Arrhenius ?4-factor from activated complex theory

Transition-state theory is one of the earliest attempts to explain chemical reaction rates from first principles. It was initially developed by Eyring [124] and Evans and Polayni [122,123], The conventional transition-state theory (CTST) discussed here provides a relatively straightforward method to estimate reaction rate constants, particularly the preexponential factor in an Arrhenius expression. This theory is sometimes also known as activated complex theory. More advanced versions of transition-state theory have also been developed over the years [401],... 

Information concerning unimolecular potential energy surfaces can be acquired from several sources. Thermochemical measurements provide bond dissociation energies Dq and heats of reaction AHq. Analyses of the vibrational spectra of a unimolecular reaction s reactants and products yields their quadratic force constants, and if the data is sufficiently complete, also, their cubic and quartic force constants. From kinetic measurements of the unimolecular rate constant at high pressure the phenomenological Arrhenius A factor Aee and activation energy can be derived. If one can show that that the activated complex theory is valid for a specific unimolecular reaction its threshold energy Eq and the entropy difference between the activated complex and molecule can be found from... 

Uncertainties about the structure of the activated complex and the assumptions involved in computing its thermodynamic properties seriously limit the practical value of the theory. However, it does provide qualitative interpretation of how molecules react and a reassuring foundation for the empirical rate expressions inferred from experimental data. The effect of temperature on the frequency factor is extremely difficult to evaluate from rate measurements. This is because the strong exponential function in the Arrhenius equation effectively masks the temperature dependency of A. C. A. Eckert and M. Boudart, Chem. Eng. Sci., 18, 144 (1963). 

Our treatment, based on both the collision and the statistical formulations of reaction rate theory, shows that there exist two possibilities for an interpretation of the experimental facts concerning the Arrhenius parameter K for unimolecular reactions. These possibilities correspond to either an adiabatic or a non-adiabatic separation of the overall rotation from the internal molecular motions. The adiabatic separability is accepted in the usual treatment of unimolecular reactions /136/ which rests on transition state theory. To all appearances this assumption is, however, not adequate to the real situation in most unimolecular reactions.The nonadiabatic separation of the reaction coordinate from the overall rotation presents a new, perhaps more reasonable approach to this problem which avoids all unnecessary assumptions concerning the definition of the activated complex and its properties. Thus, for instance, it yields in a simple way the rate equations (7.IV), corresponding to the "normal Arrhenius parameters (6.IV), which are both direct consequences of the general rate equation (2.IV). It also predicts deviations from the normal values of the apparent frequency factor K without any additional assumptions, such that the transition state (AB)" (if there is one) differs more or less from the initial state of the activated molecule (AB). ... 

If In k is plotted versus, the activation energy a corresponds to the slope of the resulting straight line, whereas the pre-exponential factor A can be determined from the intersection with the T axis. By Eyring s theory of the activated complex, rearrangement processes of the ionic atmosphere are important in electrochemical reactions. Hence it is useful to introduce the activation entropy A5. Since the pre-exponential factor A of Arrhenius equation can be expressed as a function of entropy, we get (with activation enthalpy, AH and Boltzmann constant b)-... 

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