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5.8 Reaction Mechanism and Rate Law

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A reaction mechanism is closely tied to the rate law because the observed rate of a reaction often depends on the slowest elementary step in the mechanism. This slowest step is called the rate-determining step or rate-limiting step. Since it is the bottleneck of the process, it controls how fast the overall reaction proceeds. For an elementary step, the exponents in the rate law come directly from the coefficients of the reactants in that step. This is why mechanisms are so useful: they give a molecular explanation for why the rate law has the form it does.

However, you have to be careful. You can only take coefficients directly from an elementary step, not from the overall reaction unless the overall reaction happens in one step. If the slow step involves an intermediate from an earlier fast step, then you may need additional algebra to rewrite the rate law in terms of stable reactants only. So a proposed mechanism is considered reasonable only if it produces the experimentally observed rate law and adds up to the correct overall reaction.

Example 1: Suppose the mechanism is

Step 1 (slow):
NO2+NO2→NO3+NONO_2 + NO_2 \rightarrow NO_3 + NO
Step 2 (fast):
NO3+CO→NO2+CO2NO_3 + CO \rightarrow NO_2 + CO_2

Because the first step is slow, it controls the rate. Since it is elementary, the rate law is Rate = k[NO2]2{k[NO_2]^2}

So even though CO appears in the overall reaction, it does not appear in the rate law because it is not involved in the slow step.

Example 2: Suppose the mechanism is

Step 1 (slow):
A+B→CA + B \rightarrow C
Step 2 (fast):
C+D→EC + D \rightarrow E
The slow step is elementary, so the rate law is Rate =
k[A][B]k[A][B]

The concentration of D does not appear in the rate law because D is only involved after the rate-determining step.

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