Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

OTHER REACTION ORDERS 153

An acceptable mechanism for this reaction depends upon three elementary reaction

types,initiation,chain, andtermination:

Initiation Br 2 +M

k 1

→2Br·+M

Chain Br·+H 2

k 2

→HBr+H·

Chain H·+Br 2

k 3

→HBr+Br·

Termination Br·+Br·

k− 1

→Br 2

The point of this proposed mechanism is that the cyclic chain steps can continue

indefinitely because the Br·free radicalsused in the first chain step are produced in the

second chain step. Initiation can be by a rather unlikely process such as collision with

a high-energy molecule M in the first step or impact of a photon from a flame or spark

as in chain explosions. Though initiation may not occur very often, it can have a large

effect. A hydrogen–oxygen explosion is an example. A very small spark can cause

a very large explosion. The HBr chain, though it may yield many molecules for one

initiation step, does not, of course, go on forever. Some step such as recombination of

the Br·free radicals terminates the chain or we run out of Br 2 or H 2 and the reaction

stops.

If we assume that initiation and termination are rare events by comparison to the

chain steps, for every Br·used up in the first step of the chain, one is produced in

the second chain step, so the amount of free radical present at any time during the

reaction is constant:

d[Br·]

dt

= 0

This is an example of the steady-state hypothesis. Making this assumption, a few

lines of algebra (Houston, 2006) lead to the correct rate equation given above:

1

2

d[HBr]

dt

=k[H 2 ][Br 2 ]^1 /^2

If, by a more complicated mechanism, two or more reactive species are produced on

each step, the amount of reactive species may increase rapidly. For example, if two

reactive species are produced at each step, the geometric series, 1, 2, 4, 8, 16,...is

followed. If the chain steps are fast, this kind of mechanism takes place with explosive

violence. This type of mechanism is characteristic of nuclear fission bomb reactions.

Free radical and (controlled) chain reactions are also characteristic of some bio-

chemical reactions, and they can behave in ways that are beneficial or detrimen-

tal to the organism. A hydroperoxide RCOO·free radical chain may destroy lipid

molecules in a cell wall bylipid peroxidationwith disastrous results for the cell.

Free radicals derived from tocopherol (vitamin E)antioxidantsact as sweepers in the

blood, interfering with chain propagation, thereby slowing or preventing cell degra-

dation. Free radicals have been detected in rapidly multiplying natal or neonatal cells