Preexponential factor of the rate

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. 

The preexponential factor determines the rate of incidence of the gas particles onto the free surface at a unit pressure and has a dimension of (mole sec g-1 cm-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),... 

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... 

Person 1 Determine the activation energy, Ea,n, and preexponential factor, for the rate of dissolution of Ti. 

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). 

Experiments under subcritical conditions appear to be most promising in this respect. As an example, we may cite a number of works in which different relationships at the extinction limit were used for the determination of the effective activation energy and preexponential factor of the gas-phase combustion reaction. In particular, Krishnamurthy 87) calculated the kinetic parameters of the gas-phase combustion of PMMA from the relationship between the combustion rate and the oxygen pressure and concentration at the extinction limit (Eg = 88 kJ /mol k0 = 3x 1012 cm3/mol s). Other authors 76,94) did the same by analyzing the relationship between the extinguishing oxidant flow velocity and oxidant concentration, with the help of an opposed flow diffusion flame (OFDF) apparatus. A similar relationship between flow velocity and oxidant temperature was suggested, since preheating of the oxidant was found to immediately affect the flame temperature. For PMMA, PE and polyoxymethylene (POM) Eg = 98.5, 140 and 121 kJ/mol, respectively, were reported. 

The order of activity for both cyclopropane addition and propane exchange is Rh > Pt > Pd, as found for ethane exchange (3), but the differences here reside almost entirely in the preexponential factors. Since the rates were measured only per unit weight of metal and not per unit surface area, this order may be without basic significance and will not be discussed further here. The dependence of the parameter 6 on temperature is shown... 

The activity sequence is strictly controlled by the value of the preexponential factor in the rate equation. The exceptionally low activity of palladium is explained in terms of the formation of surface hydride. 

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

The position of the isotope labels is indicated by. A is the Arrhenius preexponential factor in the rate equation E is the experimental activation energy k is the rate coefficient for elimination from the isotopically labelled substrate. Values calculated from the infrared stretching frequencies of the C-H and C-D bonds in the substrates and derived for C-T by assuming harmonicity and using the reduced mass relationship. 

Rate constants for free radical propagation increase with decreasing polymer free radical resonance stabilization (Table 20-2). The activation energies, however, are more or less independent of the constitution. Consequently the rate constants are predominantly determined by the preexponential factors of the Arrhenius equation. In addition, they also depend on the viscosity of the reaction medium to a slight extent. 

While not entirely impossible, this concept is highly improbable. It implies an even greater disagreement between the experimental Tafel slope and that predicted from the p value following from Eq. (105). Besides, the overall preexponential factor in the rate expression, if nonadiabatic proton transfer is assumed, it would give rates that are too small. A second problem of the basic model is the fact that it can only apply to protons and perhaps marginally... 

Though the overall picture is reasonably satisfactory, certain more detailed problems remain. One is the effect of coverage on the ideal heat of adsorption values discussed above. A second problem is the effect of proton tunnelling, and of other possible changes of preexponential factor in the rate expression. The latter will invalidate the assumption of constant entropy of adsorption or activation. 

According to Landau and Teller, the temperature dependence of the preexponential factor of the transition probability or the rate coefficient should be considerably weaker than that coming from the exponential. Indeed, the BSP model predicts that the preexponential factor is proportional to [15]. Eq. (11), in... 

One of the major issues in developing detailed surface reaction mechanisms is thermodynamic consistency. Even though the recently published reaction mechanisms ensure enthalpic consistency, many of them are not consistent with respect to entropy, which is due to the lack of knowledge about the transition states of the individual reaction steps. Thus, there is not sufficient information for a theory-hased determination of preexponential factors in the rate equations. However, an independent choice of the rate coefficients causes an inconsistent entropy change in the overall reaction, which leads to an incorrect prediction of equilibrium states. There are two approaches to avoid this inconsistency by adjusting the rate expressions, which are described in the Hterature (Deutschmann, 2008 Maier et al., 2011 Mhadeshwar et al., 2003). 

The enhancement of the toluene steam dealkylation reaction is feasible by microwave irradiation (Litvishkov et al., 2012). It has been found that the most likely cause of the positive effect of microwave radiation on the reaction rate is an increase in the preexponential factor of the Arrhenius equation for the temperature dependence of the reaction rate. This effect is presumably due to an increase in the active surface area of the catalyst formed by the microwave-assisted thermal treatment. 

Table 5.1 gives kinetic and vapor-liquid phase equilibrium parameters used in the numerical case considered in this chapter. The forward reaction rate parameters are the same as those used in the two-product case. The activation energy of the backward reaction is the same, but the preexponential factor of the backward reaction is changed because the backward reaction is only first order in the concentration of product C. 

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. 

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