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Nernst Equation & Electrochemical Cell Potential Calculator

Solves the Nernst equation for non-standard electrochemical half-cells and full galvanic/electrolytic cells, computing cell voltage (Ecell), reaction quotient (Q), transferred electrons (z), and Gibbs free energy (ΔG) with an interactive voltmeter display.

Nernst Equation & Electrochemical Cell Potential

Calculate non-standard electrochemical potential (Ecell), reaction quotient (Q), and Gibbs free energy (ΔG)

Standard Potential E° (V)

Electrons Transferred (z)

Reaction Quotient (Q)

Temperature (K)

Non-Standard Cell Voltage (E_cell)

1.032 Volts

Spontaneous Galvanic (Battery Discharge)

Gibbs Free Energy Change (ΔG):

-199 kJ/mol

Nernst Potential Offset (ΔE):

−0.068 V

What is the Nernst Equation?

The Nernst equation relates the reduction potential of an electrochemical reaction to the standard electrode potential (E°), temperature, and the activities or concentrations of the chemical species undergoing oxidation and reduction.

It enables electrochemists and engineers to predict cell voltages under non-standard concentration conditions, such as discharging batteries and biological membrane potentials.

Formula & Step-by-Step Calculation

E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{zF}\ln Q = E^\circ_{\text{cell}} - \frac{0.05916 \text{ V}}{z}\log_{10} Q \quad (\text{at } 298.15\text{ K})

Nernst relation with Faraday constant F = 96485 C/mol, number of electrons z, reaction quotient Q, and Gibbs free energy ΔG = -z·F·Ecell.

Worked Step-by-Step Examples

Example 1

Daniell cell (Zn + Cu²⁺ → Zn²⁺ + Cu) with E° = +1.10 V, [Cu²⁺] = 0.010 M, [Zn²⁺] = 2.0 M at 25 °C (z = 2)

Solution: Ecell = +1.032 V (Spontaneous Galvanic Cell, ΔG = -199.2 kJ/mol)

• Reaction Quotient: Q = [Zn²⁺] / [Cu²⁺] = 2.0 / 0.010 = 200

• log10(Q) = log10(200) = 2.301

• Nernst correction = (0.05916 / 2) × 2.301 = 0.02958 × 2.301 = 0.068 V

• Ecell = 1.10 V - 0.068 V = +1.032 V

• ΔG = -2 × 96485 × 1.032 = -199,145 J = -199.15 kJ/mol

Common Real-World & Academic Use Cases

✓ Battery discharge and fuel cell voltage degradation calculations
✓ Corrosion science and galvanic potential measurement
✓ Potentiometric pH meter electrode glass calibration
✓ Biological nerve impulse resting membrane potential (Nernst-Planck)

How to Use the Nernst Equation & Electrochemical Cell Potential Calculator

Input Standard Potential E°

Enter standard cell potential in Volts (e.g. +1.10 V for Daniell cell, or choose presets).

Specify Reaction Parameters

Enter number of moles of transferred electrons (z) and ion concentrations to compute reaction quotient Q.

Read Non-Standard Voltage & ΔG

View live voltmeter display, non-standard potential Ecell, Gibbs free energy change ΔG, and cell classification.

Frequently Asked Questions

Q: When does an electrochemical cell reach equilibrium?

When a battery is fully discharged, the cell reaction reaches thermodynamic equilibrium: Ecell = 0 V, ΔG = 0, and the reaction quotient Q equals the equilibrium constant K (log10 K = z·E° / 0.05916).

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