Nernst Equation - Expression

Expression

The two (ultimately equivalent) equations for these two cases (half-cell, full cell) are as follows:

E_\text{red} = E^{\ominus}_\text{red} - \frac{RT}{zF} \ln\frac{a_\text{Red}}{a_\text{Ox}} (half-cell reduction potential)
E_\text{cell} = E^{\ominus}_\text{cell} - \frac{RT}{zF} \ln Q (total cell potential)

where

  • Ered is the half-cell reduction potential at the temperature of interest
  • Eored is the standard half-cell reduction potential
  • Ecell is the cell potential (electromotive force)
  • Eocell is the standard cell potential at the temperature of interest
  • R is the universal gas constant: R = 8.314 472(15) J K−1 mol−1
  • T is the absolute temperature
  • a is the chemical activity for the relevant species, where aRed is the reductant and aOx is the oxidant. aX = γXcX, where γX is the activity coefficient of species X. (Since activity coefficients tend to unity at low concentrations, activities in the Nernst equation are frequently replaced by simple concentrations.)
  • F is the Faraday constant, the number of coulombs per mole of electrons: F = 9.648 533 99(24)×104 C mol−1
  • z is the number of moles of electrons transferred in the cell reaction or half-reaction
  • Q is the reaction quotient.

At room temperature (25 °C), RT/F may be treated like a constant and replaced by 25.693 mV for cells.

The Nernst equation is frequently expressed in terms of base 10 logarithms (i.e., common logarithms) rather than natural logarithms, in which case it is written, for a cell at 25 °C:

E = E^0 - \frac{0.05916\mbox{ V}}{z} \log_{10}\frac{a_\text{Red}}{a_\text{Ox}}.

The Nernst equation is used in physiology for finding the electric potential of a cell membrane with respect to one type of ion.

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