Reaction rate constant energy-averaged

The initial state-specific reaction rate constant for both diatom-diatom and atom-triatom reactions is calculated by averaging the corresponding cross-section over a Boltzmann distribution of translational energy ... 

Table 7 Average reaction rate constants and activation energies at 50°C for the methanolysis of soybean oil using NaOH ...

The bar over the diffusivity term indicates the product layer average. Ajuao is equal to the standard value of the formation Gibbs energy of the spinel, AGAB2oa. One finds from Eqn. (6.29) that the (parabolic) reaction rate constant (A 2 = 2-kt) is... 

Thus, the energy E has the meaning of effective activation energy. With decreasing temperature, the effective activation energy and the preexponential factor /(E ) diminish. The reaction rate constant is proportional to the averaged reaction probability. The characteristic temperature dependence of the reaction rate constant is shown in Fig. 24. 

The reaction rate constant is obtained by averaging the rate r(n) with the help of the energy distribution... 

The reaction rate constant is determined with statistic averaging of transfer rate w( ) across the initial-state energy spectrum. When this spectrum is continuous, the averaging comes down to integration [6, 7] ... 

Effective reaction rate constants for decomposition are given in Table 12.2. The temperature dependence corresponds to an activation energy of 16.7 kcal/mol. which must be an average for ihc various RMg X species present in the solution. This value is close to the dissoca-tion energy (23.4 kcal/mol) [20] calculated for a Mg—Mg bond in a singly ionized magnesium... 

The temperature dependence of the reaction rate constant The translational energy dependence of the reaction cross-section translates into the temperature dependence of the reaction rate constant. The procedure is clear take k(v) = vo-R, Eq. (3.4), and average it over a thermal distribution of velocities, k(T) = (vctr(v)). We wrote ctr(v) as a reminder that the reaction cross-section can depend on the collision velocity. 

The unraveling of the averaging that goes into the definition of a thermal reaction rate constant shows that its temperature dependence is not quite a simple matter. The state-to-state reaction rate constants vary with temperature because the state-to-state cross-section depends on the collision energy. In addition, for a system in thermal equihhrium, the populations of the different initial states are themselves temperature-dependent. Problem F shows that if an increment in the collision energy is as effective in promoting reaction as an increment in the internal energy of the reactants, then the two sources of T-dependence will be equivalent. As we have noted, such equivalence is not necessarily the case. 

G. The Tolman expression for the activation energy. The derivation of the Tohnan result for the activation energy as the difference between the mean energy of the reactive reactants and the mean energy of all reactants, Eq. (3.9), was for the special case that there was only translational energy. In Appendix 3.A we showed how to express the reaction rate constant as an average of contributions from different internal states of the reactants. Show that in this more general case we have... 

---