The Temperature and Pressure Dependence of the Equilibrium Properties of a System Introducing Thermodynamics in the Classroom Theodros Solomon Addis Ababa University, P.O.Box 1176, Addis Ababa, Ethiopia A cursory examination of the chapters on chemical thermodynami& in a random selection of some popular physical chemistry texthooks shows that only in a few of them is the snbiect matter of chemical thermodvnamics itself defined full;. Most explain what thermodyn~mics"deals with" (for example, I ) , or what it "implies" (2);others (for example, 3) define thermodynamics as the study of the transformation of energy, while some (for example, 4) simply proceed directly into a discussion of the first law of thermodynamics without eivine a fuller definition of chemical thermodynamics or witgout &ing an overview of the subject. As a result, it is not immediately clear to students what these introductory statements about thermodynamics (expressed in terms of transformations of energy) have to do in discussing phase diagrams, colligative properties, the processes of steam and fractional distillation, equilibrium constants, etc., which are among the topics discussed in the regular course of chemical thermodynamics. Levine's (51 -~ . . definition comes close to the heart of the issue. After giving two alternative definitions, a third statement is nhrased as follows: "A kev -~~ - property . . - in thermodynamics temperature, and thermodynamics is sometimes defined as the studv of the relation of temperature to the macroscopic properiies of matter." I t is this aspect of the definition that is sorelv lacking, or not given adequate emphasis, in most textbooks and that should be expanded more full\ in order toaive a better picture of the subject mntLer of chemical thermodynamics. The .purpose . of this article is thus to point out that there lies a great pedagogic advantage in starting the course with a fuller definition of chemical thermodynamics that also hints at the methods or approaches to be adopted, as well as at the contentsof thesubject. The title of this article was chosen to reflect this view., since chemical thermodvnamics is, in fact, the study of the temperature and pressure dependence of the equilibrium properties of a system. This definition admittedly does not make any explicit reference to energy or heat, which are invariably mentioned as the topics that thermodynamics deals with. However, thermodynamics is taught in the undergraduate physical chemistry course in order to help students understand the equilibrium properties of a system and how these are affected by temperature and pressure, these variables being chosen by virtue of the ease with which they can most commonly he controlled in the laboratory or industry (as oppposed to, say, internal energy or volume). t hi applications of thermodynamics to chemical systems that are discussed in all undergraduate physical chemistry textbooks focus on phase equilibria in one and multicomponent systems, properties of dilute, ideal and nonideal solutions (including colligative properties), and chemical equilibria. In all these applications, a recurrent relationship is, as pointed out by Denhigh (6),of the form (using his notation) ~
~
RT where x is an equilibrium property such as vapor pressure, solubility, equilihrium constant. I t is very essential for students to grasp that nearly all chemical thermodynamic applications lead toward relationships of the type given above. In fact. one mav eeneralize, without undue exaggeration, that, other than ;hestatementsof the laws oi ther&dynamics and the definitions of thermodvnamic functions, all that students need to learn in their first course in chemical thermodvnamics is embodied in the temperature and pressure dependence of the equilihrium properties of a system. A recognition of this important concept helps to simplify and demystify chemical thermodynamics. A few examples will help clarify these arguments. Phase diaerams of one-comnonent svstems are mostlv discussed in terms of the temperature dependence of the vapor pressure or through the use of the Clausius-Clapeyron equation
-
~
i's
~~
d lnp -=-
dT
mx.
RP
-
(in the case where the physical transformation is liquid vapor and where the vapor is assumed to behave ideally). For multicomponent systems, phase diagrams are, in fact, pictorial representations of the temperature dependence of the mole fraction solubility (or the inverse, the freezing point temperature as a function of the composition). The properties of ideal and nonideal solutions may be discussed in terms of the heat and volume changes upon mixing the components of the solution, these changes being derived through the temperature and pressure dependence of the fugacity as
~
f;lj)pa characteristicheat quantity =
RP 294
( ~ 3 )= a~ characteristic volume
Journal of Chemical Education
where the equality holds for an ideal solution and the ineaualitv for a nonideal solution exhihitine devi- negative ation from ideality. Le Chatelier's principle in chemical equilibrium can he discussed in qua&itat&e terms through-the temperature and pressure dependence of the equilihrium constant. Thus, for ideal gaseous reactions,
The above examnles have heenselected from those commonly encountered in almost all standard undergraduate physical chemistw textbooks. The argument could, however, also he extendedto more special (physical) applications such as the temperature dependence of the elasticity of rubber (or the thermal effecta accompanying its deformation), electrostriction (which can be discussed through the pressure dependence of the dielectric constant (7)),br to magnetic sys-
tems, whose properties are most commonly described in terms of the dependence of the susceptibility on temperature, pressure, and external field (8). Thus, if students were to know a t the start of the course that everytime a thermodynamic property is introduced its temperature and pressure dependence always follow, from which results of practical importancecan be derived, thenan appreciation of the subject matter and its methodology is instilled in them. In fact, they may even anticipate the course, in that they would know, well before the lectures, where they are heading. The conceptual difficulty inherent
in the subject matter is greatly simplified, and the lecturer can, in fact, make a very brief review of the subject in a couple of lectures. Literature Cited
~
Cambridge. 1966: p 3.' 7. Gugenheim, E. A. Thrrmodynomics, 5th ed.: North Holland: Amsterdam, 1967: p 335. 8. Callen, H. B. Therrnodynomics: Wiley: New York,1960; p 249.
Volume 68
Number 4
April 1991
295
