AkCalculators

Electrochemistry fundamentals — potentials, the Nernst equation, Gibbs free energy and practical electrolysis

Electrochemistry studies chemical processes that involve the movement of electrons — redox reactions — and the relationship between chemical energy and electrical energy. Key quantities include the cell potential (E), the standard potential (E°), and derived thermodynamic functions like Gibbs free energy (ΔG). Understanding these relationships allows chemists and engineers to predict the spontaneity of reactions, compute equilibrium constants, and design electrolysis systems for deposition, extraction, or synthesis.

Cell potentials and standard potentials

Electrochemical cells are composed of two half-reactions: a reduction at the cathode and an oxidation at the anode. Each half-reaction has a standard reduction potential E° (measured under standard conditions: 1 M concentration for solutes, 1 atm for gases, and 25°C). The standard cell potential is the difference between cathode and anode standard potentials:

E°_cell = E°_cathode − E°_anode

The Nernst equation — non-standard conditions

Real systems rarely operate at standard conditions. The Nernst equation adjusts the standard potential for concentrations (activities) and temperature. The general form is:

E = E° − (R T / n F) · ln(Q)

Where R is the gas constant (8.314462618 J·mol⁻¹·K⁻¹), T is temperature in kelvin, n is the number of electrons transferred, F is Faraday's constant (~96485 C·mol⁻¹), and Q is the reaction quotient (ratio of product activities to reactant activities raised to their stoichiometric coefficients). At 298.15 K the factor RT/F ≈ 0.025693 V, and it's common to use base-10 logarithm form:

E = E° − (0.05916 / n) · log₁₀(Q) (at 25°C)

Gibbs free energy and equilibrium

The electrical work available from a cell relates directly to thermodynamics. The change in Gibbs free energy for the reaction at the standard state is:

ΔG° = −n F E°

More generally for any conditions:

ΔG = −n F E

Because ΔG° = −R T ln K, we can link E° and the equilibrium constant K:

ln K = (n F E°) / (R T)

At 25°C this simplifies to:

log₁₀ K = (n E°) / 0.05916

Electrolysis and mass deposition

Electrolysis drives non-spontaneous reactions by applying a potential. The amount of substance deposited at an electrode is determined by the total charge passed. The relationship is:

m = (I · t · M) / (n · F)

Where I is current in amperes, t is time in seconds, M is molar mass (g·mol⁻¹), n is electrons transferred per formula unit and F is Faraday's constant. This formula is central to electroplating and production of metals by electrolysis.

Practical considerations and limitations

The equations here treat concentrations as activities (activity ≈ concentration for dilute solutions) and assume single-step redox stoichiometry. In concentrated or non-ideal media use activity coefficients or experimental calibration. Also note kinetic effects (overpotential, exchange current density, mass transport limitations) are not included — electrochemical cells often require additional voltage beyond the thermodynamic potential to proceed at appreciable rates.

Worked examples

Example 1 — Standard cell potential: If E°(cathode) = +0.80 V and E°(anode) = 0.00 V then E°cell = 0.80 − 0.00 = 0.80 V.

Example 2 — Nernst: For a 2-electron cell with E° = 0.80 V at 25°C and Q = 0.01, E = 0.80 − (0.05916/2)·log10(0.01) = 0.80 − (0.02958)·(−2) = 0.85916 V.

Example 3 — Mass deposited: Copper plating with I = 2 A for t = 3600 s, M(Cu)=63.546 g·mol⁻¹ and n=2: m = (2·3600·63.546) / (2·96485) ≈ 2.37 g.

Using this calculator

Use Simple Mode for quick arithmetic results and Advanced Mode for full Nernst equation calculations, solving for unknown concentrations or generating step-by-step derivations. Export results as CSV for lab records and copy results to clipboard for reports.

Electrochemistry links thermodynamics, kinetics and practical engineering. The equations in this tool let you move from measured potentials to chemical quantities and to design electrolysis processes — combine these calculations with experimental data for best accuracy.