The electrochemistry equations

Nernst equationcell potentialFaraday's law of electrolysisgalvanic cellelectroplating calculation

Standard cell potential from half-cells, the Nernst correction for real conditions, and Faraday's law for plating mass.

Standard Cell Potential from Half-Cells

E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}

Builds a galvanic cell's standard voltage by subtracting the anode's standard reduction potential from the cathode's, using tabulated half-cell values.

Nernst Equation

E = E^{\circ} - \frac{RT}{nF}\ln Q

Corrects a cell's standard potential for non-standard concentrations, the equation behind every pH meter, ion-selective probe, and battery voltage curve.

Faraday's Law of Electrolysis (m = QM/nF)

m = \frac{Q M}{n F}

Faraday's law of electrolysis: the mass plated out at an electrode from the charge passed, the molar mass, and the electrons transferred per ion.

How they fit together

These answer three different questions about the same cell. The standard potential asks what voltage the chemistry offers under textbook conditions — cathode minus anode, both taken as reduction potentials, and you subtract rather than flipping a sign yourself. Nernst asks what it actually reads at your concentrations and temperature. Faraday's law ignores voltage entirely and asks how much metal a given quantity of charge moves.

The single most common error is scaling a half-cell potential by its stoichiometric coefficient. Potentials are intensive: doubling a half-reaction does not double E°, even though it does double ΔG. The n in the Nernst equation is not a scaling factor for E° either — it is the electron count in the balanced overall reaction, and it damps the concentration correction, so a two-electron cell shifts only half as much per decade of Q as a one-electron cell. For plating and electrorefining, Faraday's law is where the n bites hardest: depositing a mole of copper from Cu²⁺ takes twice the charge of a mole of silver from Ag⁺, so getting the ion's charge wrong puts your plating time out by a clean factor of two.