Nernst Equation Calculator
Find a cell’s potential under non-standard conditions from E°, the electrons transferred, the reaction quotient, and temperature.
Correction term (E − E°): +0 V from the RT ÷ nF · ln Q shift.
The Nernst equation gives cell potential away from standard state: E = E° − (RT ÷ nF) ln Q. For a Daniell cell (E° = 1.10 V, n = 2) at 25 °C with Q = 10, E = 1.10 − (0.05916 ÷ 2) × 1 = 1.070 V. When Q = 1 the log term is zero, so E = E°.
What the Nernst equation does
Standard cell potentials (E°) assume every species is at 1 M concentration or 1 bar pressure. Real cells rarely sit at those conditions, and as a battery runs the concentrations shift. The Nernst equation corrects E° for the actual mix of reactants and products, captured by the reaction quotient Q, and for temperature T. The correction is the term −(RT ÷ nF) ln Q: it is zero at standard state (Q = 1), positive when reactants dominate (Q < 1), and negative once products build up (Q > 1).
R = 8.314 J·mol⁻¹·K⁻¹, F = 96485 C/mol, n = electrons transferred; at 25 °C this becomes E = E° − (0.05916 ÷ n) log₁₀ Q
Worked example
A Daniell cell has E° = 1.10 V and transfers n = 2 electrons. It runs until the reaction quotient reaches Q = 10, at 298.15 K (25 °C).
- 1 Gather E°, n, Q, and T. Here E° = 1.10 V, n = 2, Q = 10, T = 298.15 K. Q is products over reactants, each raised to its coefficient.
- 2 Pick the right form. At 25 °C the RT ÷ F factor collapses to 0.05916 V, so E = E° − (0.05916 ÷ n) log₁₀ Q. For any other temperature keep the full RT ÷ nF · ln Q term.
- 3 Compute the correction. (0.05916 ÷ 2) × log₁₀(10) = 0.02958 × 1 = 0.02958 V.
- 4 Subtract from E°. E = 1.10 − 0.02958 = 1.070 V. Because Q > 1, products have accumulated and E has dropped below E°.
How Q shifts the potential (n = 1, 25 °C)
Each tenfold change in Q moves a one-electron cell by 0.05916 V; divide by n for multi-electron cells.
| Reaction quotient Q | log₁₀ Q | Potential shift (E − E°) |
|---|---|---|
| 0.1 | −1 | +0.0592 V |
| 1 | 0 | 0 V |
| 10 | +1 | −0.0592 V |
What happens as the cell runs
A working cell consumes reactants and makes products, so Q climbs from its starting value toward the equilibrium constant K. Each rise in Q pushes the −(RT ÷ nF) ln Q term more negative, so E falls steadily. When Q finally equals K the cell reaches equilibrium, the correction exactly cancels E°, and E = 0 — the battery is dead. Reading it backward, the Nernst equation also links E° to K: at equilibrium 0 = E° − (RT ÷ nF) ln K.