Rate constant pre-exponential factor

A = rate constant (pre-exponential factor from Arrhenius equation k = A exp (-E /RT), sec (i.e., for a first order reaction) B = reduced activation energy, K C = liquid heat capacity of the product (J/kg K)... 

In most cases rjeact will depend on the temperature T, the concentration of deactivating components Cjeact. and/or on the activity Ucat itself (with kdeact. feodeact. and l A,deact as rate constant, pre-exponential factor and activation energy, respectively, of the deactivation). Consequently, rjeact may be expressed in quantitative terms as ... 

Now, according to the transition-state theory of chemical reaction rates, the pre-exponential factors are related to the entropy of activation, A5 , of the particular reaction [A = kT ere k and h are the Boltzmann and Planck constants, respectively, and An is the change in the number of molecules when the transition state complex is formed.] Entropies of polymerization are usually negative, since there is a net decrease in disorder when the discrete radical and monomer combine. The range of values for vinyl monomers of major interest in connection with free radical copolymerization is not large (about —100 to —150 JK mol ) and it is not unreasonable to suppose, therefore, that the A values in Eq. (7-73) will be approximately equal. It follows then that... 

The simplest approach to computing the pre-exponential factor is to assume that molecules are hard spheres. It is also necessary to assume that a reaction will occur when two such spheres collide in order to obtain a rate constant k for the reactants B and C as follows ... 

The overall requirement is 1.0—2.0 s for low energy waste compared to typical design standards of 2.0 s for RCRA ha2ardous waste units. The most important, ie, rate limiting steps are droplet evaporation and chemical reaction. The calculated time requirements for these steps are only approximations and subject to error. For example, formation of a skin on the evaporating droplet may inhibit evaporation compared to the theory, whereas secondary atomization may accelerate it. Errors in estimates of the activation energy can significantly alter the chemical reaction rate constant, and the pre-exponential factor from equation 36 is only approximate. Also, interactions with free-radical species may accelerate the rate of chemical reaction over that estimated solely as a result of thermal excitation therefore, measurements of the time requirements are desirable. 

If a data set containing k T) pairs is fitted to this equation, the values of these two parameters are obtained. They are A, the pre-exponential factor (less desirably called the frequency factor), and Ea, the Arrhenius activation energy or sometimes simply the activation energy. Both A and Ea are usually assumed to be temperature-independent in most instances, this approximation proves to be a very good one, at least over a modest temperature range. The second equation used to express the temperature dependence of a rate constant results from transition state theory (TST). Its form is... 

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... 

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... 

The rate constants are determined by fitting the PO concentrations that change with time, as shown in Fig. 1. With the rate constants at different reaction temperatures, the activation energies and the pre-exponential factors are determined by plotting In k against 1 / T. 

The pre-exponential factor for the H -i- H2 reaction has been determined to be approximately 2.3 x lO " mol cm s . Taking the molecular radii for H2 and H to be 0.27 and 0.20 nm, respectively, calculate the value of the probability factor P necessary for agreement between the observed rate constant and that calculated from collision theory at 300 K. 

A pre-exponential factor and activation energy for each rate constant must be established. All forward rate constants involving alkyne adsorption (ki, k2, and ks) are assumed to have equal pre-exponential factors specified by the collision limit (assuming a sticking coefficient of one). All adsorption steps are assumed to be non-activated. Both desorption constants (k.i and k ) are assumed to have preexponential factors equal to 10 3 sec, as expected from transition-state theory [28]. Both desorption activation energies (26.1 kcal/mol for methyl acetylene and 25.3 kcal/mol for trimethylbenzene) were derived from TPD results [1]. 

Another problem which can appear in the search for the minimum is intercorrelation of some model parameters. For example, such a correlation usually exists between the frequency factor (pre-exponential factor) and the activation energy (argument in the exponent) in the Arrhenius equation or between rate constant (appears in the numerator) and adsorption equilibrium constants (appear in the denominator) in Langmuir-Hinshelwood kinetic expressions. 

Equation 4.5 shows that the rate constant, k, is related to the activation energy, Ea, of the reaction by an inverse exponential operation. This means that the greater the activation energy, the smaller the rate constant, i.e., it is difficult to get the reactants to meet at high enough energies for the reaction to progress. The pre-exponential factor is a constant that includes information about how orientation of the reactant species to one another and the... 

His relationship of the rate constant k with temperature T in Kelvin involved a constant A known as the pre-exponential factor and the activation energy Ea ... 

Ao pre-exponential factor of reaction rate constant per attacked atom among bonds with equireactivity same units as for A... 

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. 

The pre-exponential factor depends on the reaction enthalpy, and the rate constant is equal to the following ... 

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). 

It is apparent that these reactions are close in their enthalpies, but greatly differ in the rate constants. The peroxyl radical reacts with p-cresol by four orders of magnitude more rapidly than with ethylbenzene. Such a great difference in the reactivities of RH and ArOH is due to the different activation energies of these reactions, while their pre-exponential factors are close. This situation was analyzed within the scope of the parabolic model of transition states (see Chapter 6 and Refs. [33-38]). 

It is seen that the rate constant ks is lower for compounds with electron-accepting substituents than with electron-donating substituents, which implies a dependence of the rate of Ar20 and R02 recombination on the electron density at the para- and ort/zo-positions of the benzene ring of the phenoxyl radical. The activation energies of this reaction vary from -33 to 10 kJ mol-1 however, the concurrent variation in the pre-exponential factor from 103 to 1010 L mol-1 s-1 causes a strong compensatory effect. It can also be seen that phenoxyl radicals readily react with peroxyl radicals k= 10s—109 L mol-1 s-1), whereas the disproportionation of peroxyl radicals is sufficiently slower (see Chapter 2). Hence, during the oxidation of hydrocarbons in the presence of phenols when k7[ArOH] > /c2[RH], the recombination reaction of ArO with R02 is always faster than the reaction of disproportionation of peroxyl radicals. 

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

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