Faraday's Laws

Electrolysis is the process of using electrical energy to drive a non-spontaneous chemical reaction. When an ionic compound is melted or dissolved in water, its ions become free to move and can be directed by an applied voltage to electrodes, where they undergo oxidation or reduction. Michael Faraday, working in the 1830s, was the first scientist to quantitatively relate the amount of substance deposited or liberated at an electrode to the quantity of electric charge passed through the electrolyte. His findings, known as Faraday's Laws of Electrolysis, remain cornerstones of electrochemistry today. Faraday's First Law states that the mass of a substance deposited or dissolved at an electrode is directly proportional to the total electric charge passed through the solution. Faraday's Second Law states that for the same quantity of charge, the masses of different substances deposited are proportional to their equivalent masses (molar mass divided by the number of electrons transferred per ion). Together, these two laws allow chemists and engineers to predict precisely how much product will form during electroplating, metal refining, chlorine production, and many other industrial processes. Understanding Faraday's Laws requires a firm grasp of several interconnected ideas: electric charge (measured in coulombs), electric current (measured in amperes), time, the Faraday constant, moles of electrons, and the stoichiometry of half-reactions. This article develops each idea step by step, culminating in worked calculations that mirror the types of problems you will encounter in your chemistry examinations.

Key takeaways
  • Electric Charge and Current
  • The Faraday Constant
  • Faraday's First Law
  • Faraday's Second Law
  • Half-Reactions and Stoichiometry
  • Industrial Applications

Electric Charge and Current

Electric current (I) is the rate of flow of charge. The relationship is Q = I × t, where Q is the total charge in coulombs (C), I is the current in amperes (A), and t is the time in seconds (s). For example, a current of 2 A flowing for 500 s delivers Q = 2 × 500 = 1000 C. This is the foundational quantity that links electrical measurements to chemical change.

The Faraday Constant

One mole of electrons carries a charge of 96 485 C, a value called the Faraday constant, F. This is derived from Avogadro's number (6.022 × 10²³ electrons mol⁻¹) multiplied by the charge of one electron (1.602 × 10⁻¹⁹ C). In calculations, F is rounded to 96 500 C mol⁻¹ or simply 96 485 C mol⁻¹. So if Q coulombs pass through an electrolyte, the number of moles of electrons transferred is: n(e⁻) = Q / F.

Faraday's First Law

The mass (m) of substance deposited at an electrode is directly proportional to the charge (Q) passed: m ∝ Q. Mathematically, m = (M × Q) / (n × F), where M is the molar mass of the substance (g mol⁻¹), n is the number of electrons required per atom or formula unit in the half-reaction, and F is the Faraday constant. Doubling the charge doubles the mass deposited, provided everything else stays constant. This is why electroplating baths are run for controlled times at controlled currents.

Faraday's Second Law

When the same charge Q is passed through different electrolytes in series, the masses deposited are proportional to their equivalent masses. The equivalent mass of a substance is its molar mass divided by the number of electrons involved in its half-reaction: E = M / n. So for copper (M = 63.5, n = 2): E = 31.75 g equiv⁻¹; for silver (M = 107.9, n = 1): E = 107.9 g equiv⁻¹. For the same charge, the ratio of masses deposited equals the ratio of equivalent masses. This law emphasises that it is the number of electrons, not the mass of the atom, that determines how much material is deposited.

Half-Reactions and Stoichiometry

Always write the half-reaction first to determine n. For copper plating from copper(II) sulfate solution, the cathode half-reaction is: \ce{Cu^{2+}(aq) + 2e^{-} -> Cu(s)}, so n = 2. For aluminium smelting from molten Al₂O₃, the cathode half-reaction is: \ce{Al^{3+} + 3e^{-} -> Al}, so n = 3. The full formula m = (M × I × t) / (n × F) combines both laws and current-time data into one practical equation.

