The local and observed photochemical reaction rates revisited

In a broad sense, photochemical reactions proceed through pathways involving several reaction steps. The initiation step is the absorption of energy both by the reactant or sensitizer molecules and in some cases, by the catalyst, leading to intermediate products that ultimately give rise to stable end products. Preferably, the reaction rate expression is derived from a proposed mechanism together with sound simplifying assumptions; otherwise, it may be adopted on an empirical basis. Under a kinetic control regime, the rate expression thus obtained depends on the local rate of photon absorption according to a power law whose exponent very often ranges from one half to unity. The kinetic expression should be valid at every point of the reactor volume. However, due to radiation attenuation in an absorbing and/or scattering medium, the value of the photon absorption rate is always a function of the spatial position. Therefore, the overall photochemical reaction rate will not be uniform throughout the entire reaction zone, and the distinction between local and volume average photochemical reaction rates becomes mandatory. Experimental values of reaction rates obtained from concentration measurements performed in well-mixed reaction cells are, necessarily, average values. Consequently, for validation purposes, experimental results from these cells must be compared with volume averages of the mechanistically or empirically derived local reaction rate expressions. In this work it is shown that unless the rate is first order with respect to the photon absorption rate or the attenuation in the absorbing and/or scattering medium is kept very low, when the averaging operation is not performed, significant errors may be expected.