Nernst Equation – IIT‑JEE (Main + Advanced) Study Notes
Key Idea – The Nernst equation connects the electrochemical potential (cell voltage) with the thermodynamics of the reaction and the concentrations (activities) of the reacting species.
For a redox reaction at temperature T
[ E = E^{\circ} - \frac{RT}{nF}\ln Q ] where Q is the reaction quotient, n the number of electrons transferred, R the gas constant, F Faraday’s constant, and E the cell potential.
1. Thermodynamic Background
| Symbol | Meaning | Units |
|---|---|---|
| ΔG | Gibbs free‑energy change of the reaction | J·mol⁻¹ |
| ΔG° | Standard Gibbs free‑energy change (all species at 1 M, 1 atm, 298 K) | J·mol⁻¹ |
| n | Number of electrons transferred in the balanced redox equation | mol e⁻⁻¹ |
| E | Actual cell potential (vs. a standard electrode) | V |
| E° | Standard cell potential | V |
| Q | Reaction quotient | dimensionless |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ | J·mol⁻¹·K⁻¹ |
| F | Faraday’s constant = 96485 C mol⁻¹ | C·mol⁻¹ |
1.1. Fundamental Relations
-
Electrochemical work
[ \Delta G = -nFE ] The free‑energy change equals the electrical work that can be extracted, n electrons transferred through a potential E. -
Thermodynamics of a reaction
[ \Delta G = \Delta G^{\circ} + RT\ln Q ] The Gibbs free energy at any condition is