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6.6 Elementary Reactions Involving Other Than Gas-phase Neutral Species 147

naphthol by methyl iodide, changes in solvent can shift the site of alkylation from
oxygen to carbon. The TST is altered by allowing the thermodynamic properties
to be modified by activity coefficients.
(2) Encounter frequency: Between two reactive species in solution, the encounter
frequency is slower than in the gas phase at the same concentration. The motion
in a liquid is governed by diffusion, and in one version, which assumes that there
are no long-range forces between the reactants (too simple for ionic species), the
collision rate is given by Z,, = 4s-DdABc~c~, where D is the sum of the diffu-
sion coefficients of the two species. If reaction occurs on every collision, then the
rate constant is lower in solution (even with no appreciable solvent interactions)
than in the gas phase. If reaction does not occur on every collision, but is quite
slow, then the probability of finding the two reactants together is similar to that
in the gas phase, and the rate constants are also similar. One way to think of this
is that diffusion in the liquid slows the rate at which the reactants move away
from each other to the same degree that it slows the rate of encounters, so that
each encounter lasts longer in a liquid. This “trapping” of molecules near each
other in condensed phases is sometimes referred to as the “cage effect,” and is
important in photochemical reactions in liquids, among others.
(3) Energy transfer: Because the species are continually in collision, the rate of en-
ergy transfer is never considered to be the rate-limiting step, unlike in unimolec-
ular gas-phase reactions.
(4) Pressure effects: The diffusion through liquids is governed by the number of “de-
fects” or atomic-sized holes in the liquid. A high external pressure can reduce
the concentration of holes and slow diffusion. Therefore, in a liquid, a diffusion-
controlled rate constant also depends on the pressure.

6.6.2 Surface Phenomena

Elementary reactions on solid surfaces are central to heterogeneous catalysis (Chapter
8) and gas-solid reactions (Chapter 9). This class of elementary reactions is the most
complex and least understood of all those considered here. The simple quantitative
theories of reaction rates on surfaces, which begin with the work of Langmuir in the
192Os, use the concept of “sites,” which are atomic groupings on the surface involved
in bonding to other atoms or molecules. These theories treat the sites as if they are
stationary gas-phase species which participate in reactive collisions in a similar manner
to gas-phase reactants.

6.6.2.1 Adsorption
Adsorption can be considered to involve the formation of a “bond” between the surface
and a gas-phase or liquid-phase molecule. The surface “bond” can be due to physical
forces, and hence weak, or can be a chemical bond, in which case adsorption is called
chemisorption. Adsorption is therefore like a bimolecular combination reaction:

where “s” is an “open” surface site without a molecule bonded to it, and A 0 s is a
surface-bound molecule of A. By analogy with gas-phase reactions, the collision rate
of molecules of A with a site with a reaction cross-section u on a flat surface, Z,, can
be calculated by integration of the Maxwell-Boltzmann velocity distributions over the
possible angles of impingement:

Z,/molecules site-I s-l = (1/4)aii& (6.6-2)