# Nernst Equation: Equilibrium Constant Equation

## Nernst Equation and Equilibrium ConstantÂ

Nernst equation is a general equation that relates the Gibbs free energy and cell potential in electrochemistry. Â 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:

Î”G =-nFE

Where,

Î”G= Gibbs free energy,

nÂ = number of electrons transferred in the reaction,

FÂ = Faradays constant (96,500 C/mol)

E= cell potential

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

Î”Go =-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:

Î”G=Î”Go + RT lnQ

Where,

Q= reaction quotient

R= universal gas constant

T= temperature in Kelvin

Incorporating the value of Î”G and Î”Go, from the first two equations, we get:

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: Â  Â E = Â EoÂ Â  âˆ’ (2.303RT/nF) Â log10Q

At standard temperature, T= 298K:

E = Â EoÂ Â  âˆ’ (0.0592V/n)Â log10Q

At standard temperature T = 298 K, theÂ 2.303RTF

term equals 0.0592 V and EquationÂ

can be rewritten: Â E=EoÂ âˆ’0.0592Â 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, Î”G = 0. Hence, cell potential, E = 0. Thus, the Nernst equation can be modified to:

Where,

Keq = equilibrium constant,