Page 302 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

By substituting into the rate for the second step, we obtain the following expression: 283
k A B SECTION 3.2
1
Rate = k C D = k 2 D
2
k D +k Chemical Kinetics
2 −1
If k [D] is much greater than k , the rate expression simplifies to
2 −1
k k A B D
2 1
Rate = = k A B
1
k D
2
On the other hand, if k [D] is much less than k , the observed rate expression becomes
2
−1
k k A B D
1 2
Rate =
k −1
The first situation corresponds to the first step being rate determining; in the second
case, it is the second step, with the first step being a preequilibrium.

3.2.4. Examples of Rate Expressions
The normal course of a kinetic investigation involves the postulation of likely
mechanisms and comparison of the observed rate expression with those expected for
the various mechanisms. Those mechanisms that are incompatible with the observed
kinetics can be eliminated as possibilities. One common kind of reaction involves
proton transfer occurring as a rapid equilibrium preceding the rate-determining step,
for example, in the reaction of an alcohol with hydrobromic acid to give an alkyl
bromide:

fast
k 1
ROH+H −→ ROH +
+
2
←−
k −1
slow
+
ROH +Br −→RBr +H O
−
2
2
k 2
The overall rate being measured is that of Step 2, but there may be no means of
directly measuring ROH . The concentration of the protonated intermediate ROH +
+
2 2
can be expressed in terms of the concentration of the starting material by taking into
consideration the equilibrium constant, which relates [ROH], Br , and H :
+
−
+
ROH
2
K =
ROH H
+
+
+
ROH = K ROH H
2
+
−
+
−
Rate = k K ROH H Br = k ROH H Br
2
obs
To illustrate the development of a kinetic expression from a postulated
reaction mechanism, let us consider the base-catalyzed reaction of benzaldehyde and
acetophenone. Based on general knowledge of base-catalyzed reactions of carbonyl
compounds, a reasonable sequence of steps can be written, but the relative rates of
the steps is an open question. Furthermore, it is known that reactions of this type