Electrolysis

You’ll be able to

Contrast electrolytic and galvanic cells in terms of ΔG and applied voltage
Apply Faraday's laws to relate charge, moles of electrons, and mass deposited
Calculate the mass or amount of product formed during an electrolysis

Forcing a reaction uphill

An electrolytic cell is a galvanic cell run in reverse: an external power supply pushes electrons the "wrong" way to drive a nonspontaneous reaction (ΔG > 0, E° < 0). Electrolysis is how we plate metals, purify copper, and split water or molten salts into their elements. The labels persist — oxidation is still at the anode, reduction still at the cathode — but the power source now sets the direction of electron flow.

Electrons are countable, and so is charge

Deposition is stoichiometry with electrons as a reactant. Faraday's laws say the amount of substance transformed at an electrode is proportional to the total electric charge passed. Charge is current × time (Q = I·t, coulombs = amperes × seconds), and one mole of electrons carries 96 485 C — the Faraday constant, F. Divide charge by F to get moles of electrons, then use the half-reaction's electron ratio to reach moles of product.

Faraday's laws of electrolysis

moles e⁻ = Q ÷ F = (I·t) ÷ 96 485

Then scale by the half-reaction: e.g. Ag⁺ + e⁻ → Ag needs 1 mol e⁻ per mol Ag, while Al³⁺ + 3e⁻ → Al needs 3 mol e⁻ per mol Al.

Worked example

A current of 2.00 A flows for 965 s through a solution of Ag⁺. How many grams of silver (107.87 g·mol⁻¹) plate out at the cathode? The half-reaction is Ag⁺ + e⁻ → Ag.

1.Total charge: Q = I·t = (2.00 A)(965 s) = 1930 C.
2.Moles of electrons: n(e⁻) = Q ÷ F = 1930 C ÷ 96 485 C·mol⁻¹ = 0.0200 mol e⁻.
3.The half-reaction shows 1 electron per silver ion, so moles Ag = 0.0200 mol.
4.Mass = 0.0200 mol × 107.87 g·mol⁻¹ = 2.16 g.

Answer: 2.16 g of silver.

Checkpoint

How many moles of electrons are required to deposit 1 mol of aluminum from molten Al³⁺ (Al³⁺ + 3e⁻ → Al)?

Checkpoint

Which statement correctly distinguishes an electrolytic cell from a galvanic cell?

Watch out

A doubly or triply charged ion needs proportionally more charge to deposit. Producing 1 mol of Cu from Cu²⁺ takes 2 mol e⁻; 1 mol of Al from Al³⁺ takes 3 mol e⁻. Always read the electron count straight from the balanced half-reaction.

On the exam

The classic Faraday problem gives current and time and asks for mass. Chain the units without skipping steps: A × s = C, then C ÷ 96 485 = mol e⁻, then ÷ electrons-per-ion = mol product, then × molar mass = grams. Carrying units through each arrow prevents the most common errors.

Answer the 2 checkpoints as you read.