01 · Foundations
Redox reactions and oxidation states
Electrochemistry is built on redox reactions — processes in which electrons are transferred between species. Oxidation is the loss of electrons; reduction is the gain. The two always occur together: the species that loses electrons (the reducing agent) causes another species to gain them (the oxidising agent).
OXIDATION
Loss of electrons. Oxidation state increases. The reducing agent is oxidised.
Zn(s) → Zn²⁺(aq) + 2e⁻
REDUCTION
Gain of electrons. Oxidation state decreases. The oxidising agent is reduced.
Cu²⁺(aq) + 2e⁻ → Cu(s)
Oxidation states are bookkeeping numbers that track electron ownership in a compound. Rules: free elements are 0; ions are equal to their charge; oxygen is usually −2; hydrogen is usually +1. For species in solution, balance atoms, then balance charge with electrons to write a half-equation.
For practice balancing redox equations, see the Balancing equations guide.
02 · Galvanic cells
Turning spontaneous reactions into electricity
A galvanic cell (voltaic cell) harnesses a spontaneous redox reaction to produce an electric current. The classic Daniell cell separates the Zn/Zn²⁺ and Cu/Cu²⁺ half-cells:
ANODE (−)
Zn → Zn²⁺ + 2e⁻
Oxidation occurs here. Zinc electrode dissolves.
salt bridge
⇌ ions ⇌
CATHODE (+)
Cu²⁺ + 2e⁻ → Cu
Reduction occurs here. Copper deposits.
The cell notation for the Daniell cell is:
Zn(s) | Zn²⁺(aq) ‖ Cu²⁺(aq) | Cu(s)
The cell potential under standard conditions is:
E°cell = E°cathode − E°anode
E°cell = +0.34 − (−0.76) = +1.10 V
A positive E°cell indicates that the reaction is spontaneous under standard conditions (ΔG° = −nFE°cell).
Standard electrode potential table
| Half-reaction (reduction) | E° / V |
|---|---|
| F₂(g) + 2e⁻ → 2F⁻(aq) | +2.87 |
| MnO₄⁻(aq) + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O | +1.51 |
| Cl₂(g) + 2e⁻ → 2Cl⁻(aq) | +1.36 |
| O₂(g) + 4H⁺ + 4e⁻ → 2H₂O(l) | +1.23 |
| Fe³⁺(aq) + e⁻ → Fe²⁺(aq) | +0.77 |
| Cu²⁺(aq) + 2e⁻ → Cu(s) | +0.34 |
| 2H⁺(aq) + 2e⁻ → H₂(g) | 0.00 |
| Fe²⁺(aq) + 2e⁻ → Fe(s) | −0.44 |
| Zn²⁺(aq) + 2e⁻ → Zn(s) | −0.76 |
| Li⁺(aq) + e⁻ → Li(s) | −3.04 |
Species at the top of the table are strong oxidising agents (high tendency to be reduced). Species at the bottom are strong reducing agents (high tendency to be oxidised). A spontaneous galvanic cell always has the stronger oxidising agent at the cathode.
03 · Non-standard conditions
The Nernst equation
Standard potentials apply only at 1 mol/L, 298 K, and 100 kPa. At other concentrations or temperatures, the cell potential changes. The Nernst equation makes this quantitative:
E = E° − (RT / nF) ln Q
At 298 K, the Nernst equation simplifies to:
E = E° − (0.0592 / n) log Q
When the cell reaches equilibrium, E = 0 and Q = K (the equilibrium constant). Rearranging gives the important relationship:
ln K = nFE° / RT
This connects electrochemistry to thermodynamics and equilibrium — topics explored further in the Reaction rates guide and the Acids and bases guide (Ka and Kb are equilibrium constants of the same form).
04 · Electrolytic cells
Electrolysis and Faraday's laws
An electrolytic cell uses an external power supply to drive a non-spontaneous redox reaction. The positive terminal of the supply connects to the anode; the negative terminal to the cathode — the opposite of a galvanic cell's spontaneous convention for sign.
Key industrial applications:
- Aluminium smelting — electrolysis of molten Al₂O₃ (Hall–Héroult process). Al³⁺ is reduced at the cathode; O²⁻ is oxidised at the carbon anode.
- Chlorine production — electrolysis of brine (NaCl(aq)) produces Cl₂ at the anode, H₂ at the cathode, and NaOH in solution (chloralkali process).
- Electroplating — the object to be plated is the cathode; the plating metal is the anode. Metal ions in solution deposit onto the object.
- Electrolytic refining of copper — impure copper dissolves at the anode; pure copper deposits at the cathode. Precious metal impurities fall as anode slime.
Faraday's law calculation
m = (M × I × t) / (n × F)
Worked example: A current of 2.0 A passes through a copper sulfate solution for 30 minutes. How much copper deposits?
Cu²⁺ + 2e⁻ → Cu (so n = 2)
m = (63.5 × 2.0 × 1800) / (2 × 96 485)
m = 228 600 / 192 970 ≈ 1.18 g
Electrochemistry connects directly to nuclear fusion — the fuel-cycle analysis requires understanding of how tritium (the fusion fuel) is produced by neutron bombardment, an analogue of electrolytic reduction. And in biology, the electron transport chain in mitochondria is essentially a biological galvanic cell: electrons flow from NADH (reducing agent) to oxygen (oxidising agent) through a series of redox-active proteins. See Cellular respiration for the biochemical version.
Electrochemistry — common questions
- Oxidation is the loss of electrons; reduction is the gain of electrons. The two always occur together — one species is oxidised while another is reduced. A related concept is oxidation state, which tracks the apparent charge on an atom in a compound. See also Balancing equations for redox balancing.
- A galvanic cell converts chemical energy to electrical energy spontaneously (ΔG < 0). An electrolytic cell uses an external supply to drive a non-spontaneous reaction. Batteries are galvanic cells; electroplating and aluminium smelting use electrolytic cells.
- The standard electrode potential (E°) measures the tendency of a half-cell to be reduced under standard conditions. The standard hydrogen electrode (SHE) is defined as 0.00 V. A positive E°cell = E°cathode − E°anode indicates a spontaneous reaction.
- E = E° − (RT/nF) ln Q. At 298 K this simplifies to E = E° − (0.0592/n) log Q. When Q = 1, E = E°. When the cell reaches equilibrium (Q = K), E = 0 and the cell is fully discharged.
- The key equation is: mass = (M × I × t) / (n × F), where M is molar mass, I is current (A), t is time (s), n is electrons per ion, and F = 96 485 C/mol. This links to the molar mass glossary entry.