The statistical thermodynamics of multicomponent systems

This paper describes a new statistical approach to the theory of multicomponent systems. A ‘conformal solution’ is defined as one satisfying the following conditions: (i) The mutual potential energy of a molecule of species Lr and one of species Ls at a distance ρ is given by the expression urs(ρ) = frs u00(grsρ), where u00 is the mutual potential energy of two molecules of some reference species L0 at a distance ρ, and frs and grs are constants depending only on the chemical nature of Lr and Ls. (ii) If L0 is taken to be one of the components of the solution, then frs and grs are close to unity for every pair of components. (iii) The constant grs equals ½(grr + gss). From these assumptions it is possible to calculate rigorously the thermodynamic properties of a conformal solution in terms of those of the components and their interaction constants. The non-ideal free energy of mixing is given by the equation ∆*G = E 0 ƩƩ rs xrxsdrs, where E0 equals RT minus the latent heat of vaporization of L0, xr is the mole fraction of Lr and drs denotes 2frs — frr — fss. This equation resembles that defining a regular solution, with the important difference that E0 is a measurable function of T and p, which makes it possible to relate the free energy, entropy, heat and volume of mixing to the thermodynamic properties of the reference species; and the predicted relationships between these quantities agree well with available data on non-polar solutions. The theory makes no appeal to a lattice model or any other model of the liquid state, and can therefore be applied both to liquids and to imperfect gases, and to two-phase two-component systems near the critical point.