Using existing data on the ionization energies of alkali metal atoms in small clusters of water, a thermodynamic cycle is proposed from which the hydration enthalpies of the neutral metal atoms can be estimated. Where comparisons are possible, the results are in reasonable agreement with those obtained using both experimental and ab initio methods. Application of the thermodynamic cycle to neutral alkali metal atoms solvated in ammonia yields solvation enthalpies that are significantly lower than those obtained for water.