Page 307 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

288 faster? These questions raise the issue of a relationship between the thermodynamic
and kinetic aspects of reactivity. It turns out that there frequently are such relationships
CHAPTER 3 in series of closely related reactions, although there is no fundamental requirement
Structural Effects on that this be the case. The next several sections discuss examples of such relationships.
Stability and Reactivity

3.3.2.1. Bell-Evans-Polyani Relationship. The Bell-Evans-Polyani formula deals with
the relationship between reaction rate and exothermicity for a series of related single-
step reactions. 55 Evans and Polyani pointed out that for a series of homolytic atom
transfer reactions of the general type

A −B + X·→ A ·+B−X

there was a relationship between the activation energy and the reaction enthalpy, which
can be expressed as

E = E + H (3.32)
a 0
where E is the activation energy of the reference reaction and H is the enthalpy of
0
each reaction in the series. In terms of reaction energy diagrams, this indicates that for
reactions having similar energy profiles, the height of the barrier will decrease as the
reaction becomes more exothermic (and vice versa), as illustrated in Figure 3.9.
This relationship can be explored, for example, by considering the rates of
hydrogen abstraction reactions. For example, the E for hydrogen abstraction from
a
56
simple hydrocarbons shown below can be compared with the H of the reaction, as
derived from the bond energy data in Table 3.2. The plot is shown in Figure 3.10.
R C−H + Br·→ R C·+H−Br
n n

Alkane E a H
CH 3 -H 18 3 +18 0
C 2 H 5 −H 13 4 +13 5
CH 3 2 CH−H 10 2 +11 1
C 2 H 5 CH CH 3 -H 10 2 +11 3
CH 3 3 C−H 7 5 +8 7

exothermic endothermic

Fig. 3.9. Energy profiles for series of related reactions illustrating the
Bell-Evans-Polyani relationship.
55 M. G. Evans and M. Polanyi, Trans. Faraday Soc., 34, 11 (1938).
56
G. C. Fettis and A. F. Trotman-Dickenson, J. Am. Chem. Soc., 81, 5260 (1959).