Concerning the problem of the isokinetic relationship. I. A statistical mechanical model

Abstract

The equation for the rate constant derived from the statistical theory of kinetics is compared with the common Arrhenius equation. Thereby the pre-exponential factor and the activation energy can be expressed by means of the theoretical quantities, frequency factor (Z₀), oscillator number (s), and potential barrier height (E). In these terms the isokinetic relationship can be represented by the equation (c- c) = b(E-E) where c is s- 1 and the bars denote the means in the reaction series under consideration. The empirical coefficient b, in connection with the numerical value of the isokinetic temperature, is proposed to be used as a criterion for the classification of reaction series. The model is exemplified by means of an organic S_N2 reaction.