VKC Notes · Electrochemistry · Civil Services P-I · IFoS P-I · Geo-Scientist P-II

8.2 Electrochemical Cells: Nernst Equation, EMF and Electrodes

★★★ 2021–2025: 39 parts, 326 marks (Civil Services 9 parts / 100 m · IFoS 8 / 71 m · Geo-Scientist 22 / 155 m), plus Prelims. Geo-Scientist Paper II asks two or three cell questions every year.

Syllabus lines. Civil Services and IFoS: “Galvanic cells, concentration cells; electrochemical series, measurement of e.m.f. of cells and its applications; fuel cells and batteries … ion selective electrodes and their uses”. Geo-Scientist: “Types of electrochemical cells, cell reactions, emf and Nernst equation, ΔG, ΔH and ΔS of cell reactions. Cell diagrams and IUPAC conventions. Standard cells. Half-cells / electrodes, types of reversible electrodes. Standard electrode potential … Concentration cells. Determination of ΔG°, K°, Ksp and pH”. Conductance and Debye–Hückel theory need their own notes.

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CSE 2024 Q7(a) = asked there; tap to open the solved answerSN = line kept in the short notes

8.2.1 Cells, cell diagrams, electrodes and the salt bridge ★★★

Fig. 8.2.1 The Daniell cell.

Draw it in 60 s: two beakers, a rod in each (Zn left, Cu right), an inverted U for the salt bridge, a wire on top with an arrow e⁻ left → right; write the cell diagram below.

Galvanic cell: a spontaneous reaction drives current (ΔG < 0); electrolytic cell: an outside source drives a non-spontaneous one. In both, oxidation happens at the anode and reduction at the cathode; in a galvanic cell the cathode is +, in an electrolytic cell it is −.SN
Cell diagram (IUPAC): anode on the left, | = phase boundary, ‖ = salt bridge; E_cell = E_right − E_left. A positive value means the reaction as written runs.SN
Polarity is relative: copper is + against zinc (1.10 V) but − against silver (Cu | Cu²⁺ ‖ Ag⁺ | Ag, 0.46 V) Geo 2022 Q1(j) 5m.

Reversible electrode	Example	E depends on
Metal–metal ion (first kind)	Zn \| Zn²⁺; Hg \| Hg₂²⁺	a(Mⁿ⁺)
Gas	Pt \| H₂(g) \| H⁺	a(H⁺), p(H₂)
Non-metal	Pt \| I₂(s) \| I⁻	a(I⁻)
Metal–insoluble salt–anion (second kind)	Ag \| AgCl(s) \| Cl⁻; Hg \| Hg₂Cl₂ \| Cl⁻ (calomel)	a(Cl⁻) only: steady, used as reference
Redox	Pt \| MnO₄⁻, Mn²⁺; Pt \| Fe³⁺, Fe²⁺	ratio a(ox)/a(red)

Matching electrodes to types Geo 2023 Q6(b) 5m.SN
Salt bridge: completes the circuit by ion flow, keeps each half-cell neutral, stops the solutions mixing. Saturated KCl, KNO₃ or NH₄NO₃ because cation and anion move at almost the same speed (t₊ ≈ t₋ ≈ 0.5), so the liquid-junction potential is nearly zero Geo 2021 Q15(c) 5m.SN
KCl is wrong for Ag⁺, Pb²⁺, Hg₂²⁺ or Tl⁺ half-cells: Cl⁻ precipitates AgCl, PbCl₂, the emf drifts and the bridge clogs; use KNO₃ or NH₄NO₃ Geo 2025 Q1(i) 5m.SN
Why not a voltmeter: EMF is the potential difference at zero current. A voltmeter draws current and reads E − Ir; the cell also polarises. A potentiometer (Poggendorff null method, Weston standard cell) measures at I = 0 Geo 2021 Q1(j) 5m.SN

8.2.2 Standard potentials and the electrochemical series ★★★

Fig. 8.2.2 The electrochemical series.

Draw it in 60 s: a vertical line with ten couples in order (not to scale): F₂ +2.87 on top, SHE 0.00 in the middle, Li −3.05 at the bottom; arrows: oxidising power up, reducing power down.

E° of a couple = emf of the cell SHE ‖ couple with everything at unit activity, written as a reduction. The list in order of E° is the electrochemical series CSE 2021 Q1(e) 10m.SN
Uses: high E° = strong oxidant (F₂), low E° = strong reductant (Li); a metal displaces from solution any metal above it; metals with E° < 0 liberate H₂ from dilute acid; the order of discharge in electrolysis; zinc protects iron (galvanising, sacrificial anode).SN
M₁ displaces H₂, M₂ cannot but displaces M₃: E°(M₃) > E°(M₂) > E°(M₁), with E°(M₁) < 0 < E°(M₂) IFoS 2024 Q2(d) 5m.
Fe³⁺/Fe²⁺ (0.771 V) and Sn⁴⁺/Sn²⁺ (0.154 V): only Fe³⁺ + Sn²⁺ reacts (E° = +0.617 V); Fe²⁺ + Sn⁴⁺ gives −0.617 V; Fe²⁺ + Sn²⁺ are both reductants Geo 2023 Q14(a) 10m.

✗ Adding E° values of two half-reactions to get a third. E° is intensive; add ΔG° = −nFE° instead.

