In this work a new equation which describes the time evolution of bimolecular reactions is derived and tested by experiment. The equation is general and the results show that second-order reactions of any simple type may be accurately described by a quotient of exponential functions. The model and reagent concentration dependent observed rate constants show a complex non-linear behaviour when experimental conditions deviate from pseudo-first order nevertheless reducing to the well-known linear dependence when pseudo-first order conditions are met.