Group contributions to activity coefficients from the hard sphere expansion corresponding states theory

A new method has been developed for predicting liquid activity coefficients in ternary mixtures from group contributions. In this method, activity coefficients are obtained from the excess Gibbs free energy of mixing at constant temperature and pressure. In calculating this excess function, the constituent and mixture Gibbs free energies are each represented by an expansion about a pure reference fluid in powers of ratios of hard-sphere diameters and molecular attraction parameters. When the pure component differs from the reference by a single structural group, these ratios represent, respectively, the size contribution and the attraction contribution of this group to the thermodynamic property of the pure fluid. Contributions of intermolecular repulsion to the excess Gibbs free energy are calculated directly from hard-sphere equations of state for the mixture and pure components. The effect of polar contributions calculated by a Padé approximant is also examined. Results indicate that the method developed from the hard-sphere expansion corresponding-states theory is useful for predicting activity coefficients in ternary mixtures when unlike-pair interaction parameters are fitted to binary activity coefficient data. Furthermore, the method shows promise in providing a theoretical basis for applying group contributions to activity coefficients.Nomenclature A Residual Helmholtz free energy - C _p Constant-pressure heat capacity - H _vap Heat of vaporization - P ^s Saturated vapor pressure - R Gas constant - T Temperature - U ^HS Hard-sphere internal energy - V _c Critical volume - V ^L Liquid volume - x Dimensionless residual thermodynamic property - Z Compressibility factor - d Center-to-center distance between two touching molecules - k Boltzmann constant - n Moles - x Liquid mole fraction - y Vapor mole fraction - Volume expansivity - Liquid activity coefficient - Minimum molecular attraction potential - Isothermal compressibility - Permanent dipole moment - 3.14159... - Density - Fugacity coefficient Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.