Page 102 - Mechanism and Theory in Organic Chemistry

Kinetics 91

Equations 2.27 and 2.28 constitute a mathematical model for the dynamics
of the reaction of interest. Note that the pr-e of the consti-
t u w n t L of t q eac-he
fi-oncenyted kinetics is therefore said to
lx&& In this example of a single-step mechanism, the origin of the predic-
tion of first-order kinetics is that A changes to B and B to A without the interven-
tion of any third substance. An elementary reaction step in which a single
substance changes to some other substance or substances without the intervention
of anything else is said to be a unimolecular step. It is essential to maintain a dis-
tinction between molecularity, a concept applying to the nature of a single step in
the mechanistic hypothesis, and kinetic order, a term describing the experimentally
determined dependence of rate of the reaction (which may be a complex series of
steps) on concentration. The mechanistic chemist uses kinetic order along with
other tools to try to establish a probable sequence of steps and the molecularity of
each, but the relationship between kinetic order and molecularity is often not as
simple as in the example of Equation 2.26.
Rate equations like 2.27 and 2.28, obtained from a proposed set of ele-
mentary reaction steps, are differential equations. Although for our purposes in
this book we shall require only differential rate equations, it is usually more
convenient in interpreting raw experimental data to have the equations in
integrated form. Methods of integration of rate equations can be found in the
1iteratu1-e.34

Macroscopic and microscopic rate constants Except in the simplest
mechanisms, the observed rate constant for the reaction as a whole will not
correspond to any one of the microscopic rate constants k characterizing the
individual steps. The term observed rate constant, k,,,, is used for the overall rate
constant for the complete reaction.

Simplification of kinetic equations It is a common practice in writing
mechanisms to simplify them by making various assumptions about the relative
size of rate constants. Such assumptions are justified on the basis of the same
chemical intuition that led to the mechanistic proposal in the first place, and are
properly regarded as part of the mechanism. Suppose, for example, that in
Equation 2.26 we had reason to believe that the reaction of B to A was sufficiently
slow that it would not occur to a measurable extent over the time scale being used
to study the kinetics. We might then feel justified in omitting the k- , step altogether
and writing Equations 2.29 and 2.30:

The predicted kinetics is still first-order, but the equation is simpler. Now the
observed rate constant is identical with the microscopic constant k,.

34 See for example (a) K. J. Laidler, Chemical Kinetics, 2nd ed., McGraw-Hill, New York, 1965,
chap. 1 ; (b) G. M. Fleck, Chemical Reaction Mechanisms, Holt, Rinehart, and Winston, New York, 1971.