Page 299 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

280 The calculation of the properties of transition structures is more problematic than
for stable molecules because TSs involve bond breaking. Thus computations based
CHAPTER 3 an the concept of electron pairing may not be applicable, especially for species with
Structural Effects on radical character. Nevertheless, computational studies have provided insight into many
Stability and Reactivity
reactions and we frequently use the results of these studies, as well as experimental
work, in developing the details of reaction mechanisms.

3.2.3. Reaction Rate Expressions

Experimental kinetic data can provide detailed insight into reaction mechanisms.
The rate of a given reaction can be determined by following the disappearance of
a reactant or the appearance of a product. The extent of reaction is often measured
spectroscopically, because spectroscopic techniques provide a rapid, continuous means
of monitoring changes in concentration. Numerous other methods are available and
may be preferable in certain cases. For example, continuous pH measurement or acid-
base titration can be used to follow the course of reactions that consume or generate an
acid or a base. Conductance measurements provide a means for determining the rate
of reactions that generate ionic species; polarimetry can be used to follow reactions
involving optically active materials. In general, any property that can be measured and
quantitatively related to the concentration of a reactant or a product can be used to
determine a reaction rate.
The goal of a kinetic study is to establish the quantitative relationship between
the concentration of reactants and catalysts and the observed rate of the reaction.
Typically, such a study involves rate measurements at enough different concentrations
of each reactant to determine the kinetic order with respect to each reactant. A complete
investigation allows the reaction to be described by a rate expression or rate law,
which is an algebraic formula containing one or more rate constants, as well as terms
for the concentration of all reactant species that are involved in the rate-determining
and prior steps. Each concentration has an exponent called the order of the reaction
with respect to that component. The overall kinetic order of the reaction is the sum of
all the exponents in the rate expression. The mathematical form of the rate expression
for a reaction depends on the order of the reaction. Using A , B , C , etc, for the
0
0
0
initial t = 0 t concentrations and [A], [B], [C], etc, as the reactant concentrations
0
at time t, give the following expressions 51 :
First order: Rate = k A
A −kt
o
ln = kt or A = A e (3.27)
o
A
Second order/one reactant: Rate = k A 2
1 1
kt = − (3.28)
A A 0
Second order/two reactants: Rate = k A B
1 A B
o
kt = ln (3.29)
B − A B A
o o o
51
J. W. Moore and R. G. Pearson, Kinetics and Mechanism, 3rd Edition, John Wiley & Sons, New York,
1981, Chap. 2.