Environmental Engineering Reference
In-Depth Information
photolysis reaction is represented as
B
+
hv
−→
P
1
+
S
1
.
(5.191)
The rate of the photochemical reaction is
d
[
]
d
t
=
B
−
J
[
B
]
,
(5.192)
where
J
is the first-order photochemical rate constant. Since the reaction occurs over
the entire wavelength range
λ
2
, we have to obtain an average rate constant.
The photolysis rate constant
J
can be expressed in terms of the absorption cross-
section
λ
1
to
σ
λ
(T)
, which is a function of both
λ
and
T
. The rate constant is
λ
2
λ
1
σ
J
=
(
λ
)
φ
(
λ
)I
d
λ
(5.193)
λ
or
λ
2
λ
1
σ
λ
i
ϕ
λ
i
I
J
=
λ
Δλ
,
(5.194)
where the overbar denotes the values at mid range centered at
λ
i
in the interval
Δλ
.In
using the above expression one should separately evaluate
σ
λ
i
and
I
λ
. Normally the
shortest wavelength for photochemistry in the atmosphere is 290 nm. Finlayson-Pitts
and Pitts (2000) list the values of the absorption cross-section
σ
λ
i
and the actinide
flux
I
λ
for many atmospheric reactions. The values of
J
for a number of reactions are
listed in Table 5.8.
The following two examples will illustrate the use of the above equations for
determining the photolytic rate constants in water and air environments.
E
XAMPLE
5.19 R
ATE
C
ONSTANT FOR
P
HOTOLYSIS IN THE
A
TMOSPHERE
For the case of nitrogen dioxide photolysis in air, we have the following data:
σ
λ
i
(cm
2
)
ϕ
λ
i
(Photons/cm
2
s)
λ
(nm)
I
λ
Δλ
σ
λ
i
ϕ
λ
i
I
λ
Δλ
300
2E
−
19
0.98
1.6E
+
13
3.14E
−
06
310
3E
−
19
0.972
2.81E
+
14
8.19E
−
05
320
3.5E
−
19
0.964
7.19E
+
14
0.000243
330
4E
−
19
0.956
1.29E
+
15
0.000494
340
4E
−
19
0.948
1.42E
+
15
0.000537
350
5E
−
19
0.94
1.59E
+
15
0.000748
360
5.5E
−
19
0.932
1.66E
+
15
0.000852
370
6E
−
19
0.924
2.07E
+
15
0.001146
380
6E
−
19
0.916
2.02E
+
15
0.001110
390
6E
−
19
0.908
2.06E
+
15
0.001122
400
6E
−
19
0.8
2.81E
+
15
0.001349
410
6E
−
19
0.17
3.56E
+
15
0.000363
420
6E
−
19
0.03
3.7E
+
15
6.65E
−
05
Sum:
0.008114
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