Last updated: 2026-06-16

Understanding Faraday's law of electrolysis

When an electric current flows through an electrolyte, ions are reduced or oxidised at the electrodes and matter is deposited or liberated. Michael Faraday showed in the 1830s that the amount of substance that reacts is set entirely by the electric charge passed:

Here the charge is itself the current multiplied by the time, $Q = I \, t$, so a steady current of $I$ amperes for $t$ seconds passes $I \, t$ coulombs.

The Faraday constant $F$ is the charge carried by one mole of electrons. Dividing the charge by $n \, F$ gives the moles of substance that reacted, and multiplying by the molar mass converts moles to a mass.

Worked example

A copper electroplating cell runs at $I = 2\ \text{A}$ for 30 minutes. How much copper deposits? Copper plates from $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}$, so $n = 2$, and its molar mass is $M = 63.55\ \text{g/mol}$.

First the charge passed, with the time in seconds ($30\ \text{min} = 1800\ \text{s}$):

Then the moles of copper deposited:

Finally the mass:

So roughly 1.19 g of copper plates out.

Why the charge sets the mass

Each ion that arrives at the electrode collects a fixed number of electrons from the circuit. Reducing one $\text{Cu}^{2+}$ ion takes two electrons; reducing one $\text{Ag}^+$ ion takes one. So the number of ions deposited is the number of electrons supplied divided by $n$, and the number of electrons supplied is just the total charge divided by the charge on a single electron. Counting in moles instead of individual particles, the moles deposited equal $Q / (n \, F)$. Nothing about the electrode area, the voltage, or the concentration enters the count — only the charge that has flowed.

The effect of valence

Because $n$ sits in the denominator, an ion that needs more electrons yields less metal for the same charge. The table below shows the mass deposited by 3,600 C of charge for three common plating metals.

Silver, needing only one electron per ion, deposits far more mass per coulomb than aluminium even though aluminium is the lighter element.

Using the law in practice

In electroplating and electrorefining the law works in both directions. Given a current and time you can predict the coating mass, and dividing that mass by the plated area and the metal's density gives the coating thickness. Run the calculation backwards and you can size the current or set the run time needed to hit a target mass. Real cells fall a little short of the ideal because some charge drives side reactions such as gas evolution; the fraction of charge that actually deposits the wanted product is called the current efficiency.