Pre-exponential factor tables

From data like these for SF6 a collection of diffusion coefficients (Figure 4), activation enthalpies, and pre-exponential factors (Table I) have been assembled. It was necessary to assume a value of the jump distance which seemed intuitively appropriate, the molecular diameter, for use in Equation 1. 

For the purposes of the present comparison we arc comparing not the true pre-exponential factors (Table XII.1) but rather the factors of the term here... 

Calculated pre-exponential factors (Table 15) were compared with those obtained experimentally (Table 13) and it is seen that A have lower values ( 10 times) for the cyclic form of the activated complex, if compared with the experimental values. At the same time the values of A for LC are about 200 times higher. The values of A for CC are the highest as predicted by the theory and they are lower than the experimental values. This supposes that the reaction takes place via a cyclic complex. The values of A calculated for LC in Table 15 have been obtained without taking into account the eneigy of free rotation. The latter was calculated as a sum of the rotation around H-0 and 0-0 axes (by mopac6) and it amounts to 3.1 kcal. This means that the real values in column 4 are about 200 times smaller. The comparison between the A values corrected in this way and the experimental data for the compounds I-IV reveals complete agreement. 

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... 

Table 3.6. Experimental activation energies and pre-exponential factors for CO and NO desorbing from a range of clean and well-defined single crystals. All data were obtained in the low coverage regime. [From V.P. Zhdanov, J. Pavlicek and Z. Knor, Catal. Rev.-Sci.

Table 10.2 Overview of energy barriers and pre-exponential factors derived from Arrhenius fits of the ac susceptibility data for single-molecule magnets 1-15. 

The parabolic model is, in essence, empirical because the parameter a is calculated from spectroscopic fa and v ) and atomic (/q and /q) data, while the parameter bre (or Ee0) is found from the experimental activation energies E(E= RT a(A/k)), where A is the pre-exponential factor typical of the chosen group of reactions, and k is the rate constant. The enthalpy of reaction is calculated by Equation (4.6). The calculations showed that = const, for structurally similar reactions. The values of a and bre for reactions of different types are given in Table 4.16. 

Since the reactants (R02 ketone) and the transition state have a polar character, they are solvated in a polar solvent. Hence polar solvents influence the rate constants of the chain propagation and termination reactions. This problem was studied for reactions of oxidized butanone-2 by Zaikov [81-86]. It was observed that kp slightly varies from one solvent to another. On the contrary, kt changes more than ten times from one solvent to another. The solvent influences the activation energy and pre-exponential factor of these two reactions (see Table 8.16). 

This is commonly called the Arrhenius equation. Table 4.1 gives typical values for fuels in terms of the specific rate constant, k. In Equation (4.1), m("r is taken as positive for the mass rate of fuel consumed per unit volume. Henceforth, in the text we will adopt this new sign convention to avoid the minus sign we were carrying in Chapter 3. The quantity A is called the pre-exponential factor and must have appropriate units to give the correct units to m("r. The exponents n and m as well as A must be arrived at by experimental means. The sum (n + m) is called the order of the reaction. Often a zeroth-order reaction is considered, and it will suffice for our tutorial purposes. 

Table 7.5 WGS Reaction Kinetics, Apparent Activation Energies, Eaf (Forward), and Modeled Values for the Backward Activation Energy Eab and Pre-Exponential Factors /r0f, kob, Assuming an Elementary Reaction with First-Order Kinetics of the WGS Reaction...

Arrhenius parameters calculated from the data in Tables 1-4 are shown in Table 5. The pre-exponential factors are all within the range expected for uni-molecular decompositions, with the exception of Co2(CO)6C2H2. The low value for its decomposition has been attributed to formation of a CO bridge in the transition state24. 

Table 2.9 summarizes the kinetic data which were employed by Ravindranath and co-workers in PET process models. The activation energies for the different reactions have not been changed in a decade. In contrast, the pre-exponential factors of the Arrhenius equations seem to have been fitted to experimental observations according to the different modelled process conditions and reactor designs. It is only in one paper, dealing with a process model for the continuous esterification [92], that the kinetic data published by Reimschuessel and co-workers [19-21] have been used. 

Table 13 Arrhenius activation energies and pre-exponential factors for thermal isomerization of tetraphenylethenes [42] and the standard enthalpy differences in benzene solution."...

Table IV. Pre-exponential Factors and Activation Energies of Rate...

Table V. Rate Constants (60°) for Chain Propagation and Termination and Pre-exponential Factors and Activation Energies for Methyl Ethyl Ketone Oxidation in Aqueous Solutions...

For the fresh and the specifically aged catalyst materials, the dependence of the normalized NOx storage capacity on temperature could be kept the same (Giithenke et al, 2007b). This minimized the number of parameters to be re-adapted for two catalysts with different ageing level. Thus, only the maximum NOx storage capacity and the pre-exponential factors for the reactions R1-R22 had to be re-evaluated, cf. Table III and Eq. (36). 

A study of benzocyclobutene polymerization kinetics and thermodynamics by differential scanning calorimetry (DSC) methods has also been reported in the literature [1]. This study examined a series of benzocyclobutene monomers containing one or two benzocyclobutene groups per molecule, both with and without reactive unsaturation. The study provided a measurement of the thermodynamics of the reaction between two benzocyclobutene groups and compared it with the thermodynamics of the reaction of a benzocyclobutene with a reactive double bond (Diels-Alder reaction). Differential scanning calorimetry was chosen for this work since it allowed for the study of the reaction mixture throughout its entire polymerization and not just prior to or after its gel point. The monomers used in this study are shown in Table 3. The polymerization exotherms were analyzed by the method of Borchardt and Daniels to obtain the reaction order n, the Arrhenius activation energy Ea and the pre-exponential factor log Z. Tables 4 and 5 show the results of these measurements and related calculations. 

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