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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