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.