Nernst equation

In electrochemistry, the Nernst equation gives the electrode potential (E), relative to the standard electrode potential, (E⁰), of the electrode couple or, equivalently, of the half cells of a battery. In physiology the Nernst equation is used for finding the electric potential of a cell membrane with respect to one ion.

<math>

E = E^0 - \frac{RT}{nF} \ln\frac{a_{\mbox{red}}}{a_{\mbox{ox}}} </math>

At room temperature the following is true

<math>

E = E^0 - \frac{0.0591}{n} \log\frac{[\mbox{red}]}{[\mbox{ox}]} </math>

For a cell membrane potential with respect to one ion

<math>

E = E^0 - \frac{0.0591}{n} \log\frac{[\mbox{ion out of cell}]}{[\mbox{ion inside cell}]} </math>

R is the universal gas constant, equal to 8.314510 J K^-1 mol^-1
T the temperature in kelvins. (Normal human body temperature is 310.15 Kelvins.)
a the chemical activities on the reduced and oxidized side, respectively
F is the Faraday constant, equal to 9.6485309*10⁴ C mol^-1
n is the number of electrons transferred in the half-reaction.
[red] is the concentration of oxidizing agent (the reduced species).
[ox] is the concentration of reducing agent (the oxidized species).

History

The Nernst equation is named after the German physical chemist Walther Nernst who first formulated it.