Have you ever heard of the Nernst equation yet? Did you miss out on the class when your teacher explained this concept? Well, we have got your back! In this chapter, we will cover all of the Nernst equation and also look at its derivation. You can follow the notes below to understand all about cell potential. You know what a cell in chemistry is. Don’t you? Yes! It’s that battery in your torch as well! So let’s begin.

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## 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,

ΔG^{o} =-nFE^{o}

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=ΔG^{o }+ RT lnQ

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

-nFE = -nFE^{0} + RT lnQ

E = E^{0} – (RT/nF) lnQ

Converting natural log to log_{10}, 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 = E^{o} − (2.303RT/nF) log_{10}Q

At standard temperature, T= 298K:

**E ****= ****E ^{o}**

**− (0.0592V/n) log**

_{10}**Q**

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

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## 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:

E^{0 }– (2.303RT/nF) log_{10}K_{eq }= 0

E^{0 }= (2.303RT/nF) log_{10}K_{eq}

Where, K_{eq} = equilibrium constant and F= faradays constant. Thus, the above equation gives us a relation between standard electrode potential of the cell in which the reaction is taking place and the equilibrium constant.

## Solved Examples for You

Question: State the Nernst Equation.

Answer: 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.