Faraday Electrolysis Calculator

Calculate charge, time, and mass for electrolytic cells using Faraday's laws.

Calculate

Current I (A) (A)

Time t (min) (min)

Molar mass M (g/mol) (g/mol)

Ni=58.7, Cu=63.5, Ag=107.9

Electrons n

Ni2+→Ni: n=2, Cu2+→Cu: n=2

Target mass (g) — for time/current modes (g)

Please check your inputs and try again.

Electrons as a Reagent

Faraday's law treats charge as a stoichiometric quantity. One mole of electrons is 96,485 coulombs, and the number of electrons each ion requires determines how much substance a given charge deposits.

m = (M × I × t) / (n × F)

Metal	Ion	n	Grams per faraday (96,485 C)
Silver	Ag⁺	1	107.9
Copper	Cu²⁺	2	31.8
Nickel	Ni²⁺	2	29.4
Aluminium	Al³⁺	3	9.0

That last column explains a great deal about industrial practice. Aluminium requires three electrons per atom and has low molar mass, so producing it electrolytically consumes enormous charge — roughly 13 kWh per kilogram. This is why aluminium smelters are built next to hydroelectric plants, and why recycling aluminium saves about 95% of the energy.

Solving for Time or Current

The equation rearranges in whichever direction is needed. Industrially the target is usually a coating thickness, so time is the unknown: t = mnF/(MI). Coating thickness converts to mass through the deposit area and the metal's density.

Real deposits fall short of the calculated mass because current efficiency is below 100% — some current evolves hydrogen instead. Multiply the theoretical mass by the efficiency to get the realistic figure.

Worked Examples

Example 1: Nickel plating: 5A, 30min, Ni

m=58.7×5×1800/(2×96485)

Result: m=2.74g deposited

Industrial nickel plating rate

Example 2: Deposit 1g Cu in 10min: find current

I=1×2×96485/(63.5×600)

Result: I=5.07A required

Current density calculation for plating bath design

Example 3: Coating thickness to time

Deposit 5 μm of nickel over 100 cm², density 8.9 g/cm³, at 2 A

Result: Mass = 0.445 g, t = 731 s ≈ 12 min

Volume is 0.05 cm³, giving 0.445 g. Then t = mnF/(MI) with n = 2 and M = 58.7.

Example 4: Why aluminium is energy intensive

Al³⁺ requires 3 faradays per mole, M = 27

Result: Only 9.0 g per faraday

Three electrons for a light atom means enormous charge per kilogram. Recycling avoids this entirely, saving about 95% of the energy.

Common Mistakes

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Using minutes or hours directly

An ampere is one coulomb per second, so time must be in seconds. Using minutes inflates the answer by a factor of 60.

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Forgetting the electron count

Copper from Cu²⁺ needs two electrons per atom while silver needs one. Omitting n or using the wrong value gives an answer wrong by a whole factor.

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Assuming 100% current efficiency

Some current is consumed by hydrogen evolution and side reactions. Real deposits are lighter than calculated, typically by 2 to 10% in well-run baths.

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Using the wrong oxidation state

Copper can plate from Cu⁺ or Cu²⁺. The bath chemistry determines n, and using the wrong one halves or doubles the answer.

Frequently Asked Questions

Industrial electroplating process?

Anode: dissolves to replenish metal ions. Cathode: workpiece receives deposit. Bath: metal salt solution (copper sulfate, nickel sulfate). Current density 1-5 A/dm² typical. Additive agents control deposit quality.

Coulometer application?

A coulometer is an electrolytic cell used to measure charge precisely by weighing deposited metal. Silver coulometer: deposit Ag from AgNO3, weigh. Q=m×nF/M. Historical measurement standard before electronic coulometers.

What is the Faraday constant?

96,485 coulombs per mole of electrons — Avogadro's number multiplied by the elementary charge. It converts electrical charge into moles of substance.

Why does aluminium production use so much electricity?

Each aluminium ion needs three electrons and the atom is light, so only 9 grams are deposited per faraday. Producing a kilogram consumes roughly 13 kWh.

How do I calculate plating time for a given thickness?

Convert thickness and area to volume, multiply by density for mass, then use t = mnF/(MI).

Why is the actual deposit lighter than calculated?

Current efficiency is below 100%. Some charge evolves hydrogen or drives side reactions rather than depositing metal.

Formula Explorer connections

Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.

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