Galvanic Cell — Nernst Equation

Compute the real cell potential (E_cell) of an electrochemical cell under non-standard conditions with the Nernst equation, along with K_eq, ΔG, ΔG°, and the reaction quotient Q

K ≫ 10¹⁰: reaction proceeds essentially to completion under standard conditions.

Reference Cell

Preset

Pick a classic galvanic cell or build your own

Electrons transferred

Temperature

Cell operating temperature

0100

Cathode standard potential

Standard reduction potential vs SHE (1 M, 25 °C)

-33

Cathode-ion concentration

Ion activity in the half-cell (logarithmic scale)

1.000e-45

Cathode-ion stoichiometric coef.

IUPAC cell notation

Zn(s) │ Zn²⁺(1 M) ║ Cu²⁺(1 M) │ Cu(s)

Results

E cell (Nernst, real)

1.1

E° cell (standard)

1.1

ΔG (real)

-212.3

kJ/mol

Equilibrium constant K

1.541e+37

Reaction quotient Q

Galvanic Cell — Spontaneous Process

ΔG° (standard)-212.3kJ/mol

Max. electrical work (−ΔG)212.3kJ/mol

RT/nF factor at T0.01285V

Oxidation · ANODE (−)

Zn(s) → Zn²⁺ + 2e⁻

Reduction · CATHODE (+)

Cu²⁺ + 2e⁻ → Cu(s)

Fundamentals & Explanation

Galvanic Cells and the Nernst Equation

A galvanic cell is an electrochemical device that converts the free energy of a spontaneous redox reaction into electrical work. It comprises two half-cells coupled through an external electronic conductor (the wire) and an internal ionic conductor (the salt bridge). The electrode where reduction happens is the cathode (+); the electrode where oxidation happens is the anode (−). The electromotive force (emf) under non-standard conditions is given by the Nernst equation, derived without simplifying approximations:

E° cell (standard)

E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}

E cell (Nernst)

E_{cell} = E^\circ_{cell} - \frac{RT}{nF}\,\ln Q

The Nernst equation follows from combining ΔG = ΔG° + RT·lnQ with the electrochemical identity ΔG = −nFE. The factor RT/nF is computed dynamically with the user's configured temperature.

Reaction Quotient and IUPAC Convention

For the balanced overall reaction

aA_{red} + bB_{ox} \rightarrow cC_{ox} + dD_{red}

, the reaction quotient is the ratio of product activities (≈ concentrations in dilute solutions) over reactants, raised to their stoichiometric coefficients:

Q = \frac{[\text{ion}_{anode}]^{\nu_{anode}}}{[\text{ion}_{cathode}]^{\nu_{cathode}}}

Watch the convention: the anode ion is a product of the overall reaction (the metal is oxidized and releases the ion to the solution); the cathode ion is a reactant (it is reduced back to a solid metal). Therefore increasing [cathode-ion] lowers Q, which raises E_cell — consistent with Le Châtelier's principle and full thermodynamic rigor.

Thermodynamics: ΔG, ΔG° and Equilibrium K

The real (non-standard) Gibbs free energy determines in-situ spontaneity; the equilibrium constant K is computed from the standard cell potential. The identity ΔG° = −nFE° allows the standard free energy to be obtained directly from electrochemical measurements — one of the most precise experimental methods available (see also the Gibbs-Helmholtz calculator):

Δ G real

\Delta G = -nFE_{cell}

Δ G° standard

\Delta G^\circ = -nFE^\circ_{cell}

K equilibrium

K = e^{\,nFE^\circ_{cell}/RT}

E_cell	ΔG	Thermodynamic regime
> 0	< 0	Galvanic cell — spontaneous, delivers electrical work (Wₘₐₓ = −ΔG).
≈ 0	≈ 0	Equilibrium — Q = K, no net current flow (depleted battery).
< 0	> 0	Electrolysis — requires an external source to drive the reverse process.

Notation and Model Assumptions

IUPAC cell notation

A single vertical bar │ denotes a phase change (electrode/solution); a double bar ║ represents the salt bridge. By convention the anode is on the left, the cathode on the right: e.g. Zn(s) │ Zn²⁺(1 M) ║ Cu²⁺(1 M) │ Cu(s) describes the standard Daniell cell with E° = +1.10 V.

The half-reactions shown in the calculator are the standard unit reductions (transfer of 1 mol of e⁻ per ion), as tabulated in standard reduction potential tables. They do not represent the balanced overall cell reaction — the stoichiometric coefficients for the full reaction are configured separately via the ν and n parameters.

Solvent, reference and ideal activity

The governing equations (Nernst, ΔG = −nFE, K = e^nFE°/RT) are solvent-agnostic: the calculator computes any system correctly. However, the preset E° values are tabulated vs SHE in aqueous solution at 25 °C (CRC Handbook, Atkins). For non-aqueous systems (Li-ion organic electrolytes, molten salts, ionic liquids) use custom mode with E° values consistent with your reference and solvent — do not mix aqueous-vs-SHE values with another scale.

Additionally, the model treats activities = molar concentrations, valid for dilute solutions (< 0.1 M); real solutions require correcting with γ_± coefficients (extended Debye-Hückel, valid in water). The pure solid and pure solvent have unit activity by definition and do not enter Q.

Overpotential and kinetics (not modeled)

The Nernst potential is a thermodynamic bound: the voltage actually delivered by a working cell is reduced by the overpotential (η) — kinetic dissipation at each electrode plus the IR drop across the internal resistance. This simulator assumes negligible current (potentiometric measurement).

Constant	Value	Source
R (gas)	8.314462618 J/(mol·K)	CODATA / NIST
F (Faraday)	96 485.33212 C/mol	CODATA 2019 (exact)
Standard T	298.15 K (25 °C)	IUPAC Green Book

Academic References

[1] Atkins, P. & de Paula, J. (2014). Physical Chemistry (10th ed.). Oxford University Press. Ch. 7C (Electrochemistry: equilibrium electrochemistry).
[2] Bard, A. J. & Faulkner, L. R. (2001). Electrochemical Methods: Fundamentals and Applications (2nd ed.). Wiley.
[3] IUPAC. (2019). Compendium of Chemical Terminology — Gold Book, entries galvanic cell, Nernst equation, standard electrode potential.
[4] CODATA Task Group on Fundamental Constants. Faraday constant — Recommended value after the 2019 SI redefinition (exact by definition).

Galvanic Cell — Nernst Equation

Reference Cell

Results

Fundamentals & Explanation

Galvanic Cells and the Nernst Equation

Reaction Quotient and IUPAC Convention

Thermodynamics: ΔG, ΔG° and Equilibrium K

Notation and Model Assumptions

IUPAC cell notation

Solvent, reference and ideal activity

Overpotential and kinetics (not modeled)

Academic References

You may also like:

Galvanic Cells and the Nernst Equation

Reaction Quotient and IUPAC Convention

Thermodynamics: ΔG, ΔG° and Equilibrium K

Notation and Model Assumptions

IUPAC cell notation

Solvent, reference and ideal activity

Overpotential and kinetics (not modeled)

Academic References