The Nernst equation compares the reduced potential of a cell in non-standard conditions to that of standard conditions. First, it is necessary to determine the standard potentials or conditions mentioned above. In an electrochemical cell, the standard electrode potential occurs when the temperature is 298 K, the pressure is 1 atm, and the concentration is 1 molar. The symbol which represents such a condition is ‘Eºcell”.

One of the most common uses of the Nernst equation is electrochemical cell potentials. The majority of batteries are powered by electrochemical cells and these cells can also be used to deposit small layers of materials on other surfaces, like gold plating on jewellery.

Nernst Equation for the potential of single electrode

The equation has many other practical applications too, but before moving on to that, let’s understand the nernst equation formula. 

Ecell = Eº – [RT/nF] ln Q

Now, here

• Ecell – cell potential
• Eº – cell potential under standard conditions
• R –  universal gas constant which is 8.314 J/(mol*K)
• T – temperature which is generally 298K
• n – the total number of electrons exchanged in the reaction
• F – Faraday constant which is 96485 C/mol
• Q – reaction quotient

To simplify the nernst equation formula, RT/nF can be substituted with a constant which will make the equation mostly similar to the pH equation.

Ecell = Eº – [2.303 RT/nF] log Q

Nernst Equation at 25ºC

The equation can be simplified to –

Ecell = Eº – [ 0.0592/n ] log Q

Hence, the equation can also be used to measure the rise in the cell potential when the concentration of a reactant increases. Supposedly, Q, which is the reaction quotient, is 1. It means that the cell potential will be the same as the standard cell potential. What if the value of Q is above 1? In this case, the cell potential will be less than the standard, while when the value of Q is below 1, the cell potential will be higher than the standard potential. In short, any value of Q other than 1 will alter the cell potential from that of the standard.

Derivation of the Nernst Equation

Before going to the derivation, it is important to learn what is ‘Gibbs free energy’? Because the Nernst equation has been derived from this.

Now, Gibbs free energy is a very important part of thermodynamics which tells us how spontaneous the reaction is. It is also the maximum work done in a process. And so it can be said that ΔG = -nFE and ΔG⁰ = -nFE⁰. where, Δ indicates a change. 

ΔG = ΔG⁰ + RT InQ

As explained above-

-nFE  = -nFE⁰ + RT InQ

Dividing the equation by -nF throughout will give us the Nernst equation

Ecell = Eº – [RT/nF] ln Q

Applications of Nernst Equation

The equation has many applications. Some of them are discussed below-

1. The pH of solutions and the solubility of sparingly soluble salts can both be determined using the Nernst equation. 
2. To determine the voltage and concentration of an electrochemical cell component.
3. Calculation of equilibrium constants with accuracy
4. To determine if it’s possible to generate electric potential by merging single electrodes.
5. Pourbaix diagram construction depicting the equilibrium potential between a metal and its numerous oxidised species as a function of pH.
6. To compare a substance’s reductive and oxidative abilities.
7. Calculation of a concentration cell’s potential in corrosion.
8. Unknown ionic concentrations

The equation can also be used to calculate half-cell reaction potentials or cell potentials for a variety of electrochemical cells such as voltaic and galvanic cells.

Limitations of Nernst Equation

Though the limitations are not often observed in the Nernst Equations but here are some to notice- 

1. The Nernst equation gets erroneous when concentrations are extremely high. Experiments are done to determine potentials when reactant or product concentrations are exceedingly high.
2. When there is current flowing through the cell, the equation cannot be employed. The current alters the ions’ activity or effective concentration. As a result of this impact, the equation stands incorrect.
3. The anticipated potential in extremely dilute solutions can reach infinity, which is unrealistic and should be ignored. In order to employ the Nernst equation in these situations, experimental measurements must be taken to determine the ion’s true activity.

Conclusion

The Nernst Equation has many uses not only in thermodynamics but also in Biology for important redox reactions. It also traces back its uses in physiology for estimating a cell membrane’s electric potential in relation to one type of ion. The acid dissociation constant can be linked to it. Well, the majority of the time the result is accurate except in the conditions mentioned above. 

The link between cell potential and standard potential, as well as the activities of electrically active (electroactive) species, is defined by the Nernst equation. It connects the standard cell potential to the effective concentrations (activities) of the components of a cell reaction.