Abstract

The dependence of the relative ionization constant of a weak acid on the atom fraction n of deuterium in a mixed deuterium oxide-water solvent is treated from a general point of view, with particular consideration of effects caused by the change in solvent. Various limiting formulations for comparison with experiment can be derived from the general equations, depending on the particular simplifying assumptions that are made. The GrossButler formulation, characterized by a cubic term in the denominator, results from assuming monohydrated protons and deuterons and additionally ignoring all effects, i.e., neglecting free energies of transfer of the relevant species from one to another. A linear formulation (with a first-order term in the denominator) results if one postulates nonspecific solvation for the protons and deuterons and again neglects free energy of transfer. Finally a medium formulation can be derived by assuming that the entire effect is due to free energy of transfer, i.e., that exchange fractionation is negligible. Comparison of these limiting formulations with experimental data for both ionization constants and rate coefficients of acid catalyzed reactions reveals that quite respectable fits may be obtained with each of them. However, for reactions that have K/sub H//K/sub D/more » or k/sub D//k/sub H/ values close to unity the Gross- Butler formulation fits considerably less well than the other two. Since the most likely actual situation is some superposition of contributions from effects and exchange fractionation, it seems highly doubtful that acid-base studies in mixed solvents will permit unambiguous conclusions about the state of solvation of the protons. Furthermore, in view of the likelihood that effects are of consequence, it is doubtful whether rate studies in the mixed solvents will permit choices to be made among kinetic mechanisms, a conclusion which was recently also reached by Gold from a different line of reasoning. (auth)« less

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