The hydrogen-electrode reaction in the isotopically mixed system—I. The relation between forward and backward unidirectional rates and evaluation of the stoichiometric number of the rate-determining step

A general consideration of the possible reaction routes of the hydrogen-electrode reaction leads to the classification of all the conceivable mechanisms into two groups according to the value of the stoichiometric number, ν, of the rate-determining step.

The previous treatment on the validity, in the isotopically mixed system, of the relation between the forward unidirectional rate of the over-all reaction, V_f, its backward rate, V_b, the overpotential, η, and ν; V_f/V_b = exp (− 2Fη/νRT), is re-investigated rigorously on the basis of general considerations. It is shown, in agreement with the previous conclusion, that this relation holds invariably irrespective of the isotope content and of the magnitude of the isotope effect, provided that V_f and V_b are replaced by the respective sums of contributions of both isotopes, and η by the potential of the test electrode referred to its rest potential in the same isotopically mixed system.

Based on the relation thus verified, a method is advanced that enables us to determine experimentally (a) ν by combining the rate of isotopic exchange with the polarization resistance of the electrode used as the catalyst, without neglecting the isotope effect, and (b) the magnitude of the isotope effect from similar data. For the hydrogen-electrode reaction on nickel in an alkaline solution, ν has been determined to be 1·0 and the deuterium separation factor in the hydrogen ionization reaction to be 1·5.