Chain reactions
Chain reactions are examples of complex reactions, with
complex rate expressions.
In a chain reaction, the intermediate produced in one step
generates an intermediate in another step. This process goes
on.
Sometimes, the chain carriers are radicals, they can be atoms
or ions as well.
Intermediates are called chain carriers.
1. Chain initiation
Steps in chain reaction 2. Propagation
3. Chain termination
For example, in the reaction between hydrogen and chlorine, for which the
stoichiometric equation is
H2+ Cl2 = 2HCl
chlorine atoms bring about the following reaction sequence:
In reaction (1) a chlorine atom is lost, but in reaction (2) a chlorine atom is
formed.
Similarly; in reaction (2) a hydrogen atom is consumed. but one is formed in
reaction (I).
Therefore, reactions ( l) cold (2) together constitute a closed cycle or
sequence of reactions, in which two molecules of the product HCI are
formed. There is no net loss of H or Cl atoms when the two reaction occur,
and if the cycle is repeated many times a considerable amount of product is
formed from a single chlorine atom. Provided that such a cycle of reactions
occurs more than once, the overall reaction is called a chain reaction.
Thermal hydrogen-bromine reaction
Chain initiation reaction, in which chain carriers are formed
This is followed by two chain-propagating reactions:·
Finally, there must be a termination reaction, in which chain carriers are
removed from the system. There may be other reactions, but in a chain
reaction there must always be an chain initiation reaction, a termination
reaction, and a pair of chain propagating reactions.
Chain length: the average number of-times the closed cycle of reactions
(comprising the chain-propagating steps) is repeated. Thus, it is equal to
the rate of the overall reaction divided by the rate of the initiation step in
which the chain carriers are formed.
Hydrogen-Bromine Reaction
expression for the rate of consumption of H2 or Br2 :
where k and m are constants; the value of m is about 10 and is practically
independent of temperature. This equation shows that hydrogen bromide
inhibit the reaction and that the extent of inhibition by HBr is reduced by the
addition of Br2 .
Hydrogen-Bromine Reaction
The thermal reaction was first studied by Bodenstein and Lind over
the temperature range 205-302°C. They found empirically that the
results could be fitted to the following expression for the rate of
consumption ofH2 or Br2 : .
………………..1
where k and m are constants; the value of m is about 10 and is
practically independent of temperature. This equation shows that
hydrogen bromide inhibit the reaction and that the extent of
inhibition by HBr is reduced by the addition of Br2
Their mechanism is:
There is an additional reaction, reaction (-2), which accounts for
the inhibition of the reaction by the product HBr. The fact that Br2
and HBr compete· with one another for H atoms explains why the
inhibition by HBr is reduced by Br2, that is, why [HBr]/[Br2]
appears in the denominator of Eq 1.
The steady-state hypothesis must be applied to the two
intermediates Br and H, both of which are present at very low
concentrations. The steady-state equation for H is
………………..2
for Br is
………………..3
A solution for [Br] is obtained by adding these two equations
………………..4
and therefore
………………..5
This is the equilibrium concentration of Br atoms. It is by no means
always the case that atoms and free radicals in reaction systems are
present at their equilibrium concentrations. In the present example,
the H atoms are present at much higher concentrations than their
equilibrium concentrations .
An expression for [H] can be obtained by inserting this expression
for [Br] Into Eq. 2
………………..6
………………..7
The rate of reaction is the rate of consumption of H2, which is
………………..8
From Eq. 2
………………..9
And insertion of the expression for [H] gives
………………..10
………………..11
………………..11
This is of the same form as the empirical equation 1, and we note
that the empirical k is equal to k2(k1 /k-1)1/2 and that m = k3/k-2.
………………..1
