Quadratic autocatalysis in closed vessels

If we know the initial concentrations of the reactants (let us call these a0 and b0) then because of the reaction stoichiometry, we can express the concentration of B as 

Equation (1.12) can be rearranged and integrated using partial fractions to give the explicit dependence of a on time, a(t). A special, but particularly simple, case occurs if there is no autocatalyst B present initially (i.e. b0 = 0). 

From this it follows that the reaction rate can be expressed in a similar way as a function of time  

Typical variations of concentration and rate for this case, with b0 = 10 6 mol dm-3, are shown in Fig. 1.4. There is now a finite induction 

Cubic autocatalysis and clock reactions in closed vessels 

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