Free energies of mixing

Abstract

The differences between the excess Gibbs free energy for mixing at constant pressure and the excess Helmholtz free energy for mixing subject to other constraints are considered. For three mixing processes subject to other constraints these differences are calculated directly and from approximate equations for hard-sphere mixtures and mixtures of Lennard-Jones molecules. It is found that only for mixing at ideal solution volume, i.e., “Scatchard mixing”, is the difference small, while for the other mixing processes the difference may be an order of magnitude larger than the excess Gibbs free energy. One consequence is that excess Helmholtz free energies obtained from lattice theories should be corrected to obtain excess Gibbs free energies of mixing at constant temperature and pressure, for which the approximate equation given in this communication will be useful. A second consequence is that for the calculation of the excess Gibbs free energy of mixing from computer simulations, the isobaric—isothermal ensemble is preferred over the canonical ensemble.