The standard electrode potentials are measured in their standard states when the concentration of the electrolyte solutions are fixed as **1M **and temperature is **298 K**. However, in actual practice electrochemical cells do not have always fixed concentration of the electrolyte solutions. The electrode potentials depend on the concentration of the electrolyte solutions. Nernst gave a relationship between electrode potentials and the concentration of electrolyte solutions known as **Nernst’s equation**. For a general electrode reaction,

M (aq) + ne ———-> M (s)

The Nernst’s equation is

E (M│M) = E°(M │M) – RT/ nF ln [M(s)]/[M (aq)]

Or, E (M│M) = E°(M │M) – 2.303RT/ nF log [M(s)]/[M^{n+}(aq)]

Where,

E (M│M) **= **Electrode potential

E°(M│M) = Standard Electrode potential [for IM solution of metal ions, [M^{n+}(aq)]

R = Gas constant, T Absolute temperature, F = Faraday of electricity,

n = Number of electrons gained during the electrode reaction

[M^{n+}(aq)] = Molar concentration of ions

[M(s)] = Molar concentration of metals.

Substituting the values of R = 8.314 J K^{-1}mol^{-1}, T = 298 K and F = 96500 coulombs, the Nernst equation at 25°C becomes

Or, E (M│M) = E°(M│M) – (2.303 x 8.314 x 298) / (n x 96500) log [M(s)] /[M^{n+ }(aq)]

Or, E (M│M) = E°(M│M) – 0.059/n log [M(s)] / [M^{n+ }(aq)]

It may be noted that concentration of the solid phase, [M(s)] is taken as unity. Then above expression can be written as—

** ** E (M│M) = E°(M│M) – 0.059/n log 1/ [M^{n+ }(aq)]

** **Or, E cell = E°cell – 0.059/n log 1/[M^{n+ }(aq)]