| MadSci Network: Chemistry |
Ben,
Your question is a very good one, and this is a concept that confuses
many people. For the reaction diagram that you drew, the second step is the
rate-determining step. By definition, the rate- determining step is always
the step that goes through the transition state having the highest energy.
The reason why this is the case with your reaction has to do with the
fate of the intermediate. The step with the largest activation energy is
the first step, in which the intermediate Y is produced. The crucial
question is: what is the fate of this intermediate? Since the lowest energy
pathway is for the intermediate to return to starting material, this process
will be faster than the second step, which is the forward reaction to form
the product. Therefore the intermediate Y will partition back to X much
more often than it partitions forward to Z. Hence, the step that determines
the rate at which product is formed is the second step, in which the
intermediate Y is converted into product Z.
Thus, in general, the step that is the overall rate-limiting step in a
multi-step reaction will always be the step that goes through the transition
state having the highest energy.
If you look at your reaction going in the reverse direction, the first
step (conversion of Z to Y) will be rate-limiting. This is because in the
reverse direction, the intermediate that is formed will then form product
(X) much faster than it reverts to starting material. Hence, the step that
determines the rate at which the end product is reached will now be the
first step.
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