Nernst equations are very useful for analytical chemistry and important life processes such as nerve conduction and membrane potential. The electrochemical cell, and therefore the Nernst equation, is widely used in the calculation of solution pH, solubility product, constant equilibrium and other thermodynamic properties, potentiometric titration, and  cell membrane resting potential. The Nernst equation shows the relationship between the electrode potential  and the  standard electrode potential. It is also used to calculate the free energy from Gibbs and  predict the spontaneity of  electrochemical reactions.

Expression of Nernst Equation

The Nernst equation states that the capacity (reduction potential) of an atom / ion that accepts one or more electrons  measured under any condition is 298 K and 1 mol or 1 atmospheric pressure standard condition (standard reduction potential). An expression associated with capacity.

Nernst Equation for Single Electrode Potential

Ecell = E0 – [RT/nF] ln Q

Where,

• Ecell = the cell potential of the cell
• E0 = the cell potential under the standard conditions
• R = the universal gas constant
• T = temperature
• n = number of them electrons transferred in the redox reaction
• F = the Faraday constant
• Q = the reaction quotient

The calculation of the single electrode reduction potential(Ered) from the standard single electrode reduction potential (E ° red) of an atom / ion is given by the Nernst equation.

In the case of reduction reaction Nernst equation of the reduction potential of a single electrode in the reduction reaction.

Mn+ + ne– → nM is;

Ered = EMn+/M = EoMn+/M – [2.303RT/nF] log [1/[Mn+]]

Where,

•  the gas constant R = 8.314 J/K Mole
• T =The absolute temperature,
• n = the number of mole of electron involved,
• F = 96487 (≈96500) coulomb/mole = the charged carried by the mole of electrons.
• [Mn+] = The  mass of ions. For simplicity, it can be taken as equal to molar concentration of salt.

Nernst Equation at 25oC

For measurements made at 298 K, the Nernst equation can be expressed as:

E = E0 – 0.0592/n log10 Q

Therefore,  the total potential of the electrochemical cell depends on the reaction quotient according to the Nernst equation.

Derivation of Nernst Equation

Imagine that the metal is in contact with its own aqueous salt  solution. The reaction between a metal that loses an electron and becomes an ion and an ion that acquires an electron and returns to the atomic state is also possible and is in an equilibrium state.

Mn+ + ne– → nM

In the reduction reaction, “n” moles of electrons are accepted by the ion with respect to the reduction potential of Ered.

1. Work done in movement of the electron

Wred = nFEred

Where,

• F is Faraday = 96487 coulomb = electric charge carried out by the one mole of electrons

2. Gibbs free energy changes are an indicator of  spontaneity and correspond to the most useful work done in the process (other than volume expansion). 

 Combination of work done and changes in Gibbs free energy:

Wred = nFEred = – ∆G or ∆G = – nFEred

3. The change in  free energy under standard conditions of 298 K and 1 mol / 1 atm is ΔG °. From the above relationship you can write it

∆G° = – nFE°red

Where,

• E°red is reduction potential measured at the standard conditions.

4. During the reaction, the concentration changes constantly and the potential decreases with the reaction rate. 

 To get the maximum work or the maximum change in free energy, the concentrations must be kept equal. This is only possible  by running the reaction under  reversible equilibrium conditions.

For the reversible equilibrium reaction,the vant Hoff isotherm says that:

∆G = ∆G° + RT ln K

Where,

• K is equilibrium constant
• K = Product/Reactant = [M]n/[M]n+
• The Gas constant(R) =8 .314J/K mole
• T is temperature in Kelvin scale.

5. Substituting for the free energy changes in the ant Hoff equation,

– nFEred = – nFE°red + RT ln [M]/[Mn+] = – nFE°red + 2.303 RT log [M]n/[Mn+]

Dividing the both sides by – nF,

Then we get the Nernest Equation

Ecell = E0 – [RT/nF] ln Q

Application of Nernest Equation

The Nernst equation can be used in the following calculations:

• Single electrode reduction or oxidation potential under all conditions 
•  Standard electrode potential
• Comparison of relative capacity as a reducing or oxidizing agent. 
•  Find the possibility of combining such individual electrodes to generate an electric potential.
• EMF of  electrochemical cell 
•  Unknown ion concentration 
•  The pH of the solution and the solubility of the sparingly soluble salt can be measured using the Nernst equation.

Conclusion

The activity of ions in a very dilute solution tends to be infinite and can be expressed in terms of  ion concentration. However, for  very high concentrations, the ionic concentration is not equal to the ionic activity. To be able to apply the Nernst equation in such cases, it is necessary to perform experimental measurements  to obtain the true activity of the ion. Another drawback of this equation is that it cannot be used to measure cell potential when current is  flowing through the electrodes. This is because the current flow  affects the activity of  ions on the surface of the electrode. Also, when current flows through the electrodes, additional factors such as resistance loss and overvoltage must be considered.