Page 176 - Introduction to chemical reaction engineering and kinetics

158 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

constitutes a closed sequence, which, if unbroken, or broken relatively infrequently, can
result in a very rapid rate overall.
The experimental detection of a chain reaction can be done in a number of ways:
(1) The rate of a chain reaction is usually sensitive to the ratio of surface to vol-
ume in the reactor, since the surface serves to allow chain-breaking reactions
(recombination of chain carriers) to occur. Thus, if powdered glass were added
to a glass vessel in which a chain reaction occurred, the rate of reaction would
decrease.
(2) The rate of a chain reaction is sensitive to the addition of any substance which
reacts with the chain carriers, and hence acts as a chain breaker. The addition of
NO sometimes markedly decreases the rate of a chain reaction.

Chain carriers are usually very reactive molecular fragments. Atomic species such as
Ho and Cl’, which are electrically neutral, are in fact the simplest examples of “free
radicals,” which are characterized by having an unpaired electron, in addition to being
electrically neutral. More complex examples are the methyl and ethyl radicals, CHj and
C,H;, respectively.
Evidence for the existence of free-radical chains as a mechanism in chemical reac-
tions was developed about 1930. If lead tetraethyl is passed through a heated glass
tube, a metallic mirror of lead is formed on the glass. This is evidently caused by de-
composition according to Pb(C,H,), -+ Pb + 4qHt, for if the ensuing gas passes over
a previously deposited mirror, the mirror disappears by the reverse recombination:
4C,H; + Pb -+ Pb(C,Hs),. The connection with chemical reactions was made when
it was demonstrated that the same mirror-removal action occurred in the thermal de-
composition of a number of substances such as ethane and acetone, thus indicating
the presence of free radicals during the decomposition. More recently, spectroscopic
techniques using laser probes have made possible the in-situ detection of small concen-
trations of transient intermediates.
We may use the reaction mechanism for the formation of ethylene from ethane
(GH, + C,H, + HZ), Section 6.1.2, to illustrate various types of steps in a typical
chain reaction:
chain initiation: C,H, -+ 2CHj (1)
chain transfer: CH; + C,H, + CH, + C2H; (2)
chain propagation: C,H; + C,H, + Ho (3)
Ho + C,H, + H, + C,H; (4)
chain breaking or termination: Ho + C,H; + C2H, (5)

In the first step, CHT radicals are formed by the rupture of the C-C bond in GH,.
However, CHj is not postulated as a chain carrier, and so the second step is a chain-
transfer step, from CHT to GHt, one of the two chain carriers. The third and fourth
steps constitute the chain cycle in which C,HS is first used up to produce one of the
products (C,H,) and another chain carrier (HO), and then is reproduced, to continue
the cycle, along with the other product (HZ). The last (fifth) step interrupts a chain by
removing two chain carriers by recombination. For a rapid reaction overall, the chain
propagation steps occur much more frequently than the others. An indication of this is
given by the average chain length, CL:

cL = number of (reactant) molecules reacting
number of (reactant) molecules activated
= rate of overall reaction/rate of initiation (7.1-2)