Q4(a). The polarographic wave at a dropping mercury electrode

Recording: the unstirred solution (about 10⁻³ to 10⁻⁵ M) is electrolysed between the DME, which falls at 20 to 30 drops a minute, and a large reference electrode (mercury pool or SCE). The applied potential is made steadily more negative and the current, only 10⁻⁵ to 10⁻⁶ A, is recorded. The drop is tiny and easily polarised, so the whole change in voltage appears at the drop.

Parts of the wave

1. Residual current, iᵣ: before any reduction a small current flows, mainly to charge the double layer of each new drop, with a little from traces of impurities. It rises slowly and almost linearly and forms the baseline.
2. Decomposition potential: here the species starts to be reduced, for example Cd²+ + 2e⁻ + Hg → Cd(Hg). The current rises steeply, and the concentration of the ion at the drop surface, c₀, falls below the bulk value C (concentration polarisation).
3. Limiting current, iₗ: at more negative potentials c₀=0. Every ion is reduced as soon as it arrives, so the current is set by the rate of diffusion and stops rising with potential: the plateau. iₗ=iᵣ+i_d.
4. Diffusion current, i_d=iₗ-iᵣ: given by the Ilkovič equation, i_d=607 n D^(1/2)m^(2/3)t^(1/6)C (mean current in µA; D in cm² s⁻¹, m in mg s⁻¹, t in s, C in mmol L⁻¹); 708 replaces 607 for the maximum current of each drop. For one capillary and one medium i_d=kC, so the height of the wave gives the concentration.
5. Half-wave potential, E_(1/2): the potential at i=i_d/2. For a reversible wave it is close to the standard potential of the couple and does not depend on concentration. In 0.1 M KCl against the saturated calomel electrode, Cd²+ gives about -0.60 V and Zn²+ about -1.00 V.
6. Wave equation (Heyrovský–Ilkovič): E=E_(1/2)+(0.0592)/(n)log(i_d-i)/(i) at 25°C. A plot of E against log[(i_d-i)/i] is a straight line of slope 0.0592/n V (0.0296 V for Cd²+), which gives n and tests reversibility.
7. Oscillations: the current grows as each drop grows and falls when it detaches, so the curve is saw-toothed. A slow (damped) galvanometer records the mean.

Conditions for a clean wave: a 50 to 100 times excess of supporting electrolyte (KCl) carries the migration current, so the ion arrives by diffusion only; dissolved O₂ gives its own waves and is swept out with N₂; a maximum suppressor (a trace of gelatin or Triton X-100) removes current peaks at the top of the wave.

Application. ions whose half-wave potentials differ by about 0.2 V give separate waves, so traces of Pb²+, Cd²+ and Zn²+ are determined in one run. Holding the potential on a plateau while a titrant is added gives an amperometric titration.