Faraday's Law of Electrolysis
Relates electric charge to mass deposited
Understanding Faraday's Law of Electrolysis
Faraday's law of electrolysis, formulated by Michael Faraday in 1834, establishes a quantitative relationship between the amount of electric charge passed through an electrolytic cell and the mass of substance deposited or dissolved at the electrodes. This fundamental principle revolutionized electrochemistry and laid the groundwork for modern electroplating, metal refining, battery technology, and quantitative electroanalytical chemistry. The law states that the mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity (charge) passed through the circuit.
The mathematical expression m = (Q × M) / (n × F) elegantly connects electrical and chemical quantities. The Faraday constant (F = 96,485 C/mol) represents the charge carried by one mole of electrons and serves as a bridge between the macroscopic world of grams and amperes and the microscopic world of atoms and electrons. Understanding this relationship allows chemists to precisely control deposition rates in electroplating, calculate current efficiency in industrial electrolysis, and determine the number of electrons transferred in redox reactions through coulometric analysis.
In practice, Faraday's law has countless applications: from producing pure metals like copper and aluminum through electrorefining, to electroplating jewelry and automotive parts, to manufacturing chemicals like chlorine and sodium hydroxide via the chlor-alkali process. The law also underpins the operation of batteries and fuel cells, where controlled electron transfer generates electrical energy from chemical reactions. Modern applications include nanomaterial synthesis, corrosion protection, and electroanalytical techniques for determining metal concentrations in environmental and biological samples.
Formula
m = (Q × M) / (n × F)
m = mass deposited (g)
Q = total charge (C) = I × t
M = molar mass (g/mol)
n = electrons per ion
F = 96,485 C/mol (Faraday constant)
I = current (A), t = time (s)
Detailed Step-by-Step Example
Problem: A current of 2.00 A is passed through aqueous CuSO₄ for 30.0 minutes. Calculate the mass of copper deposited at the cathode.
Step 1: Identify known values
Current I = 2.00 A
Time t = 30.0 min × 60 s/min = 1800 s
Ion: Cu²⁺, so n = 2 electrons per ion
Molar mass of Cu: M = 63.546 g/mol
Faraday constant: F = 96,485 C/mol
Step 2: Calculate total charge (Q)
Q = I × t = 2.00 A × 1800 s = 3600 C
Step 3: Apply Faraday's law
m = (Q × M) / (n × F)
m = (3600 C × 63.546 g/mol) / (2 × 96,485 C/mol)
m = 228,765.6 / 192,970 g/mol
m ≈ 1.186 g
Answer: Approximately 1.19 g of copper is deposited at the cathode.
Common Valence States (n values)
n = 1
Ag⁺, Na⁺, K⁺, H⁺
n = 2
Cu²⁺, Zn²⁺, Pb²⁺, Ni²⁺
n = 3
Al³⁺, Fe³⁺, Cr³⁺, Au³⁺
Key Applications
Electroplating
Control thickness of metal coatings by calculating mass deposited from current and time. Used in jewelry, automotive parts, and corrosion protection.
Metal Refining
Purify metals like copper through electrorefining. Impure copper anodes dissolve, and pure copper deposits at cathodes with precise mass control.
Quantitative Analysis
Coulometry uses Faraday's law to determine metal concentrations by measuring charge required for complete electrodeposition.
Notes & Pitfalls
- Use correct valence n; for Ag⁺, n = 1; for Al³⁺, n = 3.
- Ensure molar mass M corresponds to the deposited species.
- Account for efficiency if the process is not 100% current efficient.