Statistical thermodynamics of mixtures of molecules of different sizes
The central problem in the theory of mixtures is the calculation of the free energy of mixing of molecules of different sizes. An explicit calculation of this free energy is made for a mixture in which all intermolecular potentials are of the form uαα(r)=(σαα/r)n, where σαα is a distance characteristic of the interaction of two molecules of species α, and where σαβ= 1/2(σαα+σββ) when α≠β. This result follows from a solution of Percus-Yevick integral equation for the pair distribution function of a mixture of hard spheres. The form of the free energy provides a criterion by which existing theories can be judged, and it is shown that an approximation of the type originally suggested by van der Waals is superior to approximations based on the concept of random mixing. Molecules that differ only in size mix with a small and negative excess free-energy. The recommended approximation is confirmed by comparison with experiment.