Electrolysis Calculator

Background.

Electrolysis counts atoms by counting electrons. Every copper ion that plates out of a copper sulfate bath needs two electrons from the cathode, every silver ion one, every aluminium ion three, and an electric current is nothing more than a steady flow of electrons. Measure the current and the time and you know how many electrons went through the cell; divide by the number each ion needs and you know how many atoms were deposited. Michael Faraday worked out the proportionality in the 1830s, and it still sets the arithmetic for electroplating, copper refining, aluminium smelting and hydrogen production.

The bridge between electrical charge and chemical amount is the Faraday constant, the charge carried by one mole of electrons: 96,485.33 coulombs. One ampere flowing for an hour delivers 3,600 coulombs, so a mole of electrons takes about 26.8 ampere-hours. That is why plating shops and refineries think in ampere-hours. Depositing a kilogram of copper from a Cu²⁺ bath takes about 844 of them, and making a kilogram of hydrogen by splitting water about 26,590.

The answer is a theoretical ceiling. It assumes every electron does the intended job, which is 100% current efficiency. In a real cell some of the current goes on side reactions, most often hydrogen bubbling off the cathode alongside the metal, so the mass you weigh comes out lower. Comparing the two is how platers measure the efficiency of a bath.

Getting z right matters as much as the current. Copper plated from an acid sulfate bath arrives as Cu²⁺, but in cyanide baths it is Cu⁺, so the same charge deposits twice as much metal. The inputs are in SI units throughout: amperes, seconds and kilograms per mole, with the result in kilograms.

What is electrolysis calculator?

Electrolysis uses an external current to drive a chemical reaction that would not happen on its own: metal ions gain electrons and deposit on the cathode, or a compound such as water is split into its elements. Faraday's laws state that the amount of substance changed is proportional to the charge passed, and that for a given charge the mass depends on the molar mass divided by the number of electrons each formula unit takes. The result here is that mass for a perfectly efficient cell.

How to use this calculator.

1. 01Enter the cell Current in amperes, using the average if it drifted during the run, since only the total charge, amperes multiplied by seconds, affects the answer.
2. 02Enter the Duration in seconds, multiplying hours by 3,600 or minutes by 60.
3. 03Enter the Molar mass in kilograms per mole, which is the familiar grams-per-mole figure divided by 1,000: copper's 63.546 g/mol becomes 0.063546.
4. 04Enter z, the electrons transferred per atom or molecule formed: 2 for Cu²⁺, Ni²⁺ or Zn²⁺, 1 for Ag⁺, 3 for Al³⁺, and 2 per molecule of hydrogen gas.
5. 05Read the mass in kilograms, multiplying by 1,000 for grams, and expect the real deposit to be somewhat lower.

The formula.

m = I × t × M ÷ (z × F). The product I × t is the electric charge in coulombs. Dividing by the Faraday constant F = 96,485.3321 C/mol converts that charge into moles of electrons, dividing again by z converts electrons into moles of the substance, and multiplying by the molar mass M gives kilograms. F is not an empirical fit: since the 2019 redefinition of the SI it is exactly the Avogadro constant times the elementary charge, and the page uses that CODATA value. Mass rises in direct proportion to current, time and molar mass and falls in inverse proportion to z, so halving z doubles the deposit. Every input must be positive. Voltage, temperature, concentration and electrode size do not appear; they decide how well the reaction runs, not how much a given charge can deposit.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC Gold Book, Faraday laws of electrolysis.
2. [2]NIST, 2022 CODATA Recommended Values of the Fundamental Physical Constants.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.