Rule of the geometric mean : its role in the treatment of thermodynamic and kinetic deuterium solvent isotope effects

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Abstract
The results of calculations are presented for the deuterium fractionation between a monohydric solute and water, as a function of the atom fraction n of deuterium in the solvent, and on the assumption of a range of values for the equilibrium constant K of the reaction H2O + D2O 2HOD. Measurements of the deuterium fractionation between the hydroxylic hydrogen in t-butyl alcohol and water by nuclear magnetic resonance are reported and are consistent with a value of K around 3.8. Similar calculations have been performed for deuterium fractionation between the H3O group of the hydrogen ion and water, with explicit consideration of the disproportionation equilibria for H2DO and HD2O groups. The treatment is extended to the consideration of the dependence on n of the acid dissociation constants of monobasic acids. The most plausible set of assumptions about the disproportionation equilibria of HOD, H2DO and HD2O leads to results differing less from values calculated entirely on the basis of the rule of the geometric mean than those obtained using the best value for the HOD-disproportionation but assuming the rule of the geometric mean to apply to the isotopically mixed hydrogen ions.

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