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146 Chapter 6: Fundamentals of Reaction Rates

from the intuitive dynamical picture in SCT are “hidden” in the partition functions
in TST. Nevertheless, the ratio of partition functions (thermodynamics) tells how easy
(probable) the achievement of the transition state is. This ratio contains many of the
notions in collision theories, for example, (1) how close the reactants must approach
to react (equivalent to the hard-sphere cross-section in SCT), and (2) the precision of
alignment of the atoms in the transition state (equivalent to the p factor in SCT). The
combination of a smaller cross-section and more demanding configuration is equiva-
lent to a smaller entropy in the transition state. All of the dynamics in TST is contained
in kTlh, which in turn is contained in the velocity of approach in bimolecular reac-
tions in SCT. The assumption that the transition state is in thermal equilibrium with
the reactants is central to a discussion of the merits of TST. On the one hand, this as-
sumption allows a relatively simple statistical (thermodynamic) calculation to replace
the detailed dynamics. This has made transition state theory the more useful of the two
for the estimation of unmeasured rate constants. This considerable advantage of TST
is also its main weakness, and TST must fail when the assumption of thermal equilib-
rium is grossly wrong. Such an example is the behavior of unimolecular reactions at low
pressure, where the supply of energy is rate limiting. Both theories have been very use-
ful in the understanding of kinetics, and in building detailed mechanisms of important
chemical processes.

6.6 ELEMENTARY REACTIONS INVOLVING OTHER THAN GAS-PHASE
NEUTRAL SPECIES

The two simple theories SCT and TST have been developed in the context of neutral
gas-phase reactions. In this section, we consider other types of elementary reactions
listed in Section 6.2.1, and include reactions in condensed phases. The rates of this di-
verse set of reactions, including photochemistry, can be understood with the concepts
developed for gas-phase reactions.

6.6.1 Reactions in Condensed Phases

Reactions in solution proceed in a similar manner, by elementary steps, to those in the
gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are
the same. The two theories for elementary reactions have also been extended to liquid-
phase reactions. The TST naturally extends to the liquid phase, since the transition state
is treated as a thermodynamic entity. Features not present in gas-phase reactions, such
as solvent effects and activity coefficients of ionic species in polar media, are treated
as for stable species. Molecules in a liquid are in an almost constant state of collision
so that the collision-based rate theories require modification to be used quantitatively.
The energy distributions in the jostling motion in a liquid are similar to those in gas-
phase collisions, but any reaction trajectory is modified by interaction with neighbor-
ing molecules. Furthermore, the frequency with which reaction partners approach each
other is governed by diffusion rather than by random collisions, and, once together,
multiple encounters between a reactant pair occur in this molecular traffic jam. This
can modify the rate constants for individual reaction steps significantly. Thus, several
aspects of reaction in a condensed phase differ from those in the gas phase:

(1) Solvent interactions: Because all species in solution are surrounded by solvent,
the solvation energies can dramatically shift the energies of the reactants, prod-
ucts, and the transition state. The most dramatic changes in energies are for ionic
species, which are generally unimportant in gas-phase chemistry, but are promi-
nent in polar solvents. Solvation energies for other species can also be large
enough to change the reaction mechanism. For example, in the alkylation of