Environmental Engineering Reference
In-Depth Information
Ta b l e 2 . 16
Experimental values of the rate constants for mutual neutralization in pairwise colli-
sions of positive and negative ions involving nitrogen and oxygen. The rate constants are given
in units of 10
7
cm
3
/s, and
R
0
in (2.99) is expressed in
a
0
.
Process
Rate constant
R
0
,
a
0
O
C
C
O
3
˙
1
34
N
C
C
O
3
˙
1
32
O
2
C
O
2
4
˙
1
74
N
2
C
O
2
1.6
˙
0.5
28
NO
C
C
NO
2
˙
5
2
44
O
2
C
NO
2
˙
4
1
78
NO
C
C
NO
3
0.4
˙
0.1
10
O
C
C
O
2
2
28
NO
C
C
O
5
˙
2
70
2.3.6
Processes Involving Formation of a Long-Lived Complex
A long-lived complex is an intermediate state formed as a result of the collision
of two atoms. Subsequent evolution of this complex can lead to the formation of
a bound state of these particles. For example, the formation of molecular ions in
three body collisions can occur through the processes
B
k
c
!
B
)
,
A
C
B
)
τ
!
A
C
C
(
A
C
C
A
C
C
B
,
C
k
q
!
C
k
d
!
(
A
C
B
)
C
AB
C
C
C
,
A
C
B
)
C
A
C
C
B
C
C
.
(2.102)
Here (
A
C
B
)
is an autodetaching state of the colliding particles, and the quanti-
ties written over the arrows are the rate constants
k
for the collision processes or
the lifetime
of the autodetaching state (
A
C
B
)
.
Scheme (2.102) leads to the balance equations for the number densities of au-
todetaching states:
τ
[(
A
C
B
)
]
τ
d
dt
[(
A
C
B
)
]
[(
A
C
B
)
][
C
](
k
q
D
D
[
A
][
B
]
k
c
C
k
d
),
(2.103)
0
where [
X
] denotes the number density of particles
X
. The solution of this equation
gives
[
A
][
B
]
k
c
[(
A
C
B
)
]
D
.
1/
τ
C
[
C
](
k
q
C
k
d
)
Next, the balance equation for the third process (2.103) has the form
d
[
AB
C
]
dt
k
c
k
q
τ
k
q
[(
A
C
B
)
[
C
]
D
D
[
A
][
B
][
C
]
.
C
[
C
](
k
q
C
k
d
)
1
τ
