Mastering Faraday's Laws of Electrolysis Simply

Faraday's laws of electrolysis quantify exactly how much substance is deposited or liberated when electric current passes through an electrolyte. First law: the mass deposited is proportional to the quantity of electricity passed. Second law: the same charge deposits masses proportional to the substances' equivalent weights.

These laws turn electrolysis from a qualitative observation into an industrial calculation — they size electroplating baths, aluminium smelters, and copper refineries, and they underpin coulometry, the technique of analysing substances by counting electrons.

Key Concepts

• 1 faraday (F) = 96485 C = the charge carried by one mole of electrons.
• Equivalent weight E = molar mass / n-factor, where n is the electrons gained or lost per ion (Cu2+ + 2e− → Cu has n = 2).
• First law: w ∝ Q, i.e. w = ZQ, where Z = E/96500 is the electrochemical equivalent.
• Second law: passing the same Q through different cells deposits masses in the ratio of their equivalent weights.
• Real cells have current efficiency below 100% because of side reactions, so the laws give the theoretical maximum.

Formulas

• w = (E × I × t) / 96500, with w in grams, I in amperes, t in seconds, E the equivalent weight.
• Q = I × t (coulombs = amperes × seconds).
• Assumptions: 100% current efficiency and a single electrode reaction.

Worked Example

How much copper plates out when 2.0 A flows for 30 minutes through CuSO4 solution? Reaction: Cu2+ + 2e− → Cu.

1. t = 30 × 60 = 1800 s; Q = I × t = 2.0 × 1800 = 3600 C.
2. Equivalent weight of copper: E = 63.5/2 = 31.75 g per equivalent.
3. w = (31.75 × 3600)/96500 = 114300/96500 = 1.18 g.
4. Check by moles of electrons: 3600/96500 = 0.0373 mol e− → 0.0187 mol Cu → 0.0187 × 63.5 = 1.18 g. Both routes agree.

Common Misconceptions

• "Higher current always means proportionally more metal." Only with time fixed — and side reactions (like H2 evolution) can steal current, lowering efficiency.
• "One faraday deposits one mole of any metal." One faraday supplies one mole of electrons; the metal deposited is 1/n moles, where n is the ion's charge number.
• "Faraday's laws apply to galvanic cells." They describe the charge–mass relationship in electrolysis; galvanic cells are analysed with ΔG = −nFE instead.

Real-World Applications

• Electroplating: jewellers compute plating time for a target gold thickness from w = EIt/96500.
• Aluminium extraction: Hall–Héroult cells run at hundreds of kiloamperes, with output predicted by Faraday's laws.
• Copper electrorefining: impure anodes dissolve and pure copper cathodes grow at Faraday-law rates.

Faraday's laws are chemistry's currency exchange between electricity and matter: count the coulombs, divide by 96500, multiply by the equivalent weight — and you know exactly how many grams the current has built.