Reaction-rate preexponential factor

Under these circumstances the use of calculated preexponentials in kinetic model development is likely to lead to significant errors, in addition to those inherent in the use of calculated heats of adsorption. These problems are reflected in the attempt to model magnetite kinetics using observed heats of adsorption and estimated frequency factors, which gave rise to a calculated reaction rate a factor of 10 too low. The development of mechanistically sound, kinetic models will therefore remain dependent on the direct determination of the heats of adsorption, activation energies, and frequency factors for the forseeable future. 

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. 

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

Some workers in this field have used Eyring s equation, relating first-order reaction rates to the activation energy d(7, whereas others have used the Arrhenius parameter E. The re.sults obtained are quite consistent with each other (ef. ref. 33) in all the substituted compounds listed above, AG is about 14 keal/mole (for the 4,7-dibromo compound an E value of 6 + 2 keal/mole has been reported, but this appears to be erroneous ). A correlation of E values with size of substituents in the 4- and 7-positions has been suggested. A/S values (derived from the Arrhenius preexponential factor) are... 

The attention of the authors was particularly directed toward the increased activity of the nickel catalyst film when copper was added. This increase is revealed in a change of the initial reaction rate of copper itself and of all the alloys (except those containing 25-35% nickel) they are more active than nickel itself. A respectively similar difference was observed for the activation energy and the preexponential factor. 

By using the kinetic equations developed in Sect. 5.2, the degradation yield as a function of strain rate and temperature can be calculated. The results, with different values of the temperature and preexponential factor, are reported in Fig. 51 where it can be seen that increasing the reaction temperature from 280 K to 413 K merely shifts the critical strain rate for chain scission by <6%. 

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... 

Relationships between reaction rate and temperature can thus be used to detect non-classical behaviour in enzymes. Non-classical values of the preexponential factor ratio (H D i 1) and difference in apparent activation energy (>5.4kJmoRi) have been the criteria used to demonstrate hydrogen tunnelling in the enzymes mentioned above. A major prediction from this static barrier (transition state theory-like) plot is that tunnelling becomes more prominent as the apparent activation energy decreases. This holds for the enzymes listed above, but the correlation breaks down for enzymes... 

Arrhenius proposed his equation in 1889 on empirical grounds, justifying it with the hydrolysis of sucrose to fructose and glucose. Note that the temperature dependence is in the exponential term and that the preexponential factor is a constant. Reaction rate theories (see Chapter 3) show that the Arrhenius equation is to a very good approximation correct however, the assumption of a prefactor that does not depend on temperature cannot strictly be maintained as transition state theory shows that it may be proportional to 7. Nevertheless, this dependence is usually much weaker than the exponential term and is therefore often neglected. 

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),... 

Enthalpies, Preexponential Factors, and Rate Constants of Reaction InH Calculated by IPM method [110]—continued... 

The estimation based on the equations of the parabolic model indicates that a reaction of the type (ArO + H02 —> ArOH + 02) involving phenoxyl radicals also requires no activation energy (in this case, AH> A emin = 57kJ mol-1). However, the addition of the peroxyl radical to the aromatic ring of the phenoxyl radical occurs very rapidly. Hence, the rate constant for this reaction is determined by diffusion processes. The data on the Ee0 values are also consistent with this. For the ArO + HOOR reactions with the O H O reaction center and for Am + HOOR reactions with the N H O reaction center, these values are 45.3 and 39.8 kJ mol-1, respectively [23]. At the same time, the calculation of the preexponential factor in terms of the parabolic model indicates that the rate constant k 7 for the reaction of ROOH with the participation of the aminyl radical is several times higher than that for the reaction involving the phenoxyl radical, where the enthalpies of these reactions... 

We observe that both the activation energy and preexponential factor increase with the polarity of the solvent. That is probably due to the polar structure of reactants and TS. In hexane, this reaction proceeds via two routes at the total rate v. 

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... 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

Strong interactions are observed between the reacting solute and the medium in charge transfer reactions in polar solvents in such a case, the solvent effects cannot be reduced to a simple modification of the adiabatic potential controlling the reactions, since the solvent nuclear motions may become decisive in the vicinity of the saddle point of the free energy surface (FES) controlling the reaction. Also, an explicit treatment of the medium coordinates may be required to evaluate the rate constant preexponential factor. 

The simultaneous desorption peaks observed at 560-580 K in TPR are of reaction-limited desorption. The peak temperatures of these peaks do not depend on the coverage of methoxy species, indicating that the desorption rate (reaction rate) on both surfaces has a first-order relation to the coverage of methoxy species. Activation energy (Ea) and the preexponential factor (v) for a first-order process are given by the following Redhead equation [12] ... 

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