This electrolysis calculator applies Faraday’s laws: charge passed (current × time) becomes moles of electrons, and moles of electrons — divided by the electrons per ion in the half-reaction — become grams of metal deposited, grams dissolved, or gas evolved.

–

Faraday’s Two Laws in One Chain

Faraday’s first law: deposited mass is proportional to charge passed. Second law: for a fixed charge, masses are proportional to molar mass divided by ion charge (the “chemical equivalent”). Both fuse into one chain: Q = I·t → moles e⁻ = Q / 96,485 (the Faraday constant, one mole of electrons’ charge) → moles product = moles e⁻ / n → grams = moles × M. The defaults electroplate copper from Cu²⁺ at 2 A for an hour: Q = 7,200 C = 0.0746 F → 0.0373 mol Cu → 2.37 g of copper. Every electroplating thickness spec, chlor-alkali tonnage and aluminum smelter’s energy bill runs on this chain — Hall–Héroult cells pass hundreds of thousands of amps precisely because grams-per-coulomb is so stingy (a single amp-hour deposits just 1.19 g of copper).

The n input carries the chemistry: Ag⁺ needs 1 electron (107.87 g per Faraday — silver plates FAST), Cu²⁺ 2, Al³⁺ 3 (aluminium’s 8.99 g per Faraday explains the industry’s power hunger: a tonne of Al requires ~3 million amp-hours before efficiency losses). Gases read off the same chain: water electrolysis at the defaults’ charge would evolve 0.0373 mol H₂ (0.84 L at STP — note H₂’s n = 2 as well) at the cathode and half that of O₂ at the anode. Competing reactions are the real-world footnote: aqueous NaCl gives H₂, not Na, at the cathode because water wins the reduction contest — Faraday counts electrons faithfully, but the half-reaction you feed it must be the one that actually runs (potentials, via the Nernst page, referee that contest).

Worked Examples (Verified)

  • Copper plating (defaults): 2 A × 3,600 s → 2.371 g Cu.
  • Silver’s speed: same charge, Ag⁺ (n = 1, M 107.87): 0.0746 mol → 8.05 g Ag — 3.4× the copper mass, the equivalent-weight effect in one line.
  • Chromium’s patience: hard-chrome from Cr⁶⁺ (n = 6): one Faraday plates only 52.00/6 = 8.67 g (silver gets 107.87 g) — why chrome plating is slow, hot and inefficient in practice.

Electrolysis Discipline

  • n is the electrons in the HALF-REACTION as written (Cu²⁺ + 2e⁻ → Cu: n = 2; 2H₂O + 2e⁻ → H₂ + 2OH⁻: n = 2 per H₂) — recount when the product is a molecule built from multiple ions.
  • Current efficiency is real: quote Faraday output as theoretical; multiply by the cell’s measured efficiency (plating shops track it) for production numbers.
  • Seconds, not minutes, feed Q = I·t — this calculator takes minutes for convenience and converts; manual problems die on this unit more than any other.
  • Series cells share the same charge: the same Q plates proportional equivalents in every cell of the string — the basis of coulometer measurements.
  • Voltage doesn’t enter Faraday’s mass law at all (it sets energy cost and which reactions run) — a 3 V and a 30 V supply at equal current deposit equal mass.

Related Tools

Frequently Asked Questions

How do you calculate mass from electrolysis?

m = (I × t × M) / (n × F), with F = 96,485 C/mol. Defaults — 2 A, 60 min, Cu²⁺ (n = 2, M = 63.55): (2 × 3,600 × 63.55)/(2 × 96,485) = 2.37 g. This calculator walks the chain — charge, moles of electrons, moles of product, grams — and adds the STP gas volume when relevant.

What is the Faraday constant?

96,485 coulombs per mole of electrons — Avogadro’s number of elementary charges (6.022 × 10²³ × 1.602 × 10⁻¹⁹ C). It is the exchange rate between the electrical world (amps, seconds) and the chemical world (moles). One “faraday” of charge deposits exactly one mole-equivalent: M/n grams of any substance.

Why does silver plate faster than copper at the same current?

Equivalent weight: Ag⁺ takes ONE electron and weighs 107.87 g/mol, so each Faraday plates 107.87 g of silver; Cu²⁺ takes two electrons, so a Faraday plates 63.55/2 = 31.78 g of copper. Ratio ≈ 3.4× — Faraday’s second law. The defaults’ 7,200 C would plate 8.05 g Ag vs 2.37 g Cu.

How much gas does electrolysis of water produce?

From the same chain: moles H₂ = Q/(2F) at the cathode, moles O₂ = Q/(4F) at the anode — a 2:1 volume ratio. 7,200 C → 0.0373 mol H₂ = 0.84 L at STP and 0.42 L O₂. Multiply moles by 22.414 L for STP volume, or use PV = nRT at your conditions.

What is current efficiency?

The fraction of charge doing the intended reaction. Real cells lose charge to side reactions (water decomposition, re-dissolution, oxide formation) and heat; well-run plating baths achieve 90–98%, hard chrome famously 15–25%. Faraday’s law gives the 100% benchmark; production math multiplies by the measured efficiency.

Does voltage affect how much is deposited?

Not in the mass law — only current × time sets the amount. Voltage decides WHICH reactions are thermodynamically driven (the cell must exceed the decomposition potential), how fast side reactions intrude, and the energy bill (power = V × I). Two cells at 2 A deposit identically whether run at 3 V or 30 V; the 30 V one just wastes ten times the energy as heat.

How is plating thickness calculated?

Mass from Faraday → volume via density → thickness = volume ÷ area. Example: 2.37 g Cu (density 8.96 g/cm³) over 50 cm² → 0.265 cm³ → 0.0053 cm ≈ 53 µm. Uniformity assumptions flatter real parts (edges plate thicker — current density concentrates there), but the Faraday average is the spec’s starting point.

Is this electrolysis calculator free?

Yes — free, instant, no sign-up. Enter current, time, electrons per ion and molar mass for the deposited mass, charge in coulombs and faradays, and gas volume.