Equilibrium statistical mechanics activated complex theory

The activated complex theory of reaction rates in dilute gas mixtures is based on the statistical mechanical theory of chemical equilibrium. 

In transition-state theory, the absolute rate of a reaction is directly proportional to the concentration of the activated complex at a given temperature and pressure. The rate of the reaction is equal to the concentration of the activated complex times the average frequency with which a complex moves across the potential energy surface to the product side. If one assumes that the activated complex is in equilibrium with the unactivated reactants, the calculation of the concentration of this complex is greatly simplified. Except in the cases of extremely fast reactions, this equilibrium can be treated with standard thermodynamics or statistical mechanics . The case of... 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

Equations (1.3-14) and (1.3-15) thus give the prediction from transition-state theory for the rate of a reaction in terms appropriate for an SCF. The rate is seen to depend on (i) the pressure, the temperature and some universal constants (ii) the equilibrium constant for the activated-complex formation in an ideal gas and (iii) a ratio of fugacity coefficients, which express the effect of the supercritical medium. Equation (1.3-15) can therefore be used to calcu-late the rate coefficient, if Kp is known from the gas-phase reaction or calculated from statistical mechanics, and the ratio (0a 0b/0cO estimated from an equation of state. Such calculations are rare an early example is the modeling of the dimerization of pure chlorotrifluoroethene = 105.8 °C) to 1,2-dichlor-ohexafluorocyclobutane (Scheme 1.3-2) and comparison with experimental results at 120 °C, 135 °C and 150 °C and at pressures up to 100 bar [15]. 

The transition State Theory (TST) applies the principle of statistical mechanics and thermodynamic to a system in which activated complexes are effectively in equilibrium with... 

A more complete analysis based on the theory of activated complexes and on statistical mechanics has been given by Zener (1951,1952). He considered the system or an atom in its initial equilibrium condition and in the activated state at the top of the potential barrier which separates the initial position from its neighbouring equilibrium position. The rate of transition from one equilibrium site to another is given by... 

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