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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2022/paper-1/section-a-iii/6/i/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section A(iii) / 6 / i / Solution by

Codex  0 2026-10-20

Take unit activity of each dissolved metal ion, unit activity of each metal,

p_{H_{2}} = 1 bar

and

T = 298 K

. The hydrogen-electrode Nernst equation gives

E_{H^{+} / H_{2}} = - \frac{RT l n 10}{F} pH = - 0.059117 pH V .

Thus

E_{H} = - 0.05912 V

at pH 1 and

- 0.82764 V

at pH 14. For corrosion coupled to hydrogen evolution,

M + z H^{+} ⟶ M^{z +} + \frac{z}{2} H_{2}, E_{cell} = E_{H} - E_{M}^{\circ}, Δ G = - z F E_{cell} .

For alkaline solution the same electron balance can be written

M + z H_{2} O \to M^{z +} + z O H^{-} + (z /2) H_{2}

, before allowing for metal-ion hydrolysis or complexation. Using

z = 2

for zinc and lead, and

z = 1

for lithium, the results per mole of metal are

metal Zn Pb Li pH = 1 E_{cell} (V) 0.7009 0.07088 3.0409 pH = 1 Δ G (kJ mo l^{- 1}) - 135.3 - 13.68 - 293.4 pH = 14 E_{cell} (V) - 0.06764 - 0.6976 2.2724 pH = 14 Δ G (kJ mo l^{- 1}) + 13.05 + 134.6 - 219.3

Lithium is strongly unstable against hydrogen evolution in both media in this model. The positive alkaline values for zinc and lead apply to the stipulated unit-activity free-ion products; they are not complete predictions of alkaline corrosion once hydroxide precipitation and complexation change the product chemical potentials.

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