CALCULATION OF IDEAL OR EMPIRICALLY MODIFIED MASS-ACTION EQUILIBRIA IN HETEROVALENT, MULTICOMPONENT ION-EXCHANGE

For chemical-engineering design purposes, it is useful, where possible, approximately to characterize the equilibrium between an ion-exchange material and any two exchangeable ion species involved by a constant selectivity coefficient. This can be done with the ideal or empirically modified mass-action law, but the application of even this simplified model to systems involving more than two exchangeable ion species, some of which differ in their valences, can lead to extremely cumbersome calculations. To overcome this difficulty, a successive-approximation algorithm is presented, and specifically applied in the form of a program for a small electronic calculator.