Nernst equation

A fresh battery reads a healthy voltage; a nearly dead one reads less, even though it is the same chemistry inside. The difference is concentration — the reactants are running low. The Nernst equation is the formula that adjusts a cell's standard voltage for the actual concentrations present, telling you what voltage it really delivers right now.

Standard electrode potentials assume tidy textbook conditions: every dissolved species at 1 molar, gases at 1 bar. Real cells almost never match that. The Nernst equation, E = E° − (RT/nF) ln Q, starts from the standard voltage E° and corrects it using Q, the ratio of products to reactants, where n is the number of electrons transferred and F is the Faraday constant. As reactants get used up, Q rises and the voltage falls — smoothly, all the way to zero when the cell reaches equilibrium.

This equation ties electrochemistry to the rest of chemistry. It is why a concentration cell — two identical electrodes in solutions of different strength — can produce a voltage from concentration alone, and it underlies the pH meter and the ion-selective sensors that read a single ion's concentration as a voltage. At equilibrium, with the voltage gone, it even hands you the reaction's equilibrium constant.