Environmental Engineering Reference
In-Depth Information
Ta b l e 4 . 10
The ratio of experimental mobilities of the ions given in Table 4.9 to those according
to the Dalgarno formula (4.88) [43].
Ion, gas
He
Ne
Ar
Kr
Xe
H
2
N
2
Li
C
1.27
1.17
1.06
1.07
1.06
1.02
0.89
Na
C
1.38
1.24
1.07
1.06
1.09
1.13
0.97
K
C
1.35
1.28
1.08
1.10
1.07
1.14
0.98
Rb
C
1.29
1.26
1.08
1.07
1.0
1.14
0.99
Cs
C
1.19
1.18
1.07
1.08
1.07
1.15
0.99
where the same notation is used as in (4.88), and the accuracy of 10% reflects the
coincidence of its results with experimental data. For instance, the ratio of exper-
imental mobilities of alkali metal ions in helium to those according to (4.89) is
1.13
0.06. One can conveniently use (4.89) for estimation of the ion mobility in
a foreign gas. In addition, Table 4.11 contains statistically averaged experimental
values
K
exp
of the mobilities for molecular ions of inert gases in parent gases, and
theoretical data for these mobilities
K
pol
according to the Dalgarno formula (4.88).
On the basis of (4.89) for the ion mobility and the Einstein relation (4.38) we
obtain the following expression for the diffusion coefficient of ions
D
i
in foreign
gases if an electric field is absent
˙
1.0
0.1
p
αμ
˙
D
i
D
,
(4.90)
where the diffusion coefficient is expressed in square centimeters per second and
is reduced to the normal number density of atoms, and the other notations are the
Ta b l e 4 . 11
The zero-field mobilities of molecular ions of inert gases in a parent gas [51].
T
,
K
exp
,cm
2
/(V s)
K
pol
,cm
2
/(V s)
D
i
N
a
,10
18
cm
1
s
1
Ion
He
2
295
16.7
˙
0.1
21
˙
2
13
˙
1
He
2
77
16.4
˙
0.3
21
˙
2
3.3
˙
0.3
He
3
77
18.1
˙
0.1
20
˙
2
3.7
˙
0.4
He
4
77
17.9
˙
0.1
19
˙
2
3.6
˙
0.4
Ne
2
295
6.5
˙
0.6
6.8
˙
0.7
5.0
˙
0.5
Ne
2
77
5.4
6.8
˙
0.7
1.1
˙
0.1
Ne
3
77
5.4
˙
0.1
6.4
˙
0.6
1.1
˙
0.1
Ar
2
295
1.86
˙
0.04
2.4
˙
0.2
1.4
˙
0.1
Ar
2
77
1.8
˙
0.1
2.4
˙
0.2
0.36
˙
0.04
Ar
3
77
1.7
˙
0.1
2.2
˙
0.2
0.34
˙
0.03
Kr
2
295
1.1
˙
0.1
1.3
˙
0.1
0.86
˙
0.09
Xe
2
295
0.75
˙
0.05
0.59
˙
0.06
0.59
˙
0.06
