Microscopic interpretation of Arrhenius parameters

We return to the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor (A) and the activation energy (Ea) known from classical chemical kinetics. 

In Chapter 2, the first chapter of the gas-phase part of the book, we began the transition from microscopic to macroscopic descriptions of chemical kinetics. In this last chapter of the gas-phase part, we will assume that the Arrhenius equation forms a useful parameterization of the rate constant, and consider the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor (A) and the activation energy (Ea) defined by the Arrhenius equation k(T) = Aexp(—Ea/kBT). 

In the previous chapters, we have seen that the rate constant for unimolecular as well as bimolecular elementary reactions can be written in a form similar to the Arrhenius equation, provided we allow for a (weak) temperature dependence of the pre-exponential factor A. Experimentally the parameters may be determined from an Arrhenius plot, that is, a plot of ln[ (T)] versus 1 /T, which according to the Arrhenius equation will be a straight line with slope —Ea/R and an intercept of In A. The question is what is the molecular origin of these parameters  

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In Chapter 7 we turn to the other basic type of elementary reaction, i.e., uni-molecular reactions, and discuss detailed reaction dynamics as well as transition-state theory for unimolecular reactions. In this chapter we also touch upon the question of the atomic-level detection and control of molecular dynamics. In the final chapter dealing with gas-phase reactions, Chapter 8, we consider unimolecular as well as bimolecular reactions and summarize the insights obtained concerning the microscopic interpretation of the Arrhenius parameters, i.e., the pre-exponential factor and the activation energy of the Arrhenius equation. 

The kinetics of dehydration [128] of Na2S203.5H20 were difficult to interpret because the course of the reaction was markedly influenced by the perfection of the initial reactant surface and the reaction conditions. No reliable Arrhenius parameters could be obtained. The mechanism proposed to account for behaviour was the initial formation of a thin superficial layer of the anhydrous salt which later reorganized to form dihydrate. The first step in the reaction pentahydrate - dihydrate was satisfactorily represented by the contracting area (0.08 < or, < 0.80) expression. The second reaction, giving the anhydrous salt, fitted the Avrami-Erofeev equation (n = 2) between 0.05 < 2< 0.8. The product layer offers no impedance to product water vapoiu escape and no evidence of diffusion control was obtained. The mechanistic discussions are supported by microscopic observations of the distributions and development of nuclei as reaction proceeds. 

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