Environmental Engineering Reference
In-Depth Information
by solar radiation (
<
240 nm). In the presence of a third body, Z, the oxygen atoms
react with O
2
to produce ozone.
λ
O
2
h
−
J
1
2O,
Z
k
2
Z
∗
)
.
2
(
O
+
O
2
+
−→
O
3
+
(6.169)
2O
3
. The species Z
∗
in the above case represents
vibrationally excited O
2
or N
2
molecule. UV radiation also splits up O
3
into O
2
and O.
The overall reaction is 3O
2
→
O
3
h
−
J
3
O
2
+
O.
(6.170)
The above reaction is the predominant mechanism by which ozone performs the
function of shielding the earth from harmful UV light.
Ozone also reacts with O atom to give rise to O
2
as follows:
O
k
4
O
3
+
−→
2O
2
.
(6.171)
The above set of four reactions constitutes what is called the
Chapman mechanism
for ozone formation and dissociation in the upper stratosphere.
Let us now consider the rates of formation and destruction of ozone in the
stratosphere. The monoatomic O species obeys the following rate expression:
d
[
]
d
t
=
O
2
J
1
[
O
2
]+
J
3
[
O
3
]−[
O
]
(k
2
[
O
2
][
Z
]+
k
4
[
O
3
]
)
,
(6.172)
where
J
i
is the photolysis rate constant given by
i
φ
i
(
as described
in Chapter 5. We prefer to distinguish this from the chemical rate constants expressed
as
k
2
and
k
4
.
For ozone the equation is
λ
)I
i
(
λ
)
σ
i
(
λ
)
Δλ
d
[
O
3
]
d
t
=
k
2
[
O
][
O
2
][
Z
]−
J
3
[
O
3
]−
k
4
[
O
3
][
O
]
.
(6.173)
At steady state we can write d[O]
/
d
t
=
d
[
O
3
]
/
d
t
=
0. Hence,
2
J
1
[
O
2
]+
J
3
[
O
3
]
[
O
]=
,
k
2
[
O
2
][
]+
k
4
[
O
3
]
Z
(6.174)
k
2
[
O
][
O
2
][
Z
]
[
O
3
]=
.
J
3
+
k
4
[
O
]
The ozone concentration can be obtained by simultaneously solving the above equa-
tions. A quadratic in [O
3
] will result. Retaining only the positive square root for the
solution, we obtain after some simplification,
1
1
.
J
1
2
J
3
1
/
2
4
J
3
k
2
[
Z
]
[
O
3
]=[
O
2
]
+
−
(6.175)
J
1
k
4
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