theory that there is a range of energies for molecules at any given temperature).
More formally, an initiation reaction should indicate this energy input, which
can be in the form of heat, light, or some other process:
energy
reactants →intermediates (initiation)For termination reactions, the formation of a stable product implies that en-
ergy is released (that is, it is an exothermic process). The energy given off must
go somewhere. Typically, the energy is either given off as photons or, more
commonly, a third body is needed to absorb the energy given off as the reac-
tive intermediates react to form a stable product. If the third body is given the
symbol M, then a termination reaction between two free radicals Rcan be
written as
RRM →R–R M* (termination)where M* is an energetically excited third body. Third bodies can be reactant
or product molecules, some other species like an inert gas (an example of
homogeneous termination), or even the walls of the container defining the sys-
tem (an example ofheterogeneous termination).
Under some conditions, intermediate reactions that actually generate
more reactive intermediates can contribute significantly to the propagation
of the reaction. These reactions are more properly called branching reac-
tions.One example, from the mechanism of the reaction between H 2 and O 2
gases, is
HO 2 →HOO (branching)In this example, the reaction goes from having one reactive free radical to two
reactive free radicals. These two reactive products can participate in their own
propagation reactions, like
HOH 2 →H 2 O H
O HO→O 2 Hor other steps. Branching reactions contribute to an increase in the number
of propagation reactions, and if more branching reactions occur, more and
more propagation reactions will occur as a result. Under the right conditions,
branching reactions can contribute to a geometric increase in the number of
propagation processes that occur (that is, 2 → 4 → 8 → 16 → 32 →as
shown in Figure 20.19). Since most propagation reactions are exothermic, a
geometric increase in the number of propagation reactions is accompanied
by a geometric increase in the amount of energy released. The result is an
explosion.
Not all explosions are caused by branching reactions, and not all chain re-
action mechanisms lead to explosions. But a branching chain reaction is one
cause for a gas-phase explosion, under the right conditions. If there are enough
inert bodies or the area of the walls of the container is large enough with re-
spect to the volume, enough termination reactions can occur to minimize the
effect of branching reactions, and no explosion occurs. If the concentrations of
the reactants are not in the right proportions, not enough branching reactions
will occur to cause a geometric increase in the energy given off by the overall
reaction, and no explosion occurs. As an example, the H 2 /O 2 system has been
studied extensively, and the relative partial pressures, temperatures, and other
variables have been mapped to determines conditions under which explosions716 CHAPTER 20 Kinetics