232. Write Nernst equation for single electrode potential.

The concentration of all species involved in the species involved in the electrode reaction is unity.This need not be always true.
Nernst shows that for the electrode reaction:
${\mathrm{M}}^{\mathrm{n}+}\left(\mathrm{aq}\right) +{\mathrm{Ne}}^{-}\to \mathrm{M}\left(\mathrm{s}\right)$

the electrode potential at any concentration measured with respect to standard hydrogen electrode can be represented by:
${\mathrm{E}}_{\raisebox{1ex}{${\mathrm{M}}^{\mathrm{n}+}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{M}$}\right.} = {\mathrm{E}}_{\raisebox{1ex}{${\mathrm{M}}^{\mathrm{n}+}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{M}$}\right.}^{-} - \frac{\mathrm{RT}}{\mathrm{nF}}\mathrm{In} \frac{\left[\mathrm{M}\right]}{\left[{\mathrm{M}}^{\mathrm{n}+}\right]}$
but concentration of solid M is taken as unity as we have
${\mathrm{E}}_{\raisebox{1ex}{${\mathrm{M}}^{\mathrm{n}+}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{M}$}\right.} = {\mathrm{E}}_{\raisebox{1ex}{${\mathrm{M}}^{\mathrm{n}+}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{M}$}\right.}^{-} - \frac{\mathrm{RT}}{\mathrm{nF}}\mathrm{In} \frac{1}{\left[{\mathrm{M}}^{\mathrm{n}+}\right]}$

R is gas constant (8.314 JK–1 mol–1),
F is Faraday constant (96487 C mol^–1), T is temperature in kelvin and [Mⁿ⁺] is the concentration of the species, Mn

Let us take a electrode reaction
${\mathrm{Zn}}^{2+}+ 2{\mathrm{e}}^{-} \to \mathrm{Zn}$
The Nernst equation of this electrode
$\mathrm{E} =\mathrm{E}° -\frac{ 2.303\mathrm{RT}}{\mathrm{nF}}\log \frac{{\mathrm{A}}_{\mathrm{product}}}{{\mathrm{A}}_{\mathrm{reactant}}}$
Instead of activity, we can take molar concentration.
$\mathrm{E} = \mathrm{E}°- \frac{0.05916}{\mathrm{n}}\log \frac{\left[\mathrm{Zn}\right]}{\left[{\mathrm{Zn}}^{2+}\right]}$
For pure solid and liquid molar concentration is taken as unity.
$\mathrm{E} = \mathrm{E}°- \frac{0.05916}{\mathrm{n}}\log \frac{1}{\left[{\mathrm{Zn}}^{2+}\right]}$