The Proton's Absolute Aqueous Enthalpy and Gibbs Free Energy of Solvation from Cluster-Ion Solvation Data

A method is presented to determine the absolute hydration enthalpy of the proton, ΔHaq°[H+], from a set of cluster-ion solvation data without the use of extra thermodynamic assumptions. The absolute proton hydration enthalpy has been found to be ∼50 kJ/mol different than traditional values and has been more precisely determined (by about an order of magnitude). Conventional ion solvation properties, based on the standard heat of formation of H+(aq) set to zero, have been devised that may be confusing to the uninitiated but are useful in thermochemical evaluations because they avoid the unnecessary introduction of the larger uncertainties in our knowledge of absolute values. In a similar strategy, we have motivated the need for a reassessment of ΔHaq°[H+] by the trends with increased clustering in conventional cluster-ion solvation enthalpy differences for pairs of oppositely charged cluster ions. The consequences of particular preferred values for ΔHaq°[H+] may be evaluated with regard to cluster-ion properties and how they connect to the bulk. While this approach defines the problem and is strongly suggestive of the currently determined proton value, it requires extra thermodynamic assumptions for a definitive determination. Instead, a unique reassessment has been accomplished without extra thermodynamic assumptions, based on the known fraction of bulk absolute solvation enthalpies obtained by pairs of oppositely charged cluster ions at particular cluster sizes. This approach, called the cluster-pair-based approximation for ΔHaq°[H+], becomes exact for the idealized pair of ions that have obtained the same fraction of their bulk values at the same cluster size. The true value of ΔHaq°[H+] is revealed by the linear deviations of real pairs of ions from this idealized behavior. Since the approximation becomes exact for a specific pair of oppositely charged ions, the true value of ΔHaq°[H+] is expected to be commonly shared on plots of the approximation vs the difference in cluster-ion solvation enthalpy for pairs of ions sharing the same number of solvating waters. The common points on such plots determine values of −1150.1 ± 0.9 kJ/mol (esd) for ΔHaq°[H+] and −1104.5 ± 0.3 kJ/mol (esd) for ΔGaq°[H+]. The uncertainties (representing only the random errors of the procedure) are smaller than expected because the cluster data of 20 different pairings of oppositely charged ions are folded into the determination.