Time dependence of pseudo-steady states

Because we also know exactly how the concentration of the reactant varies in time, we can estimate the way in which the concentrations of the intermediates, A and B will change during an experiment. Simply by substituting into 

These time-dependent, or pseudo-steady-state, results are shown in Fig. 2.2. The numerical values correspond to the data in Table 2.1, but the curves are qualitatively correct for any values of the rate constants etc. b t) falls exponentially throughout the reaction whilst a(t) builds up to a maximum before decaying. 

The time at which the curves for a and b cross will be that at which the concentration p has fallen from its initial value to that given by eqn (2.12), i.e. tcross satisfies 

Predicted pseudo-stationary-state evolution of the intermediate species concentrations a(t) and b(t), as given by eqns (2.15) and (2.16). Specific numerical values correspond to the rate data in Table 2.1. The time at which the two concentrations become equal and that at which a(t) attains its maximum are indicated. 

In a similar way, the maximum in a(t) will occur at time rmax, given by 

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