Industrial Applications

Faraday's Laws underpin major industries. The chlor-alkali process electrolyses brine (NaCl solution) to produce chlorine gas, hydrogen gas, and sodium hydroxide simultaneously. Electroplating uses Faraday's First Law to deposit a precise thickness of metal (e.g., gold, chromium) onto a substrate. The Hall–Héroult process for aluminium production operates at ~100 000 A and uses Faraday's Laws to calculate daily aluminium output. Electrorefining of copper produces 99.99% pure copper for electrical wiring, with impurities falling as 'anode mud'.

The Key Equation

m=M×I×tn×Fm = \frac{M \times I \times t}{n \times F}
  • m — Mass deposited (g): Mass of substance produced or consumed at the electrode
  • M — Molar mass (g mol⁻¹): Mass of one mole of the substance being deposited or dissolved
  • I — Current (A (amperes)): Steady electric current flowing through the electrolytic cell
  • t — Time (s (seconds)): Duration for which the current flows; note Q = I × t
  • n — Number of electrons (dimensionless): Electrons transferred per ion in the electrode half-reaction (e.g., n = 2 for Cu²⁺)
  • F — Faraday constant (C mol⁻¹): Charge carried by one mole of electrons; F = 96 485 C mol⁻¹

Worked Example

Problem. A current of 3.00 A is passed through a solution of copper(II) sulfate for 40.0 minutes. (a) Calculate the mass of copper deposited at the cathode. (b) If the same charge is simultaneously passed through a silver nitrate solution, calculate the mass of silver deposited. (Molar masses: Cu = 63.5 g mol⁻¹, Ag = 107.9 g mol⁻¹; F = 96 485 C mol⁻¹)

m(Cu)=2.37 g,m(Ag)=8.05 gm(\text{Cu}) = 2.37\text{ g},\quad m(\text{Ag}) = 8.05\text{ g}

Answer. Mass of copper deposited = 2.37 g; Mass of silver deposited = 8.05 g

Figure
Diagram
Electrolytic Cell — Faraday's LawsCuSO₄(aq) ElectrolyteCathode (−)Anode (+)Cu²⁺Cu²⁺Cu²⁺SO₄²⁻SO₄²⁻Cu(s)depositedCu²⁺ + 2e⁻ → CuCu → Cu²⁺ + 2e⁻Power Supplye⁻ →← e⁻Faraday's First Law: m ∝ Q = I × tm = (M × I × t) / (n × F)F = 96 485 C mol⁻¹ | n = electrons per ion in half-reaction
Origins · 1 minMichael Faraday and how this was discovered
MF
Michael Faraday
1791–1867 · British

Faraday formulated his two quantitative laws of electrolysis in 1833–1834, published in his Experimental Researches in Electricity. He coined the terms electrode, anode, cathode, electrolyte, and ion — vocabulary still used daily by chemists. He also discovered electromagnetic induction and the laws of electromagnetism, laying the groundwork for electric motors and generators. Faraday had no formal university education and began his scientific career as a bookbinder's apprentice. He taught himself chemistry by reading the books he was binding, then wrote to the great chemist Humphry Davy asking for a job — and was hired as Davy's laboratory assistant at the Royal Institution.

  • Half-Reactions and Electrode Processes — Faraday's Laws require writing the correct cathode or anode half-reaction to determine n, the number of electrons transferred per ion.
  • Electrolysis: Setup and Products — Understanding which products form at each electrode (discharge of ions) is the qualitative foundation on which Faraday's quantitative laws are applied.
  • Galvanic Cells and Standard Electrode Potentials — Electrolytic cells are the reverse of galvanic cells; the same half-reactions appear in both, and the Faraday constant is central to energy calculations in both types of cell.
  • The Mole and Molar Mass — Converting between moles of electrons, moles of atoms deposited, and mass in grams is essential for every Faraday's Laws calculation.
  • Electric Current and Charge (Q = It) — The relationship Q = I × t is the starting point of every Faraday calculation; it links the physics of electric circuits to the chemistry of electrolysis.