Using first-principles calculations, we studied the adsorption of alkali ions in pure silica Linde Type A (LTA) zeolite. The probability of adsorbing alkali ions from solution and the driving force for ion exchange between Na+ and other alkali ions at the different adsorption sites were analyzed. From the calculated ion exchange isotherms, we show that it is possible to exchange Na+ with K+ and Rb+ in water, but that is not the case for systems in a vacuum. We also demonstrate that a solvation model should be used for the accurate representation of ion exchange in an LTA and that dispersion interactions should be introduced with care