Multicomponent ion-exchange equilibria. II. Prediction of ternary equilibria for the system Ca²⁺-Mg²⁺-H⁺ from the data of the component binary systems

A scheme for treatment of multicomponent ion-exchange equilibria is present. Binary and ternary ion-exchange equilibria involving Ca2+, Mg2+ and H+ studied using the strong-acid cation exchanger Amberlite IR 120. Considering the nonideal nature of the component binary exchange equilibria and applying the above-mentioned multicomponent ion-exchange framework to these systems, resinate-ion interaction parameters and activity coefficients of the ions in the exchanger phase have been determined. The activity coefficient values thus determined are compared with those obtained through use of the so far most commonly used equations, derived from the solid-solution model, and also by using somewhat modified forms of those equations deduced herein. The exchanger phase ionic activity coefficients and the activities in the ternary system Ca2+-Mg2+-H+, both on the basis of equivalent fraction and mole fraction, have been predicted by using the predicted resinate ion concentrations (derived from the component binary data) and the binary interaction parameters in the resin phase. The ΔG° values of the three-component binary exchange reactions have been found to be in good agreement with each other. The predicted ternary data based on the pair of binary exchange results containing the most preferred ion have found to be consistent with the experimentally obtained results pertaining to this system