ChemBench

Nernst Equation Calculator

Standard electrode potentials tell you the starting point — the Nernst equation tells you what really happens.

E° (standard cell potential)

Electrons transferred (n)

Temperature

Reaction quotient (Q)

Cell potential E

1.159

What you entered

E° (standard cell potential): 1.1Electrons transferred (n): 2Temperature: 298Reaction quotient (Q): 0.01

1
ln(Q)
ln(0.01)= -4.6052
2
RT ÷ (nF)
(8.314 × 298) ÷ (2 × 96485)= 0.0128
3
E = E° − (RT/nF)·ln(Q)
1.1 − -0.0591= 1.1591 V

Result

Cell potential E: 1.159

At 298 K with Q = 0.01, the cell potential is 1.159 V (standard E° = 1.1 V).

Cell potential away from standard conditions

The Nernst equation corrects the standard cell potential for actual concentrations. Excess product lowers the voltage; excess reactant raises it.

E standard	Electrons (n)	Temperature	Q	Cell potential
1.10 V	2	298.15 K	0.01	1.1592 V
1.10 V	2	298.15 K	1	1.1000 V
1.10 V	2	298.15 K	100	1.0408 V
1.10 V	1	298.15 K	0.1	1.1592 V
1.10 V	2	350 K	0.01	1.1694 V
0.34 V	2	298.15 K	1	0.3400 V

At Q = 1 the correction term vanishes and the cell sits at its standard potential. A cell reaches equilibrium, and stops producing current, when Q rises far enough to drive the potential to zero.

Why standard conditions aren't enough

Standard electrode potentials (E°) are measured at 25°C, 1 M concentrations, and 1 atm — real batteries and electrochemical cells almost never operate under those conditions. The Nernst equation adjusts E° for actual concentrations and temperature, predicting the real voltage a cell produces.

The link to Gibbs free energy

The Nernst equation connects electrochemistry to thermodynamics: E = E° − (RT/nF)ln(Q). When Q = K (equilibrium), E = 0 and the battery is dead. When Q < K, the reaction is spontaneous (positive E) and the cell produces electricity.

Frequently asked questions

A Zn/Cu cell has E° = 1.10 V. With [Zn²⁺] = 0.01 M and [Cu²⁺] = 1.0 M at 25°C, what is E?

E = 1.10 - (0.02569/2) × ln(0.01/1.0) = 1.10 - 0.01285 × (-4.605) = 1.10 + 0.059 = 1.16 V. The non-standard concentrations increase the cell potential slightly.

How is the Nernst equation related to the Gibbs free energy calculator?

ΔG = -nFE, so a positive cell potential means negative ΔG (spontaneous). At equilibrium, E = 0 and ΔG = 0. The Nernst equation and Gibbs free energy describe the same thermodynamic reality from different angles.

What happens to cell potential as a battery discharges?

As the reaction proceeds, reactant concentrations drop and product concentrations rise, increasing Q. The Nernst equation shows E decreasing as Q approaches K, until E = 0 at equilibrium — the battery is dead.