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)]/[Mn+(aq)]
Where,
E (M│M) = Electrode potential
E°(M│M) = Standard Electrode potential [for IM solution of metal ions, [Mn+(aq)]
R = Gas constant, T Absolute temperature, F = Faraday of electricity,
n = Number of electrons gained during the electrode reaction
[Mn+(aq)] = Molar concentration of ions
[M(s)] = Molar concentration of metals.
Substituting the values of R = 8.314 J K-1mol-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)] /[Mn+ (aq)]
Or, E (M│M) = E°(M│M) – 0.059/n log [M(s)] / [Mn+ (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/ [Mn+ (aq)]
Or, E cell = E°cell – 0.059/n log 1/[Mn+ (aq)]