Nernst Equation
Calculate cell potential under non-standard conditions.
Adjusts voltage for concentration and temperature.
The Formula
E = E° - (RT / nF) × ln(Q)
At 25°C: E = E° - (0.0592 / n) × log₁₀(Q)
At 25°C: E = E° - (0.0592 / n) × log₁₀(Q)
The Nernst equation adjusts the standard cell potential for real-world conditions. When concentrations are not 1 M or pressures are not 1 atm, this formula gives the actual voltage.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| E | Cell potential under actual conditions | Volts (V) |
| E° | Standard cell potential | Volts (V) |
| R | Gas constant (8.314 J/mol·K) | J/(mol·K) |
| T | Temperature | Kelvin (K) |
| n | Number of electrons transferred | (unitless) |
| F | Faraday's constant (96,485 C/mol) | C/mol |
| Q | Reaction quotient [products]/[reactants] | (unitless) |
Example 1
Zn-Cu cell (E° = 1.10 V, n = 2) with [Cu²⁺] = 0.01 M and [Zn²⁺] = 1.0 M at 25°C
Q = [Zn²⁺] / [Cu²⁺] = 1.0 / 0.01 = 100
E = 1.10 - (0.0592/2) × log₁₀(100)
= 1.10 - 0.0296 × 2
= 1.04 V
Example 2
At equilibrium (E = 0), find the equilibrium constant K for the Zn-Cu cell
0 = 1.10 - (0.0592/2) × log₁₀(K)
log₁₀(K) = 1.10 / 0.0296 = 37.16
K = 10³⁷·¹⁶ ≈ 1.45 × 10³⁷
When to Use It
Use the Nernst equation when:
- Calculating actual battery voltage at non-standard concentrations
- Predicting cell potential during discharge (as concentrations change)
- Relating cell potential to the equilibrium constant
- Designing concentration cells and pH meters