Page 289 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

270 the minimum energy pathway. To the extent that the calculations accurately reflect
the molecular reality, this provides a structural description of the reaction path and
CHAPTER 3 transition state. Thus we can refer to the transition structure, that is, the structural
Structural Effects on description of the reacting ensemble at the transition state. 41 We use the abbreviation
Stability and Reactivity
TS to refer to transition structures. We use the term transition state in the context
of energetic analysis where there is no explicit consideration of the structure. In
Section 3.7 we focus attention on another aspect of reactivity—the use of catalysts to
accelerate reaction.

3.2. Chemical Kinetics

3.2.1. Fundamental Principles of Chemical Kinetics

Thermodynamic data give us a means of quantitatively expressing stability. Now
we need to explore the relationship between structure and reactivity. The quantitative
description of reactivity is called chemical kinetics. A fundamental thermodynamic
equation relates the equilibrium constant for a reaction to the free-energy change
associated with the reaction:
G =−RT ln K (3.12)

The free energy contains both enthalpy and entropy terms:

G = H −T S (3.13)

Thus we see that thermodynamic stability, as measured by free energy, places a limit
on the extent of a chemical reaction. However, it does not directly determine the rate
of the reaction.
The nature of the rate constants k for individual steps in a chemical reaction
r
can be discussed in terms of transition state theory, which is a general approach for
analyzing the energetic and entropic components of a reaction process. In transition
state theory, a reaction is assumed to involve the attainment of an activated complex
that goes on to product at an extremely rapid rate. The rate of decomposition of
the activated complex has been calculated from the assumptions of the theory to be
12 −1
about 6–10 s at room temperature. The observed rate constant k is given by the
r
expression 42

k T − H /RT S /R
‡
‡
B
k = e e (3.14)
r
h
41 Although the terms transition state and transition structure are often used interchangeably, if the transition
state is taken as defined by transition state theory, it may differ in structure from the maximum energy
obtained by computation; K. N. Houk, Y. Li, and J. D. Evanseck, Angew. Chem. Int. Ed. Engl., 31, 682
(1992).
42
For a more complete development of these relationships, see M. Boudart, Kinetics of Chemical Processes,
Prentice-Hall, Englewood Cliffs, NJ, 1968, pp. 35–46; or I. Amdur and G. G. Hammes, Chemical
Kinetics: Principles and Selected Topics, McGraw-Hill, New York, 1966, pp. 43–58; J. W. Moore and
R. G. Pearson, Kinetics and Mechanism, Wiley, New York, 1981, pp. 159–169; M. M. Kreevoy and
D. G. Truhlar, in C. F. Bernasconi, Investigation of Rates and Mechanisms of Reaction: Techniques of
Organic Chemistry, 4th Edition, Vol. VI, Part 1, Interscience, New York, 1986.