Beyond the Beer–Lambert law: The dependence of absorbance on time in photochemistry

•The Beer–Lambert law is shown to be inadequate in photochemistry.•Absorber concentration depends on time as light intensity depends on distance.•A fundamental law governing photochemistry is derived and solved.•We demonstrate how quantum yields may be measured exactly.•Simulation supports our derivations.

The photochemical law governing chemical conversion of a photoactive species is derived and solved analytically. In the absence of solution mixing, the law predicts a remarkable symmetry in which the dependence of light intensity on distance matches the dependence of concentration on time. An exact method is described whereby a time sequence of experimental transmittance/absorbance data obtained during a light-induced chemical process can provide a value of the quantum yield for the photoreaction. It is demonstrated that this procedure is not invalidated by solution mixing.