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, ΔG_hyd of Mⁿ⁺, and the standard heat of vaporization (ΔH_vap) 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 ΔG_hyd values not reported before. Together with previously determined values, the compiled lists of ΔG_hyd 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 ΔG_hyd(H⁺) = -1100 kJ/mol and SHE = +4.44 V, but can be easily adjusted to other reference states as appropriate. Some of the new ΔG_hyd 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 ΔG_hyd 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.