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

Abstract

A method is presented to determine the absolute hydration enthalpy of the proton, ∆H aq °[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 ∆H aq °[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 ∆H aq °[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 ∆H aq °[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 ∆H aq °[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 ∆H aq °[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 ∆H aq °[H + ] and -1104.5 ( 0.3 kJ/mol (esd) for ∆G aq °[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.

Response to “Comment on ‘Ab initio molecular dynamics calculation of ion hydration free energies’ [J. Chem. Phys. 133, 047103 (2010)]”

“…Regarding comparison with Marcus' tabulated experimental data, 3 these ⌬G hyd and those of Tissandier et al 2 appear to differ by values very similar to the theoretical SPC/E surface potential ͑ϳ−0.65 eV͒. For example, the two Li + ⌬G hyd differ by Ϫ0.56 eV.…”

“…7 With DFT methods, we have so far unambiguously calculated q . 1 2 Even better agreement is obtained when comparing neutral ion pairs where ambiguities in cancel. To reiterate, no parameters in our model are adjusted to achieve a fit to experiment.…”

“…To evaluate the quality of these predictions, we made a proper apples-to-apples comparison to tabulated data from experimental work. 2,3 The comment by Chen and Chen 4 reflects confusion about our choice of observable used to achieve a consistent comparison of predicted 1 and tabulated 2,3 ⌬G hyd , perhaps incorrectly implies that we adjusted free parameters to achieve a fit to experimental data, and overstates the utility of the Born hydration formula for ion hydration. Some of their apparent disagreement with our work appears more philosophical than technical in nature, but we welcome the opportunity to clarify our results in light of recent developments in this field.…”

“…4 This ambiguity may partly account for differences in the tabulated values of ⌬G hyd for single ions, including protons. 2,3 The theoretical can be rigorously decomposed into dipolar ͑ d ͒ and quadrupolar ͑ q ͒ contributions. 7 With DFT methods, we have so far unambiguously calculated q .…”

Phase Transitions Involving Dissociated States of Water at the Electrochemical Ni(111)/H2O Interface

“…Following recent experimental and theoretical literature [36][37][38][39] we adopted a value of -1080 kJ/mol for proton solvation at 300 K and 1 M concentration, and subsequently derived a value of -970 kJ/mol for proton solvation at 600 K and 1 M concentration using high temperature parameters developed by Criss and Cobble [62][63][64] . Entropies of the reference H + (g) state at 1 atm were calculated using the Sackur-Tetrode equation.…”