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Most students of physical chemistry, as well as their teachers, regard
equilibrium chemical thermodynamics as an impressive, useful, and
stable subject that was "finished" long ago. As part of their
education, students in physical chemistry have been taught the importance
and the usefulness of the Gibbs function (formerly called the Gibbs
free energy function). The antiquity of the subject and the presumed
mastery of its basics by physical chemistry teachers are taken for
granted as given parts of the educational and scientific scene in
chemical education. It comes as a surprise to occasionally discover
that even those who teach this venerable subject sometimes disagree,
not merely in matters of style or organization of the subject, or
in matters of mathematical elegance, but in matters of real substance.
The following four papers are examples of this. My role here is simply
to introduce this set of papers and to provide some orientation regarding
their contents.
The authors have been in private communication with each other for
a period of over four years about the use and the proper definition
of the Gibbs function. The lengthy period of correspondence has not
resulted in any significant agreement. The Editor of this Journal
was unable to settle the resulting controversy by normal review
procedures. In an attempt to break the deadlock he asked me, as an
impartial outsider to the situation, for assistance in deciding an
appropriate literary form in which the authors could present their
own points of view as well as comments on the views of the other authors.
The original hope was that agreement could eventually be reached on
disputed points by the give and take of the interchange of further
correspondence, and that the outcome would be published in the form
of a "paper symposium" on the subject, with me as the "chairman"
of the symposium.
It must be said at the outset that the prolonged correspondence has
not produced much agreement among the authors. This is surprising
(and disappointing) since (a) all of these authors are experienced
teachers of physical chemistry and thermodynamics, and (b) most readers
of this Journal would suppose that the nature of the Gibbs
function and the manner in which it is to be used are issues that
have been settled long ago, and that there are no disagreements of
any significance between practitioners of thermodynamics regarding
these matters.
Historical Background
The beginning of the controversy was occasioned by a paper of Schomaker
and Waser (1), in which they dealt with an ancient problem
going back to Bates. This problem is by now variously described as
the "Ether Problem", or the "Bates Problem", or the "Bates-Tykodi Problem".
It considers the change occurring when a two-phase system of liquid (e.g., ether) and its vapor, coexisting at equilibrium at a given temperature, is allowed to expand into a larger space (originally evacuated), with a final state consisting
of the liquid and vapor still at equilibrium at the same temperature,
but now occupying a larger volume (with the volumes of the liquid
and vapor phases being smaller and larger, respectively, than in the
original state). Since the initial and final states of the ether are
both two-phase liquid/vapor systems at the same temperature and pressure,
then of course deltaG = 0 for the ether itself; but how should
the spontaneous nature of this process be expressed thermodynamically?
Schomaker and Waser showed straightforwardly that when the ether and
its surroundings are considered together, then deltaS > q/T
as required by the Second Law. They further showed that deltaA
< 0 for the system that consists of the original two-phase liquid-vapor
system and the originally evacuated space into which the ether
expands. This is also a traditional result since for a system whose
volume remains constant at a given temperature, the Second Law condition
for a spontaneous process is that deltaA < 0. Schomaker and Waser
took things a step further and by so doing initiated the discussion
and controversy that eventually led to the following four papers.
In this step they took as the thermodynamic system of interest not
just the ether but the ether together with the entire container that
separates it from the surrounding constant-temperature, constant-pressure
fluid. For this system, they argued, the criterion deltaG < 0
is valid.
This conclusion of theirs has been seriously criticized, especially
by Tykodi (2), and later by Noyes (3). Extensive discussion
ensued, including several other people who were drawn into the controversy,
of whom only Wood and Battino (4) chose to submit a manuscript
as part of this symposium.
The original controversy dealt with the question: is deltaG for
the Bates process negative as argued by Schomaker and Waser (1),
or zero (or almost so), as argued by Tykodi (2)? This led to
concerns by Noyes about how the pressure should be defined (3)
and by Wood and Battino that it is not appropriate to utilize the
Gibbs function in describing the Bates process (4). The various
authors not only disagreed, sometimes sharply, on these matters but
eventually carried the discussion into related but somewhat more distant
areas including the following:
- The role of the container walls, which experience
a change in the differential pressure on the inside and outside surfaces
(5).
- The question of whether it is possible to define
a Gibbs function for anisotropic solids (6) and if it is, how
it should be done (5,7).
- The use of "Global" intensive properties
(in particular pressure) of the surroundings to characterize a system
in which such properties may not be uniform (5).
- The relationship of the variance (in the sense of
the phase rule) of a system to its most appropriate thermodynamic
function (4).
- A historical issue--exactly what did J. W. Gibbs
say regarding the definition of a Gibbs function for systems in which
the pressure was not uniform and/or there were anisotropic solids
present (5-7)?
When it finally became apparent that there was to be no resolution
of the disputed points it was decided to publish the papers in the
present form, which allows each contributor to make his positions
as forcefully and clearly as possible, along with his assessment of
the deficiencies of the other papers as seen from his own perspective.
