Activation free energy heterogeneous rate constant

The final step of the convolution analysis is the determination of the transfer coefficient a. This coefficient, sometimes called the symmetry factor, describes how variations in the reaction free energy affect the activation free energy (equation 26). The value of a does not depend on whether the reaction is a heterogeneous or a homogeneous ET (or even a different type of reaction such as a proton transfer, where a is better known as the Bronsted coefficient). Since the ET rate constant may be described by equation (4), the experimental determination of a is carried out by derivatization of the ln/Chet-AG° and thus of the experimental Inkhei- plots (AG° = F E — E°)) (equation 27). 

The B coefficient corresponds to the logarithm of the rate constant at Tis, i-e. to the reaction proceeding on the pseudo-homogeneous surface. It is likely, that Tis and B constants may be useful characteristics of heterogeneous surface active sites reactivity towards a test gas reactant. For example, as it follows from Table 5, Tis value increases with enhancement of the chemisorption activation energy for interaction of organosilicon compounds with the free surface of pyrogenic parent and mixed oxides. 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

Figure 11.25. Photocurrent dependence on the Gibbs free energy of electron transfer for the photo-oxidation of ferrocene derivatives (a) and photoreduction of quinone-type molecules (h) at the water/DCE interface. AG ( is evaluated from Equation (11.47), employing the formal redox potentials summarised in Table 11.1 and the applied Galvani potential difference. A deconvolution of the photocurrent relaxation in the presence of the electron acceptors was performed in order to estimate the flux of election injection g. The second-order rate constant for the photoninduced heterogeneous electron transfer is also calculated assuming values of 1 nm for dec and 5 x 10 s for A ,. The trends observed in both set of data were rationahsed in terms of a single solvent reorganisation energy and activation-less limit for the rate constant. Reprinted with permission from refs.[101] and [60]. Copyright (2002/2003) American Chemical Society.

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