Electrolysis Calculator – Faraday's Laws, Electrolysis Cells and Electroplating
Electrolysis uses an electric current to drive a reaction that would not run on its own: copper plating out of a blue solution, water splitting into hydrogen and oxygen, aluminium smelted from its oxide. How much forms is set by the charge alone. This calculator applies Faraday's laws of electrolysis in three ways: one product solved for any variable, every product of a classic electrolysis cell, and the time, thickness or current of an electroplating job.
Faraday's two laws
Michael Faraday published his laws of electrolysis in 1833–34. The first says the mass formed at an electrode is proportional to the charge passed. The second says that the same charge forms different substances in proportion to their molar mass divided by the electrons each needs, M/z. Together they give m = I·t·M / (z·F). A charge of 900 C, from 0.500 A for 30 minutes, deposits 0.2964 g of copper but only 0.0839 g of aluminium, because aluminium is light and needs three electrons per atom.
The mole of electrons
The Faraday constant, F = 96 485 C/mol, is the charge on one mole of electrons: Avogadro's number times the charge of one electron. Dividing a charge by F turns coulombs into moles of electrons, and the rest is ordinary stoichiometry, shown in the tool as a chain from current and time to grams or litres.
Finding z: where most mistakes happen
z is the number of electrons per formula unit of the product, read from its half-reaction, not the charge printed on a nearby ion. Cu²⁺ + 2e⁻ → Cu gives z = 2. Each O₂ molecule needs 4 electrons. Hard chromium is plated from chromic acid, where chromium starts at +6, so it takes 6 electrons per atom. Gold and copper from cyanide baths are held as +1 and need only 1, and tin from a stannate bath needs 4. The Molar mass solve identifies an unknown metal from a measured deposit.
What forms at each electrode
A molten salt can only give its own ions: molten sodium chloride gives sodium and chlorine. In water there is competition. Concentrated brine gives chlorine rather than oxygen because chloride is abundant and oxygen evolution needs a large overpotential. Zinc can be deposited from acid, below hydrogen in the series, because hydrogen evolves slowly on zinc. The Electrolysis cell tab draws these classic setups.
Water splitting and the 2 : 1 ratio
In a Hoffman voltameter, each H₂ molecule takes 2 electrons and each O₂ gives up 4, so the same charge makes twice as many moles of hydrogen. At the same conditions that is twice the volume. Gas collected over water also holds water vapour; switch on the wet-gas correction under custom conditions, or use the Dalton's Law Calculator for the full treatment.
Industry and energy
Chlor-alkali plants, aluminium smelters and copper refineries follow the same arithmetic. The electrical energy is E = V·Q: at an illustrative 3.0 V, a tonne of chlorine takes about 2270 kWh. The thermodynamic minimum voltage comes from the Standard Cell Potential Calculator.
Electroplating thickness and time
Platers work in current density, j = I/A, usually in A/dm². At a fixed current density the thickness grows at a rate that does not depend on the part's area: δ = η·j·t·M / (z·F·ρ). Current efficiency η matters: an acid copper bath runs near 100 %, while a hard chrome bath turns most of its current into hydrogen. A handy rule of thumb is the charge per micrometre per square decimetre, which the tool reports in A·h.
Not to be confused with Faraday's law of induction
Faraday's law of induction is about a changing magnetic flux inducing a voltage, a different law with the same name. For that, use the Faraday's Law EMF Calculator.
The formulas
Q = I · t charge passed (C)
n(e⁻) = η · Q / F F = 96 485.33212 C/mol
n = n(e⁻) / z z from the half-reaction
m = n · M = η·I·t·M / (z·F)
V(gas) = n · V_m
δ = η · j · t · M / (z · F · ρ) plating thickness