Bearing in mind that although the set of papers originally had
as basis the "expansion of ether into a vacuum" problem, the
set of questions and the interests eventually addressed by the various
authors diverged somewhat as discussion proceeded. Here we merely
point out some of the main issues addressed in the four papers in
order to guide the reader to a quicker path to reading them in context.
Some Main Issues Considered in the Four Papers
Schomaker and Waser
- These authors emphasize the importance of "global variables"
of a system. By this term they mean that the pressure and temperature
of the surroundings are the values that determine the thermodynamic
properties of the system (even if there might be variations of the
pressure within the system). From their point of view, the
pressure "of" a system is the pressure exerted on
it by the surrounding fluid with which it is in thermal and mechanical
equilibrium, and is therefore the pressure that is appropriate to
such expressions as G= U + pV - TS.
They believe that this takes care of the possibility that regions
within a system may have different pressures, or even have pressures
that are undefined; all that is required is that the pressures within
the system are functions of the external pressure (that of the surroundings).
- As one of their main convictions, Schomaker and Waser hold that
if the surroundings of a system are kept at fixed temperature and
pressure, then any process that is isothermostatic and isobarostatic
(in their sense) will conform to the condition deltaG is less than or equal to
0 in a quite general sense, even in the special case of a system confined
to a fixed volume by an ideally rigid container.
- Schomaker and Waser have given considerable attention to the thermodynamic
properties of systems that are exposed simultaneously to different
pressures, such as is the case for the walls of a container for which
the inner and outer pressures differ. To deal with this they applied
elasticity theory to irregularly shaped solids. Although I requested
that the details of such calculations be omitted from their manuscript,
they did introduce the notion that the container walls may contribute
significantly to the overall change in the Gibbs function.
- Although it is not a subject of controversy between the authors
of the other papers, Schomaker and Waser also emphasize a distinction
between the changes in the values of the energy, entropy, etc.
and the changes in the corresponding functions, cf. their discussion
of the difference between deltau and deltaU in sections
I and II of their paper.
Tykodi
Tykodi's contribution is largely a reaction to the work of Schomaker
and Waser. In particular:
- Tykodi has also considered in detail just how the changes in the
Gibbs function for container walls should be evaluated; here, too,
I requested that the details be omitted from the manuscript. His conclusion--the
contribution of the walls to the overall value of deltaG can
not be evaluated (or even defined) in the general case but for the
special case of ideally rigid walls it is not negative, and is very
small.
- He contends that the way in which Schomaker and Waser define the
Gibbs function for a system that has a different pressure from its
surroundings is misleading, and that what they call the Gibbs function
for a composite system is really the Availability function. His views
on the Availability function have been published previously (8).
Noyes
- Whereas both Schomaker and Waser and Tykodi have regarded the
original Bates problem as an incentive to extend the traditional views
regarding the Gibbs function to systems in which pressure differentials
may exist, Noyes has concluded that such efforts are misguided and
meaningless. He holds that certain statements of J.Willard Gibbs should
be interpreted in this sense (Schomaker and Waser disagree). Noyes
has even concluded that it is not meaningful to attempt to define
a Gibbs function for systems in which anynonuniformity of
pressure may exist, e.g., systems that contain anisotropic solids.
- He also concludes that a system should be defined in a way that
excludes the walls of its container.
Wood and Battino
- Wood and Battino stay closer to the issues raised directly by
the original Bates problem. They are primarily concerned to emphasize
various traditional points regarding the definition of a system, definitions
of spontaneity and reversibility, the relationship between the external
constraints of a system, and the corresponding thermodynamic potential
that is appropriate for the simplest description.
- Their most provocative idea, perhaps, is that the Gibbs function
is not an appropriate function for the description of changes in a
one-component system containing two phases at constant temperature
and pressure. They therefore conclude that the whole controversy occurs
because of a misguided effort to use the Gibbs function in an inappropriate
situation.
Conclusion
It is hoped that readers of these symposium papers will profit from
the experience of seeing how even experts in thermodynamics can argue
themselves into positions that although plausible from the individual
author's standpoint, are nevertheless difficult to reconcile. As is
usual in science, time will tell which of the sharply expressed and
tenaciously held views present in these papers can be maintained.
In the meantime, perhaps teachers of thermodynamics may be inspired
to greater efforts to clarify basic concepts in their own teaching
and be inclined to greater tolerance in dealing with their students'
attempts to express their own understanding.
Literature Cited
- Schomaker, V.; Waser, J. J.Chem. Educ. 1988,
65, 968; 1990, 67, 384.
- Tykodi, R. J. J.Chem. Educ. 1990, 67,
383.
- Noyes, R. M. J.Chem. Educ. 1992, 69,
470.
- Wood, S. E.; Battino, R. J.Chem. Educ. 1996,
73, 408.
- Schomaker, V.; Waser, J.J. Chem. Educ. 1996,
73, 396.
- Noyes, R. M. J. Chem. Educ. 1996, 73,
404.
- Tykodi, R. J. J. Chem. Educ. 1996, 73,
398.
- Tykodi, R.J. J.Chem. Educ. 1995, 72,
103.
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