Abstract
Chemical clock reactions are characterized by a relatively long induction period followed by a rapid ‘switchover’ during which the concentration of a 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.
Highlights
Chemical clock reactions are characterized by a relatively long induction period followed by a rapid ‘switchover’ during which the concentration of a clock chemical rises rapidly
Given by Chien [6]; this work exhibited a number of analytical techniques including solving a Riccati- 2 type equation resulting from quadratic reaction kinetics
This study focused on the vitamin C clock reaction, the dynamics of which are governed by substrate-depletion without autocatalysis
Summary
Chemical clock reactions are characterized by a relatively long induction period followed by a rapid ‘switchover’ during which the concentration of a clock chemical rises rapidly. Asymptotic analysis 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. ‘Clock reactions’ encompass many different chemical processes in which, following mixing of the reactants, a long induction period of repeatable duration occurs, followed by a rapid visible change These reactions have been studied for over a century, with early examples including the work of H. Further review and history of the field can be found in [1,8]
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