We have adapted a grand ensemble Monte Carlo simulation method to directly compute, for the first time to our knowledge, univalent cation exchange isotherms in zeolites. The computed isotherms for the exchange of sodium in NaY faujasite by lithium, potassium, rubidium, and cesium ions, respectively, are in good agreement with the experimental ones. They display the three main types of behavior observed in zeolites, namely, a monotonous evolution of selectivity throughout the exchange process (Li(+)), a selectivity reversal (K(+)), and an incomplete exchange (Rb(+) and Cs(+)). The initial stage of the cation exchange is shown to be dominated by the hydration energy of the cations in the external aqueous solution. The final part of the process is. often dominated by the cation-framework and cation-cation interactions. A crossover between these two regimes explains the frequently observed reversal of selectivity phenomenon. The incomplete exchange observed in the case of Rb(+) and Cs(+) is shown to correspond to a blocked state of the system for highest accessible composition of the aqueous solution. This stable state is shown not to be linked to an inability of the cesium cations to cross the six-ring window in order to penetrate into the smallest cages.