Free Energies of Hydration for Metal Ions from Heats of Vaporization

Consistent thermochemical data are of major importance for predicting and rationalizing stability and reactivity throughout chemistry. The free energy of hydration (ΔGhyd) substantially defines the aqueous chemistry of metal ions and aids our understanding of the properties of water and has thus been widely studied both theoretically and experimentally.

This paper first shows that the experimental standard half reduction potential for the process Mn+ + n e- → M is accurately described using a simplified version of Trasatti's thermochemical cycle involving the ionization potentials, ΔGhyd of Mn+, and the standard heat of vaporization (ΔHvap) of M. This approximation, which neglects entropy, is shown to be valid both by actual performance (uncertainty ~0.1 V, R2 ~0.99-1.00 for available data for M3+ and M2+ ions) and by application of Trouton's rule for entropies of vaporization.

Second, application of the formula allows the identification of many ΔGhyd values not reported before. Together with previously determined values, the compiled lists of ΔGhyd are the most complete so far reported and are all thermochemically consistent, i.e. they agree with their corresponding thermochemical cycles.

The numbers use the convention ΔGhyd(H+) = -1100 kJ/mol and SHE = +4.44 V, but can be easily adjusted to other reference states as appropriate. Some of the new ΔGhyd values established here are for the catalytically important d-transition metal ions Rh3+, Re3+, Ir3+, Mo3+, W3+, Ge2+, Tc2+, Nb3+, Ta3+, Os3+, and Ru2+.

Some, such as Ir3+, are among the most inert aqua ions known. The ΔGhyd values have an accuracy of ~10 kJ/mol and are recommended for use in thermochemical calculations, for interpretation of the aqueous chemistry of the metal ions, and as benchmarks for theoretical chemistry.