Page 301 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

282 If we specify that the first step is a very rapid but unfavorable equilibrium, and that
k << k , then the second step is rate determining. Under these circumstances, the
2 3
CHAPTER 3 overall rate of the reaction will depend on the rate of the second step. In the reaction
Structural Effects on under consideration, the final step follows the rate-determining step and does not affect
Stability and Reactivity
the rate of the overall reaction; k does not appear in the overall rate expression. The
3
rate of the reaction is governed by the second step, which is the bottleneck in the
process. The rate of this step is equal to k multiplied by the molar concentration of
2
intermediate C, which is small and may not be measurable. It is therefore necessary
to express the rate in terms of the concentration of reactants. In the case under
consideration, this can be done by recognizing that [C] is related to [A] and [B] by an
equilibrium constant:
C
K =
A B

Furthermore, K is related to k and k by the requirement that no net change in
1 −1
composition occur at equilibrium
k C = k A B
−1 1
k 1
C = A B
k −1
The rate of Step 2 can therefore be written in terms of [A] and [B]:
d D k 1
= k C = k 2 A B = k A B
2
obs
dt k −1
Experimentally, it would be observed that the reaction rate would be proportional to
both [A] and [B]. The reaction will be first order in each reactant and second order
overall.
A useful approach that is often used in analysis and simplification of kinetic
expressions is the steady state approximation, which can be illustrated by a hypothetical
reaction scheme:
k 1
A +B −→ C
←−
k −1
k 2
C+D −→ E +F
A +B+D → E +F

If C is a reactive, unstable species, its concentration will never be very large. It must
be consumed at a rate that closely approximates the rate at which it is formed. Under
these conditions, it is a valid approximation to set the rate of formation of C equal to
its rate of destruction:

k A B = k C D +k C
1 2 −1
Rearrangement of this equation provides an expression for [C]:

k A B
1
= C
k D +k
−1
2