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

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.