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Statistical Thermodynamics
book

Statistical Thermodynamics

by Iwao Teraoka
March 2019
Intermediate to advanced content levelIntermediate to advanced
352 pages
9h 26m
English
Wiley
Content preview from Statistical Thermodynamics

14Regular Solutions

In this chapter, we learn about thermodynamics of a binary mixture. If you remember such words as a critical temperature and a miscibility gap, you should have learned in physical chemistry the thermodynamics of mixing, at least phenomenologically. Here we apply canonical‐ensemble formulation to a system of an A–B binary mixture in a liquid state. Examples include a water–acetone mixture and a water–pentanol mixture. Unlike a mixture of gas molecules, we cannot add or remove a molecule without changing the volume, that is, the mixture is incompressible. We neglect a small‐volume change upon mixing due to a packing change.

First, we consider a simple mixture of A molecules and B molecules that have an equal size. Subsequently, we consider a binary mixture of different sizes. For both mixtures, we adopt a mean‐field approximation for the interaction between the molecules. This model is called a Hildebrand regular solution.

14.1 Binary Mixture of Equal‐Size Molecules

14.1.1 Free Energy of Mixing

Suppose we mix NA molecules of A and NB molecules of B. Here, NA is not the Avogadro's number. The mixture fills a box consisting of N sites (N = NA + NB), each being occupied by either an A molecule or a B molecule (see Table 14.1). Since the two molecules have an equal size, the mole fraction xj = Nj/N (j = A, B) is identical to the volume fraction.

Table 14.1 Numbers of molecules and mole fractions in an A–B mixture.

Molecule Number of molecules Mole fraction ...
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Publisher Resources

ISBN: 9781118305119Purchase book