On the statistical mechanics of dilute and of perfect solutions

1.Introduction and Definitions .—In a previous paper the author discussed the laws of dilute and of perfect solutions. It was pointed out that the laws of dilute solutions take different forms according to the concentration scale used, these forms becoming identical only at infinite dilution. Of these various sets of laws that corresponding to the mole-fraction scale of concentration has in certain respects simpler properties than the others and is more symmetrical between solvent and solute. In particular only in this form is it possible for the laws of dilute solutions to hold at all concentrations, in which case they become the laws of perfect solutions. It was shown how this set of laws of perfect solutions could be deduced by thermodynamic reasoning from certain assumptions about the additivity of energies and volumes on mixing, but these assumptions were not of a very simple form. Nor was any reason found why the laws of dilute solutions should take the particular form corresponding to the mole-fraction scale of concentration, except analogy with the laws of perfect solutions. In the present paper an attempt will be made to remedy this omission by considerations of statistical mechanics. The method used will be that of partition functions described in Fowler’s text-book. This method is more elegant than Gibbs’ method of the canonical ensemble, does not suffer from the logical inconsistencies of Boltzmann’s method of “thermodynamic probability,” and is more powerful than either of these.