# 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.

$At \hspace{2mm} 25^0 C; E_{cell} = E^0_{cell}- \dfrac{0.059}{n}\log \dfrac{M]}{[M^{n+}]} or \dfrac{1}{[M^{n+}]} \\[5mm] E_{cell} = E^0_{cell}- \dfrac{0.059}{n} \log [\dfrac{\text{Products}}{\text{Reactants}}] or Q. \\[5mm] E_{cell} = E^0_{cathode}- E^0_{anode}- \dfrac{0.059}{n} \log \dfrac{[P]}{[R]}$

Related posts:

1. Standard Electrode Potential It is potential difference developed between metal electrode and the...
2. Worksheet on Electrode potential The electromotive force of a cell built on two electrodes...
3. Electrode Potential When a metal rod is placed in a solution of...
4. Henderson’s Equation Henderson derived an equation to calculate the pH value of...
5. Worksheet based on Electro-Chemistry The study of chemical reaction that takes place in a...