VKC Notes · Electrochemistry · Civil Services P-I · IFoS P-I

8.4 Electrode Kinetics: Double Layer, Overpotential, Butler–Volmer and Tafel Equations, Polarography and Voltammetry

★★★ 2021–2025: 6 Mains parts, 53 marks (Civil Services 4 parts / 40 m · IFoS 2 / 13 m). Polarography is the favourite long answer (10–15 marks); the rest are overvoltage, limiting current and Butler–Volmer reasoning.

Syllabus lines. Civil Services (Electrochemistry): “Processes at electrodes; double layer at the interface; rate of charge transfer, current density; overpotential; electroanalytical techniques: amperometry, ion selective electrodes and their uses”. IFoS: the same, with “voltammetry, polarography, amperometry, cyclic voltammetry, ion selective electrodes”. Cells and emf: 8.2; conductance and Debye–Hückel: 8.3.

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

8.4.1 The electrode–solution interface: the double layer ★★

A charged electrode attracts a sheet of oppositely charged ions (and oriented water dipoles): an electrical double layer of separated charge, across which the potential changes from φ_metal to φ_solution. It behaves as a capacitor and must be charged before any faradaic current flows.SN
Helmholtz: a rigid layer of ions at the outer Helmholtz plane (OHP, the centres of the nearest solvated ions); the potential falls linearly across it, like a parallel-plate capacitor. It ignores thermal motion.SN
Gouy–Chapman: a diffuse ionic atmosphere (Debye–Hückel at a plane); the potential falls exponentially, φ ∝ e^−κx, over the Debye length 1/κ (about 0.3 nm/√(I/mol dm⁻³) for a 1 : 1 salt at 25 °C), so it thins as ionic strength rises. It ignores ion size.SN
Stern (and Grahame): a compact Helmholtz layer followed by a diffuse Gouy–Chapman layer; specifically adsorbed ions (inner Helmholtz plane) can even reverse the sign. The potential at the start of the diffuse layer is close to the zeta potential of electrokinetic effects (11.2).SN
Electrocapillarity (Lippmann): the surface tension of a mercury electrode against potential is an inverted parabola whose maximum is the potential of zero charge; the slope gives the surface charge.

Fig. 8.4.1 Three models of the double layer at a positive electrode: Helmholtz (linear fall), Gouy–Chapman (exponential), Stern (both).

Draw it in 60 s: three panels, a + plate on the left; (a) a column of − ions and a line falling straight then flat; (b) scattered ions and a curve; (c) a column plus a cloud and a straight-then-curved line.

8.4.2 Rate of charge transfer: the Butler–Volmer equation ★★★

(8.4.1)

Current density j = current/area is the rate of an electrode reaction (j/nF in mol m⁻² s⁻¹). For O + ne⁻ ⇌ R the cathodic rate is k_c[O]_s and the anodic rate k_a[R]_s ([ ]_s at the surface, outside the double layer).SN
Moving the electrode potential by η changes the activation Gibbs energy: the fraction α (transfer coefficient, usually ≈ 0.5) of Fη helps the cathodic step and 1 − α the anodic step (transition state partway across the double layer). Subtracting the two rates at the same surface concentrations gives Eq. 8.4.1.SN
At equilibrium (η = 0) the anodic and cathodic currents are equal and opposite: the exchange current density j₀. It measures the intrinsic speed of the couple: H⁺/H₂ on Pt j₀ = 0.79 mA cm⁻², on zinc only about 50 pA cm⁻².SN

Low overpotential (η ≪ 25 mV): expand the exponentials: j = j₀fη, Ohm-like; the charge-transfer resistance is R_ct = 1/fj₀ (33 Ω cm² for H₂ on Pt).SN
High overpotential (|η| > ~120 mV): one exponential wins; ln j = ln j₀ + (1 − α)fη (anodic) or ln(−j) = ln j₀ − αfη (cathodic): the Tafel region (8.4.3).SN

Fig. 8.4.2 Butler–Volmer curve, α = 0.5, 25 °C (computed): the net current is the difference of two exponentials; linear near η = 0.

