The Nernst equation, E = E° − (RT/nF)·lnQ, extends the idea of a standard electrode potential to the real, non-standard conditions every actual battery, sensor, or biological cell operates under. Named after Walther Nernst, who developed it in 1889, it explains why cell voltage drifts as a battery discharges, why pH meters work, and how concentration differences alone can generate a voltage. This article covers where the equation comes from, its practical short form, how to invert it to find a reaction quotient, and where the simple model needs care.
Why cell potential depends on concentration
A standard electrode potential E° is defined for one specific set of conditions — every species at 1 M (or 1 atm for gases) and 298 K. Real cells almost never sit exactly at those conditions: reactant concentrations fall and product concentrations rise as a battery discharges, and industrial or biological systems rarely start at 1 M anyway. The Nernst equation's −(RT/nF)·lnQ term is a correction that shifts the potential away from E° in proportion to how far the actual reaction quotient Q is from 1. When Q < 1 (more reactant-like conditions than standard), the term becomes positive and E rises above E°; when Q > 1, E falls below E°. This is exactly why a battery's voltage sags as it discharges — Q climbs as reactants are consumed and products accumulate.
The 298 K short form and when it applies
Because R, F, and ln(10) are all constants, the natural-log Nernst equation can be rewritten with a base-10 logarithm: E = E° − (0.05916/n)·log₁₀Q, where 0.05916 V is simply RT/F·ln(10) evaluated at 298.15 K. This is the version most often taught first because log₁₀ is more intuitive for concentration ratios that are themselves powers of ten. The catch is that 0.05916 is only correct at room temperature — at body temperature (310 K) or a hot industrial process, the coefficient is measurably different, and the full formula with the actual T should be used instead. The Cell Potential tab above computes both so you can see exactly how close they are at your chosen temperature.
Solving backward: finding Q from a measured voltage
Because a voltmeter can measure E directly, the Nernst equation is often used in reverse: given E°, n, T, and a measured cell potential, solve for Q = exp((E° − E)·nF/RT). This is the working principle behind concentration-based sensors, including the glass pH electrode, which is really a concentration cell whose measured voltage is converted into a hydrogen-ion concentration via exactly this inversion. The Reaction Quotient tab implements this rearrangement directly.
Concentration cells: voltage without a net reaction
An easy way to see the Nernst term in isolation is a concentration cell — two half-cells built from the identical electrode and identical ion, differing only in concentration. Because both half-reactions are the same, E° = 0 exactly, yet the cell still produces a real, measurable voltage driven entirely by the concentration difference through the lnQ term. This same principle — a voltage arising from an ion-concentration gradient rather than a chemical reaction — is also how resting membrane potentials work in nerve and muscle cells (the Nernst equation applied to a single ion species is sometimes called the Nernst potential in that biological context).
Limits of the equation
The Nernst equation assumes ideal behavior — that concentrations can be used directly in place of thermodynamic activities. At high ionic strengths (concentrated solutions), the difference between concentration and activity becomes significant and the equation's predictions drift from measured values; more rigorous work substitutes ion activities corrected by an activity coefficient. The equation also assumes the electrode reaction is at equilibrium locally (no significant current is being drawn) — under load, additional voltage losses from resistance and reaction kinetics (overpotential) make the actual terminal voltage lower than the Nernst prediction. Despite these caveats, the equation remains the standard starting point for battery voltage, corrosion potentials, and any sensor built on an electrochemical half-cell.