Environmental Engineering Reference
In-Depth Information
The
initiation
step involves decomposition of one of the reactants. Usually this
will occur for the reactant with the smallest bond energy. For example, between H
2
and Br
2
, with dissociation energies of 430 and 190 kJ/mol, respectively, Br
2
will
dissociate easily as
k
1
−→
Br
2
2Br.
(5.92)
The propagation step consists of the following reactions:
k
2
−→
H
2
+
Br
HBr
+
H,
(5.93)
k
3
−→
H
+
Br
2
HBr
+
Br,
where it should be noted that the Br radical is consumed and regenerated. In complex
reactions of this type HBr can also react with H to give H
2
and Br:
k
4
−→
H
+
HBr
H
2
+
Br.
(5.94)
This is called an
inhibition
step since the H radical is consumed by a reaction other
than by chain termination. The reason why HBr reacts with H and not with Br is that
the former is an exothermic reaction (67 kJ/mol) whereas the latter is an endothermic
reaction (170 kJ/mol). The
termination
step occurs by the reaction
k
5
−→
2Br
+
M
Br
2
+
M,
(5.95)
where M is a third body that absorbs the energy of recombination and thereby helps
to terminate the chain.
To derive the overall rate expression we must first note that the concentrations of
the intermediates H and Br radicals are at steady state, and hence
d
[
H
]
d
t
=
0
=
k
2
[
Br
][
H
2
]−
k
3
[
H
][
Br
2
]−
k
4
[
H
][
HBr
]
(5.96)
and
[
]
d
t
=
d
Br
2
.
(5.97)
=
2
k
1
[
Br
2
]−
k
2
[
][
H
2
]−
k
3
[
][
Br
2
]−
k
4
[
][
]−
2
k
5
[
]
0
Br
H
H
HBr
Br
Upon solving these equations simultaneously, we get
k
1
[
1
/
2
Br
2
]
k
5
[
Br
]=
(5.98)
and
k
2
(k
1
/k
5
)
1
/
2
1
/
2
[
H
2
][
Br
2
]
[
]=
H
.
(5.99)
k
3
[
Br
2
]−
k
4
[
]
HBr
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