Absorbance, Light Intensity, Mass Transfer, and Sampling Time Effects in a Proposed Mechanism for the Photolysis of Phenyl Azide

In the concentrated phenyl azide solutions in which Costantino et al. have reported apparent quantum yields for azide disappearance {formula-omited} on the order of 1000 and interpreted their results in terms of a branching-chain mechanism, the optical penetration depth is sufficiently small that the proposed chain-initiation reaction is effectively confined to a very thin layer near the front optical window. Simple calculations show that this layer is sufficiently thin that diffusive mass transfer is important on the time scale of the experiments. On the basis of the mechanism of Costantino et al., we develop and investigate a model consisting of three nonlinear integro-partial differential equations accounting for the nonuniform light absorption, photochemical kinetics, and diffusive mass transfer. The dependence of {formula-omited} on initial azide concentration is shown to be in good qualitative agreement with experiment. The model predicts that the apparent quantum yield is sometimes a strong function of the time at which the reaction mixture is sampled. The relatively simple mechanism proposed by Costantino et al. is consistent with their results, as well as the more recent measurements of Liang and Schuster, in which quantum yields in excess of unity were not observed. In terms of the proposed branching-chain mechanism, the apparent discrepancies between the results of Costantino et al. and Liang and Schuster can be attributed to the use of different light intensities.