Electrochemistry

In this chapter: galvanic cells and the Daniell cell, electrode potential and the standard hydrogen electrode, the Nernst equation, E°_cell, ΔG° and K, conductivity and molar conductivity, Kohlrausch's law, electrolysis and Faraday's laws, products of electrolysis, batteries, fuel cells and corrosion.

Galvanic cells

A galvanic (voltaic) cell converts the chemical energy of a spontaneous redox reaction into electrical energy. The Daniell cell uses the reaction

The zinc rod dips in ZnSO₄ solution and the copper rod in CuSO₄ solution. The two half-cells are joined by a wire through a voltmeter and by a salt bridge (an inverted U-tube with KCl or KNO₃ set in agar-agar gel). The salt bridge completes the circuit and keeps both solutions electrically neutral.

• Anode: oxidation takes place (Zn → Zn²⁺ + 2e⁻). In a galvanic cell it is the negative electrode.
• Cathode: reduction takes place (Cu²⁺ + 2e⁻ → Cu). It is the positive electrode.
• Electrons flow from anode to cathode in the external wire; conventional current flows from cathode to anode.

If an external potential opposing the cell is applied and slowly raised, the reaction continues until the external potential reaches 1.1 V. At exactly 1.1 V no current flows. Above 1.1 V the reaction runs backwards (zinc is deposited, copper dissolves) and the device becomes an electrolytic cell.

Electrode potential and the SHE

The potential difference between an electrode and its solution is the electrode potential. By IUPAC convention, electrode potentials are written as reduction potentials. When all species are at unit concentration (1 M) and gases at 1 bar, it is the standard electrode potential, E°.

A single electrode potential cannot be measured on its own, so the standard hydrogen electrode (SHE) is taken as the reference and assigned zero at all temperatures: Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M), E° = 0.00 V. It consists of a platinum electrode coated with platinum black, dipped in acid, with pure hydrogen bubbled through it.

A more positive E° means a greater tendency to be reduced, so the species on the left is a stronger oxidising agent. A more negative E° means the metal is a stronger reducing agent. A metal with negative E° can displace hydrogen from dilute acids; copper, with positive E°, cannot.

The Nernst equation

For an electrode reaction Mⁿ⁺(aq) + ne⁻ → M(s), the potential at any concentration is

For a general cell reaction aA + bB → cC + dD, E_cell = E°_cell − (0.059/n) log Q, where Q = [C]^c[D]^d ÷ [A]^a[B]^b.

Worked example: Find the emf at 298 K of the cell Zn | Zn²⁺(0.1 M) || Cu²⁺(0.01 M) | Cu, given E°_cell = 1.10 V.
Solution: n = 2. E_cell = 1.10 − (0.059/2) log (0.1/0.01) = 1.10 − 0.0295 × 1 = 1.07 V (1.0705 V). The cell voltage drops slightly because the product ion is more concentrated than the reactant ion.

E°_cell, equilibrium constant and Gibbs energy

At equilibrium E_cell = 0 and Q = K_c. The electrical work a cell can do equals the decrease in Gibbs energy.

For the Daniell cell, log K_c = (2 × 1.1) ÷ 0.059 = 37.3, so K_c ≈ 2 × 10³⁷. Its Δ_rG° = −2 × 96500 × 1.1 = −212300 J mol⁻¹ = −212.3 kJ mol⁻¹. A positive E°_cell means a negative ΔG°, a spontaneous reaction and K greater than 1.

Conductance of electrolytic solutions

Conductivity of an electrolyte depends on the nature of the electrolyte, the size and solvation of its ions, the solvent and its viscosity, the concentration and the temperature (it increases with temperature). Resistance of a solution is measured with a conductivity cell in a Wheatstone bridge using alternating current, since direct current would electrolyse the solution. The cell constant is found first with a KCl solution of known conductivity.

Variation with concentration

• Conductivity (κ) decreases on dilution for both strong and weak electrolytes, because the number of ions per unit volume falls.
• Molar conductivity (Λ_m) increases on dilution. It is the conductance of the whole volume containing 1 mol of electrolyte, and that volume increases faster than κ falls. The limiting value as c → 0 is Λ°_m.
• Strong electrolytes: Λ_m increases slowly and almost linearly: Λ_m = Λ°_m − A c^½. Λ°_m is found by extrapolating the straight line to zero concentration. The constant A depends on the type of electrolyte (1-1, 2-1 and so on) and on the solvent and temperature.
• Weak electrolytes: Λ_m rises steeply at low concentration because the degree of dissociation increases sharply. The curve cannot be extrapolated, so Λ°_m is obtained from Kohlrausch's law.

Kohlrausch's law of independent migration of ions

The limiting molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its cation and anion, each multiplied by the number of such ions in one formula unit: Λ°_m = ν₊λ°₊ + ν₋λ°₋.

