On the functional forms of activity coefficients and their properties

A complete system of partial differential equations is obtained for the logarithms of activity coefficients of real chemical mixtures. All solutions of these equations are obtained under mild regularity conditions and the conditions that the limit of ln (f_α), as n_α/n tends to unity, is equal to zero. It is shown that all of the functions ln (f_α) can be determined if any one of them is a known function of temperature, pressure and the independent mole fractions. These results are used to compute the deviations of partial and total volume, entropy and specific heats at constant pressure, and the laws of mass action from what would be given for ideal mixtures. Conditions for static and dynamic stability of equilibrium are obtained, and a forward time integration procedure is given for satisfaction of the laws of mass balance and the full form of the laws of mass action.