Using the SSA to Predict Changes in Kinetic Order

Lef s examine the result obtained when k i k2, and the concentrations of Pi and B are comparable and in excess at the beginning of the study. Since Pi is a product of the first reaction, its concentration necessarily increases during the reaction. However, we are free to add this product in advance of performing the reaction as a means to keep its concentration nearly constant. With excess Pi and B present from the start, their concentrations do not change appreciably during the reaction (hence [Pi] = [Pilo, [B] = [Bjo, and k i[Pi] 2(6]). Under these conditions the term k2(B] in Eq. 7.57 can be neglected, and the rate law reduces to Eq. 7.58. Now the reaction is found to be second order overall with respect to the reactants that is, first order in both A and B. The rate of the reaction would be inversely proportional to the concentration of [Pi] that was added at the beginning. 

This same result can also be achieved regardless of the relative sizes of and k2 as long as we can add enough excess of Pi so that fc i[Pi] k2[B], In this case we have manipulated the rates of the individual steps by controlling the concentrations of the reactants. This is only possible with second order or higher reactions where at least one of the terms in the denominator is concentration dependent. 

In contrast, when the T2[B] term is much greater than the I -i[Pi] term, we can neglect the Li[Pi] term. Neglecting LJPi] in Eq. 7.57 cancels the /C2[B] term in the numerator and denominator, giving Eq. 7.59. This scenario occurs when 2 k i and the concentrations of Pi and B are comparable, or when B is added in such a large excess that its associated term overwhelms the P] term. Under any of these conditions the reaction is found to be first order in A and zero order in B, and the concentration of Pi does not affect the rate. 

The reduction of Eq. 7.57 to Eqs. 7.58 or 7.59, depending upon the experimental conditions, gives us the ability to test if the kinetics of the reaction under study responds in the manner predicted by these mathematical analyses. If the kinetics gives the behavior discussed, the data tell us that a mechanism involving A in the first step to give P] and a reactive intermediate that then reacts with B is plausible. This shows how one can experimentally control the form of the rate law and thereby test mechanistic postulates, such as the sequence of steps and the existence of an intermediate. 

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