Md. Tissandier et al., THE PROTONS ABSOLUTE AQUEOUS ENTHALPY AND GIBBS FREE-ENERGY OF SOLVATION FROM CLUSTER-ION SOLVATION DATA, The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory, 102(40), 1998, pp. 7787-7794
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.