242. Write a Nernst equation for the half-cell reaction: Mⁿ⁺(aq) + ne^– → M(s)

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}$}\right.}^0 -\frac{\mathrm{RT}}{\mathrm{nF}} \mathrm{In} \frac{\mathrm{M}}{{\mathrm{M}}^{\mathrm{n}+}}$

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}$}\right.}^0 -\frac{\mathrm{RT}}{\mathrm{nF}} \mathrm{In} \frac{1}{{\mathrm{M}}^{\mathrm{n}+}}$

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.