How this instrument works
Faraday's law of electrolysis says the mass deposited or dissolved at an electrode is set by the charge that passes through the cell and by how much of that charge each ion actually needs. Push a known current for a known time and you know the charge, I·t, in coulombs. Divide by the Faraday constant, F ≈ 96,485.332 coulombs per mole of electrons, and you have the moles of electrons delivered. Divide again by the valence n — the electrons each ion swaps to plate out — and you have moles of metal; multiply by molar mass and the answer is a mass on a scale, not an abstraction.
The formula's shape follows directly from that chain of reasoning: m = ItM ⁄ (nF). Charge in, moles of electrons out, moles of substance out, grams out — four unit conversions strung end to end, none of them adjustable. Faraday arrived at this in 1834 without knowing electrons existed; he measured that the same charge always released the same chemical equivalent weight, and later physics simply explained why — each ion genuinely does trade a fixed number of electrons for a fixed number of atoms.
The equation assumes every electron that crosses the electrode goes into the reaction you're counting, which real cells rarely deliver perfectly. In aqueous copper plating, some current is lost to hydrogen evolving at the cathode instead of copper depositing, so plants apply a measured current efficiency — often 95 to 98 percent for acid copper baths — on top of this ideal figure. Faraday's number is the ceiling; the plating shop's meter tells you how close production gets to it.
- Enter the cell's Current in amperes — the steady reading off the power supply or rectifier.
- Set Time to how long that current runs, in seconds, minutes, or hours.
- Enter the Molar mass, g ⁄ mol of the metal being deposited or dissolved — 63.546 for copper, 107.868 for silver.
- Set Valence (electrons transferred) to the ion's charge number — 2 for Cu²⁺, 1 for Ag⁺, 3 for Al³⁺.
- Read Mass deposited, g — the theoretical yield, at 100 percent current efficiency.
Worked example — copper plating for one hour
Run 2 A through a copper sulfate bath for exactly one hour: t = 3600 s. Charge passed is I·t = 7200 coulombs. Copper's molar mass is M = 63.546 g ⁄ mol and Cu²⁺ carries valence n = 2, so m = (2 × 3600 × 63.546) ⁄ (2 × 96,485.33212) = 2.37098836656 g — call it 2.371 g of copper plated onto the cathode.
That figure is exactly what a hobbyist electroplater or a school electrochemistry lab measures on a lab balance after an hour-long run at 2 A, which is why Faraday's 1834 result is still the reference calculation stamped into electroplating handbooks — modern rectifiers and modern balances have only made it easier to confirm.
Questions
What is the Faraday constant and where does 96,485 come from?
It's the charge carried by one mole of electrons, F = 96,485.33212 coulombs per mole. Since the 2019 redefinition of the SI, it is an exact value: the elementary charge e (1.602176634×10⁻¹⁹ C) multiplied by the Avogadro constant N_A (6.02214076×10²³ per mole). Before 2019 it was measured; now it is fixed by definition.
Why does the valence n matter so much to the result?
Valence n is how many electrons each ion trades to plate out — 1 for Ag⁺, 2 for Cu²⁺, 3 for Al³⁺. The same charge buys fewer moles of a high-valence metal, because each atom costs more electrons. Double n and, all else equal, the deposited mass halves; get n wrong and every answer downstream is wrong by that same factor.
Does the calculator account for real-world current efficiency?
No, it returns the ideal, 100 percent efficient mass that Faraday's law predicts. Real electrolytic cells lose some current to side reactions, commonly hydrogen evolution at the cathode in aqueous baths, so measured deposits usually run a few percent under this figure. Industrial platers multiply the ideal mass by a measured efficiency factor, often 0.90 to 0.98, to plan bath time.
Can I use this for metals other than copper, like silver or nickel?
Yes, change Molar mass, g ⁄ mol and Valence (electrons transferred) to match the ion. Silver (Ag⁺) uses M = 107.868, n = 1; nickel (Ni²⁺) uses M = 58.693, n = 2; trivalent chromium uses M = 51.996, n = 3. The Current and Time fields work the same way regardless of which metal is depositing.
Why do current and time combine as a simple product, I times t?
Because what actually drives the chemistry is charge, not current or time separately, and charge is current integrated over time. At constant current that integral collapses to the product I·t, in coulombs. Doubling the time deposits exactly as much extra metal as doubling the current would, because both double the same underlying charge.
What did Faraday actually measure in 1834 to find this law?
He passed identical charge through different electrolytic cells wired in series and weighed what each deposited or released. The masses always matched the ratio of their chemical equivalent weights — proof that a fixed quantity of electricity always does a fixed amount of chemical work, decades before anyone knew that quantity was a count of electrons.