12.2 Elementary Processes in Liquid Solutions 527
Termolecular Gas-Phase Reactions
A termolecular elementary process in the gas phase involves a three-body collision,
which we picture as a collision of a third particle with a pair of molecules that is
undergoing a two-body collision. The number of three-body collisions is proportional
to the number of such pairs and is also proportional to the number of “third” particles.
The rate of three-body collisions of a single substance is therefore proportional to the
third power of the number density. The rate of three-body collisions of two particles
of type 1 and a particle of type 2 is proportional toN 12 N 2 , and so on. If we again
assume that the fraction of three-body collisions that lead to reaction depends only on
temperature, we obtain a second important result:Gaseous termolecular elementary
processes are third order overall, and the order with respect to any substance is equal
to the number of molecules of that substance involved in the three-body collision.Unimolecular Elementary Processes
These processes involve a single reactant molecule. We assert thatgaseous unimolec-
ular elementary processes are first order.We will discuss unimolecular processes in
Section 12.4 and will find that this assertion applies to gaseous unimolecular processes
only under certain conditions.General Statement
Our results for gas-phase elementary reactions are summarized as follows:For a
gaseous elementary process, the order with respect to any substance is equal to the
molecularity of that substance, and the overall order is equal to the sum of the molecu-
larities of all substances.This equality of order and molecularity holds only for elemen-
tary processes. The order of a reaction does not imply anything about its molecularity
unless it is an elementary process.12.2 Elementary Processes in Liquid Solutions
There are at least three steps involved in a chemical reaction in a liquid solution: The
reactants diffuse together, they react chemically, and the products diffuse apart. We
will speak of a process that has an elementary chemical part as an elementary process
in spite of the occurrence of the diffusion processes.
If the chemical part of a reaction is rapid, the rate of the reaction is controlled by
the diffusion of the reactants. If so, a reaction in solution can occur very rapidly. For
example, the reaction between hydrogen ions and hydroxide ions in aqueous solution is
a second-order process with a rate constant at 25◦C equal to 1. 4 × 1011 L mol−^1 s−^1 .If
solutions could be mixed instantaneously to give a solution containing hydrogen ions
at 0.10 mol L−^1 and hydroxide ions at 0.10 mol L−^1 , the reaction would have a half-life
of 7× 10 −^11 s.Exercise 12.4
Verify the half-life value just given.