Global Master Equation Analysis of Rate Data for the Reaction C₂H₄ + H ⇄ C₂H₅: Δ_fH₀^⊖C₂H₅

While forward and reverse rate constants are frequently used to determine enthalpies of reaction and formation, this process is more difficult for pressure-dependent association/dissociation reactions, especially since the forward and reverse reactions are usually studied at very different temperatures. The problems can be overcome by using a data-fitting procedure based on a master equation model. This approach has been applied to existing experimental pressure-dependent forward and reverse rate coefficients for the reaction C₂H₄ + H ⇄ C₂H₅ (k₁, k_-1) using the MESMER code to determine Δ_fH₀^⊖C₂H₅ from the enthalpy of the reaction. New measurements of k₁, k_-1 were included in analysis. They are based on laser flash photolysis with direct observation of H atom time profiles by vacuum ultraviolet laser-induced fluorescence under conditions where the approach to equilibrium could be observed. Measurements were made over the temperature range 798-828 K and with [He] from 2.33 to 7.21 × 10¹⁸ molecule cm^-3. These data were then combined with a wide range of existing experimental data with helium as the bath gas (112 measurements of k₁ and k_-1, covering the temperature range 285-1094 K, and [He] = 7.1 × 10¹⁵-1.9 × 10¹⁹ molecule cm^-3) and fitted using the master equation solver MESMER. The required vibrational frequencies and rotational constants of the system were obtained from ab initio calculations, and the activation threshold for association (ΔE_thresh), enthalpy of reaction (Δ_rH₀^⊖), imaginary frequency (υ_imag), and helium energy-transfer parameters (⟨ΔE⟩_d,298(T/298)) were optimized. The resulting parameters (errors are 2σ) are ΔE_thresh = 11.43 ± 0.34 kJ mol^-1, Δ_rH₀^⊖ = -145.34 ± 0.60 kJ mol^-1, υ_imag = 730 ± 130 cm^-1, ⟨ΔE⟩_d,298 = 54.2 ± 7.6 cm^-1, and n = 1.17 ± 0.12. A value of Δ_fH_298.15^⊖(C₂H₅) = 120.49 ± 0.57 kJ mol^-1 is obtained by combining Δ_rH₀^⊖ with standard enthalpies of formation for H and C₂H₄ and making the appropriate temperature corrections. The dependence of these parameters on how the internal rotor and CH₂ inversion modes are treated has been explored. The experimental data for other bath gases have been analyzed, and data sets compatible with the potential energy surface parameters determined above have been identified. The parameters are virtually identical but with slightly smaller error limits. Parameterization of k₁, k_-1 using the Troe formalization has been used to investigate competition between ethyl decomposition and reaction with oxygen under combustion conditions.