Nernst Equation

Nernst equation is a general equation that relates the Gibbs free energy and cell potential in electrochemistry.  It is very helpful in determining cell potential, equilibrium constant etc.

It takes into account the values of standard electrode potentials, temperature, activity and the reaction quotient for the calculation of cell potential. For any cell reaction, Gibbs free energy can be related to standard electrode potential as:

ΔG =-nFE

Where, ΔG= Gibbs free energy, n = number of electrons transferred in the reaction, F = Faradays constant (96,500 C/mol) and E= cell potential. Under standard conditions, the above equation can be given as,

ΔGo =-nFEo

According to the theory of thermodynamics, Gibbs free energy under general conditions can be related to Gibbs free energy under the standard condition and the reaction quotient as:

ΔG=ΔGo + RT lnQ

Where, Q= reaction quotient, R= universal gas constant and T= temperature in Kelvin. Incorporating the value of ΔG and ΔGo, from the first two equations, we get:

-nFE = -nFE0 + RT lnQ

E = E0 – (RT/nF) lnQ

Converting natural log to log10, the above equation is known as the Nernst equation. Here, it relates the reaction quotient and the cell potential. Special cases of Nernst equation:

E =  Eo   − (2.303RT/nF)  log10Q

At standard temperature, T= 298K:

E =  Eo   − (0.0592V/n) log10Q

At standard temperature T = 298 K, the 2.303RTF, term equals 0.0592 V.