Thermodynamic modeling of activity coefficient and prediction of solubility: Part 1. Predictive models

A new activity coefficient model was developed from excess Gibbs free energy in the form G(ex) = cA(a) x(1)(b)...x(n)(b). The constants of the proposed model were considered to be function of solute and solvent dielectric constants, Hildebrand solubility parameters and specific volumes of solute and solvent molecules. The proposed model obeys the Gibbs-Duhem condition for activity coefficient models. To generalize the model and make it as a purely predictive model without any adjustable parameters, its constants were found using the experimental activity coefficient and physical properties of 20 vapor-liquid systems. The predictive capability of the proposed model was tested by calculating the activity coefficients of 41 binary vapor-liquid equilibrium systems and showed good agreement with the experimental data in comparison with two other predictive models, the UNIFAC and Hildebrand models. The only data used for the prediction of activity coefficients, were dielectric constants, Hildebrand solubility parameters, and specific volumes of the solute and solvent molecules. Furthermore, the proposed model was used to predict the activity coefficient of an organic compound, stearic acid, whose physical properties were available in methanol and 2-butanone. The predicted activity coefficient along with the thermal properties of the stearic acid were used to calculate the solubility of stearic acid in these two solvents and resulted in a better agreement with the experimental data compared to the UNIFAC and Hildebrand predictive models.