The Nernst equation and electrode potentials

The standard electrode potential of a half-reaction, tabulated at standard conditions (1 M concentration, 1 atm pressure, a fixed reference temperature, and referenced against the standard hydrogen electrode), is a fixed, well-defined quantity — but a real electrochemical cell operating under ordinary, non-standard conditions has a voltage that generally differs from the value calculated by simply combining standard electrode potentials, and that voltage is not constant over time as the cell discharges. The Nernst equation supplies the correction: E = E° − (RT/nF)ln(Q), where E° is the standard cell potential, n is the number of electrons transferred in the balanced cell reaction, F is Faraday's constant, and Q is the reaction quotient — the same ratio of product to reactant concentrations (or activities) that appears in the equilibrium constant expression, but evaluated at the cell's actual, instantaneous concentrations rather than at equilibrium.

This single equation explains two related, practically important facts about real cells. First, as a battery discharges, reactants are consumed and products accumulate, so Q grows continuously, and because Q sits inside a logarithm subtracted from E°, a growing Q steadily pulls the cell potential down from its initial value — this is exactly why a battery's voltage sags gradually rather than staying constant until it abruptly runs out. Second, and more fundamentally, the Nernst equation reveals what "cell potential" actually measures: it is a measure of how far the cell's overall redox reaction is from equilibrium, in the same sense that Gibbs energy measures distance from equilibrium for any reaction. As the reaction proceeds and Q approaches the equilibrium constant K, the potential E approaches zero, and E = 0 exactly when Q = K — that is, a "dead" cell that can no longer do electrical work is not out of material in some vague sense, but has specifically reached chemical equilibrium in its cell reaction, at which point there is no remaining thermodynamic driving force to push electrons through an external circuit.

The Nernst equation's dependence on concentration also makes it a practical measurement tool: since E responds predictably to the concentration of a species involved in the electrode reaction, measuring a cell's potential provides a way to determine an unknown concentration (or activity, dissociation constant, or solubility product) — the basis of potentiometric measurement techniques including pH electrodes and ion-selective electrodes used throughout analytical chemistry.