Page 180 - Introduction to chemical reaction engineering and kinetics

162 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

Two radicals (OH’ and Ho) are produced from the reaction of one radical (0’). This
allows the reaction rate to increase without limit if it is not balanced by corresponding
radical-destruction processes. The result is a “runaway reaction” or explosion. This can
be demonstrated by consideration of the following simplified chain mechanism for the
reaction A + . . . + P.

initiation: A&R’
chain branching: R’ + A%P + nR* (FZ > 1)

(If 12 = 1, this is a linear-chain step)

termination: R’k3-X

The rate of production of R’ is

rR. = klcA + (n - l)k2cAcR. - k3cR.
(7.1-4)
= klcA + [(n - 1) kZcA - k3]cR.

A runaway reaction occurs if

drRJdc,.[= (n - l)k2cA - k3] > 0

or (n - l)k,c, > k3

which can only be the case if 12 > 1. In such a case, a rapid increase in cn. and in the
overall rate of reaction (rp = k2cAcR.) can take place, and an explosion results.
Note that the SSH cannot be applied to the chain carrier R* in this branched-chain
mechanism. If it were applied, we would obtain, setting rRo = 0 in equation 7.1-4,

c,.(SSH) = kc, <o
k3 - (n - l)kzCA
if (n - 1) kZcA > k3

which is a nonsensical result.
The region of unstable explosive behavior is influenced by temperature, in addition
to pressure (concentration). The radical destruction processes generally have low acti-
vation energies, since they are usually recombination events, while the chain-branching
reactions have high activation energies, since more species with incomplete bonding
are produced. As a consequence, a system that is nonexplosive at low T becomes ex-
plosive above a certain threshold T . A species Y that interferes with a radical-chain
mechanism by deactivating reactive intermediates (R* + Y + Q) can be used (1) to
increase the stability of a runaway system, (2) to quench a runaway system (e.g., act as
a fire retardant), and (3) to slow undesirable reactions.
Another type of explosion is a thermal explosion. Instability in a reacting system
can be produced if the energy of reaction is not transferred to the surroundings at a
sufficient rate to prevent T from rising rapidly. A rise in T increases the reaction rate,
which reinforces the rise in T . The resulting very rapid rise in reaction rate can cause an
explosion. Most explosions that occur probably involve both chain-carrier and thermal
instabilities.