Pre-exponential factor in rate constant

A Pre-exponential factor in rate constant Ea Activation energy... 

Aromatic lump containing i carbon atoms (i 6) Pressure effect exponent for reaction class j Pre-exponential factor in rate constant (1/s) Activity factor for reaction group x Beta distribution shape parameter Benzene... 

Enthalpies, Pre-exponential Factors, and Rate Constants of Reaction InH + 02 —> In + H02 Calculated by IPM method [110]... 

Calculate the value of pre-exponential factor and rate constant at 298 K in following... 

AlA pre-exponential factor in equilibrium constant Arrhenius rate constants of forward and back reactions constants in a form of f = [I + 2... 

Let us consider the last statement in more detail. Keeping in mind serious doubts stated in Section III.B, we nevertheless assume that pre-exponential factors for rate constants of collision-type reactions between gas species and surface sites can be evaluated as a gas-surface collision frequency (v). The dimension (or cross-section) of the surface sites (surface area (3), as well as a steric factor (c) should also be taken into account. The latter value shows the probability of reciprocal orientation of two reactants optimal for the reaction to proceed during the collision. As a result, the pre-exponential factor can be calculated as follows ... 

It is frequently stated that kinetics and thermodynamics are two completely different subjects. This is an oversimplification which is misleading if it conveys the impression that thermodynamics is useless in the study of reaction rates. First of all, as was seen in Chapter 2, the theory of reaction rates is essentially an equilibrium theory. It permits us to evaluate pre-exponential factors of rate constants of elementary steps, at least in order of magnitude. As to the estimation of activation barriers, this can be done in certain cases, as will be seen shortly, by means of correlations between activation barriers and heats of reactions. Finally, in the treatment of reactions in concentrated acid solutions, it is frequently possible to relate rate constants to a purely thermodynamic quantity, the acidity function, which will also be introduced in this chapter. 

Here a and b are considered as fitting parameters depending on temperature. De-excitation rate constants (s < 0) are obtained from the detailed balance principle. AH fitting laws differ in the pre-exponential factor in Eq. (5.70). In the PEG model... 

As a consequence of these various defined quantities, care must be taken in assigning values of rate constants and corresponding pre-exponential factors in the analysis and modeling of experimental data. This also applies to the interpretation of values given in the literature. On the other hand, the function [ [ c and the activation energy EA are characteristics only of the reaction, and are not specific to any one species. 

For a temperature of 1000 K, calculate the pre-exponential factor in the specific reaction rate constant for (a) any simple bimolecular reaction and (b) any simple unimolecular decomposition reaction following transition state theory. 

The rate constant for decomposition of the activated complex is simply the pre-exponential factor in the high-pressure Arrhenius fit to kun. This constant may be available from experimental measurement. Alternately, Eq. 10.98 provides an estimate for A,, . We can use this result and Eq. 10.150 to obtain an expression for kd. ... 

Ai, A2 pre-exponential factors in the rate constants Ac area of cooling surface... 

In these formulas a is a numerical constant which is to be found by integration (see 9), B and D are the pre-exponential factors in the expressions for the equilibrium constant and the rate coefficient. 

The parameter A( = pZ) is called the frequency factor (or pre-exponential factor). In accord with the minus sign in the exponent, the rate constant decreases as Ea increases and increases as T increases. 

The partial rate factor is equal to a ratio of rate constants. It may be used as a measure of the substituent effect on the activation energy for the reaction, provided it is assumed that the pre-exponential factors in the kinetic equation for the reaction with benzene and its derivatives are the same. On the basis of the Arrhenius equation and the theory of absolute reaction rates the rate constant can be expressed as... 

Gas phase terminations generally have very low, zero or negative activation energies, and their rate constants are governed by their pre-exponential factors. In contrast, surface terminations have a much wider range of activation energies. 

Finally, these expressions can be related to the Arrhenius equation, where the activation energy Ea is identified from RT2d n k/dT. Although the rate constant is independent of volume (or pressure), we note that the exponential factor, as well as the pre-exponential factor, in Eq. (6.61) depends on volume (or pressure). Thus, we choose to perform the differentiation under constant pressure. Using that l/ce = V/N = ksTIp, we get... 

The second classification concerns the adiabaticity of the e.t. reaction. Conceptually, the reaction is adiabatic if the probability of reaction for each passage through the intersection region (point X of Fig. 2) between the potential surfaces of the reactants and products is close to unity [16]. If this probability is small, then the system remains on the initial state potential surface and the reaction is nonadiabatic . In the quantitative formulation of Jortner and Bixon [16], the pre-exponential factor in the rate constant equation is given as follows, for the case of an adiabatic e.t. ... 

In the estimation methods discussed so far the quantities estimated have either been the rate constant or the pre-exponential factor in the Arrhenius expression. Methods for estimating the activation energy of bimolecular reactions are much less developed. Theoretical prediction, at the level required, is beyond current computational techniques except in some exceptional, simple cases. However, there have been empirical attempts to relate the activation energy for a series of related reactions e.g., H abstraction by methyl radicals from hydrocarbons, to the thermodynamics of the process. 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

To use this equation it is necessary to know how the energies associated with the states of several vibrational modes vary along the minimum energy path. This model explains why the pre-exponential factors in the rate constant expressions, as well as the activation energies, depend on the vibrational state of the reagents. 

K , equilibrium constant of main reaction Ki adsorption constant of i component ki kinetic coefficient of poisoning rate, [eqn.(8)] k2 kinetic coefficient of deactivation rate, [eqn. (9)] kgi mass transfer coefficient of i component ko pre-exponential factor in eqn. (6)... 

The complete current-potential relation under illumination has already been derived in Section 7.3.3 (Eq. 7.68). In this case it was assumed that the cathodic dark current is only due to the injection of holes into the valence band of an n-type electrode. It was further shown that the current-potential relation could be simplified if the recombination is the rate-determining step (Eq. 7.73). The pre-exponential factor in Eq. (7.73), y o, mainly depends on material parameters such as diffusion constant and length of minority carriers as given by Eq. (7.65). For instance, the recombination is fast if the diffusion length is short, which leads to high /o values and thereby to large cathodic dark currents (Eq. 7.73). As already mentioned, there arc many cases where the photocurrent is due to a hole transfer to occupied states of the redox system but the dark current corresponds to an electron transfer from the conduction band to the empty states of the redox system. In this case the current-potential dependence for an n-type electrode has in principle the same shape... 

Setting the time scale for the escape rate constant, Choi and colleagues used the longest Rouse time to replace the pre-exponential factor in Eq. 37 ... 

Thus, the pre-exponential factor in the rate constant of a reaction following collision of a molecule with a surface has the dimensions of a linear velocity. The probability factor, which, as seen in a previous section, might be unity, for simple condensation of an atom on a surface, will in general be smaller than unity. It will be small if the reactant loses freedom upon reaching the transition state. A calculation of P would be tantamount to a calculation of A5 . ... 

Comparing this equation with eq.(3.3-19), we see that the parameter g is simply the pre-exponential factor in the Clausius-Clapeyron vapor pressure equation. It is reminded that the parameter g is the ratio of the rate constant for desorption to that for adsorption of the second and subsequent layers, suggesting that these layers condense and evaporate similar to the bulk liquid phase. 

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