydersen’s group contribu-
tion scheme, added several new functional groups, and determined new contribution
values. His relations for the critical properties are
2
Ϫ
1
T (K) ϭ T 0.584 ϩ 0.965 N (tck) Ϫ N (tck) (2-2.1)
͸͸
ͫͭͮͭͮͬ
cb k k
kk
Ϫ
2
P (bar) ϭ 0.113 ϩ 0.0032N Ϫ N (pck) (2-2.2)
͸
ͫͬ
c atoms k
k
3
Ϫ
1
V (cm mol ) ϭ 17.5 ϩ N (vck) (2-2.3)
͸
ck
k
where the contributions are indicated as tck, pck and vck. The group identities and
Joback’s values for contributions to the critical properties are in Table C-1. For T
c
,

a value of the normal boiling point, T
b
, is needed. This may be from experiment
or by estimation from methods given in Sec. 2-4; we compare the results for both.
An example of the use of Joback’s groups is Example 2-1; previous editions give
other examples, as do Devotta and Pendyala (1992).
Example 2-1 Estimate T
c
, P
c
, and V
c
for 2-ethylphenol by using Joback’s group
method.
solution 2-ethylphenol contains one —CH
3
, one —CH
2
—, four
ϭ
CH(ds), one
ACOH (phenol) and two
ϭ
C(ds). Note that the group ACOH is only for the OH and
does not include the aromatic carbon. From Appendix Table C-1