Nernst equation
/ NERNST /
Think of an electrode's voltage as a kind of pressure that depends on how crowded a solution is with a certain ion: pack more of the ion in, and the voltage shifts in a predictable, orderly way. The Nernst equation is the exact rulebook for that shift — the formula that links the potential of an electrode to the concentration (activity) of the species involved. It is the bridge that turns a voltage reading into a number you can report.
Formally, the Nernst equation gives the potential E of a half-reaction as its standard potential E° plus a term proportional to the temperature and to the logarithm of a ratio of activities of products to reactants, divided by the number of electrons transferred. At room temperature it simplifies to a slope of about 59 millivolts per decade for a single-electron, single-charge ion: every tenfold change in activity shifts the potential by roughly 59 mV.
It matters because it is the engine behind potentiometry: pH meters, ion-selective electrodes, and reference electrodes all rely on Nernstian behavior to convert voltage into concentration. The caveat is twofold — the equation is written in terms of activity, not concentration, so ionic strength matters, and it assumes the system is at electrochemical equilibrium, which slow or irreversible reactions can violate.
Why does a pH electrode read in convenient pH units? Because the Nernst equation says its voltage changes by about 59 mV for each unit of pH (each tenfold change in hydrogen-ion activity), so the meter just rescales that steady 59 mV-per-pH slope into a pH display.
About 59 mV per tenfold change in activity at room temperature.
The 59 mV/decade slope is for a singly charged ion; a doubly charged ion such as calcium gives about half that, near 29.5 mV per tenfold change, because the slope is divided by the ion's charge.