Q4(a)(ii). Principle of polarography; the half-wave potential
Discuss the principle of polarographic analysis. Explain the meaning and significance of half wave potential.
Answer in brief
The current is recorded while the potential of a dropping mercury electrode (DME) is made more negative in an unstirred solution with excess supporting electrolyte. Reducible species give S-shaped waves: the wave height (diffusion current) is proportional to concentration; the half-wave potential E_(1/2), the potential at half the wave height, is characteristic of the species and independent of concentration.
Key points
- The DME (small, renewed every few seconds, easily polarised) and a large non-polarisable reference electrode (SCE or mercury pool) dip in the test solution. The whole applied voltage acts at the drop.
- A small residual current flows until the decomposition potential is reached; then the ion is reduced, e.g. Cd²+ + 2e⁻ + Hg → Cd(Hg), and the current rises steeply.
- The ion is removed at the drop surface faster than it arrives (concentration polarisation). At more negative potentials its surface concentration is zero, and the current is limited by diffusion alone: the plateau.
- A large excess of supporting electrolyte (KCl) carries the migration current, so the ion reaches the drop only by diffusion; dissolved O₂ is removed with N₂; a maximum suppressor (gelatin) smooths the wave.
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
Principle
- The DME (small, renewed every few seconds, easily polarised) and a large non-polarisable reference electrode (SCE or mercury pool) dip in the test solution. The whole applied voltage acts at the drop.
- A small residual current flows until the decomposition potential is reached; then the ion is reduced, e.g. Cd²+ + 2e⁻ + Hg → Cd(Hg), and the current rises steeply.
- The ion is removed at the drop surface faster than it arrives (concentration polarisation). At more negative potentials its surface concentration is zero, and the current is limited by diffusion alone: the plateau.
- A large excess of supporting electrolyte (KCl) carries the migration current, so the ion reaches the drop only by diffusion; dissolved O₂ is removed with N₂; a maximum suppressor (gelatin) smooths the wave.
- The diffusion current i_d (limiting minus residual) follows the Ilkovič equation; for a given capillary i_d=kC, the basis of quantitative analysis.
Half-wave potential
- Meaning: the potential at which i=i_d/2. From the wave equation, E=E_(1/2)+(0.0592)/(n)log(i_d-i)/(i) (25°C), so at i=i_d/2 the log term vanishes.
- Significance: for a reversible wave E_(1/2) is close to the standard potential of the couple and is independent of concentration and of the capillary. It identifies the species (qualitative analysis): in 0.1 M KCl against SCE, Cd²+ about -0.60 V, Zn²+ about -1.00 V.
- A shift of E_(1/2) on adding a ligand measures the stability constant of the complex formed; the slope of E against log[(i_d-i)/i] gives n.
Application. ions whose E_(1/2) differ by about 0.2 V give separate waves, so Pb²+, Cd²+ and Zn²+ are determined together in one run (trace metals in water and alloys).
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All parts of Question 4
- 4(a)(i) Stark–Einstein law; quantum yield and why it is often low15 marks
- 4(a)(ii) Principle of polarography; the half-wave potential10 marks
- 4(b) Schrödinger wave equation in three dimensions; meaning of ψ and ψ²15 marks
- 4(c) Equilibrium constant of A + B ⇌ C from two relaxation times10 marks