Oscillatory chemical reactions in closed vessels

A skeleton kinetic scheme representing the simplest model for oscillatory chemical reactions in a closed vessel can be built around an autocatalytic feedback step $\text{precursor decay} P \rightarrow A k_0 p,\\ \text{uncatalysed step} A \rightarrow B k_3 a,\\ \text{autocatalysis} A + 2B \rightarrow 3B k_1ab^2,\\ \text{catalyst decay} B \rightarrow C k_2 b.$ The first intermediate A is formed via the slow decay of a reactant or precursor species P, initially in large excess. A is converted to B via two routes: a slow pseudo-first order process and a step in which B acts as its own catalyst. The autocatalyst B is then capable of a simple first order decay to a stable product C. The concentrations of the various species at first change steadily, with that of P decreasing while A, B and C increase. This period is followed by the onset and growth of oscillations in the concentrations of the intermediates A and B. The behaviour at long times depends upon the uncatalysed conversion of A to B. Provided k$_3$ is not taken as zero, the oscillations finally diminish in amplitude and die out leaving a steady decay of P, A and B until everything has been converted to C. The simplicity of the model allows the first self-consistent test of the 'pool chemical approximation', an approach commonly used in the analysis of mechanisms in closed systems in which the precursor concentration is assumed to be constant and set equal to its initial value. The results presented here reveal the range of applicability of the approximation and show clearly how and why it can break down to give unphysical predictions.