Concepts of Elementary Reaction Act Theory

Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia 

Experimental studies of electrode kinetics resulted in the formnlation of the basic empirical relationship, the Volmer-Butler equation, (6.10) or (6.13), describing the dependence of the electric current on the electrode potential. This eqnation involves the potential E, the rate constants, and the concentrations. 

Equation (6.13), in fact, reflects the physical nature of the electrode process, consisting of the anode (the first term) and cathode (the second term) reactions. At equilibrium potential, E = Eq, the rates of both reactions are equal and the net current is zero, although both anode and cathode currents are nonzero and are equal to the exchange current f. With the variation of the electrode potential, the rate of one of these reactions increases, whereas that of the other decreases. At sufficiently large electrode polarization (i.e., deviation of the electrode potential from Eg), one of these processes dominates (depending on the sign of E - Eg) and the dependence of the net current on the potential is approximately exponential (Tafel equation). 

Important parameters involved in the Volmer-Butler equation are the transfer coefficients a and (1. They are closely related to the Bronsted relation [Eq. (14.5)] and can be rationalized in terms of the slopes of the potential energy surfaces [Eq. (14.9)]. Due to the latter, the transfer coefficients a and P are also called symmetry factors since they are related to the symmetry of the transitional configuration with respect to the initial and final configurations. 

In general, the potential dependence of the current is determined by both the potential dependence of the concentrations of the reacting particles near the electrode surface and the potential dependence of the reaction rate constant itself (i.e., the probability of the elementary reaction act per unit time, W). 

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The theory of steady-state reactions operates with the concepts of "a path of the step , "a path of the route , and "the reaction rate along the basic route . Let us give their determination in accordance with ref. 16. The number of step paths is interpreted as the difference of the number of elementary reaction acts in the direct and reverse directions. Then the rate for the direct step is equal to that of the paths per unit time in unit reaction space. One path along the route signifies that every step has as many paths as its stoichiometric number for a given route. In the case when the formation of a molecule in one of the steps is compensated by its consumption in the other step, the steady-state reaction process is realized. If, in the course of this step, no final product but a new intermediate is formed, then it is this... 

Thus, the above analysis shows that the regularities of the kinetic isotope effect in enzymatic hydrolysis reactions confirm the basic results of the quantum-mechanical theory of an elementary act and contradict the results of the bond-stretching model. The concepts of the quantum-mechanical theory are found to be useful for discussing some specific aspects of the action of enzymes. Hence it is important to discuss the general corollaries of the theory as applied to enzymatic reactions and other biological processes. Some aspects of this problem will be discussed in the following section. 

These conceptions have given impetus to the development of two trends that must complement each other studies of the kinetic regularities of elementary acts and construction of the kinetic theory for complex reactions. 

In the preceding chapter, we gave a brief account of the modern theory of an elementary act of charge transfer reactions and, in particular, of electrode reactions. This new theory basically differs from the concepts generally accepted for a long time, and especially from the Horiuti-Polanyi model, in that it takes into account the dynamic role of the solvent and the difference in the behavior of classical and quantum degrees of freedom. This difference should be manifested most clearly in proton transfer reactions, since the proton is a particle which behaves essentially in a quantum-mechanical manner. Therefore, our primary task was to study experimentally an elementary act of proton donor discharge. 

The investigation of enzymatic processes accompanied by a proton transfer, especially with the help of the kinetic isotope effect, is quite interesting from two complementary points of view. Firstly, it is essential to study the applicability of the quantum-mechanical theory of an elementary act to this very important class of biochemical processes, and thus create a certain experimental basis for further application and development of the theory for analyzing biological phenomena. Secondly, enzymatic reactions are found to be more convenient, to a certain extent, than ordinary chemical homogeneous reactions for the verification of certain concepts of the theory. 

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