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Faraday's Law of Electrolysis Calculator

Applies Faraday's laws of electrolysis: from current and time it computes the charge passed, moles of electrons, moles and mass of substance deposited or evolved (m = Q·M / (z·F)), or, for a target mass, the electrolysis time required at the given current.

When to use

You need how much metal is plated or gas is evolved by a current over a time, or how long an electrolysis must run at a given current to produce a target mass.

Do not use when: The current efficiency is well below 100% (side reactions such as hydrogen evolution reduce the real yield), or you need the cell voltage rather than the amount of product (use nernst-equation).

Formula

Q = I × t; n_e = Q / F; n = n_e / z; m = n × M = I × t × M / (z × F) with F = 96485.33212 C/mol; time for a target mass: t = m × z × F / (M × I)

Assumes 100% current efficiency (all charge goes into the stated product) and a constant current; real plating baths typically run at 90–98% efficiency.

Inputs

ParameterTypeUnitRequiredDescription
current_anumberAyesConstant electrolysis current in amperes. Range: > 0
timenumbernoDuration of electrolysis in time_unit. Leave empty to solve it from target_mass_g. Range: > 0
time_unitenum: seconds | minutes | hoursdefault secondsUnit of the time input.
electrons_per_ionintegeryesMoles of electrons per mole of product: Ag⁺ → Ag 1, Cu²⁺ → Cu 2, Al³⁺ → Al 3, 2H⁺ → H2 2, 2H2O → O2 4, 2Cl⁻ → Cl2 2. Range: ≥ 1, ≤ 12
formulastringnoFormula of the substance deposited or evolved (Ag, Cu, Al, H2, O2, Cl2) for its molar mass. Alternative to molar_mass_g_mol.
molar_mass_g_molnumberg/molnoMolar mass of the substance; use instead of formula when it is already known. Range: > 0, ≤ 10000000
target_mass_gnumbergnoMass of product wanted; when given, the calculator solves the time needed at current_a (the time input is ignored). Range: > 0

Outputs

OutputTypeUnitDescription
charge_cnumberCQ = I × t.
moles_electronsnumbermolQ / F (F = 96 485.33 C/mol).
moles_substancenumbermolmoles_electrons / z.
mass_gnumbergmoles_substance × molar mass.
gas_volume_stp_lnumberLmoles_substance × 22.414 L/mol; meaningful only for gaseous products such as H2, O2 or Cl2.
time_snumbersElectrolysis time in seconds.
time_minnumberminElectrolysis time in minutes.
time_hnumberhElectrolysis time in hours.
molar_mass_g_molnumberg/molMolar mass of the product used.
solved_forstringmass_g (from current and time) or time_s (from target mass).

Example

Silver plating at 10.23 A for 1 hour: {"current_a":10.23,"time":1,"time_unit":"hours","electrons_per_ion":1,"formula":"Ag"} → {"charge_c":36828,"moles_electrons":0.381695,"moles_substance":0.381695,"mass_g":41.1735,"time_s":3600,"molar_mass_g_mol":107.87,"solved_for":"mass_g"}

Time to deposit 10.0 g of copper at 5.0 A: {"current_a":5,"electrons_per_ion":2,"formula":"Cu","target_mass_g":10} → {"moles_substance":0.157366,"moles_electrons":0.314733,"charge_c":30367.08,"time_s":6073.42,"time_min":101.224,"time_h":1.68706,"solved_for":"time_s"}

GET https://tttkmbb.com/api/v1/calculate/faraday-electrolysis?current_a=10.23&time=1&time_unit=hours&electrons_per_ion=1&formula=Ag

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FAQ

How do I choose z?

z is the number of electrons per atom or molecule of product in the half-reaction: the ion charge for metals (Cu²⁺ + 2e⁻ → Cu gives 2), 2 for H2 or Cl2, 4 for O2 from water.

What if the current is not constant?

Use the total charge instead: enter the average current and the total time, since Q = ∫I dt; a coulometer reading divided by any time gives the equivalent constant current.

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