598
13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics
ϩ
ϩ
ϩ
ϩ
ϩ
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
1.0
0.8
0.6
0.4
0.2
0.0
(a)
(b)
/
0
0 510 mV
(limiting exponential form)
0 5100 mV
0 51000 mV
x / Å
Outer
Helmholtz
plane
Inner
Helmholtz
plane
Solvated cation
Diffuse layer
Metal
Specifically absorbed anion
5Solvent molecule
x 1 x 2
Figure 13.14 The Electrical Double Layer. (a) The structure of the double layer
(schematic). From Bard and Faulkner, op. cit., p. 8. (b) The electric potential in the diffuse
double layer. From Bard and Faulkner, op. cit., p. 505.
E X A M P L E 13.7
Find the Debye length at 298.15 K for an aqueous solution of HCl with a molality of
0.0200 mol kg −1 .
Solution
The permittivity of water at this temperature is 6.954 × 10 −10 C 2 N −1 m −2 and the density
of water is 997 kg m −3 .
κ e
2N Av ρ 1 I
εk B T
1/2
13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics
ϩ
ϩ
ϩ
ϩ
ϩ
0
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
1.0
0.8
0.6
0.4
0.2
0.0
(a)
(b)
/
0
0 510 mV
(limiting exponential form)
0 5100 mV
0 51000 mV
x / Å
Outer
Helmholtz
plane
Inner
Helmholtz
plane
Solvated cation
Diffuse layer
Metal
Specifically absorbed anion
5Solvent molecule
x 1 x 2
Figure 13.14 The Electrical Double Layer. (a) The structure of the double layer
(schematic). From Bard and Faulkner, op. cit., p. 8. (b) The electric potential in the diffuse
double layer. From Bard and Faulkner, op. cit., p. 505.
E X A M P L E 13.7
Find the Debye length at 298.15 K for an aqueous solution of HCl with a molality of
0.0200 mol kg −1 .
Solution
The permittivity of water at this temperature is 6.954 × 10 −10 C 2 N −1 m −2 and the density
of water is 997 kg m −3 .
κ e
2N Av ρ 1 I
εk B T
1/2