Arrhenius energy coupled reactions

Transition state theory yields rate coefficients at the high-pressure limit (i.e., statistical equilibrium). For reactions that are pressure-dependent, more sophisticated methods such as RRKM rate calculations coupled with master equation calculations (to estimate collisional energy transfer) allow for estimation of low-pressure rates. Rate coefficients obtained over a range of temperatures can be used to obtain two- and three-parameter Arrhenius expressions ... 

When P(E) is not perturbed by the reaction, so that the distribution of critically energized molecules is that characteristic of equilibrium, the RRK model leads to a specific first-order rate constant of the form k = A exp —E /RT) where A is the frequency of internal energy transfer between oscillators. The Slater formulation in these circumstances gives k = V exp —E /RT ), both results being similar in form to the Arrhenius equation. The A factor in the RRK model represents the frequency of energy transfer between oscillators, which Jor weakly coupled oscillators would be of the order of their beat frequencies, or about 10 to 10 sec In the Slater model, V represents a weighted rms frequency of the normal frequencies which describe the decomposition [Eq. (X.6.1)]... 

Finally, another area of overlap is the potential presence of a false activation energy. This occurs when film diffusion is coupled with, say, a hrst-order reaction at the catalyst surface. The mass transfer rate r = k a ic - Cj). In contrast, the inherent reaction rate is r = These two can be combined to give an expression for the snrface concentration c, = kf cl(k + k, which is difficult to measure. This expression can be snbstitnted in the original reaction rate expression to give r = with an effective rate constant of = ll(llk, + k. Thns, if the inherent rate obeys the Arrhenius dependence on temperatnre, k, = A exp(-A yR7), and if kf is constant, the observed Arrhenius activation energy, AEq = RT d In k(/d(l/T), would be deceptively low. 

Also included on Fig. 8 is the rate constant determination for reaction (2) in a flame by Fenimore and Jones (9). The line drawn in this region for the temperature dependence of the direct reaction (2) corresponds to an Arrhenius form. It has a frequency factor 2 x 10" cm sec and activation energy of 9 kcal/mole, estimated respectively by the OH + CH A-factor and an estimate of AH for reaction (2) coupled with a 2 kcal/mole barrier. While this forms a reasonable description of the two experimental results, it would be desirable to measure points intermediate in temperature. 

Many examples of Arrhenius plots are found in the literature, but for an electrochemical flavor the one shown in Fig. 3.2, taken from a paper by Kreysa and Medin, refers to the chemical step in the indirect electrochemical oxidation of p-methoxytoluene to p-methoxybenzaldehyde using a Ce /Ce redox couple. This reaction has an activation energy obtained from the slope of Fig. 3.2 ... 

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