Page 300 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

3
Third order/one reactant: Rate = k A 281
1 1 1 SECTION 3.2
kt = − (3.30)
2 A 2 A 2 Chemical Kinetics
o
2
Third order/two reactants: Rate = k A B
2 1 1 2 B A
o
kt = − + ln (3.31)
2 B − A A A 2 B − A 2 A B
o
o
o
o
o
o
Integrated expressions applicable to other systems are available. 52
The kinetic data available for a particular reaction are examined to determine if
they fit a simple kinetic expression. For example, for a first-order reaction, a plot of
log [A] versus t yields a straight line with a slope of −k/2 303. For second-order
reactions, a plot of 1/[A] versus t is linear with a slope of k. Figure 3.7 shows such
plots. Alternatively, the value of k can be calculated from the integrated expression
over a sufficient time range. If the value of k remains constant, the data are consistent
with that rate expression.
Many organic reactions consist of a series of steps involving several interme-
diates. The overall rate expression then depends on the relative magnitude of the rate
constants for the individual steps. The relationship between a kinetic expression and a
reaction mechanism can be appreciated by considering the several individual steps that
constitute the overall reaction mechanism. The expression for the rate of any single
step in a reaction mechanism contains a term for the concentration for each reacting
species. Thus, for the reaction sequence:

k k 2 k 3
A + B 1 C D E + F
k –1

the rates for the successive steps are:
d C
Step 1: = k A B −k C
1
−1
dt
d D
Step 2: = k C
2
dt
d E d F
Step 3: = = k D
3
dt dt

Log c 1/c

t t

Fig. 3.7. Linear plots of log c versus t for a first-order reaction (a) and
1/c versus t for a second-order reaction.
52
C. Capellos and B. N. J. Bielski, Kinetic Systems, Wiley-Interscience, New York, 1972.