Hydration Energies and Entropies for Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ from Gas-Phase Ion−Water Molecule Equilibria Determinations

The sequential enthalpies, free energies, and entropies for the hydration reaction M(H 2 O) n - 1 2+ + H 2 O = M(H 2 O) n 2+ were determined in the gas phase for M = Mg, Ca, Sr, Ba. The gas-phase ion hydrates were produced by electrospray, and the hydration equilibria were determined in a reaction chamber attached to a mass spectrometer. The exothermicities of the ( n − 1, n ) reactions at low n ( n = 1 to n = 5) are very high, and the corresponding equilibria require very high temperatures and could not be determined. For these low n, good theoretical results are available for Mg 2+ and Ca 2+ (Siegbahn and co-workers). A combination of the theoretical data with the experimental results (from n = 6 to n = 14) provides information on the inner and outer hydration shell structure and energetics of the hydrates. Very good agreement is observed between the theoretical and experimental energies where they overlap. For Mg, Ca, and Sr the first six molecules go into the inner shell while the seventh and higher molecules go into the outer shell(s). However, the sequential energies indicate crowding in the inner shell of Mg. Six or seven molecules can be filled in the inner shell of Sr, while for Ba the inner shell number may be as high as 8 or 9. The observed entropy changes are, in general, consistent with the assigned shell structures. In particular, there is a large change of Δ S n - 1, n on transition from the inner ( n = 6) to the outer ( n = 7) shell for Mg, Ca, and Sr. The difference between the gas-phase total enthalpies (Ca 2+ ) − (Mg 2+ ) is within 3 kcal/mol of the total hydration difference (Ca 2+ ) − (Mg 2+ ) for liquid water. A similar result is obtained also for the hydration free energies. Extension of the determinations to ligands that model bonding and coordination in biocomplexes of Mg 2+ and Ca 2+ is discussed.