Electrolysis and Faraday’s Law Formulas

Faraday’s law formulas for electroplating: the mass deposited by a current in a time, the coating thickness on an area and the time for a target thickness.

The formulas

M is the molar mass of the metal in g/mol, I the current in amperes, t the time in seconds, z the number of electrons per ion, F = 96,485 C/mol the Faraday constant and η the current efficiency as a fraction. ρ is the density of the metal in g/cm³ and A the plated area in cm². The result is the mass in grams and the thickness in cm, which the page turns into micrometres. The formula assumes an even coating, and real plating is thicker at the edges and corners. The efficiency, the current and the area here are examples.

Worked example: copper at 10 A for 1 h with a current efficiency of 95%

1. At 100% efficiency, m = 63.55 × 10 × 3,600 / (2 × 96,485) = 11.86 g
2. At 95%, m = 11.86 × 0.95 = 11.26 g
3. On 100 cm², th = 11.26 / (8.96 × 100) = 125.7 µm

Worked example: the time to plate 25 µm of copper on 100 cm² at 10 A

1. m = 25 × 10⁻⁴ cm × 100 cm² × 8.96 g/cm³ = 2.24 g
2. t = 2.24 × 2 × 96,485 / (63.55 × 10 × 0.95) = 716 s, which is 11.93 min

Mass deposited by one ampere-hour at 100% efficiency

Frequently asked questions

Why is the efficiency below 100%?

Some of the current goes into side reactions, such as the release of hydrogen, so less metal is deposited than the law gives.

Why does the charge number matter?

A metal that needs two electrons per ion deposits half the mass of the same moles that need one. The mass is inversely proportional to z.

Is the coating even?

No. The current density is higher at the edges and the corners, so those parts plate faster. A shield, an auxiliary anode or a pulse supply can improve it.

Does the formula work for other processes?

Yes. It holds for any electrolysis, such as refining, anodising or the production of hydrogen, with the molar mass, the charge number and the efficiency of that process.

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