Chain reactions apparent activation energy

The apparent activation energy for the y-ray induced formation of carbonyl difluoride is calculated to be 18.0 kj moP . The kinetics results indicate a chain mechanism in which primary radicals formed from the irradiation of CjF, induce its copolymerization with Oj-The resulting long-chain peroxide radicals decompose by splitting off COFj or CjF O, depending upon whether a carbon-carbon, or oxygen-oxygen bond is broken. The perfluorinated cyclopropane is considered to be formed independently, in a minor side-reaction [420]. 

The apparent activation energy of the overall chain reaction is thus not the same as the activation energy for the propagation step, nor is it a direct function of the activation energy for the initiation step. In fact, the apparent activation energy can be considerably smaller than due either to if > 0 or second-order termination where w = 2. For this reason, a chemical transformation may occur by a chain mechanism even if the chain involves an initiation step with higher activation energy than the alternative direct reaction. 

The mechanism of hydroquinone autoxidation likely proceeds by a radical chain pathway. Kinetic studies carried out under relevant reaction conditions support a second-order rate law for the reaction, rate =Ar[QH2] [Oj], with an apparent activation energy of = 15 kcal/mol [21]. Based on these kinetic findings, as well as DFT studies [22], anthrahydroquinone autoxidation has been proposed to occur through initial, rate-limiting, direct H-atom abstraction from the hydroquinone species by O2 (Eq. (14.2)). The semiquinone species then react readily with triplet O2 (Eq. (14.3)), and hydroperoxy radical, HO2, has been proposed to act as a radical chain carrier (Eq. (14.4)). 

In the case of catalysis by iron complexes with HMPA, which does not transformed in the course of oxidation, it is possible to estimate the apparent activation energies for micro steps of ethylbenzene oxidation - chain initiation (activation by O2) and propagation (Cat + R02 ) at two temperatures, 80 and 120°C. These are EJ w =24.53 and 13.03 kcal/mol and (Wp ) =21.46 and 17.63 kcal/mol in the absence and presence of HMPA, respectively. The gain in activation energy of the initiation reaction 11.5 kcal/mol via the coordination of HMPA is approximately equal to the energy 10 kcal/mol of ligand addition to metal acetylacetonates [139]. The difference in between the initiation and propagation reactions in the presence of HMPA is presumably responsible for tendency of oxidation selectivity to increase with decrease in temperature. 

---