Kinetics of the phenyl radical reaction with ethylene: An RRKM theoretical analysis of low and high temperature data

The kinetics of the reaction of phenyl radical with ethylene has been investigated with the cavity-ring-down method at six temperatures between 297 and 523 K under a constant pressure of 20 torr Ar. A test performed at 60-torr pressure revealed no noticeable change in the measured rate constant value. The second-order rate constant determined by directly monitoring the decay of the phenyl radical under excess ethylene concentration conditions could be effectively represented by the Arrhenius equation imagek”C2H4 = 10− 11.92± 0.35 exp (−2,250 ± 630/T) cm3/s where the errors represent one-standard deviation evaluated with the weighting factor wi = (ki/σi)2. This low-temperature and comparatively high-pressure result can be satisfactorily correlated by means of the RRKM theory with the high-temperature (1000–1300 K) and low-pressure (1–10 mtorr) styrene formation data reported by Fahr and Stein (Ref. 15), k″C6H5C2H3 = 4.2 × 10−12exp(−3120/T)cm3/s. The result of our multichannel RRKM calculation based on the mechanism imageimage suggests that the rate constant for the production of styrene under the conditions employed by Fahr and Stein (kb) is essentially the same as the total rate constant, k″C2H4 = kb + kc, because kb much greater-than kc at high temperatures (T > 1000 K) and low pressures (P < 20 torr). Under atmospheric combustion conditions, however, both kb and kc are comparable and strongly dependent on T and P. The total rate constant for the C6H5 + C2H4 reaction can be given by the following expression: imagek”C2H4 = 1.2×10− 17 T 1.62 exp (−1490/T) cm3/s for the temperature range 300–2000 K, effectively encompassing both sets of kinetic data.