Juro Horiuti

THEORY OF REACTION RATES AS BASED ON THE STOICHIOMETRIC NUMBER CONCEPT

The order of elementary processes bears an obvious relation to the total number of participants, insofar as they behave individually, statistically independent except at the moment of the elementary process; the elementary process of first, second, or third order is thus that of one, two, or three participants, respectively, and so on. This rule has proved to be a useful key for the analysis of homogeneous reactions that are favored with statistical independence of the participants. That is, however, often carelessly applied to heterogeneous reactions and encounters difficulties. Elementary processes are termed steps, and the complete set of its participants at the state before or after the step are the initiai or the final system; overall reactions are each considered to be composed of steps. The hydrogen electrode reaction

On the Theory of Heterogeneous Catalysis

Publisher Summary This chapter discusses the formulation of the rate of elementary reaction and the theory of steady reaction consisting of elementary reactions with emphasis on heterogeneous ones. The chapter presents the rate of a heterogeneous elementary reaction, in the absence of interaction, as exactly proportional to the product of activities of the species composing the initial system and of the populations or probabilities of adsorption sites being kept vacant. The chapter develops the theory of construction of an over-all reaction from elementary reactions based on the steady state approximation, in which the rate of creation of each intermediate is assumed as balanced with that of its consumption in the course of the progress of the over-all reaction.

Significance and experimental determination of stoichiometric number

Abstract The concept of Stoichiometric number is introduced with special reference to the applicability of the classical theorem k′ k″ = K to the relation between the forward and the backward rate constants, k ′ and k ″, and the equilibrium constant K . The significance of the Stoichiometric number ν r of the rate-determining step in determining the mechanism is illustrated. The theoretical background of ν r and theorems on ν r derived from its definition are reviewed and on their basis the experimental determination of ν r is illustrated in several cases.

35 A Theorem on the Relation between Rate Constants and Equilibrium Constant

A theorem k/—k = K 1/ v(r) is shown valid for any thermal reaction having a rate-determing step r , where v(r) is the stoichiometric number of r , k or — k the rate constant of the forward or the backward reaction, and K the equilibrium constant. The theorem includes the classical one, k/—k = K as a special case when v(r) = 1 and states that a catalyst varies with k/--k, according to whether shifts the part of r from one step to the other of different v(r) or not, and that the difference of the activation energies of the forward and the backward reactions equals 1/ v(r) times the negative heat of reaction.

Catalyzed Reactions by Solid Surfaces and Adsorption

Usual assumption that participants of an elementary reaction (step) behave statistically independent of one another leads to a relation between the order of the step and the number of its participants, which is used as a handy key to the analysis of reactions. This assumption was shown, however, unreliable when applied to reactions on solid surfaces. The statistical mechanical method of dealing with the rate of steps was obliged to be generalized to take the interaction of participants on one another coherently into account. The generalized method thus developed was summarized and its application were exemplified in treatments of the hydrogen electrode reaction, the flash desorption spectrum and the isotopic shift of sticking probability respectively of hydrogen on W(100).

THE MECHANISM OF THE HYDROGEN EVOLUTION REACTION

Abstract The dual mechanism of the hydrogen evolution reaction is an alternative of the catalytic or the electrochemical mechanism operative depending on the experimental conditions and electrode material, as advanced by one of the present authors. The hydrogen evolution reaction consists of a set of steps H+ + + e → H(a) and 2H(a) → H2 or 2H+ + e → H+2 (a) and H+2 (a) + e → Hs2 respectively according to the catalytic or the electrochemical mechanism, where H+ denotes a proton associated with Bronsted base H2O or OH-, e is a metal electron, H(a) or H+2(a) is a hydrogen atom or hydrogen molecule-ion respectively adsorbed on the electrode surface and A is the rate-determining step. The slow discharge mechanism is expressed by the above notations as H+ + e → H(a), 2H(a) → H2, which appeared once before quite conclusive. Experimental and theoretical investigations, to which the dual and the slow discharge mechanisms have ever since been subjected, are reviewed. The dual mechanism is thus shown to be verified with regard to the effect of overvoltage or of pH on the rate, differential capacity of electrode, electrolytic separation factor of hydrogen isotopes and alternative operation of the catalytic and the electrochemical mechanisms on the same electrode depending on experimental conditions. The slow discharge mechanism is disproved by several points raised against it, which give, on the other hand, further evidence for the dual mechanism.