THE PROTONS 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, Delta H-aq(o)[H+], from a set of cluster-ion solvation dat a without the use of extra thermodynamic assumptions. The absolute pro ton hydration enthalpy has been found to be similar to 50 kT/mol diffe rent than traditional values and has been more precisely determined (b y about an order of magnitude). Conventional ion solvation properties, based on the standard heat of formation of H+(aq) set to zero, have b een devised that may be confusing to the uninitiated but are useful in thermochemical evaluations because they avoid the unnecessary introdu ction of the larger uncertainties in our knowledge of absolute values. In a similar strategy, we have motivated the need for a reassessment of Delta H-aq(o)[H+] by the trends with increased clustering in conven tional cluster-ion solvation enthalpy differences for pairs of opposit ely charged cluster ions. The consequences of particular preferred val ues for Delta H-aq(o)[H+] may be evaluated with regard to cluster-ion properties and how they connect to the bulk. While this approach defin es the problem and is strongly suggestive of the currently determined proton value, it requires extra thermodynamic assumptions for a defini tive determination. Instead, a unique reassessment has been accomplish ed without extra thermodynamic assumptions, based on the known fractio n of bulk absolute solvation enthalpies obtained by pairs of oppositel y charged cluster ions at particular cluster sizes. This approach, cal led the cluster-pair-based approximation for Delta H-aq(o)[H+], become s exact for the idealized pair of ions that have obtained the same fra ction of their bulk values at the same cluster size. The true value of Delta H-aq(o)[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 o f Delta H-aq(o)[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 kT/mol (esd) for Delta H-aq(o)[H+] and -1104.5 +/- 0.3 KJ/mol (esd) for Delta G(aq) (o)[H+]. The uncertainties (representing only the random errors of the procedure) are smaller than expected because the cluster data of 20 d ifferent pairings of oppositely charged ions are folded into the deter mination.