Transition-state Theory Applied to SCFs

The theory then considers that this species breaks up by a first-order process and describes the rate of formation of one of the immediate products, P, in terms of the amount of the activated complex and an appropriately defined rate coefficient, k  

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

The theory then assumes that the equilibrium between the reagents, A and B, and the activated complex, C, is governed by an equilibrium constant. In a near-critical fluid, the most convenient approach is to define the equilibrium in terms of fugacities, fi/p, referred to the standard state of p, typically 1 atmosphere  

The quantity is an equilibrium constant for the ideal-gas state and is thus equal to that used for dilute-gas reactions. The fugacities are given in terms of the mole fractions, x,-, the fugacity coefficients, f i, and the pressure, P, by 

The substitution of eq (1.3-10) and (1.3-11) into equation (1.3-9) gives the following expression for the rate of increase of the product P  

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