Table Of ContentButterworths Monographs in Chemistry
Butterworths Monographs in Chemistry is a series of occasional texts by
internationally acknowledged specialists, providing authoritative treatment
of topics of current significance in chemistry and chemical engineering
Series Editorial Panel
J E Baldwin, FRS
Waynflete Professor of Chemistry, University of Oxford
A D Buckingham, FRS
Professor of Chemistry, University of Cambridge
S Danishefsky
Professor of Chemistry, University of Yale, USA
G W Kirby
Regius Professor of Chemistry, University of Glasgow
W G Klemperer
Professor of Chemistry, Columbia University, New York, USA
J W Mullin
Professor of Chemical Engineering, University College, London
R Stevens
Professor of Chemistry, University of California, USA
T S West
Professor, The Macaulay Institute for Soil Research, Aberdeen
R N Zare
Professor of Chemistry, Stanford University, USA
Published titles
Kinetics and Dynamics of Elementary Gas Reactions
Prostaglandins and Thromboxanes
Silicon in Organic Synthesis
Solvent Extraction in Flame Spectroscopic Analysis
Forthcoming titles
Compleximetric Titration
Coordination Catalysis in Organic Chemistry
Strategy in Organic Synthesis
Butterworths Monographs in Chemistry
Liquids and Liquid Mixtures
J S Rowlinson
Dr Lee's Professor of Chemistry
University of Oxford
F L Swinton
Professor of Chemistry
New University of Ulster
Third edition
Butterworth Scientific
London · Boston · Sydney · Wellington · Durban · Toronto
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First published 1982
© Butterworth & Co (Publishers) Ltd 1982
British Library Cataloguing in Publication Data
Rowlinson, J. S.
Liquids and liquid mixtures.—3rd ed.—
(Butterworths monographs in chemistry
and chemical engineering)
1. Liquids
I. Title II. Swinton, F. L.
530.4'2 QC145.2
ISBN 0-408-24192-6
0-408-24193-4 Pbk
Filmset by Northumberland Press Ltd, Gateshead, Tyne and Wear
Printed and bound in Great Britain
by Page Bros (Norwich) Ltd
Preface to the Third Edition
The aim of this book remains unchanged: to give an account of the
equilibrium properties of liquids and liquid mixtures, and to relate these to
the properties of the constituent molecules by the methods of statistical
thermodynamics.
Much has happened in the twelve years since the publication of the second
edition. The properties of pure and mixed fluids near their critical points
have now been thoroughly studied and methods of describing such states
thermodynamically have been worked out. Tricritical points have received
much attention. Measurements of the excess properties of mixtures have
grown beyond number, and, in some cases, are now of an accuracy that was
not even attempted in the 1960s. The study of liquid mixtures at high
pressures has not shown the same quantitative increase, although the accuracy
of a higher proportion of the work than hitherto now approaches that of
the leading workers.
The interpretation of this material has been put on a much better footing
by the use of the methods of computer simulation and by the developments
of perturbation theories of liquids and mixtures. Both techniques were in
their infancy in 1969. The use of simulated data for testing theories has
eliminated the dangerous step of guessing at the intermolecular forces. These
are now known accurately for the inert gases and some of their mixtures,
but it is our ignorance of their form and strength that looks like being the
main bar to progress in the interpretation of the properties of less simple
systems. If we knew the forces more accurately, it now seems that there would
be no real difficulties in the way of a full statistical interpretation of the
thermodynamic properties.
We thank many friends and colleagues for useful comments and for sending
us work before publication. We are particularly indebted to S. Angus,
J. C. G. Calado, M. L. McGlashan, I. A. McLure, R. L. Scott, L. A. K.
Staveley, W. B. Streett, D. J. Tildesley and C. J. Wormald. A grant from
the Leverhulme Trust greatly assisted the co-operation of two authors who
normally work on different islands. Finally, we thank Miss H. McCollum
and Miss W. E. Nelson for typing the manuscript.
J.S.R.
June 1981 F.L.S.
v
Chapter 1
Introduction
1.1 The liquid state
Everyone can recognize a liquid. It is popularly defined as the state of
matter which, when placed in a closed vessel, conforms to the shape of the
vessel but does not necessarily fill the whole of its volume. The first
property distinguishes it from a solid and the second from a gas. Although
this simple definition is adequate for many purposes, it does not go very
deeply into the relationship between the three principal states of matter,
solid, liquid and gas.