Draw it in 60 s: axes j/j₀ and η; two dashed exponentials (one rising to the right, one falling to the left); a solid S-curve through the origin that follows them at the ends.

8.4.3 Tafel equation; fast and slow systems ★★★

(8.4.2)

Tafel plot: log|j| against η is straight at high |η|; the slope gives α, and extrapolating to η = 0 gives log j₀ (Fig. 8.4.3). Tafel found η = a + b log j by experiment (1905); Butler–Volmer explains it.SN
Fast system (large j₀, e.g. H⁺/H₂ on platinised Pt, Ag⁺/Ag): a tiny overpotential drives a large current; the steady-state curve rises steeply through j = 0 at E_eq and soon reaches the diffusion plateaux. Slow system (small j₀, H⁺/H₂ on Hg or Zn): flat near equilibrium; a large η is needed before current flows, so the wave is drawn out. With the same open-circuit potential and the same limiting currents, both curves cross zero at the same point and end on the same plateaux IFoS 2025 Q1(e) 8m.SN

Fig. 8.4.3 Tafel plot, α = 0.5 (computed): straight branches of slope 1 decade per 118 mV, extrapolating to log j₀.

Draw it in 60 s: axes log|j| and η; a V with rounded bottom; extend the straight arms (dashed) to meet at η = 0: that height is log j₀.

Fig. 8.4.4 Steady-state curves for a fast and a slow system with the same E_eq and limiting currents (Butler–Volmer with mass-transport limits, computed).

Draw it in 60 s: two S-curves between the same two dashed plateaux, both through the origin: one almost vertical (fast), one flat in the middle and rising only far out (slow).

8.4.4 Overpotential (overvoltage) and its uses ★★★

Overvoltage η = E_applied − E_reversible: the extra potential, beyond the equilibrium value, needed for an electrode reaction to go at a measurable rate CSE 2024 Q1(d)(ii) 5m. Kinds: activation (slow charge transfer, Tafel), concentration (reactant depleted at the surface, 8.4.5), resistance (iR drop in solution and films). Decomposition voltage = E_rev + η_a + |η_c| + iR: water at smooth Pt needs about 1.7 V, not 1.23 V.SN
Hydrogen (bubble) overvoltage at cathodes in N H₂SO₄: platinised Pt ≈ 0.00, Au 0.02, Fe 0.08, smooth Pt 0.09, Ag 0.15, Ni 0.21, Cu 0.23, Cd 0.48, Sn 0.53, Pb 0.64, Zn 0.70, Hg 0.78 V. It depends on the metal, its surface, the current density and temperature.SN
Uses: zinc, cadmium, tin and nickel can be plated from acid solutions, and the lead–acid battery can be charged, because H₂ is held back on those metals; the mercury cathode of the chlor-alkali cell gives sodium amalgam, not H₂; at the anode Cl₂ is evolved before O₂ because the oxygen overvoltage is larger; the dropping mercury electrode reaches about −2 V in polarography; electrolytic reductions of organic compounds use high-overvoltage cathodes.SN

Solved PYQ IFoS 2025 Q4(c)(ii) 5m

E°(Zn²⁺/Zn) = −0.76 V; H₂ discharge on Pt has j₀ = 0.79 mA cm⁻². Can Zn be plated on Pt? Unit activities, α = 0.50, 25 °C.

Zn deposits only when the cathode is at or below −0.76 V. At that potential the H⁺/H₂ couple (E° = 0) has a cathodic overpotential of −0.76 V.
Tafel: |j| = j₀ e^αf|η| = 0.79 × 10⁻³ × e^{0.5 × 38.92 × 0.76} = 0.79 × 10⁻³ × 2.65 × 10⁶ ≈ 2 × 10³ A cm⁻².
Hydrogen would be evolved at an enormous rate long before −0.76 V is reached: zinc cannot be plated on platinum. On zinc itself (j₀ ≈ 50 pA cm⁻²) the same overpotential gives only 1.3 × 10⁻⁴ A cm⁻², so once zinc covers the cathode it deposits; this is why zinc is plated on high-overvoltage cathodes.SN

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