General rate equations for calculating quantum yields of unimolecular photoprocesses

Abstract

The closed-form solution to the differential equation describing the rate of a unimolecular photoprocess occurring in a well-stirred medium is reported for the first time for the general case of a single reactant yielding any number of absorbing products and where any number of nonreactive absorbing species are present. The final equation can be used to obtain an accurate quantum yield for the photoreaction. This method for the calculation of quantum yields does not require special experimental conditions of either very high or very low total absorbance nor is it limited to low conversion. An approximate form of this equation has also been derived. The approximate equation can be rapidly solved by hand and is accurate to 3% or better over a wide range of experimental conditions, including absorbance values between 0.2 and 1.0 and conversions as high as 50%. In addition, the application of this approximate equation to the calculation of quantum yields for solid-phase photoreactions is discussed. The accuracy of the approximation is again high, but over a relatively smaller range of experimental conditions. © 1984 American Chemical Society.