Determining Rate Laws From Mechanistic Steps

Consider the following mechanism for the overall reaction A+B→C

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How do we find the overall rate law for this reaction? 

First of all, we need to know the Rate Determining Step (RDS) to write the rate law. Note that this is the slow step, as the part of the overall mechanism that proceeds the slowest will ultimately determine the overall rate of the reaction. Since this is an elementary step, we can write the rate law for the RDS directly from the coefficients: 

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However, we have a problem here because we cannot define a rate in terms of an intermediate. Here, our intermediate is D because it is a product of one step and then used as a reactant in another step in the mechanism.  

Thus, we need to write [D] (the intermediate) in terms of [A] (our reactant in the overall reaction). To do so, use the equilibrium step. We know that when a system is at equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction. Thus, we can write:

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Rearranging this, we get that

Screen Shot 2019-02-05 at 12.09.58 AM.png

Now we can substitute this into our original rate law:

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We combine all of the rate constants, k, into k’ to symbolize the overall rate constant. Thus, the rate law is:

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Ally CollardComment