When a crystalline solid is heated, it changes to either a liquid or a gas at
a temperature which is a function of the applied pressure. At this melting,
or sublimation, temperature one of the fluid states and the solid state can
exist in equilibrium. Only at a fixed temperature and pressure, the triple
point, can the three phases of a pure substance, solid, liquid and gas, remain
in mutual equilibrium (Figure 1.1). This restriction is a consequence of
Gibbs's phase rule, which requires that the sum of the number of degrees of
freedom and the number of phases shall be three for a pure substance. Thus,
in a two-dimensional phase diagram of pressure as a function of tempera-
ture (Figure 7.7(b)), a single phase is represented by an area, two coexistent
phases by a line and three by the intersection of three lines at a point.
Figure 7.7(a) represents the volume of a given amount of a substance, say
one mole, as a function of pressure and temperature. If this amount is
placed in a vessel of the pressure, volume and temperature represented by
the point x, then the vessel will contain liquid characterized by the point y
and gas (or vapour) characterized by the point z. That is, the liquid and gas
have, respectively, the pressure, temperature and volume per mole of these
points. Since the overall molar volume is that of the vessel, x, it follows that
the ratio of the masses of the two phases (m /m) is the ratio of the lengths
y z
(xz/xy).
A line that joins two coexistent phases in such a way that the position of
a point on the line is a measure of the relative amounts of the phases is
called a tie-line. Thus all points on the line B C are liquid states for they are
2
states of the fluid in equilibrium with infinitesimal amounts of gas, and all
points on B C represent vapour in equilibrium with infinitesimal amounts
3
1
2 Introduction
Figure LI (a) The (p, V, T) surface for a given mass of a simple substance, and(b) the
(p, T) projection of this surface
A volume of the solid at absolute zero
AB vapour-pressure curve of the solid
1
B B andB volumes of the solid, liquid and gas at the triple point
19 2 3
BD and BC melting curve of the solid and vapour-pressure curve of the liquid' the
letter ends at the critical point C
of liquid. BC and B C are thus the locus of bubble points and dew points
2 3
respectively. The line BC is also often called the orthobaric liquid curve or
2
the saturation curve and this latter term can be conveniently applied both to
B C (a saturated liquid) and to BC (a saturated gas). All points on the
2 3
curved surface to the right of BD represent the fluid state, which cannot
2 2
be divided into liquid and gas in any but an arbitrary way except for points
along the continuous curve BCB . Thus a fluid at point p, which might be
2 3
said to be 'obviously' a liquid, can be changed to point s, 'obviously' a gas,
first by heating at constant volume to q, expanding at constant temperature
to r, and then cooling at constant volume to s. At no point in this three-
stage transformation has a change of phase occurred, and no dividing
meniscus, such as that which separates y and z, would have been observed.
There is, in fact, no qualitative physical test that could distinguish fluid at
point p from that at point 5 without making a change of pressure, volume
1.1 The liquid State 3
or temperature that brings the fluid into the two-phase region of BCB .
2 3
The two fluids differ only in degree. At higher temperatures and pressures
and particularly in the vicinity of C, the gas-liquid critical point, any
attempt to divide the fluid state must become even more artificial. It would,
however, be pedantic to describe all states except BC and B C as fluids
2 3
every time they are mentioned, and so in this book the word liquid is used
freely for fluids at or near the line BC and the word gas for fluids of low
2
density, in contexts where the meaning is clear.
Over the past few decades much evidence has accumulated to show that
the fluid states, gas and liquid, possess many structural similarities and that
both are quite distinct from the crystalline solid state of the same substance.
Some of this evidence has resulted from the computer simulation of
assemblies of particles that interact with particularly simple intermolecular
potentials, but most of it is a consequence of the direct experimental
investigation into the structure of liquids and highly-compressed gases
using x-ray and neutron diffraction1.
