The thermodynamic theory of ion exchange selectivity at an air/solution interface is rigorously derived. The free energy change driving ion exchange is shown to be a sum of terms arising from counterion interactions with the solvent, chemical interactions with the surfactant, and mechanical effects at the surface. Each of these terms can be explicitly calculated and the solvation interaction is shown to dominate the exchange free energy. These results may be extended to provide a qualitative description of ion exchange in other systems, such as resins or micelles. A partial dehydration model of ion exchange is presented and is shown to provide falsifiable, quantitative predictions concerning ion exchange selectivity. Most available ion exchange data for anion and cation exchange, both within a valence group and between ions of different valences, are unified in this model.