• Λ° of a weak electrolyte from strong ones: Λ°(CH₃COOH) = Λ°(CH₃COONa) + Λ°(HCl) − Λ°(NaCl).
• Degree of dissociation of a weak electrolyte: α = Λ_m ÷ Λ°_m, and the dissociation constant K_a = cα² ÷ (1 − α).

Worked example: Λ° for HCl, NaCl and CH₃COONa are 425.9, 126.4 and 91.0 S cm² mol⁻¹. If Λ_m of 0.01 M ethanoic acid is 16.4 S cm² mol⁻¹, find its degree of dissociation and K_a.
Solution: Λ°(CH₃COOH) = 91.0 + 425.9 − 126.4 = 390.5 S cm² mol⁻¹. α = 16.4 ÷ 390.5 = 0.042. K_a = (0.01 × 0.042²) ÷ (1 − 0.042) = 1.84 × 10⁻⁵ mol L⁻¹.

Electrolytic cells and Faraday's laws

In an electrolytic cell, external electrical energy drives a non-spontaneous reaction. The anode is still where oxidation happens, but here it is the positive electrode (connected to the positive terminal of the battery), and the cathode is negative.

• First law: the mass of substance deposited or liberated at an electrode is proportional to the charge passed: m = Z I t, where Z is the electrochemical equivalent.
• Second law: when the same charge passes through different electrolytes, the masses liberated are proportional to their chemical equivalent weights (atomic mass ÷ number of electrons needed).
• Charge on one mole of electrons = 1 Faraday (F) = 96487 C mol⁻¹ ≈ 96500 C mol⁻¹. Deposition of 1 mol Ag⁺, Cu²⁺ and Al³⁺ needs 1 F, 2 F and 3 F respectively.

Worked example: A current of 5.0 A is passed through CuSO₄ solution for 1930 s. What mass of copper is deposited? (Cu = 63.5 g mol⁻¹)
Solution: Q = 5.0 × 1930 = 9650 C = 0.1 F. Cu²⁺ + 2e⁻ → Cu, so 0.1 F deposits 0.05 mol Cu = 0.05 × 63.5 = 3.18 g.

Products of electrolysis

When more than one reaction is possible at an electrode, the one with the higher reduction potential usually occurs at the cathode, and at the anode the species with the lower reduction potential (the one more easily oxidised) reacts. Overpotential can change this, since some electrode reactions are kinetically slow.

Batteries

A primary battery cannot be recharged once used up; a secondary battery can be recharged by passing current in the opposite direction.

Fuel cells

Fuel cells convert the energy of combustion of fuels such as hydrogen or methane directly into electricity. In the H₂-O₂ fuel cell (used in the Apollo space programme, where the water produced was used for drinking), the gases are bubbled through porous carbon electrodes containing finely divided platinum or palladium, into concentrated aqueous NaOH.

Fuel cells run as long as reactants are supplied, are pollution free and have an efficiency of about 70%, compared with about 40% for thermal power plants.

Corrosion

Corrosion is an electrochemical process in which a metal is slowly oxidised by its surroundings. In the rusting of iron, one spot on the surface acts as the anode and another as the cathode, with a film of water containing dissolved CO₂ and O₂ as the electrolyte.

Fe²⁺ is further oxidised by air to Fe³⁺, which appears as rust, hydrated ferric oxide Fe₂O₃·xH₂O. Prevention: painting or coating to keep out air and water; covering with a more easily oxidised metal such as zinc (galvanisation) or connecting a sacrificial electrode of Mg or Zn that corrodes in place of iron.

Common mistakes: (1) Mixing up signs: the anode is negative in a galvanic cell but positive in an electrolytic cell. Oxidation at the anode holds in both. (2) Multiplying E° when a half-reaction is multiplied. E° is an intensive property and does not change. (3) Writing E°_cell = E°_anode − E°_cathode. (4) Forgetting to convert κ from S m⁻¹ to S cm⁻¹ before using the factor 1000 in Λ_m. (5) Saying conductivity increases on dilution; it is molar conductivity that increases.

JEE and NEET focus

• Cell notation, E°_cell from the table of reduction potentials, and predicting whether a reaction is feasible.
• Nernst equation for electrodes and full cells, including the hydrogen electrode at a given pH (E = −0.059 pH at 298 K for 1 bar H₂).
• Relations between E°_cell, Δ_rG° and K, with correct n.
• κ, Λ_m and cell constant numericals; Kohlrausch's law for Λ° of weak electrolytes and for α and K_a.
• Faraday's laws with charge in faradays, and products at each electrode, including aqueous NaCl.
• Electrode reactions of dry cell, mercury cell, lead storage battery and H₂-O₂ fuel cell; rusting as an electrochemical cell.

Practice questions