# Nernst Equation

It describes the quantitative relationship between electrode potential and concentrations and temperature of the substance involved in the half cell reaction.

Consider a simple general reaction: $M^{n+} + ne^- \to M$

Nemst deduced the following mathematical expression for the above reaction: $E_{cell} = E^0_{cell} - \dfrac{2.303 RT}{nF} \log \dfrac{[M]}{[Mn^{n+}]}$

where, E = Electrode potential of the metal, $E^0$ = standard electrode potential, R = gas constant, T = temperature in K, F = Faraday constant $(96500 C mol^{-1})$, n = number of electrons involved in the half reaction, [M] = activity of metal in the solid phase or liquid phase and is taken as unity for pure metals, $[M^{n+}]$ = activity of metal ions in the solution and is taken equal to its molarity. $At \hspace{2mm} 25^0 C; E_{cell} = E^0_{cell}- \dfrac{0.059}{n}\log \dfrac{M]}{[M^{n+}]} or \dfrac{1}{[M^{n+}]} \\[5mm] E_{cell} = E^0_{cell}- \dfrac{0.059}{n} \log [\dfrac{\text{Products}}{\text{Reactants}}] or Q. \\[5mm] E_{cell} = E^0_{cathode}- E^0_{anode}- \dfrac{0.059}{n} \log \dfrac{[P]}{[R]}$

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