Modeling Sorbent Phase Nonideality for the Accurate Prediction of Multicomponent Ion Exchange Equilibrium with the Homogeneous Mass Action Law

In this Article the ion exchange equilibrium of binary and multicomponent systems was modeled with homogeneous mass action law using activities and taking account of the partial dissociation of salts according to Kester and Pytkowicz's approach. The activity coefficients in the solution were estimated by the Pitzer model and in the sorbent by Wilson, nonrandom two-liquid (NRTL), and universal quasichemical (UNIQUAC) models. Wilson has already been adopted in the literature, while NRTL and UNIQUAC were investigated here for the first time. The modeling procedure relied on the analysis of experimental data for the constitutive binary systems to fit the equilibrium constants and the binary parameters of the activity coefficients for the sorbent, which were then applied to predict the multicomponent isotherms. The models were tested with 22 binary, 14 ternary, 5 quaternary, and 1 quinary systems, totalizing 1494 points. The results showed that NRTL and Wilson provide reliable and very similar predictions (average deviations equal to 11.35 % and 11.53 %, respectively) while UNIQUAC performs poorly (16.02 %). The ideal model, which assumes unitary activity coefficients, achieved the largest error (34.20 %), thus emphasizing the chief nonidealities. The extension of ion association also proved to be very important, attaining values near 60 %.