Electrolysis & Faraday's Laws
Ions carry the current and deposit matter.
Lesson at a glanceShow the key points
- Cations move to the cathode, anions to the anode; matter is liberated at the electrodes.
- First law: m = Zit (33.7); second law: m ∝ chemical equivalent A/v.
- m = EQ/K, K = e/m_u = 9.6485 × 10⁷ C/kg (33.8).
- F = 96 485 C/mol; one faraday liberates one gram-equivalent.
- Voltameters measure charge by the mass deposited.
In a solution, current is carried by ions rather than electrons, and as they give up their charge at the electrodes, matter is deposited. Faraday found exactly how much.
How an electrolyte conducts
Solutions of salts, dilute acids and bases conduct electricity. Such a liquid is an electrolyte, and its container with electrodes is an electrolytic cell. Current enters through the anode and leaves through the cathode.
Take silver nitrate solution with silver electrodes. Some AgNO₃ molecules split into ions: Ag⁺ (a positive ion, a cation) and NO₃⁻ (a negative ion, an anion). With a battery connected, the field in the solution points from anode to cathode, so cations drift to the cathode and anions to the anode.
- At the cathode: Ag⁺ + e → Ag. Silver is deposited.
- At the anode: NO₃⁻ → NO₃ + e; the NO₃ reacts with the anode’s silver to form AgNO₃, which dissolves. Silver leaves the anode.
The solution’s concentration stays the same; silver is simply moved from anode to cathode. Every electron the anode receives passes round through the battery to the cathode, so the charge through the circuit equals the charge given up at each electrode. This process, chemical change driven by a current, is electrolysis.
Faraday’s laws
- The mass of a substance liberated at an electrode is proportional to the charge passed.
- For a given charge, the mass liberated is proportional to the substance’s chemical equivalent.
What steady current deposits 1.20 g of copper in 1.5 h? (ECE of copper = 3.29 × 10⁻⁷ kg/C.)
Verifying the laws
First law: weigh a clean cathode, pass current i₁ for time t, wash, dry and weigh again; repeat with i₂. You find m₁/m₂ = i₁/i₂, and at fixed current m₁/m₂ = t₁/t₂, so m ∝ it.
Second law: put a copper cell (CuSO₄) and a silver cell (AgNO₃) in series so the same current flows through both. The deposits satisfy m₁/m₂ = E₁/E₂.
Why: the ionic picture
An ion of valency v carries charge ve. If charge Q passes, N = Q/ve ions are neutralised, each of mass A mu (A = relative atomic mass, mu = 1.6605 × 10⁻²⁷ kg):
So K = e/mu = 1.6022 × 10⁻¹⁹ / 1.6605 × 10⁻²⁷ = 9.6485 × 10⁷ C/kg: Faraday’s laws follow from charge coming in lumps of e.
A current of 0.50 A flows through a silver voltameter for 40 min. How much silver is deposited? (Z for silver = 1.118 × 10⁻⁶ kg/C.)
The silver voltameter above is in series with a copper voltameter. How much copper is deposited?
Voltameters
Since i = m/Zt, weighing a deposit measures a current or a charge. Used this way an electrolytic cell is a voltameter (or coulombmeter).
- Copper voltameter (routine lab use): CuSO₄ in water (about 1:4 by weight); a central copper cathode between two joined copper anodes, so both faces of the cathode are coated.
- Silver voltameter (high accuracy, standards labs): AgNO₃ solution (1:5 to 1:6) in a platinum cup that is the cathode; a silver anode in the middle inside a porous porcelain cup that keeps anode impurities away.
- 1Electrolytes conduct by ions: cations to the cathode, anions to the anode.
- 2First law: m = Zit (33.7). Second law: m ∝ chemical equivalent A/v.
- 3Combined: m = EQ/K, K = e/m_u = 9.6485 × 10⁷ C/kg (33.8).
- 4Faraday constant 96 485 C/mol; one faraday liberates one gram-equivalent.
- 5Voltameters measure charge by weighing the deposit.
Check yourself
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