Nernst Equation
E = E° - (RT/nF)ln(Q) or E = E° - (0.0592/n)log(Q) at 25°C
The Nernst equation calculates cell potential under non-standard conditions by accounting for concentration effects. It shows how cell voltage changes with reaction quotient Q.
Variables
Potential under actual conditions in volts
Potential at standard conditions in volts
8.314 J/(mol·K)
Temperature in Kelvin
Number of moles of electrons in balanced equation
96485 C/mol
[products]/[reactants] at current conditions
Example Calculation
Scenario
For Zn|Zn2+(0.10 M)||Cu2+(2.0 M)|Cu with E° = 1.10 V, calculate E at 25°C.
Given Data
Calculation
Q = [Zn2+]/[Cu2+] = 0.10/2.0 = 0.050; E = 1.10 - (0.0592/2)log(0.050) = 1.10 - (0.0296)(-1.30)
Result
E = 1.10 + 0.038 = 1.14 V
Interpretation
The actual cell potential (1.14 V) is higher than standard (1.10 V) because Q < 1, meaning the reaction has further to go to reach equilibrium.
When to Use This Formula
- ✓Calculating cell potential at non-standard concentrations
- ✓Finding equilibrium constant from E°
- ✓Understanding concentration cells
- ✓Predicting effect of concentration on cell voltage
Common Mistakes
- ✗Using wrong n (must match balanced equation)
- ✗Getting Q upside down (products over reactants)
- ✗Confusing ln and log (factor of 2.303)
- ✗Forgetting to include all species in Q
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Common questions about this formula
At equilibrium, E = 0 and Q = K. So 0 = E° - (RT/nF)ln(K), giving E° = (RT/nF)ln(K), or at 25°C: E° = (0.0592/n)log(K). This connects electrochemistry to thermodynamics.
A concentration cell has identical electrodes with different concentrations. E° = 0, but E > 0 due to concentration difference. Voltage drives ion migration until concentrations equalize (Q approaches 1).