The diffraction pattern of a liquid is very similar to that of the same
substance in the gaseous form when it is above the critical temperature and
compressed to a comparable density, and both are totally different to that
of the crystalline solid. Diffraction studies on compressed gases are difficult
to carry out and the majority of such measurements have been performed
only over the past two decades. Previously, because dilute gases possess no
x-ray diffraction patterns apart from those due to internal molecular
structure, diffraction studies were used as evidence for the contrary pos-
tulate, the similarity of the solid and liquid states. During the same period
this misconception was compounded by the application to the liquid state
of statistical theories based on the cell model2 in which the individual
molecules are imagined to be confined, and to move, within cells composed
of their nearest neighbours. Such a model is solid-like in nature and
imposes too great a degree of structure on the fluid. When applied to more
appropriate systems such as clathrate compounds that actually do possess a
cage-like configuration, such theories are extremely successful3, but their
extensive use in the field of liquids and particularly liquid mixtures has been
singularly unhelpful.
In the neighbourhood of the triple point the change from the solid state
to the fluid or from the liquid to the gas is a sharp one, at which the
characteristic equilibrium properties of the substance change discon-
tinuously at a so-called first-order transition. The changes for the molar
entropy, heat capacity and volume of argon are shown in Figure 1.2 and
other properties such as the coefficients of thermal expansion and of
compressibility, refractive index and dielectric constant show similar be-
haviour. The relative values of the three thermodynamic properties shown
in this figure are typical of almost all substances, but a few, of which water
and the elements antimony, bismuth, gallium and germanium are the most
familiar, are atypical and contract on melting so that K(s) > V(\).
For all substances in the region of the triple point, the change from solid
4 Introduction
s(g)
o
E
T3
iool·
5(1)
Cp(D
Cp(S)
cp(g)
70 80 90 Γ, K
A v(g)9960
30
v{lï
v(s)
20
Figure 1.2 Changes of molar entropy (s), heat capacity (c) and volume (v) at the
p
triple point of argon. The entropy is measured from an arbitrary zero
to liquid is less drastic than that from liquid to gas. However, at high
pressures the situation is very different, for whereas the solid-fluid discon-
tinuities are but little affected by pressure, as is shown by the near-vertical
slope of BD in Figure 1.1, the size of the liquid-gas discontinuities de-
creases, slowly at first, but then with increasing rapidity as the two states
become indistinguishable at the critical point C. A fascinating account of
the early experimental attempts to establish the unity, or continuity, of the
fluid states has been given recently by Levelt Sengers4.
The continuity of the two fluid states contrasts sharply with the apparent
lack of continuity between the fluid and the solid state. It is, of course,
impossible to prove that the lines B D and B D of Figure 7.7(a) never
X X 2 2
meet at a critical point but the solid-fluid transition has been followed
experimentally to, for example, 7400 bar and 50 K for helium and to
12000bar and 330K for argon without changing its character in any way5.
Computer simulation of model systems under extreme conditions also fails
to give evidence for a solid-fluid critical point.
The temperatures of the triple points of substances range from 14 K for
hydrogen to temperatures too high for accurate measurement for sub-
stances such as diamond6. Triple-point pressures are never very high, that
of carbon dioxide being one of the highest known at 5.2 bar. Higher
pressures have been reported only for the elements carbon, phosphorus and
1.1 The liquid State 5
arsenic, for which the triple points are not well established. Most pressures
are of the order of 10"3 bar and a few, such as that of n-pentane, are as low
as 10"7 bar. The triple point differs slightly from the normal melting point
in the presence of air at atmospheric pressure, both because of the finite
slope of BD in Figure 7.7(a), which represents the change of the melting
2 2
point with pressure, and also because of the solubility of air in the liquid.
The former effect is usually the larger and for water lowers the melting
temperature by 0.0075 K whereas the air solubility depresses the melting
temperature by a further 0.0025 K, a total of 0.010 K. The triple point is
more reproducible than the normal melting point and that of water,
273.1600 K, is now used as the single thermometric fixed point that defines
the kelvin7.
Gas-liquid critical temperatures also extend over an enormous range8,
starting with 5.2 K for helium and rising to 2079 K for caesium, the highest
experimentally-determined value and to an estimated 23 000 K for tung-
sten9. Critical pressures are more uniform, with most substances possessing
values around 50 bar but with those of helium and hydrogen being un-
usually low at 2.3 bar and 13 bar, that of water being unusually high for a
non-metallic substance at 221 bar, and the experimentally-determined value
for mercury extremely high at 1510 bar.
