Nernst Equation Calculator: Cell Potential Under Real Conditions

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E = 1.100 V — ΔG = −212.3 kJ/mol

At standard conditions (Q = 1, T = 298 K), the Nernst correction vanishes and E equals E°. The Daniell cell produces 1.1 V, sufficient to drive electron flow from zinc to copper.

Formula

E = E° − (RT / nF) × ln(Q)
ΔG = −nFE
K = exp(nFE° / RT)

The Voltage of Chemistry

Every battery, every fuel cell, and every corrosion process operates at a voltage determined by the Nernst equation. Published by Walther Nernst in 1889, this equation extends the concept of standard electrode potential to real-world conditions where concentrations deviate from the ideal 1 M standard state. It reveals that cell voltage is not fixed — it shifts continuously as reactants are consumed and products accumulate.

Inside the Equation

The Nernst equation E = E° − (RT/nF) ln Q contains two competing terms. The standard potential E° represents the intrinsic driving force of the redox couple. The correction term (RT/nF) ln Q accounts for the actual concentrations via the reaction quotient Q. When Q < 1, the correction boosts the voltage; when Q > 1, it reduces it. At equilibrium (Q = K), the cell potential drops to zero.

Temperature and Electron Count

The sensitivity of the cell to concentration changes depends on both temperature and the number of electrons transferred. A one-electron reaction at 298 K shifts by about 59 mV per tenfold change in Q, while a two-electron reaction shifts by only 30 mV. This is why multi-electron cells tend to have more stable voltages and why high-temperature fuel cells behave differently from room-temperature batteries.

From Theory to Technology

The Nernst equation underpins pH meters (which measure hydrogen ion activity), reference electrodes, concentration cells, and the design of every commercial battery. Engineers use it to predict how much voltage a lithium-ion cell loses as it discharges, and analytical chemists use it to quantify ion concentrations in solution with millivolt precision.

FAQ

What is the Nernst equation?

The Nernst equation E = E° − (RT/nF) ln Q calculates the actual cell potential of an electrochemical cell under non-standard conditions. E° is the standard potential, R is the gas constant, T is temperature, n is the number of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.

What happens when Q equals 1?

When Q = 1, ln(Q) = 0 and the Nernst correction term vanishes, so E = E°. This corresponds to standard-state concentrations where all species are at unit activity.

How does temperature affect cell potential?

Temperature appears in the RT/nF term. Higher temperature increases the magnitude of the concentration-dependent correction, making the cell voltage more sensitive to changes in Q. At 298 K, the factor is approximately 0.0257/n volts.

What is the relationship between E and Gibbs free energy?

ΔG = −nFE connects cell potential to thermodynamic spontaneity. A positive E means negative ΔG (spontaneous). At equilibrium, E = 0 and ΔG = 0.

Sources

Embed

<iframe src="https://homo-deus.com/lab/electrochemistry/nernst-equation/embed" width="100%" height="400" frameborder="0"></iframe>
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