Nernst equation

For a balanced cell reaction involving transfer of n electrons, the Nernst equation is E = E° − (RT/nF) ln Q. Here E is the cell potential under the stated conditions, E° is the standard cell potential for the same reaction, R is the gas constant, T is absolute temperature, F is the Faraday constant, and Q is the reaction quotient. Q is written from the activities of products and reactants, each raised to its stoichiometric coefficient; pure solids and liquids are omitted. For dilute solutions, concentrations are often used as practical approximations to activities. The equation applies to a specified redox reaction and consistent potential conventions.

When temperature is 298.15 K, the equation can be written E = E° − (0.05916 V/n) log₁₀ Q, with the numerical factor rounded to 0.0592 V in many introductory calculations. The logarithm base and numerical factor must be used as a matched pair: the RTF form uses the natural logarithm, while the 0.0592 V form uses the base-10 logarithm and is specific to 25 °C. At other temperatures, use the general equation or recompute the corresponding factor.

The equation follows by combining ΔG = −nFE, ΔG° = −nFE°, and ΔG = ΔG° + RT ln Q. It shows how a change in the reaction mixture changes the electrical potential from its standard value. For a cell reaction at equilibrium, ΔG and E are zero and Q equals the equilibrium constant K. Substitution gives E° = (RT/nF) ln K, linking standard potential to the position of equilibrium.

The Nernst equation is used to estimate cell potentials in nonstandard mixtures, interpret concentration cells, and connect electrochemical measurements with equilibrium constants. It also provides the idealized basis for relating an electrode potential to the activity of an ion in solution. Accurate calculations require a correctly balanced reaction, the right value of n, a properly constructed reaction quotient and consistent standard-state conventions. Concentration substitutions are approximations when solutions are non-ideal, because chemical activities can differ from concentrations.