Preexponential factor of the rate constants

A similar interpretation holds for the preexponential factor of the rate constants for the dissociative adsorption, desorption, reaction between the adspecies and their migration. The CM is distinguished by the fact that the preexponential factor is dependent on the properties of the starting reagents only and is independent of the transition state whereas the rate constant depends on the activation barrier height, which is governed by the transition state energy. 

Interestingly, the preexponential factor of the rate constants is practically the same for all intermediates (Kq = 10" s ), whereas the activation energy slightly... 

Wul-6 (In contrast to Marcus-Hush which refers to the theory of electron transfer activation, the Mulliken-Hush equation describes the preexponential factor of the rate constant. We spell out Mulliken-Hush each place it occurs in this chapter and use the acronym MH to refer to only Marcus-Hush.) In practice, however, FCWD(O) cannot be extracted from experimental spectra, and one needs a theoretical model to calculate FCWD(O) from experimental band shapes measured at the frequencies of the corresponding electronic transitions. This purpose is achieved by a band shape analysis of optical lines. 

If the preexponential factors of these rate constants are comparable in magnitude, further simplification is possible. 

This reaction occurs in solution with an extremely low preexponential factor with the rate constant k= 1.6 x 102 exp(—29.0/R7) L mol-1 s-1 (benzene, 293-333 K [28]). Reactants are dissolved and react in the amorphous phase of the polymer. The PP matrix retards the... 

Knowing which of the Sy are large in magnitude can be very helpful to a modeler, but Eq. (24a) requires some care. First, in systems where T and P are not constant, one usually means the sensitivity with respect to the preexponential factor in the rate constant, i.e. a uniform scaling of kfT,P) at all T,P (Kee et al., 1989). 

Some of the rate constants discussed above are summarized in Table VI. The uncertainties (often very large) in these rate constants have already been indicated. Most of the rate constants have preexponential factors somewhat greater than the corresponding factors for neutral species reactions, which agrees with theory. At 2000°K. for two molecules each of mass 20 atomic units and a collision cross-section of 15 A2, simple bimolecular collision theory gives a pre-exponential factor of 3 X 10-10 cm.3 molecule-1 sec.-1... 

We assume that neither the preexponential factor of the conditional electrode reaction rate constant nor the charge transfer coefficient changes markedly in a series of substituted derivatives and that the diffusion coefficients are approximately equal. In view of (5.2.52) and (5.2.53),... 

Again the preexponential factor is seen to be temperature dependent, but for large activation energies, the exponential term dominates the temperature dependence of the rate constant. 

In general, the activation energies are estimated with a fair accuracy, whereas the estimates of the preexponential factors suffer from the problem discussed above because the experimental temperature range is rather limited. Nevertheless, it must be underlined that this problem does not affect very much the estimates of the rate constants inside the examined experimental range of temperature. 

The principal dependence of the rate constant on temperature is incorporated in the exponential term including the enthalpy of activation. Thus, we may assume that the rate constant is approximately equal to a product of a preexponential factor, /l Alj, and a term involving the activation energy AB ... 

For an elementary reaction the temperature dependency of the rate constant is given by the Arrhenius equation, Equation (6), which accounts only for elementary reactions. It is important to note that this equation gives the dependency of the rate constant k on the temperature, not the dependency of r. The preexponential factor P also shows a dependency on the temperature, but its dependency is weak compared to the exponential dependency of k ... 

An additional and much more reliable method for the calculation of preexponential factors presents itself when one of the rate constants for a reversible reaction is known and it is desired to compute the factor for the reverse reaction. Such a calculation depends on a knowledge or calculation of the entropy change in the reaction. An illustration of this type of calculation will also be presented. 

We see that this simple model well describes the characteristic S-shaped profiles of local polarization curves far from the channel inlet, detected in experiments [197, 200]. Physically, these maxima result from the effect of oxygen starvation . Qualitatively, Eq. (154) shows that local current is a product of two factors. The preexponential factor a describes the growth of local current with the increase in rj due to exponential dependence of the rate constant of ORR on rj (Tafel law). The second (exponential) term in Eq. (154) describes oxygen consumption upstream from the given point z. 

V.P. Zhdanov. Effect of the Lateral Interaction of Adsorbed Molecules on Preexponential Factor of the Desorption Rate Constant. Surf. Sci. 111 L662 (1981). 

A brief qualitative consideration of the inverse reaction, namely, the production of ions, or ionization, is illuminating. Since the products are ions and the reactant is usually a neutral molecule, the transition state has an intermediate structure. This means that the transition state is more polar than the reactants and therefore more solvated. But such a situation causes a large entropy decrease, and ionization processes should have relatively large negative entropies of activation or abnormally small preexponential factors. Raising the dielectric constant should, of course, increase the rate of reaction. These predictions have been well verified by experiment [13]. 

It is clear that kinetic studies cannot distinguish between the two mechanisms. One possibility is that a consideration of the preexponential factors and activation energies of the rate constants / and / might lead to a decision. From experiments in aqueous solution at an ionic strength of 0.0376 M (Svirbely and Warner [19]),... 

The data in Table P3.4 are typical of those reported by Abdalla. Use these data to determine the orders of the reaction with respect to the concentrations of the ester and hydroxide ions, the value of the rate constant at 298 K, the activation energy for the reaction and the preexponential factor. You may assume that the rate expression can be written in the general nth-order form, but you may not assume that the orders are integers. 

Determine the activation energy and the preexponential factor for this reaction. Because the tabulated values of the rate constant correspond to values corrected for the inhibitory effect of water, the value of the rate constant determined in part (a) will not be consistent with the data for part (b). 

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