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Faraday's Law Calculator

Calculate the mass of substance deposited or dissolved during electrolysis using Faraday's law: m = (I x t x M) / (n x F), where F = 96,485 C/mol.

Common Electrolysis Ions Reference

Faraday’s law of electrolysis

Faraday’s law is the stoichiometry of electrolysis: it counts electrons the same way you count moles of a reactant. The quantitative form is m = (I × t × M) / (n × F), where I is current, t is time, M is the molar mass of the deposited or dissolved species, n is the number of electrons in the relevant half-reaction, and F is 96,485 C/mol — the charge of one mole of electrons.

The logic underneath the equation is straightforward. I × t gives total charge in coulombs. Divide by F to convert that charge into moles of electrons. Divide by n to convert moles of electrons into moles of the chemical species (each ion needs n electrons to be reduced or oxidized). Multiply by M to get mass. The single-line formula collapses all four steps. The same expression works at the cathode, where cations are reduced and metal plates out, and at the anode, where neutral atoms are oxidized and dissolve; only the half-reaction (and therefore n and M) changes.

What the calculator does

  1. Enter current in amperes.
  2. Enter the run time and pick the unit; the calculator converts to seconds.
  3. Enter n from the half-reaction. Common ions are listed in the reference table.
  4. Enter the molar mass of the species being deposited or dissolved.
  5. The output is mass in grams, with each step shown: total charge, moles of electrons, moles of substance, mass.

Worked examples

Copper electroplating. 3.00 A through CuSO4 for 2.00 hours.

  • Half-reaction: Cu^2+ + 2e- → Cu, so n = 2, M = 63.546 g/mol
  • t = 2.00 × 3600 = 7200 s
  • m = (3.00 × 7200 × 63.546) / (2 × 96,485) = 7.10 g Cu

Silver electroplating. 1.50 A through AgNO3 for 30 minutes.

  • Half-reaction: Ag+ + e- → Ag, so n = 1, M = 107.868 g/mol
  • t = 1800 s
  • m = (1.50 × 1800 × 107.868) / (1 × 96,485) = 3.02 g Ag

Aluminum production (Hall–Héroult). 100,000 A for 24 hours in molten cryolite.

  • Half-reaction: Al^3+ + 3e- → Al, so n = 3, M = 26.982 g/mol
  • t = 86,400 s
  • m = (100,000 × 86,400 × 26.982) / (3 × 96,485) = 805.6 kg Al

The aluminum case is why smelters draw enormous current: n = 3 means three electrons per atom, and the molar mass is small, so the kg-per-coulomb yield is low and you compensate with raw current.

Frequently Asked Questions

What is Faraday's law of electrolysis?
Faraday's law says the mass deposited or dissolved at an electrode is proportional to the total charge passed. Quantitatively, m = (I × t × M) / (n × F), where I is current in amperes, t is time in seconds, M is molar mass in g/mol, n is the number of electrons in the half-reaction, and F is the Faraday constant, 96,485 C/mol. Charge is the bridge between the electrical side and the chemical side.
What is Faraday's constant?
F is the charge carried by one mole of electrons: 96,485 coulombs per mole. It is the product of Avogadro's number (6.022 × 10^23 electrons/mol) and the elementary charge (1.602 × 10^-19 C/electron). Whenever you convert moles of electrons into coulombs (or vice versa) in an electrochemistry problem, F is the conversion factor.
How do you determine n (electrons transferred) for electrolysis?
n is read directly from the half-reaction at the electrode of interest. Cu^2+ + 2e- → Cu has n = 2. Ag+ + e- → Ag has n = 1. Al^3+ + 3e- → Al has n = 3. For polyatomic processes like the oxidation of water at the anode (2H2O → O2 + 4H+ + 4e-), n equals the electrons in the balanced half-reaction, which is 4 here.
What is the relationship between current, charge, and time?
Charge in coulombs equals current in amperes times time in seconds: Q = I × t. One ampere is one coulomb per second by definition. So 3.0 A flowing for 2.0 hours delivers 3.0 × 7200 = 21,600 C. That total charge, divided by F, gives the moles of electrons that crossed the electrode interface during the run.
Can Faraday's law predict the volume of gas produced in electrolysis?
Yes — Faraday's law gives moles of gas, then PV = nRT gives volume. For water electrolysis, 2 moles of electrons reduce to 1 mole of H2 at the cathode (2H+ + 2e- → H2), and 4 moles of electrons oxidize to 1 mole of O2 at the anode. So the H2:O2 mole ratio is 2:1, matching the stoichiometry of water itself.