Hydration energies and entropies for Mg2+, Ca2+, Sr2+, and Ba2+ from gas-phase ion-water molecule equilibria determinations

The sequential enthalpies Delta H(n-1,n)degrees free energies Delta G(n-1, n)degrees, and entropies Delta S-n-1,S- (n)degrees for the hydration reaction M(H2O)(n-1)(2+) + H2O = M(H2O)(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 st 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 Mg2+ and Ca2+ (Siegbahn and coworkers). 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 shelf 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 Delta S-n-1,S- 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 Delta H(0, 14)degrees(Ca2+) - Delta H(0.14)degrees(Mg2+) is within 3 kcal/mol of the total hydration difference Delta H(h)degrees(Ca2+) - Delta H(h)degrees(Mg2+) for liquid water. A similar result is obtained also for the hydration free energies. Extension of the determinations to ligands that model bending and coordination in biocomplexes of Mg2+ and Ca2+ is discussed.