Galvanic (voltaic) cells
A galvanic cell converts the chemical energy of a spontaneous redox reaction into electrical energy. The classic example is the Daniell cell:
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
Anode (negative terminal): oxidation, Zn → Zn²⁺ + 2e⁻.
Cathode (positive terminal): reduction, Cu²⁺ + 2e⁻ → Cu.
Electrons flow through the external wire from anode to cathode.
A salt bridge (for example, KCl in agar) completes the circuit and keeps the solutions electrically neutral.
Cell notation: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s), with the anode on the left and the cathode on the right.
Electrode potential and the SHE
The tendency of an electrode to gain electrons is its reduction potential. Absolute values cannot be measured, so all potentials are measured against the standard hydrogen electrode (SHE), whose potential is defined as 0 V.
E°_cell = E°_cathode − E°_anode
For the Daniell cell: E°(Cu²⁺/Cu) = +0.34 V and E°(Zn²⁺/Zn) = −0.76 V, so E°_cell = 0.34 − (−0.76) = 1.10 V.
The electrochemical series lists standard reduction potentials. A more negative E° means a stronger reducing agent (for example, lithium). A more positive E° means a stronger oxidising agent (for example, fluorine).
The Nernst equation
For an electrode reaction Mⁿ⁺ + ne⁻ → M at 298 K:
E = E° − (0.059/n) log (1/[Mⁿ⁺])
For a complete cell reaction with reaction quotient Q:
E_cell = E°_cell − (0.059/n) log Q
At equilibrium, E_cell = 0 and Q = K_c, so E°_cell = (0.059/n) log K_c.
Cell potential and Gibbs energy
ΔG = −nFE_cell, and ΔG° = −nFE°_cell
where F = 96 487 C mol⁻¹ (the Faraday constant). A positive E_cell means a negative ΔG, so the reaction is spontaneous.
For the Daniell cell: ΔG° = −2 × 96 487 × 1.10 ≈ −212 kJ mol⁻¹.
Conductance of electrolytic solutions
Conductivity κ is the conductance of a solution placed between electrodes 1 cm² in area and 1 cm apart. Unit: S m⁻¹.
Molar conductivity Λ_m = κ / c, the conductivity per mole of electrolyte.
On dilution: conductivity κ decreases, because there are fewer ions per unit volume. Molar conductivity Λ_m increases, because ions move more freely and (for weak electrolytes) more of the electrolyte dissociates.
For strong electrolytes, Λ_m rises slightly and linearly with √c, so a plot can be extrapolated to find Λ°_m.
For weak electrolytes, Λ_m rises steeply at low concentration and cannot be extrapolated.
Kohlrausch's law: at infinite dilution, each ion contributes independently: Λ°_m = ν₊λ°₊ + ν₋λ°₋. This lets us find Λ°_m for weak electrolytes, and their degree of dissociation α = Λ_m / Λ°_m.
Electrolysis and Faraday's laws
In an electrolytic cell, electrical energy drives a non-spontaneous reaction.
First law: the mass deposited is proportional to the charge passed, m = Z I t.
Second law: for the same charge, the masses of different substances deposited are proportional to their equivalent masses.
Products depend on the competing electrode reactions. Electrolysis of aqueous NaCl gives H₂ at the cathode (water is reduced more easily than Na⁺) and Cl₂ at the anode (because of overpotential for O₂).
Batteries, fuel cells and corrosion
Primary cells (not rechargeable): the dry cell (Leclanché cell) and the mercury cell.
Secondary cells (rechargeable): the lead–acid battery and the nickel–cadmium cell.
Fuel cells convert the energy of fuels such as H₂ and O₂ directly into electricity with high efficiency. They were used in the Apollo space programme.
Corrosion of iron is electrochemical. Iron is oxidised at anodic spots, and oxygen is reduced at cathodic spots, with moisture acting as the electrolyte. Sacrificial protection (coating with zinc or connecting to a magnesium block) protects iron because the more reactive metal corrodes first.