What is a Nernst Equation?

Nernst Equation corresponds to any change in the Gibbs free energy G directly correspond to changes in free energy for processes at constant temperature and pressure, change is the maximum non-expansion work obtainable under these conditions in a closed system; ΔG is negative for spontaneous process, positive for nonspontaneous process, and zero for processes at equilibrium.

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

ΔG =-nFE

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

                                                                          ΔG^o =-nFE^o

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

ΔG=ΔG^o + RT lnQ

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

-nFE = -nFE⁰ + RT lnQ

E = E⁰ – (RT/nF) lnQ

By conversion of Natural log to log₁₀, the above equation is called as the Nernst equation. Here, it shows the relation of the reaction quotient and the cell potential. Special cases of Nernst equation:

E = E^o   − (2.303RT/nF) log₁₀Q

At standard temperature, T= 298K:

E = E^o   − (0.0592V/n) log₁₀Q

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

Nernst Equation Under Equilibrium Condition

As the redox reaction in the cell progresses, the concentration of reactants decreases while the concentration of products increases. This process goes on until equilibrium is achieved. At equilibrium, ΔG = 0. Hence, cell potential, E = 0. Thus, the Nernst equation can be modified to:

E⁰ – (2.303RT/nF) log₁₀K_eq = 0

E⁰ = (2.303RT/nF) log₁₀K_eq

Where, K_eq = equilibrium constant and F= faradays constant. Therefore, the above equation gives us a relation between standard electrode potential of the cell where the reaction takes place and the equilibrium constant.

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