Nernst Equation Calculator

Frequently Asked Questions

What does the Nernst equation do?

It gives the electrode or cell potential away from standard conditions: E = E° − (RT/nF)·ln(Q).

What is Q here?

The reaction quotient from the ion concentrations; at equilibrium E = 0 and Q equals the equilibrium constant.

Why does temperature appear?

Potential depends on RT/nF; the common 0.0592/n form at 25 °C is just the equation evaluated at 298 K.

Where is it used?

Battery voltage prediction, pH and ion-selective electrodes, corrosion analysis, and electroplating.

What is a concentration cell?

A cell with the same electrode and reaction on both sides, so the standard potential E° = 0. The entire voltage comes from the concentration difference: E = −(RT/nF)·ln Q, where Q is the ratio of the two ion concentrations. To model one here, enter E° = 0 and set Q to (dilute side) ÷ (concentrated side). The cell drives current until the two concentrations equalize and E falls to zero.

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How This Calculator Works

The Nernst equation gives the actual cell potential under non-standard conditions: E = E° − (RT ÷ nF) · ln Q, where E° is the standard cell potential (V), R = 8.314 J/(mol·K), T is absolute temperature (K), n is the number of electrons transferred, F = 96,485 C/mol is the Faraday constant, and Q is the reaction quotient (products over reactants, each raised to its stoichiometric power). At 25°C the prefactor simplifies to the familiar E = E° − (0.0592 ÷ n) · log₁₀ Q. This calculator accepts °C, converts to kelvin, and reports E in volts and millivolts plus the Nernstian slope in mV per decade of Q. The rounded R = 8.314 and F = 96,485 shown in the prose keep the algebra readable; internally the tool carries the full-precision CODATA values (R = 8.314462618 J/(mol·K), F = 96485.33212 C/mol), so its output matches reference calculations exactly.

Worked Example: A Daniell Cell

For Zn | Zn²⁺ || Cu²⁺ | Cu, E° = 1.10 V and n = 2 electrons. Suppose Q = [Zn²⁺] ÷ [Cu²⁺] = 0.01. At 25°C, T = 298.15 K, and RT ÷ nF = (8.314 × 298.15) ÷ (2 × 96485) ≈ 0.01285 V. Then E = 1.10 − 0.01285 × ln(0.01) = 1.10 − 0.01285 × (−4.605) = 1.10 + 0.0592 ≈ 1.159 V. The simplified form gives E = 1.10 − (0.0592 ÷ 2)·log₁₀(0.01) = 1.10 + 0.0592 = 1.159 V; identical, as it must be at 25°C.

Real-World Uses

pH and ion-selective electrodes: a glass electrode's 59 mV/pH response is pure Nernst behavior.

Battery & fuel-cell modeling: open-circuit voltage as electrolyte concentration changes during discharge.

Corrosion science: predict galvanic potentials and protection requirements.

Biology: the resting membrane potential of neurons follows the same equation for ion gradients.

Common Mistakes

The 0.0592 ÷ n shortcut is valid only at 25°C; using it at body temperature or in a hot reactor introduces error, so this tool uses the full RT÷nF term. Writing Q upside-down (reactants over products) flips the sign of the correction. Forgetting to raise concentrations to their stoichiometric coefficients in Q is common. Pure solids and liquids and the solvent are excluded from Q (activity = 1). Note the equation uses natural log (ln) with RT÷nF but log₁₀ with the 0.0592 form; mixing them drops a factor of 2.303.

Limitations & Related

The Nernst equation assumes ideal-dilute behavior, using concentrations as proxies for activities; at high ionic strength, activity coefficients deviate and the predicted potential drifts. It describes equilibrium / open-circuit potential, not the voltage under current draw, which is reduced by overpotential and internal resistance (kinetics, not thermodynamics). A special case is the concentration cell, where E° = 0 and the entire voltage arises from a concentration gradient (E = −(RT÷nF)·ln Q). Related tools include the cell-potential, half-reaction, and pH calculators.

Nernst Equation Calculator

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