Electrochemistry

1. Galvanic Cell & Cell Notation

A galvanic (voltaic) cell converts the energy of a spontaneous redox reaction into electrical energy. An electrolytic cell does the reverse: electrical energy forces a non-spontaneous reaction.

Golden rule: Anode = oxidation, Cathode = reduction in both cells. Only the signs swap.

Cell notation: anode on the left, cathode on the right; a single line | for a phase boundary, a double line || for the salt bridge. Example: $\text{Zn}\,|\,\text{Zn}^{2+}(1\text{ M})\,||\,\text{Cu}^{2+}(1\text{ M})\,|\,\text{Cu}$

Salt bridge: a U-tube of inert electrolyte (KCl, NH₄NO₃, KNO₃) in agar. It (i) completes the circuit and (ii) keeps both half-cells electrically neutral. Its ions must not react with the cell solutions and should have nearly equal ionic mobilities (this is why KCl is used, not NaCl).

2. Electrode Potential & the E° Series

• The potential of a single electrode cannot be measured, so it is measured against the Standard Hydrogen Electrode (SHE), assigned $E^\circ = 0.00$ V (Pt, H₂ at 1 bar, 1 M H⁺).
• Standard conditions: 1 M concentration, 1 bar pressure, 298 K.
• All tabulated values are reduction potentials.

$$E^\circ_{cell}=E^\circ_{cathode}-E^\circ_{anode}\quad(\text{both as reduction potentials})$$

Reading the series:

• More positive $E^\circ$ = stronger oxidising agent (e.g. F₂, +2.87 V).
• More negative $E^\circ$ = stronger reducing agent (e.g. Li, −3.05 V).
• A metal displaces another from its salt solution if its $E^\circ$ is lower (more negative). Metals above H (negative $E^\circ$) liberate H₂ from dilute acids; Cu, Ag, Au (positive $E^\circ$) do not.

3. Nernst Equation, ΔG° and Equilibrium Constant

For $aA+bB\rightarrow cC+dD$ with $n$ electrons transferred, at 298 K:

$$E_{cell}=E^\circ_{cell}-\frac{0.0591}{n}\log Q,\qquad Q=\frac{[C]^c[D]^d}{[A]^a[B]^b}$$

• Pure solids and liquids (Cu, Zn, H₂O) are omitted from Q. Gases enter as partial pressure.
• For a single electrode $M^{n+}+ne^-\rightarrow M$: $E=E^\circ-\frac{0.0591}{n}\log\frac{1}{[M^{n+}]}$.
• At equilibrium, $E_{cell}=0$ (a "dead" battery) and $Q=K_c$.

The three linked equations (learn them together):

$$\Delta_rG^\circ=-nFE^\circ_{cell}\qquad \Delta_rG^\circ=-RT\ln K\qquad E^\circ_{cell}=\frac{0.0591}{n}\log K_c$$

with $F=96500$ C mol⁻¹. Spontaneous ⇒ $E^\circ_{cell}>0$, $\Delta G^\circ<0$, $K>1$.

Worked example (2023 board): Mg | Mg²⁺(0.1 M) || Cu²⁺(0.01 M) | Cu, $E^\circ=2.71$ V, $n=2$:

$$E=2.71-\frac{0.0591}{2}\log\frac{0.1}{0.01}=2.71-0.02955=2.68\text{ V}$$

4. Conductance & Kohlrausch's Law

Electrolytic (ionic) conductance uses AC (to avoid electrolysis) and depends on ion concentration, charge, size and temperature.

Variation with dilution (very important):

• Conductivity ($\kappa$) decreases on dilution (fewer ions per unit volume).
• Molar conductivity ($\Lambda_m$) increases on dilution (more dissociation for weak electrolytes; less inter-ionic attraction for strong ones).

• Strong electrolytes: Debye-Hückel-Onsager equation $\Lambda_m=\Lambda_m^\circ-A\sqrt c$. Extrapolate the line to $c=0$ to get $\Lambda_m^\circ$.
• Weak electrolytes: the curve is too steep to extrapolate, so use Kohlrausch's law.

