Environmental Engineering Reference
In-Depth Information
The rate of disappearance of each species is given below:
d
[
A
]
d
t
=
k
1
[
A
][
B
]−
k
−
1
[
A
−−
B
]
,
−
d
[
A
−−
B
]
d
t
=
k
1
[
A
][
B
]−
k
1
[
A
−−
B
]−
k
2
[
A
−−
B
][
Z
]
,
(5.57)
−
d
[
AB
]
d
t
=
k
2
[
A
−−
B
][
Z
]
.
To simplify the analysis we make use of the concept of steady state for [A
−−
B].
Thus, d[A
−−
B]/d
t
=
0 and hence [A
−−
B
]
∗
=
k
1
[A][B]/(
k
1
+
k
2
[Z]). Thus we
−
have the following differential equation for [A
−−
B]:
d
[
A
−−
B
]
d
t
k
1
k
2
[
A
][
B
]
k
1
+
k
2
[
Z
]
[
Z
]=
k
[
A
][
B
]
,
=
(5.58)
−
with
k
=
k
1
k
2
[
Z
]
/(k
−
1
+
k
2
[
Z
]
)
is a constant since [Z] is in excess and varies little.
As [Z]
]=
k
0
[Z]. In the
high-
pressure limit
, [Z] is very large, and
k
4
=
k
1
and is independent of [Z]. From
k
0
and
k
4
one can obtain
k
=
k
0
[
1
+
(k
0
/k
∞
0, we have the
low-pressure limit
,
k
0
=
(k
1
k
2
/k
−
1
)
[
→
Z
)
]
−
1
. Table 5.2 lists the rate constants for a typical
atmospheric chemical reaction. Note that the values are a factor of two lower under
stratosphericconditions.Thegeneralsolutiontotheordinarydifferentialequationabove
is the same as that for reaction A
+
B
→
products as in Table 5.1. From the integrated
rate law one can obtain the concentration-time profile for species A in the atmosphere.
TABLE 5.2
Low- and High-Temperature Limiting
k
Values for the Atmospheric
Reaction OH
Z
→
+
SO
2
HOSO
2
[Z]
(molecule/
k
0
/(cm
6
/
k
∞
/(cm
3
/
k
/(cm
3
/
s/cm
3
)
molecule
2
/s)
T
(K)
P
(Torr)
molecule/s)
molecule/s)
10
19
(
3.0
10
−
31
(
2.0
10
−
12
1.1
10
−
12
300
(troposphere)
760
2.4
×
±
1.5
)
×
±
1.5
)
×
×
1.7
×
10
18
8.7
×
10
−
31
2.0
×
10
−
12
5.2
×
10
−
13
−
219
(stratosphere)
−
39
Source:
Finlayson-Pitts, B.J. and Pitts, J.N. 1986.
Atmospheric Chemistry
. NewYork, NY:
John Wiley & Sons, Inc.
5.3.4 P
ARALLEL
R
EACTIONS
Inenvironmentalreactionstherealsoexistcaseswhereamoleculecansimultaneously
participate in several reactions. For example,
A
k
1
−→
C,
(5.59)
A
k
2
−→
D.
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