Transition-State Theory of Reaction Rates

The transition state theory of reaction rates [21] provides the link between macroscopic reaction rates and molecular properties of the reactants, such as translational, vibrational, and rotational degrees of freedom. For an extensive discussion of transition state theory applied to surface reactions we refer to books by Zhdanov [25] and by Van Santen and Niemantsverdriet [27]. The desorption of a molecule M proceeds as follows ... 

In this chapter, we discuss TPR and reduction theory in some detail, and show how TPR provides insight into the mechanism of reduction processes. Next, we present examples of TPO, TP sulfidation (TPS) and TPRS applied on supported catalysts. In the final section we describe how thermal desorption spectroscopy reveals adsorption energies of adsorbates from well-defined surfaces in vacuum. A short treatment of the transition state theory of reaction rates is included to provide the reader with a feeling for what a pre-exponential factor of desorption tells about a desorption mechanism. The chapter is completed with an example of TPRS applied in ultra-high vacuum (UHV), in order to illustrate how this method assists in unraveling complex reaction mechanisms. 

The distinction between kinetic and thermodynamic stability is important and is explained by the concept of the free energy of activation necessary to convert the substrate to its transition state. In order for the substrate to form products, its internal free energy must exceed a certain value i.e., it must surmount an energy barrier. The energy barrier is that of the free energy of the transition state, AG. The transition-state theory of reaction rates introduced by H. Eyring relates the rate of the reaction to the magnitude of AG. ... 

There are two classes of reactions for which Eq. (10) is not suitable. Recombination reactions and low activation energy free-radical reactions in which the temperature dependence in the pre-exponential term assumes more importance. In this low-activation, free-radical case the approach known as absolute or transition state theory of reaction rates gives a more appropriate correlation of reaction rate data with temperature. In this theory the reactants are assumed to be in equilibrium with an activated complex. One of the vibrational modes in the complex is considered loose and permits the complex to dissociate to products. Figure 1 is again an appropriate representation, where the reactants are in equilibrium with an activated complex, which is shown by the curve peak along the extent of the reaction coordinate. When the equilibrium constant for this situation is written in terms of partition functions and if the frequency of the loose vibration is allowed to approach zero, a rate constant can be derived in the following fashion. 

The Eaci is an important parameter in the collision theory of reaction rates, and it approximates the energy of activation in the transition state theory of reaction rates [94]. As indicated earlier, diffusion reactions for keratin fibers generally involve mutual diffusion coefficients because... 

According to the transition-state theory of reaction rates (Evans and Polanyi, 1935 Wjmne-Jones and Eyring, 1935 see Glasstone et al., 1941) the rate constant ib of a one-stop chemical reaction is given by... 

The transition state theory of reaction rates forms the basis of the quantitative theory of isotope effects (Bigeleisen, 1949 Bi-geleisen and Wolfsberg, 1959). It considers reaction rates in terms of the assumption that reactants are in equilibrium with the transition state. For two isotopic species Ai and A2 reacting with a nonisotopic species B, the reactions will be given by Eqs. (5) and (6) (Saunders, 1961) ... 

The transition state theory of reaction rates is discussed in Chapter 5. 

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