Instant Notes: Analytical Chemistry

As the cadmium plates out, the layer around the electrode is depleted and

more cadmium ions must diffusein from outside through the diffusion

layerof thickness d. This will cause a current, I,to flow, which depends on

the concentration gradient between the bulk solution and the surface.

Eventually, the surface concentration becomes zero, and the limiting diffu-

sion current is reached:

Id=constant (c(bulk))/d=kS(c(bulk))

The constant, kS, depends on the number of electrons transferred, the diffu-

sion coefficient of the ion in the solution, and the characteristics of the

cathode.

(iii) If the potential is increased further, the current does not increase unless

other reducible ions are present. These three regions are shown in Figure2.

The potential difference, E, across the cell at any stage is:

E =ESCE-EDME or

E =ESCE-(EnCd+(RT/2F) ln [(a(Cd^2 +, surface)/a(Cd(Hg))]

From the equations above, the concentrations may be substituted by the

currents, since the concentration of reduced species in the mercury depends on

the current Iand the diffusion constant in the amalgam, kA

I =kA(c(Cd(Hg))

E =ESCE-(EnCd+(RT/2F) ln (kA/kS)) +(RT/2F) ln [(Id-I)/I]

When I =^1 ⁄ 2 Id, that is at the half-wave position, the DME has the half-wave

potential, E (^1) ⁄ 2
EDME, (^1) ⁄ 2 =ESCE-(E (^1) ⁄ 2 +(RT/2F) ln [^1 ⁄ 2 Id/^1 ⁄ 2 Id] =E (^1) ⁄ 2
The half-wave potential is usually quoted relative to the SCE, and, like the
standard electrode potential, is characteristic of the electrode reaction. Typical
values are shown in Table 1.
100 Section C – Analytical reactions in solution
–0.5 –0.7 –0.9
E/(V)
E1/2
Id
–1.1
Current,
I
Limiting current
Residual current
Fig. 2. Current-voltage curve for 10-^4 M cadmium sulfate solution.