Reduction of Iodine by Phosphorus(I): Integration of the Rate Equation

The reduction of iodine by phosphorus(I) (hypophosphorous acid) yields iodide and phosphorus(III) (phosphorous acid). The reaction is autocatalytic in hydrogen ion, autoinhibitory in iodide ion, and zero order in iodine over a wide concentration range. We return to the original article by A. D. Mitchell that presents a mechanism to account for these facts and devise a method to integrate numerically the complex rate equation for this reaction. Integration is combined with nonlinear curve-fitting to determine the rate-limiting rate constant and provide a fit to the data that is considerably improved over the original. The entire exercise provides an excellent case study for introducing the student to numerical integration and curve-fitting of complex nonlinear reaction dynamics.