Prediction of ion-interaction parameters of binary 2:1 and 2:2 ion-exchange systems by the coupling of the Margules model with a linear free energy correlation approach

The Gibbs free energy of exchange (ΔG∘ΔG∘, T = 303 K; TN = 0.005 N) for aqueous binary mixtures of Na+, Cu2+, Zn2+, and Pb2+ previously calculated using Pitzer’s and Margules (MM) models for aqueous (γi’s) and solid phase (Aij  ) cationic parameters, respectively, were equated with a linear free energy correlation approach, ΔGLCA∘, which correlates thermodynamic parameters with cation properties. The resulting linear relationships between ΔGMM∘ and ΔGLCA∘ for the binary mixtures permitted the evaluation of the Margules parameters (A12, A21) for other (1:2)- and (2:2)-exchange systems, as well as to predict the ion-exchange isotherm profile. These findings, consequently, allowed the prediction of selectivity trends of clinoptilolite for different groups of divalent cations without the need of empirical data. In general, clinoptilolite showed greater affinity for univalent cations of bigger ionic radii, which corresponds to its more negative non-solvation energies. The higher affinity of clinoptilolite for divalent cations of bigger ionic radii is probably owing to greater framework stabilization provided by higher charge density and polarizability. Homoionic Ca- and Mg-clinoptilolite showed greater affinity for any other divalent cation compared to the exhibited by its Na-form of the exchange, which is useful for practical applications.