(8.2.1)

Cr³⁺ + e⁻ → Cr²⁺ (−0.424) and Cr²⁺ + 2e⁻ → Cr (−0.90): E°(Cr³⁺/Cr) = [1(−0.424) + 2(−0.90)]/3 = −0.741 V CSE 2023 Q1(e)(i) 5m.SN
Fe³⁺/Fe²⁺ (0.772) and Fe³⁺/Fe (−0.036): E°(Fe²⁺/Fe) = [3(−0.036) − 1(0.772)]/2 = −0.440 V Geo 2021 Q10(a) 5m.
O₂ in base: O₂ + 2H₂O + 4e⁻ → 4OH⁻ = acid half-reaction + 4(H₂O → H⁺ + OH⁻); E°_b = 1.23 − 0.0591 pK_w = +0.40 V CSE 2025 Q2(b) 15m.
E° from thermal data: ΔG° = ΔH° − TΔS°, then E° = −ΔG°/nF. Na⁺ + ½H₂ → Na + H⁺: ΔG° = 240.1 − 298(−0.0731) = +261.9 kJ → E° = −2.71 V Geo 2023 Q1(i) 5m. 2M + 6H⁺ → 2M³⁺ + 3H₂: ΔfG°(M³⁺) = −15.83 kcal, E°(M³⁺/M) = −0.229 V Geo 2025 Q13 20m.

8.2.3 Nernst equation, ΔG° and K ★★★

(8.2.2)

(8.2.3)

Derivation in one line: reaction isotherm ΔG = ΔG° + RT ln Q, with ΔG = −nFE; divide by −nF. For one electrode written as a reduction ox + ne⁻ → red: E = E° + (RT/nF) ln(a_ox/a_red). Pt | Cr⁶⁺, Cr³⁺: E = E° + 0.0197 log(a_Cr⁶⁺/a_Cr³⁺) Geo 2022 Q1(i) 5m.SN
E° > 0 ⇔ ΔG° < 0 ⇔ K > 1 Geo Pre 2021 Q57. At equilibrium E = 0 and Q = K.SN

Cell	n	E°_cell / V	ΔG° / kJ mol⁻¹	K (298 K)	Asked
Zn + Cu²⁺ (Daniell)	2	1.10	−212	≈ 10³⁷	CSE 2022 Q1(e) 10m Geo 2024 Q1(i) 5m
3Mg + 2Al³⁺	6	0.71	−411	≈ 10⁷²	IFoS 2024 Q1(e) 8m
2Fe³⁺ + Sn²⁺	2	0.617	−119	7.4 × 10²⁰	Geo 2023 Q14(b) 10m
Zn + 2Ag⁺ (E = 1.62 V measured)	2	1.531	−295	6 × 10⁵¹	IFoS 2021 Q1(e) 8m

Solved PYQ CSE 2021 Q4(a) 10m

at 25 °C. E°(Cu²⁺/Cu) = 0.34 V.

Reaction: H₂ + Cu²⁺ → 2H⁺ + Cu, n = 2; E° = 0.34 − 0 = 0.34 V.
Q = [H⁺]²/([Cu²⁺] p_H₂) = 10⁻⁴/0.1 = 10⁻³.
E = 0.34 − (0.05916/2)(−3) = 0.429 V; ΔG = −nFE = −82.7 kJ mol⁻¹: runs as written.SN

K_sp from E°: Ag in saturated AgI with a_I⁻ = 1: a_Ag⁺ = K_sp, E = 0.799 + 0.05916 log(8.3 × 10⁻¹⁷) = −0.152 V (this is E° of AgI | Ag | I⁻) Geo 2024 Q12(b) 10m.SN

8.2.4 ΔG, ΔH and ΔS from emf ★★★ Geo-Scientist favourite

(8.2.4)

Derivation: a reversible cell gives maximum non-expansion work nFE = −ΔG. Since (∂ΔG/∂T)_P = −ΔS, differentiating ΔG = −nFE gives ΔS = nF(∂E/∂T)_P; then ΔH = ΔG + TΔS (Gibbs–Helmholtz) Geo 2025 Q7 10m Geo Pre 2021 Q58.SN
Sign of dE/dT = sign of ΔS. q_rev = TΔS: dE/dT < 0 means the working cell gives out heat.

Cell	E / V	dE/dT / V K⁻¹	ΔG / kJ	ΔS / J K⁻¹	ΔH / kJ	Asked
Pb \| PbCl₂ \| AgCl \| Ag (n = 2)	0.490	−1.86 × 10⁻⁴	−94.6	−35.9	−105.3	Geo 2021 Q6 10m
Cd \| CdCl₂(sat) ‖ AgCl \| Ag (n = 2)	0.675	−6.5 × 10⁻⁴	−130.3	−125.4	−167.6	Geo 2024 Q11(c) 5m
Fe \| Fe²⁺ ‖ Fe³⁺, Fe²⁺ \| Pt (n = 2)	–	+1.14 × 10⁻³	–	+220	–	Geo 2025 Q7

Cell reactions: Pb + 2AgCl → PbCl₂ + 2Ag; Cd + 2AgCl → CdCl₂ + 2Ag; Fe + 2Fe³⁺ → 3Fe²⁺. All-solid cells: E = E°, no concentration term.

H₂–O₂ fuel cell: ΔrH° = −285.83 kJ, ΔrS° = 69.91 − 130.68 − ½(205.14) = −163.34 J K⁻¹; ΔrG° = −285.83 + 48.70 = −237.13 kJ; E° = 237 130/(2 × 96 485) = 1.23 V. Maximum efficiency ΔG/ΔH = 83 % (a heat engine is limited by Carnot) CSE 2023 Q3(c) 20m.SN

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