Nernst Equation Calculator
Calculate the actual cell potential E at non-standard concentrations using the Nernst equation.
Works at any temperature.
The Nernst equation gives the cell potential under non-standard conditions (concentrations ≠ 1 mol/L).
General form:
E = E° − (RT/nF) × ln Q
At 25°C (simplified):
E = E° − (0.05916/n) × log Q
Where:
- E° = standard cell potential (V)
- R = 8.314 J/mol·K
- T = temperature (K)
- n = moles of electrons transferred
- F = 96,485 C/mol (Faraday constant)
- Q = reaction quotient (same form as K, but with current concentrations)
At equilibrium: E = 0, Q = K, so:
0 = E° − (RT/nF) ln K
E° = (RT/nF) ln K = (0.05916/n) log K at 25°C
Examples:
-
Daniell cell (Zn|Zn²⁺||Cu²⁺|Cu), E° = 1.10 V, n = 2: If [Zn²⁺] = 2.0 M and [Cu²⁺] = 0.50 M: Q = [Zn²⁺]/[Cu²⁺] = 4 E = 1.10 − (0.05916/2) × log(4) = 1.10 − 0.0178 = 1.082 V
-
Concentration cell (same metal, different concentrations): E° = 0, so E = −(0.05916/n) × log([low]/[high]) = (0.05916/n) × log([high]/[low])
Biological applications: The Nernst equation is used to calculate membrane potential in nerve and muscle cells. The resting potential (−70 mV) across a neuron membrane results from different K⁺ and Na⁺ concentrations inside and outside the cell.