Kohlrausch's law of independent migration of ions: at infinite dilution each ion contributes a fixed amount, irrespective of the counter-ion.

$$\Lambda_m^\circ=\nu_+\lambda_+^\circ+\nu_-\lambda_-^\circ$$

Applications (both are board favourites):

1. Get $\Lambda_m^\circ$ of a weak electrolyte: $\Lambda^\circ_m(\text{CH}_3\text{COOH})=\Lambda^\circ(\text{CH}_3\text{COONa})+\Lambda^\circ(\text{HCl})-\Lambda^\circ(\text{NaCl})$.
2. Degree of dissociation and dissociation constant of a weak electrolyte:

$$\alpha=\frac{\Lambda_m}{\Lambda_m^\circ},\qquad K_a=\frac{c\alpha^2}{1-\alpha}=\frac{c\Lambda_m^2}{\Lambda_m^\circ(\Lambda_m^\circ-\Lambda_m)}$$

Worked example (2024 board): cell constant from 0.05 M KCl: $G^*=\kappa R=1.35\times10^{-2}\times100=1.35$ cm⁻¹. For AgNO₃ (R = 90 Ω): $\kappa=1.35/90=1.5\times10^{-2}$ S cm⁻¹ and $\Lambda_m=\dfrac{1.5\times10^{-2}\times1000}{0.02}=750$ S cm² mol⁻¹.

5. Electrolysis & Faraday's Laws

Faraday's first law: mass deposited is proportional to the charge passed.

$$m=Z\,I\,t=\frac{M}{nF}\times Q,\qquad Q=I\times t\ (\text{coulomb})$$

Faraday's second law: for the same charge through different electrolytes in series, masses deposited are proportional to their equivalent weights ($M/n$).

Useful numbers: 1 F = 96500 C = charge on 1 mol of electrons. Charge needed to deposit 1 mol: Ag⁺ = 1 F, Cu²⁺ = 2 F, Al³⁺ = 3 F.

Which species is discharged? (Products in aqueous solutions)

• Cathode: the species with the higher reduction potential is reduced first. Cu²⁺ (+0.34 V) beats H₂O; Na⁺, K⁺, Ca²⁺ (very negative E°) lose to water, so H₂ is evolved.
• Anode (inert electrode): the species that is easier to oxidise (lower $E^\circ$) goes first, but O₂ evolution from water needs extra voltage (overpotential), so Cl⁻ is oxidised in brine.

6. Batteries & Fuel Cells

Primary cells (not rechargeable): Dry (Leclanché) cell — Zn anode, graphite rod cathode with MnO₂ + NH₄Cl paste; about 1.5 V. Mercury cell — Zn(Hg) anode, HgO/C cathode, KOH-ZnO paste; constant 1.35 V because the overall reaction $\text{Zn(Hg)}+\text{HgO}\rightarrow\text{ZnO}+\text{Hg}$ involves no ion whose concentration changes. Used in watches and hearing aids.

Secondary cells (rechargeable):

• Lead-acid accumulator: Pb anode, PbO₂ cathode, ~38% H₂SO₄.
  • Discharge: $\text{Pb}+\text{PbO}_2+2\text{H}_2\text{SO}_4\rightarrow2\text{PbSO}_4+2\text{H}_2\text{O}$ (about 2 V per cell; acid density falls).
  • Charging reverses this.
• Ni-Cd cell: longer life (~1.4 V), but costlier.

Fuel cells convert the energy of combustion directly into electricity. Reactants are fed continuously.

Advantages of the H₂–O₂ fuel cell: high efficiency (~70%), pollution-free (product is water), continuous operation, and the water can be consumed by astronauts.

Primary vs secondary battery (asked in 2025-style questions): a primary battery is used once and cannot be recharged (dry cell, mercury cell); a secondary battery can be recharged by passing current in the reverse direction (lead-acid, Ni-Cd).

7. Corrosion

Corrosion is an electrochemical process: a tiny galvanic cell forms on the metal surface in the presence of moisture and air.

• Anode: $\text{Fe}\rightarrow\text{Fe}^{2+}+2e^-$ ($E^\circ=-0.44$ V)
• Cathode: $\text{O}_2+4\text{H}^++4e^-\rightarrow2\text{H}_2\text{O}$ ($E^\circ=+1.23$ V)
• Then Fe²⁺ is oxidised by air and forms rust, $\text{Fe}_2\text{O}_3\cdot x\text{H}_2\text{O}$.

Prevention: paint or oil coating; galvanisation (Zn); electroplating; sacrificial anode (Mg, Zn), cathodic protection; alloying (stainless steel).

8. Formula Sheet & Last-Minute Checklist

Before the exam, check:

1. Can I write cell notation from a reaction (anode on the left)?
2. Do I remember to omit solids from Q and to use the balanced n?
3. Do I know the direction of current, and the difference between primary and secondary cells?
4. Can I state Kohlrausch's law and one application in two lines?
5. Do I know why Cl₂ (not O₂) forms in brine and why the mercury cell has constant voltage?