Kinetics of coupled reactions: Lumping pentadecylbenzene pyrolysis into three parallel chains

The pyrolysis of pentadecylbenzene (PDB) was used as a vehicle example with which to develop a general methodology for the formulation of an analytical rate expression for the reaction of a single substrate to a complex product spectrum. The methodology organizes reaction products into pairs that form from closed-chain sequences, and allows chain transfer by both μ and β radicals to determine quantitative product selectivities. Including initiation steps and termination by all possible combinations of μ and β radicals provides quantitative reaction rates. PDB pyrolysis was modeled as three coupled parallel chains that led to the product pairs toluene plus 1-tetradecene, styrene plus tridecane, and minor products. Estimates of the rate constants for each elementary step allowed comparison with experimental data on the concentration dependence of a pseudo-first-order rate constant and product selectivities. Qualitative agreement between the model and the experiments was always good, and quantitative agreement was excellent at high PDB concentrations. The model and experiments demonstrated that chain transfer by μ radicals can influence both product selectivities and the apparent kinetics, and a criterion whereby its importance can be discerned is presented.