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.