Faraday's Laws of Electrolysis
Faraday's laws of electrolysis, formulated by Michael Faraday in 1833–1834, quantitatively describe the relationship between the amount of substance deposited or dissolved at an electrode and the quantity of electric charge passed through the electrolyte. The first law states that the mass of substance liberated is directly proportional to the charge passed; the second law states that for a given charge, the masses of different substances liberated are proportional to their equivalent masses. Together, these laws enable the precise calculation of the amount of product formed in any electrolytic process.
Key Formula
m = (I × t × M) / (n × F)
LaTeX: m = \frac{Q \cdot M}{n \cdot F} = \frac{I \cdot t \cdot M}{n \cdot F}
| Symbol | Meaning | Unit |
|---|---|---|
| m | Mass of substance deposited | g |
| I | Current | A (amperes) |
| t | Time | s (seconds) |
| M | Molar mass of substance | g mol⁻¹ |
| n | Number of electrons in the half-reaction | mol |
| F | Faraday constant (96485) | C mol⁻¹ |
Worked Example
Problem
A current of 2.0 A is passed through a solution of CuSO₄ for 30 minutes. Calculate the mass of copper deposited at the cathode. (M_Cu = 63.5 g mol⁻¹, n = 2, F = 96485 C mol⁻¹)
Solution
Step 1: Convert time to seconds: t = 30 × 60 = 1800 s Step 2: Calculate charge: Q = I × t = 2.0 × 1800 = 3600 C Step 3: Apply Faraday's law: m = Q × M / (n × F) = 3600 × 63.5 / (2 × 96485) Step 4: m = 228600 / 192970 = 1.185 g
Answer
m ≈ 1.19 g of copper
Faraday's Two Laws of Electrolysis Summary
| Law | Statement | Mathematical Form | Key Variable |
|---|---|---|---|
| First Law | Mass ∝ charge passed | m ∝ Q | Charge Q (coulombs) |
| Second Law | Mass ∝ equivalent mass | m ∝ M/n | Equivalent mass M/n |
| Combined | Both laws unified | m = ItM/(nF) | All variables |
| Faraday constant F | 1 mole of electrons = 96485 C | F = N_A × e | 96485 C mol⁻¹ |
Interactive Tools
PhET Electrolysis Simulation
Visualise electrolysis and observe mass deposition with changing current and time
Open ToolKhan Academy – Faraday's Laws
Lessons and problem sets on Faraday's first and second laws with worked examples
Open ToolWolfram Alpha – Electrolysis Calculation
Compute mass deposited using Faraday's law with numeric inputs
Open Tool
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Related Terms
Electrolysis
Electrolysis is a process in which an electric current is passed through an electrolyte (an ionic compound in solution or molten state) to drive non-spontaneous chemical reactions, decomposing the electrolyte into its constituent elements or ions at the electrodes. At the cathode, cations are reduced by gaining electrons, while at the anode, anions are oxidised by losing electrons. Electrolysis has wide industrial applications including the production of chlorine and sodium hydroxide (chlor-alkali process), extraction of aluminium (Hall–Héroult process), electroplating, and water splitting to produce hydrogen fuel.
Electrolytic Cell
An electrolytic cell is an electrochemical device that uses an external electrical energy source to drive non-spontaneous redox reactions, converting electrical energy into chemical energy. Unlike a galvanic cell, the anode is connected to the positive terminal of the power supply and the cathode to the negative terminal, and oxidation still occurs at the anode while reduction occurs at the cathode. Electrolytic cells are used industrially in processes such as electroplating, electro-refining of metals, chlor-alkali production, and the electrolysis of water.
Galvanic Cell
A galvanic cell (also called a voltaic cell) is an electrochemical device that converts chemical energy into electrical energy through spontaneous redox reactions occurring at two electrodes separated by an electrolyte. The oxidation half-reaction occurs at the anode (negative terminal) and the reduction half-reaction occurs at the cathode (positive terminal), with electrons flowing through an external circuit. Galvanic cells are the basis of all batteries and are fundamental to understanding energy storage and conversion in chemistry.
Named after Michael Faraday (1791–1867), the English chemist and physicist who discovered electromagnetic induction and formulated the laws of electrolysis in 1833. "Faraday" as a unit (F) honours his contribution to electrochemistry.