Preexponential factor and

In Eq. (6-1), A is called the preexponential factor and is the activation energy. In this section we are concerned with the experimental evaluation of A and and with their uses. 

When the temperature of the analyzed sample is increased continuously and in a known way, the experimental data on desorption can serve to estimate the apparent values of parameters characteristic for the desorption process. To this end, the most simple Arrhenius model for activated processes is usually used, with obvious modifications due to the planar nature of the desorption process. Sometimes, more refined models accounting for the surface mobility of adsorbed species or other specific points are applied. The Arrhenius model is to a large extent merely formal and involves three effective (apparent) parameters the activation energy of desorption, the preexponential factor, and the order of the rate-determining step in desorption. As will be dealt with in Section II. B, the experimental arrangement is usually such that the primary records reproduce essentially either the desorbed amount or the actual rate of desorption. After due correction, the output readings are converted into a desorption curve which may represent either the dependence of the desorbed amount on the temperature or, preferably, the dependence of the desorption rate on the temperature. In principle, there are two approaches to the treatment of the desorption curves. 

Figure 8.18. Effect of catalyst potential and work function on the apparent activation energy, E, and on the logarithm of the preexponential factor r° rfi is the open-circuit preexponential factor and T0, T are the two isokinetic points of C2H6 oxidation on Pt/YSZ for positive and negative potentials respectively.27 Reprinted with permission from Academic Press.

At high coverages, adsorbate interactions will always be present, implying that preexponential factors and activation energies are dependent on coverage. In the following we shall assume that the mean-field approximation is valid, but one should be aware that it may be a source of error. The alternative to this approximation is to perform Monte Carlo simulations (see Chapter 7). 

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

To set up the calculation, we take a quartz sand of the same porosity as in the calculations in Section 26.1 and assume that the quartz reacts according to the same rate law (Eqn. 26.1). We let the rate constant vary with temperature according to the Arrhenius equation (Eqn. 26.7), using the values for the preexponential factor and activation energy given in Section 26.2. As in the previous section, we need only be concerned with the time available for water to react as it flows through the aquifer. We need not specify, therefore, either the aquifer length or the flow velocity. 

The thermal decomposition of dimethyl mercury in the presence of radical scavengers has been thoroughly investigated61-65. The basic mechanism, the preexponential factor and the activation energy are all well established. There is still considerable doubt about the mechanism of the pyrolysis in the absence of chemically active additives. Consequently, the quantitative interpretation of rate data from such systems is of doubtful value. Systems using effective scavengers will be discussed first. The quantitative results from these systems will be used in assessing the data obtained in the absence of additives. 

Commonly, the temporal luminescence of sensors in carriers is expressed in terms of preexponential factors and lifetimes... 

Intrinsic Frenkel disorder, in which some of the oxygens are displaced into normally unoccupied sites, is responsible for the oxide ion conduction in, for example, Zr2Gd207, Fig. 2.11. The interstitial oxygen concentration is rather low, however, and is responsible for the low value of the preexponential factor and for the rather low (by -Bi203 standards ) conductivity. 

In the second approach, the chemical equilibrium between the reactant(s) and the transition state is expressed in terms of conventional thermodynamic functions, i.e., enthalpy and entropy changes. This method is easier to implement and provides useful insights for estimating both the preexponential factors and the activation energies. Consequently, we shall utilize the thermodynamic formulation of the TST in this paper. 

Figure 834 Arrhenius plot of reaction rates for equilibrium of analcite + quartz al-bite in NaCl, and NaDS-bearing solutions, after Matthews (1980). Preexponential factors and activation energies can be deduced from the fitting expression. NaDS = Na2Si205.

AG is the free energy change of the forward energy transfer and kj and AG are the preexponential factor and the free energy of activation of its rate coefficient, respectively. 

Note that only the product of the preexponential factors and the sum of the energies enter into the equation. It is a very general problem in the interpretation of TPD spectra that the A s and E s appear so that the A or E for a single step cannot be determined. 

Better fits were obtained for n = 1 which gave linear reduced rate-conversion plots up to 20-30 % conversion, followed by a downward curvature. The apparent preexponential factors and activation energies associated with Kt and K2 were A, = 6.53 x 10s s-1, E, = 80.4kJ/mole, A2 = 3.01 x 10s s 1, and E2 = 71.3 kJ/mole. These kinetics can be explained in terms of a bimolecular rate-determining step between hydroxylic catalyst species and either amine or a rapidly-formed amine-epoxide adduct. An analysis similar to that of Horie et al. yields the kinetic Eq. 

One of the important limitations in the use of DSC for the study of expls is that decompn is often accompanied by, or is a consequence of, melting or sublimation. Data analysis of such systems results in kinetic orders which have no significance. The problem was examined by Rogers (Ref 32) who noted that organic expls decomp normally more rapidly in the melt and, therefore, show very high apparent activation energies and preexponential factors, and that, therefore, compds which decomp without autocatalysis decomp in a DSC at a rate which is max when the melt is complete. For this reason Rogers used only the data above the ATmax peak. He performed the decompn iso thermally and ob-... 

The rate of coke burning is given in equation (7.28) and the value of the preexponential factor and activation energy are... 

In the formula (70) k0 and E i are the preexponential factor and the activation energy for thermal process of bond breaking, a V is the work made by elastic pressure during the elementary process ([Pg.420]

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