EXCESS GIBBS FREE-ENERGY OF MIXING

The statistical mechanical approach to developing excess Gibbs free en ergy models for liquids using lattice theories in the Canonical ensemb le is reexamined numerically in the light of the fundamental observati ons of Sandler et al. (S.I. Sandler et al., 1989. Fluid Phase Equilibr ia, 45: 251-265). Calculations are carried out for mixtures of hard sp here fluids and model mixtures of Lennard-Jones (LJ) molecules to find the effect of varying the relative size of the hard sphere molecules and the unlike interaction parameters for LJ mixtures on the differenc e between the excess Gibbs free energy at constant pressure and the ex cess Helmholtz free energy under different mixing constraints. It is s hown that for engineering purposes lattice theories can only provide m athematical expressions that fit mixture data accurately provided thes e expressions contain one or two adjustable parameters. Further, for f itting excess Gibbs free energy data it is shown that expressions for the excess Helmholtz free energy under any of the constraints (''Scatc hard mixing'', mixing under constant number density or constant reduce d density) are equally useful.