Evaluation of the activity coefficients of ternary molecular solutions from osmotic coefficient data

A method is proposed for the evaluation of the activity coefficients of a solution constituted by a solvent (1) and two non-volatile molecular solutes (2,3) from the experimental dependence of the osmotic coefficient of the ternary solution (1,2,3) on composition. A generalized analytical expression is derived to describe such dependence, based on the sum of the weighted contributions of both binary systems and the contribution due to the mixing effect. With the resulting expression and using the solution of the Gibbs-Duhem differential equation for ternary systems, the equations that allows the evaluation of the corresponding experimental activity coefficients of both solutes in ideal dilute solution reference state (molality scale) are derived. From the comparative analysis and discussion of the results obtained for three ternary systems, it was possible to verify that the proposed methodology provides a rigorous alternative to evaluate suitable values ​​of activity coefficients from experimental data of osmotic coefficients. Finally, in order to facilitate the correlation of these values with equations originated in molecular solution modelling (NRTL, UNIQUAC, etc.), the relationships between the corresponding reference states and concentration scales were established.