Mathematical modelling of the vitamin C clock reaction

TL;DR

This paper develops a mathematical model for the vitamin C clock reaction, analyzing its dynamics and validating the model with experiments, providing insights into reaction timing and concentration effects.

Contribution

It introduces a nonlinear ODE model for the vitamin C clock reaction and derives an approximate formula for switchover time, validated by experiments.

Findings

Asymptotic approximations match numerical solutions closely.

Derived formula accurately predicts switchover time based on initial conditions.

Model provides a useful educational and industrial chemistry tool.

Abstract

Chemical clock reactions are characterised by a relatively long induction period followed by a rapid `switchover' during which the concentration of a \emph{clock chemical} rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via `kitchen sink chemistry' experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry.