To provide a thermodynamic basis for understanding zeolite-water interactions in geologic systems, ion-exchange experiments were conducted at 25 degrees C between clinoptilolite, which is the predominant zeolite mineral in altered pyroclastic and volcaniclastic rocks, and aqueous mixtures of Na+/K+ and Na+/Ca2+. Isotherm points were obtained by equilibrating Na-clinoptilolite, which was prepared from clinoptilolite-rich tuff from Death Valley Junction, California, USA, and Na+/K+ and Na+/Ca2(+) chloride solutions having different ionic concentration ratios, but constant total normalities of 0.5, 0.05, or 0.005 N. The experimental data were interpreted using a Margules thermodynamic formulation for zeolite solid solutions, coupled with the Fitter model for aqueous activity coefficients. The isotherm data for 0.5 N Na+/K+ and Na+/Ca2(+) solutions were used to derive equilibrium constants and Gibbs free energies for the ion-exchange reactions, as well as parameters for the Margules model. Using the same parameters derived from the 0.5 N data, isotherms were calculated for the 0.05 and 0.005 N solutions. The predicted values agree very well with experimental data, including other data at 0.05 N solution concentration with nitrate as the supporting anion. The results of this study indicate that a Margules solid solution model for zeolites, coupled with an activity coefficient model for aqueous solutions (e.g., Pitzer model), can successfully describe and predict binary ion-exchange equilibria between aqueous solutions and the zeolite mineral clinoptilolite over a wide range of solution composition and concentration, and may provide a foundation for quantitative understanding of ion-exchange equilibria in multicomponent geochemical systems.