Nernst Equation: Equilibrium Constant Equation

Nernst Equation and Equilibrium Constant 

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)

E= cell potential

Under standard conditions, the above equation can be given as,

ΔGo =-nFEo

According to 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

T= temperature in Kelvin

Incorporating the value of ΔG and ΔGo, from the first two equations, we get:

Nernst equation_1

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 and Equation 

can be rewritten:  E=Eo 0.0592 Vnlog10Q

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

Nernst equation _4

Where,

Keq = equilibrium constant,

F= faradays constant

Thus, the above equation gives us a relation between the standard electrode potential of the cell in which the reaction is taking place and the equilibrium constant. For vibrant video lessons, download Byju’s -The Learning App. Also, learn and practice questions related to the Nernst equation and equilibrium constant.


Practise This Question

In a cell that utilizes the reaction Zn(s)+2H+(aq)Zn2+(aq)+H2 (g) addition of H2SO4 to cathode compartment, will