# Mathematical modelling of the vitamin C clock reaction: a study of two kinetic regimes

## TL;DR

This paper models a vitamin C clock reaction to better understand how hydrogen peroxide affects its timing and behavior.

## Contribution

A more detailed and validated mechanistic model of the vitamin C clock reaction is developed and analyzed.

## Key findings

- The model explains the effect of hydrogen peroxide concentration on the clock reaction's switchover time.
- The model resolves discrepancies in the literature about the slow reaction's kinetic order.
- The model is validated across a wide range of hydrogen peroxide concentrations.

## Abstract

Chemically reacting systems exhibiting a repeatable delay period before a visible and sudden change are referred to as clock reactions; they have a long history in education and provide an idealization of various biochemical and industrial processes. We focus on a purely substrate-depletive clock reaction utilizing vitamin C, hydrogen peroxide, iodine and starch. Building on a recent study of a simplified two-reaction model under high hydrogen peroxide concentrations, we develop a more detailed model which breaks the slow reaction into two steps, one of which is rate-limiting unless hydrogen peroxide levels are very high. Through asymptotic analysis, this model enables the effect of hydrogen peroxide concentration to be elucidated in a principled way, resolving an apparent discrepancy with earlier literature regarding the order of the slow reaction kinetics. The model is analysed in moderate and high hydrogen peroxide regimes, providing approximate solutions and expressions for the switchover time which take into account hydrogen peroxide concentration. The solutions are validated through simultaneously fitting the same set of parameters to several experimental series, then testing on independent experiments across widely varying hydrogen peroxide concentration. The study thereby presents and further develops a validated mechanistic understanding of a paradigm chemical kinetics system.