Nernst Equation & Cell Potential
Build a galvanic cell from two half-reactions to get the standard cell potential, ΔG° and whether it runs spontaneously — then apply the Nernst equation to find the potential at any concentration, pressure or temperature.
How to use this tool
The Standard cell tab combines two standard reduction potentials into a cell; the Nernst tab corrects that potential for non-standard conditions. The "Apply Nernst" button carries E° and n across in one click.
What to enter
- Cathode: the half-reaction that is reduced (gains electrons) — usually the more positive E°.
- Anode: the half-reaction that is oxidised (its potential is subtracted).
- Nernst tab: E° (V), the electrons transferred n, the reaction quotient Q, and temperature (K).
Reading the result
E°cell = E°(cathode) − E°(anode). A positive E°cell (negative ΔG°) means the cell reaction is spontaneous as written. In the Nernst tab, E shifts by RT·ln10/(nF) — about 0.0592/n V — per ten-fold change in Q at 25 °C.
Worked example
Daniell cell: cathode Cu²⁺/Cu (+0.34 V), anode Zn²⁺/Zn (−0.76 V) → E°cell = +1.10 V, spontaneous, ΔG° ≈ −212 kJ.
Result
E°cell is the maximum voltage at standard conditions; the Nernst equation tells you the live voltage as the cell discharges and Q changes.
Methodology
Standard cell
The standard cell potential is E°cell = E°(cathode) − E°(anode), using tabulated standard reduction potentials (vs the standard hydrogen electrode). Standard free energy is ΔG° = −nFE°cell with F = 96 485 C/mol; a positive E°cell gives a negative ΔG° and a spontaneous reaction. n is the electrons transferred in the balanced cell reaction (the lowest common multiple of the two half-reaction electron counts).
Nernst equation
E = E° − (RT/nF) ln Q. At 25 °C this is E = E° − (0.0592/n) log₁₀ Q. Q is the reaction quotient in the same form as the equilibrium constant.
Sources
- CRC Handbook / IUPAC standard electrode (reduction) potentials at 25 °C.
- Atkins, P. & de Paula, J. Physical Chemistry — electrochemistry.
Known limits
- Standard potentials are 25 °C, aqueous, unit-activity values; real cells deviate with temperature, ionic strength and junction potentials.
- Q uses concentrations as a proxy for activities (ideal-dilute assumption).