Electrolysis and Faraday's Law

Finds how much substance an electrolysis deposits. The charge passed is converted to moles of electrons, divided by the charge on the ion, and multiplied by the molar mass. The charge carried by one mole of electrons is the Faraday constant.

The amount of substance deposited at an electrode is exactly proportional to the charge passed. Faraday established this.

There are three steps. Current and time give the charge, the charge gives the moles of electrons, and dividing by the charge on the ion gives the moles of substance.

n_e = \dfrac{I t}{F} \qquad n = \dfrac{n_e}{z} \qquad w = n M

$I$ is the current in amperes and $t$ the time in seconds
$F$ is the Faraday constant, 96485 C/mol
$n_e$ is the moles of electrons and $n$ the moles deposited
$z$ is the charge on the ion, $M$ the molar mass and $w$ the mass deposited

The Faraday constant is the charge carried by one mole of electrons. It is the elementary charge times the Avogadro constant, and since both are defined values, $F$ is exact.

Dividing by the charge on the ion reflects how many electrons are needed to turn one ion back into an atom. A copper ion carries a charge of 2, so two electrons make one copper atom.

Example

The default input passes 2 A for 60 minutes to deposit copper.

The charge is $2 \times 3600$ , or 7200 C. The moles of electrons are $7200 \div 96485$ , about 0.07462 mol.

Copper's charge of 2 halves that to about 0.03731 mol of copper. Multiplying by the molar mass of 63.55 gives about 2.371 g.

Checking against silver

One ampere for one hour deposits about 4.0248 g of singly charged silver.

That figure has history. The ampere was once defined as the current depositing 0.001118 g of silver per second. Over 3600 seconds that is 4.0248 g, matching the calculation exactly and confirming the formula against the experimental definition itself.

Points to watch

The calculation assumes every electron goes into the intended reaction. In practice side reactions such as the electrolysis of water consume some of the current and reduce the deposit. That fraction is the current efficiency, which in plating may sit in the nineties or considerably lower.

Time is entered in minutes and converted to seconds internally. Mixing the units up throws the answer out by a factor of 60.

Plating, the electrolytic refining of copper and the smelting of aluminium all rest on this law. Aluminium smelting is so power-hungry because its ions carry a charge of 3 and its molar mass is small, and both work against you.