Nernst Equation

The Nernst equation gives the voltage across a membrane at which an ion is at equilibrium, when the electrical force on it exactly balances the pull of its concentration difference. It is named for the German chemist Walther Nernst, who received the 1920 Nobel Prize in Chemistry.

For an ion of charge z, the equilibrium potential is E = (RT / zF) ln([out] / [in]), where R is the gas constant, T the absolute temperature and F the Faraday constant. At body temperature, 37 °C, and using base-10 logarithms, this becomes about 61.5 millivolts divided by z, times log([out]/[in]). The same relationship follows from the balance of chemical potential and electrical energy, and it underlies much of thermodynamics and Gibbs free energy.

A typical neuron has much more potassium inside than outside, so the Nernst potential for K⁺ is about −90 millivolts, close to the resting membrane potential. Sodium is concentrated outside, giving a Nernst potential of about +60 millivolts. Because the real resting voltage lies near the potassium value, the membrane is mostly permeable to potassium at rest. The ions are kept out of equilibrium by pumps that use ATP.

When several ions can cross the membrane, the Goldman-Hodgkin-Katz equation weights each ion's Nernst potential by its permeability. In energy conversion, the same logic relates the voltage across the mitochondrial membrane to the proton gradient used in bioenergetics. It is also used in biophysics to interpret electrical signals in the nervous system.

• Biophysics — the field that applies it
• Gibbs Free Energy — the energy balance behind it
• Cell Membrane — the barrier across which it applies