Page 1012 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

996 The data required are the relative magnitudes of k and k . When both B−X and
Y
X
B−Y are present in the reaction system, they will be consumed at rates that are a
CHAPTER 11 function of their reactivity and concentration.
Free Radical Reactions
−d B−X
= k A· B−X
x
dt
−d B−Y
= k A· B−Y
y
dt
k d B−X / B−X
x
=
k y d B−Y / B−Y
Integration of this expression with the limits [B–X]=[B–X] to [B−X] , where t is a
in
t
point in time during the course of the reaction gives
k x ln B−X / B−X
in
t
=
k y ln B−Y / B−Y
in
t
This relationship permits the measurement of the ratio k /k . The initial concen-
Y
X
trations [B−X] and [B−Y] are known from the conditions of the experiment. The
in
in
reaction can be stopped at some point when some of both B−X and B−Y remain
unreacted, or an excess of B−X and B−Y can be used so that neither is completely
consumed when A−A has reacted completely. Determination of [B−X] and [B−Y] t
t
then provides the information needed to calculate k /k . It is clear that the reactions
Y
X
being compared must be of the same kinetic order. If they are not, division of the two
rate expressions would leave uncanceled concentration terms.
Another experiment of the competition type involves the comparison of the
reactivity of different atoms in the same molecule. For example, gas phase chlorination
of butane can lead to 1- or 2-chlorobutane. The relative reactivity (k /k
of the
p
s
primary and secondary hydrogens is the sort of information that helps to characterize
the details of the reaction process.
kp
.
Cl . + CH CH CH CH 3 HCl + CH CH CH CH 3
2
2
2
2
2
3
Cl 2 + . CH CH CH CH 3 Cl . + ClCH CH CH CH 3
2
2
2
2
2
2
Cl . + CH CH CH CH 3 ks HCl + CH CHCH CH 3
2
3 .
3
2
2
.
CHCH CH
Cl 2 + CH 3 . 2 3 Cl + CH CHCH CH 3
2
3
Cl
The value of k /k can be determined by measuring the ratio of the products
p
s
1-chlorobutane:2-chlorobutane during the course of the reaction. A statistical correction
must be made to take account of the fact that the primary hydrogens outnumber the
secondary ones by 3:2. This calculation provides the relative reactivity of chlorine
atoms toward the primary and secondary hydrogens in butane:
k p 2 1-chlorobutane
=
k 3 2-chlorobutane
s
Techniques for measuring the rates of very fast reactions have permitted absolute
84
rates to be measured for fundamental types of free radical reactions. Some examples
84
M. Newcomb, Tetrahedron, 49, 1151 (1993).