Page 209 - Instant notes

The kinetics of real systems 195

Explosions

Chain reactions which contain chain branching steps, i.e. reactions which increase the
total number of chain carriers, have the potential for runaway reaction propagation and,
under the right conditions, for explosion. Familiar examples are H 2/O 2 gas mixtures, or
the hydrocarbon/O 2 mixtures that provide the explosive power in the cylinders of a car
engine.
The H 2/O 2 reaction can be initiated in a number of ways, one of which is bimolecular
collision between the two species to produce an H atom radical:
H 2+O 2→H+HO 2

The H atom instigates a series of propagation and branching reactions so that after just a
few reaction steps the number of H atoms has trebled:
H+O 2 →OH+O Propagation and branching
OH+H 2 →H+H 2 O Propagation
O+H 2 →OH+H Propagation and branching
OH+H 2 →H+H 2 O Propagation
Net: H+O 2 +3H 2 →3H+2H 2 O

This reaction scheme illustrates the ability of branching reactions to create extremely
rapid growth in the number of chain carriers and the number of parallel elementary
reactions. Whether or not a chain reaction ultimately leads to explosion depends on a
number of factors such as the ratio of chain termination to chain branching processes,
the initial concentration of reactants (which is a function of pressure for gas reactants
such as H 2 and O 2), the temperature, and the rate at which energy (principally heat) can
dissipate from the system. The complex dependence of H 2/O 2 explosion on pressure and
temperature is shown in Fig. 1. The presence of a complex boundary between steady
reaction and explosion reflects competition between the rates of different temperature and
pressure dependent reactions in the mechanism. The system is difficult to interpret
analytically because the steady state approximation (in which concentrations of
reaction intermediates are assumed to remain constant) is not valid under the non-linear
conditions of chain branching.