Decomposition reaction rate of BCl₃-C₃H ₆(propene)-H₂ in the gas phase

The decomposition reaction rate in the BCl₃-C₃H ₆-H₂ gas phase reaction system in preparing boron carbides was investigated based on the most favorable reaction pathways proposed by Jiang et al. [Theor. Chem. Accs.2010, 127, 519] and Yang et al. [J. Theor. Comput. Chem.2012, 11, 53]. The rate constants of all the elementary reactions were evaluated with the variational transition state theory. The vibrational frequencies for the stationary points as well as the selected points along the minimum energy paths (MEPs) were calculated with density functional theory at the B3PW91/6-311G(d,p) level and the energies were refined with the accurate model chemistry method G3(MP2). For the elementary reaction associated with a transition state, the MEP was obtained with the intrinsic reaction coordinates, while for the elementary reaction without transition state, the relaxed potential energy surface scan was employed to obtain the MEP. The rate constants were calculated for temperatures within 200-2000 K and fitted into three-parameter Arrhenius expressions. The reaction rates were investigated by using the COMSOL software to solve numerically the coupled differential rate equations. The results show that the reactions are, consistent with the experiments, appropriate at 1100-1500 K with the reaction time of 30 s for 1100 K, 1.5 s for 1200 K, 0.12 s for 1300 K, 0.011 s for 1400 K,or 0.001 s for 1500 K, for propene being almost completely consumed. The completely dissociated species, boron carbides C₃B, C₂B, and CB, have very low concentrations, and C₃B is the main product at higher temperatures, while C₂B is the main product at lower temperatures. For the reaction time 1 s, all these concentrations approach into a nearly constant. The maximum value (in mol/m³) is for the highest temperature 1500 K with the orders of -13, -17, and -23 for C₃B, C₂B, and CB, respectively. It was also found that the logarithm of the overall reaction rate and reciprocal temperature have an excellent linear relationship within 700-2000 K with a correlation coefficient of 0.99996. This corresponds to an apparent activation energy 337.0 kJ/mol, which is comparable with the energy barrier 362.6 kJ/mol of the rate control reaction at 0 K but is higher than either of the experiments 208.7 kJ/mol or the Gibbs free energy barrier 226.2 kJ/mol at 1200 K.