Page 101 - Mechanism and Theory in Organic Chemistry

solvents as characterizing the solvents, and then to see whether these parameters
will yield a linear correlation with rates of some closely related reaction in those
same solvents. This method is the basis of the Grunwald-Winstein = Y scale, which
we shall discuss further in Chapter 5. Another method is to measure the energy
change of an electronic transition in a reference molecule between two states that
differ in their ability to interact with solvent. Kosower's Z scale is of this kind.32
These solvent scales are linear free-energy relationships entirely analogous to
those discussed in Section 2.2. They give only limited insight into the molecular
basis of solvation, but are particularly useful in assessing reaction mechanisms.

2.5 KINETICS

The study of reaction rates has two purposes : first, to compare the form of the rate
equation with predictions of the various mechanisms under consideration, and
second, to measure numerical values of rate constants and to interpret them in
terms of elementary reaction steps.

The Rate Equation
The interpretation of kinetic data begins with a hypothetical sequence of ele-
mentary reaction steps, each characterized by two microscopic rate constants, one for the
forward and one for the reverse reaction. From this proposed mechanism a rate
equation is derived, predicting the dependence of the observed reaction rate on
concentrations and on microscopic rate constants, and its form is tested against
the observations. If the form of the rate equation meets the test of experiment, it
may be possible to derive from the data numerical values for the microscopic rate
constants of the proposed elementary reaction steps. While inconsistency is clear
grounds for modifying or rejecting a mechanistic hypothesis, agreement does
not prove the proposed mechanism correct.

The unimolecular reaction Suppose we postulate that a given reaction
consists of the single step

The rate of disappearance of A, - d[A]/dt, is given by Equation 2.27 and the rate
of disappearance of B, - d[B]/dt, by Equation 2.28.33

For the rate equation to compare with experiment we could choose either of
these, depending upon whether the time dependence of [A] or of [B] is more
convenient to measure.

3a Kosower, An Introduction to Physical Organic Chemisty, p. 293.
33 It is merely a matter of convenience whether rates are expressed as rates of appearance, + d [X]/dt,
or as rates of disappearance, - d[X]/dt, of a reactant or product.