The normal liquid range of a substance is sometimes defined as the
temperature interval between the normal melting point and the normal
boiling point, the latter being the temperature at which the vapour pressure
is one atmosphere. This is an artificial definition which has little to
recommend it. As may be seen from the large range of triple-point and
critical pressures quoted above, a pressure of one atmosphere has no
fundamental significance and refers to quite different relative conditions for
different substances. In this book no undue emphasis is placed on that part
of the liquid state which happens to lie below one atmosphere pressure.
The triple or melting point of a substance is much more susceptible to
small variations in the symmetry of the intermolecular potential than is the
critical point. For example, the isomeric hydrocarbons n-octane and
2,2,3,3-tetramethylbutane have the very comparable critical temperatures
of, respectively, 568.8 and 567.8 K but their melting points of 216.4 and
373.9 K are quite different. Often highly-symmetric, pseudo-spherical mol-
ecules such as adamantane (melting point 541.2 K) have unusually high
melting temperatures and, therefore, small liquid ranges, and many such
substances (e.g., hexachloroethane, melting point 460.0 K) sublime directly at
atmospheric pressure.
Such materials undergo a first-order transition in the solid state from a
normal crystalline solid to a so-called plastic crystal or rotator-phase solid
stable between the transition temperature and the melting point10. In the
plastic crystalline phase the molecules possess a considerable degree of
rotational motion although full three-dimensional translational order is
maintained under normal pressures.
The wide variation in the properties of liquids makes it useful to attempt
6 Introduction
a qualitative classification of liquids before discussing any of their proper-
ties in detail. A satisfactory classification can be made only in terms of the
intermolecular forces, for it is these forces that are the sole determinants of
all the physical properties discussed in this book. At low temperatures, the
strength and symmetry of these forces determine the properties of the
crystal. In the fluid states at higher temperatures, the symmetry becomes
less important.
The equilibrium properties of a substance, whether it is solid or fluid, are
the result of a balance between the cohesive or potential energy on the one
hand, and the kinetic energy of the thermal motions on the other. The
translational kinetic energy is the same for all molecules at a given
temperature—the classical principle of the equipartition of energy—and so
it is solely the differences in the strength and types of the intermolecular
energies that cause the properties of one substance to differ from those of
another at this fixed temperature. If liquids are compared, not at the same
temperature, but at the same fraction of, say, their critical temperatures,
then it is found that it is differences in type and symmetry of the in-
termolecular energies that are responsible for the differences. The following
classes of liquids may be distinguished, in increasing order of complexity:
(1) The noble gases The molecules are monatomic and so, in isolation,
spherically symmetrical. The force between a pair of molecules is
entirely central; that is, the force acts through the centres of gravity and
neither molecule exerts a torque on the other.
(2) Homonuclear diatomic molecules such as hydrogen, nitrogen, oxygen and
the halogens, and heteronuclear diatomic molecules with negligible dipole
moments, such as carbon monoxide The internuclear distances are here
much smaller than the mean separation of the molecules in the liquid,
and so the intermolecular forces do not depart greatly from spherical
symmetry.
(3) The lower hydrocarbons and other simple non-polar substances such as
carbon tetrachloride The lower hydrocarbons are comparable in sym-
metry with diatomic molecules, but as the number of carbon atoms
increases, the maximum internuclear distance within one molecule cea-
ses to be small when compared with the mean intermolecular sepa-
ration. That is, the forces depart greatly from spherical symmetry.
(4) Simple polar substances such as sulphur dioxide and the hydrogen and
methyl halides These molecules have a direct electrostatic interaction
between permanent dipole moments superimposed on a force field
which is otherwise reasonably symmetrical. Molecules with large quad-
rupole moments, such as carbon dioxide and acetylene (ethyne), are few
in number but must be included in this class.
(5) Molecules of great polarity or electrical asymmetry Water, hydrogen
fluoride and ammonia are in this class. The polarity is often localized in
one part of the molecule, as in organic alcohols, amines, ketones and
nitriles.
