Faraday's Law Calculator (Electrolysis)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
Faraday's law gives m = (I × t × M) ÷ (n × F), where F is Faraday's constant (96,485 C/mol). For a copper deposit with a 2 A current over 5000 seconds, the mass deposited is about 3.29 g.
Explanation
Electrolysis uses an electric current to drive a chemical reaction that wouldn't happen spontaneously, notably depositing a metal on a surface (electroplating, gilding, silvering) or dissolving it. Faraday's laws precisely relate the amount of substance deposited or dissolved to the amount of electricity that passed through the solution: the stronger the current and the longer the electrolysis runs, the greater the total electric charge transported (Q = I × t), and so the greater the mass of substance transformed, in a strictly proportional relationship. The number of electrons exchanged per ion (n) reflects the charge of the metal ion involved: a copper ion Cu²⁺ needs 2 electrons to be reduced to metallic copper, versus just one for a silver ion Ag⁺, meaning that at equal electric charge, electrolysis deposits more silver atoms than copper atoms (though the final mass also depends on each metal's molar mass). Faraday's constant (96,485 C/mol) represents the electric charge carried by one mole of electrons, a conversion bridge between the macroscopic world of measurable electric current and the microscopic world of the number of charged particles involved in the reaction — the same kind of bridge Avogadro's number establishes between a measurable mass and a number of particles, already used in our molar concentration calculator. The real yield of an industrial electrolysis generally stays below 100%, a gap quantified by our reaction yield calculator.
Example: copper deposit, 2 A over 5000 seconds
Inputs
Current: 2 A. Duration: 5000 s. Molar mass (Cu): 63.55 g/mol. Electrons exchanged (Cu²⁺): 2.
Calculation
Q = 2 × 5000 = 10,000 C. m = (10,000 × 63.55) ÷ (2 × 96,485) = 635,500 ÷ 192,970 ≈ 3.2933 g.
Result
This electrolysis deposits about 3.29 g of copper.
Frequently asked questions
Why does the number of electrons exchanged differ from one metal to another?
It depends on the charge of the metal ion involved in the reaction, itself determined by the element's electron configuration: copper commonly occurs as the Cu²⁺ ion (needing 2 electrons to be reduced to metallic copper), silver as the Ag⁺ ion (just 1 electron), and aluminum as the Al³⁺ ion (3 electrons). This value is found in electrochemical data tables for each element and its oxidation state considered.
At equal electric charge, why does the mass deposited differ by metal?
Because the mass deposited depends both on the number of electrons needed per ion (n) and the metal's molar mass (M): a metal with a high molar mass but requiring few electrons per ion (like silver) gets deposited in a greater mass, at equal electric charge, than a lighter metal requiring more electrons per ion.
Does this law also apply to the electrolysis of water?
Yes, the same principle applies to any electrochemical reaction, including the electrolysis of water to produce hydrogen and oxygen gas: the amount of gas produced at each electrode stays proportional to the total electric charge transported, with a number of electrons exchanged specific to each half-reaction (2 electrons to produce one molecule of hydrogen gas, for example).