Mathematical Modelling Of Chemical Reactions: The Vitamin C Clock Reaction

Abstract

The thesis presents a mathematical model and accompanying analysis to gain insights into the chemical clock reaction associated with vitamin C, hydrogen peroxide and iodine. Chemical clock reactions are identified by a reproducible induction period that is followed by in a rapid change in a solution triggered by a rise in a specific chemical concentration. In the vitamin C clock reaction, vitamin C converts iodine to iodide (the fast reaction) and simultaneously hydrogen peroxide converts iodide to iodine (the slow reaction). The fast reaction dominates until the vitamin C is depleted, at which point the iodine concentration rises, resulting in a rapid colour change in the system. Three new models are presented. Firstly, both the fast and slow reactions are considered under the assumption that hydrogen peroxide levels are moderate. Secondly, the slow reaction is considered in isolation and in more detail, revealing the effect of hydrogen peroxide concentration on the reaction kinetics and resolving differences in the existing literature. Thirdly, the fast reaction is reincorporated with the more detailed slow reaction to create a unified model that can capture the clock reaction dynamics under both moderate and high hydrogen peroxide regimes. All models are studied through numerical and asymptotic analysis. Using asymptotic analysis, formulae are derived that can predict the length of the induction period. Finally, experiments are carried out to generate data to parameterise the models and test the associated formulae, which are shown to be accurate for both hydrogen peroxide regimes.