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 k"_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 w_i = ( k_i σ_i)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 C₆H₅ + C₂H₄ a ⇌ C₆H₅CH₂CH₂ b → C₆H₅C₂H₃ + H c → C₆H₅C₂H₄ +(M) suggests that the rate constant for the production of styrene under the conditions employed by Fahr and Stein (k_b) is essentially the same as the total rate constant, k″_C2H4 = k_b + k_c, because k_b ≫ k_c at high temperatures (T > 1000 K) and low pressures (P < 20 torr). Under atmospheric combustion conditions, however, both k_b and k_c 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: k"_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.