Transition state theory and supercritical fluids

Transition-state theory, that is treatment of chemical reactions as steady state processes, first devised by Evans and Polanyi [72] in 1935, has been widely used in modelling the absolute rate coefficients of reactions in both gases and liquids. Eyring s extension defining the volume of activation [73], has also been employed to interpret the pressure variation of rate coefficient data, often with mechanistic application. Activation volume is the particular facet of transition-state theory which has received application to reactions in supercritical fluids, especially in the immediate vicinity of the solvent gas-liquid critical point. Some of this work is reviewed below, beginning with a discussion of the validity of the use of transition-state theory in near-critical and supercritical fluids. 

Transition-state or activated-complex theory describes the rate of formation of an immediate product, P, in terms of the amount of the activated complex and an appropriately defined rate coefficient  

In this equation the total molar amounts, Wk rather than concentrations are used. This is valid because the process is first order and necessary in a near-critical fluid because the volume change on reaction could be substantial. However, it is more convenient to use mole fractions, Xk and (as can be easily shown by differentiation) if s is the total number of product molecules formed from the activated complex. 

if only one product molecule is formed from the activated complex, it becomes true that 

The theory assumes that the activated complex is formed in a rapid preequilibrium with the reagents. For example, for the common case of a bimole-cular reaction. 

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