THERMODYNAMICS OF CATION EXCHANGE .6. SELECTIVITY AND ACTIVITY COEFFICIENTS IN MODERATELY CONCENTRATED SOLUTIONS

The cation-exchange equilibria of Na+-H+, Na+-Cs+, and Na+-Sr2+ have been examined on the relatively low-capacity and highly swollen phenolsulfonic acid exchanger Zeo-Karb 315 in the form of a coherent disk. Measurements on each ion pair have been made at two concentrations, one dilute and one moderately concentrated. Coion uptake and water uptake have also been studied in detail. A thorough thermodynamic analysis of the results has been carried out to elucidate the effects of coion sorption and changes in water activity on the thermodynamic properties of homoionic and heteroionic resins and on the exchange equilibria. The activity of any particular homoionic resin in a solution at nonzero concentration is affected by the activity of water and by the coion sorption. When the resin in equilibrium with an infinitely dilute solution is taken as standard state, a decrease in the water activity raises the activity coefficient, while coion sorption lowers it. The effect of the water activity is the more important at low concentrations, and the activity coefficient becomes greater than unity. Coion sorption becomes increasingly important as concentration increases, and its effect on the activity coefficient eventually outweighs that of the water activity. Thus the activity coefficient passes through a maximum and falls to values less than unity at sufficiently high concentrations. Thermodynamic equilibrium constants of uni-univalent exchange reactions are only slightly affected by allowing for coion uptake and swelling changes. The coion term is the more important. In the uni-bivalent exchange, the effect of the water activity term on the equilibrium constant is quite large because the activity of water in the external solution at constant coion concentration is sensitive to the valency of the counterions. The activity coefficients of the two cationic forms in a heteroionic resin are a measure of the ideality of the resin mixture. Allowances for coion sorption and water activity are always important in calculating these activity coefficients. When compared on the rational mole fraction scale, the departures from ideality are no greater for Na+-Sr2+ than for Na+-Cs+. They are greatest for Na+-H+, although the selectivity coefficient is close to unity in this system.