Gibbs free energies of transfer of K(I) ion from water to water-dimethyl sulfoxide mixtures corrected to zero ionic strength have been used to deduce information concerning states of solvation of K+ ion in the purely aqueous phase and in the mixed solvent phase. It was found that the largest number of water molecules which needed to be assigned to the solvent cage of K+ was 11 in either phase. The partition equilibrium constant, /?0, for the distribution of K(H20)H+ between the two phases was found as a function of the mole fraction of dimethyl sulfoxide in the mixed solvent phase. The largest number of dimethyl sulfoxide molecules which needed to be assigned to the solvent cage was 10. The number of solvent molecules in the solvent cage was allowed to be variable and the overall formation constants of all K(H20)j((CH3)2S0)k+ ions contributing to the free energy of transfer were determined. The results are compared with the results from molecular dynamics computer simulations for K+ where possible