Faraday's Law of Electrolysis

Use m = M·I·t/(z·F). First calculate the charge: Q = I·t with the time in seconds. Divide by the Faraday constant F = 96,485 C/mol to obtain the amount of electrons, and by z, the number of electrons per deposited particle. Finally multiply by the molar mass. Example copper: I = 2.0 A for one hour gives Q = 2.0·3600 = 7200 C. With z = 2 (Cu²⁺ + 2 e⁻ → Cu) it follows that n = 7200/(2·96,485) = 0.0373 mol and m = 0.0373·63.5 ≈ 2.37 g. The most common error is a time in minutes or hours instead of seconds.

The Faraday constant is the electric charge of one mole of electrons: F = N_A·e = 6.022×10²³ mol⁻¹ · 1.602×10⁻¹⁹ C ≈ 96,485 C/mol. It is thus the bridge between the electrical world (charge in coulombs, measurable via current and time) and the material world (amount of substance in moles). If 96,485 C flow during an electrolysis, exactly one mole of electrons has been transferred; how much substance that deposits depends on z: one mole of silver (z = 1), but only half a mole of copper (z = 2) or a third of a mole of aluminium (z = 3). As a rule of thumb it pays to keep F ≈ 96,500 C/mol in your head.

z is the number of electrons transferred per deposited particle in the electrode reaction. You read it from the half-equation, not from the overall equation: Cu²⁺ + 2 e⁻ → Cu means z = 2, Ag⁺ + e⁻ → Ag means z = 1, Al³⁺ + 3 e⁻ → Al means z = 3. Caution with gases: for hydrogen, 2 H⁺ + 2 e⁻ → H₂ applies, so z = 2 per H₂ molecule; setting z = 1 here wrongly halves the charge. Rule of thumb: z corresponds to the charge number of the discharged ion, or the change in oxidation number times the number of atoms in the particle formed.

Rearrange Faraday's law for the time: t = m·z·F/(M·I). Example silver plating: for 1.00 g of silver (M = 107.9 g/mol, z = 1) at I = 0.50 A you need Q = m·z·F/M = 1.00·96,485/107.9 ≈ 894 C, so t = Q/I = 894/0.50 ≈ 1790 s, about 30 minutes. The calculation also shows why industrial electrolysis needs enormous currents: a single mole of aluminium (27 g, z = 3) requires almost 290,000 C; even at 1000 A that takes nearly five minutes. Real processes take longer because the current efficiency is below 100 %, for example due to side reactions such as hydrogen evolution.

Wherever current deposits or decomposes substances. In electroplating they determine the layer thickness in chrome, zinc or gold plating: charge, area and density fix the thickness exactly. Copper refining deposits high-purity copper (over 99.99 %) from anode copper; aluminium production uses molten-salt electrolysis with gigantic current demand. In water electrolysis for green hydrogen the law links charge and gas volume: 2·96,485 C produce one mole of H₂, about 24.8 L at room conditions. In analytics, coulometry measures amounts of substance directly via the charge, and when charging batteries the same relation describes the material turnover at the electrodes.