Nernst Equation

It is possible to calculate standard cell potentials in the presence of average temperature and pressure conditions. On the other hand, the Nernst equation is used to compute cell potentials in non-standard situations. Walther Hermann Nernst developed an equation that connects the Gibbs free energy to the cell potential, known as the Nernst equation.

Nernst Equation

The Nernst equation describes the link between the potential of a cell and the standard potential and the activities of electrically active (electroactive) species in a given situation. It is a relationship between the effective concentrations (actions) of the components of a cell reaction and the standard cell potential.

Using the equation, you may compute the cell potential at any point during a reaction under any situation except the normal state. The equation assesses concentration cells in corrosion investigations and generates Pourbaix diagrams, both valuable tools.

E(Mª¯/M)=Eº (M³+ /M) RT/nF In [M]/ [M¹+]

How to Derive Nernst’s Equation?

For a general electrochemical reaction-

Nernst equation can be written as:

Where,

Ecell = cell potential of the cell

E0 = cell potential under standard conditions

R  is the gas constant  (8.314JK–1mol–1)

F is Faraday constant (96,500Cmol–1)

T is the temperature in kelvin 

Q is the reaction quotient.

N is the number of moles of electrons transferred.

This is how Gibbs free energy and standard electrode potential are linked in any cell reaction:

ΔG=–nFE Eqn(1)

Here, G is called the Gibbs free energy.

number of electrons transferred in the reaction is n

In chemistry, F stands for Faraday’s constant (96,500C/mol), and m stands for mole.

When you think about a cell, you think about its “potential.”

When things are normal, Eqn (1) can be written down as,

standard Gibbs free energy is 

               Δ G0=–nFE0 Eqn (2)

E0 is the standard cell potential for a given type of cell.

It happens when E0 is positive, and it doesn’t happen when E0 is negative.

In thermodynamics, the reaction quotient, Gibbs free energy, and standard Gibbs free energy are all linked together:

As shown in this equation, 

ΔG=ΔG0+RtlNQ Eqn (3)

universal gas constant R is the name of this number

In Kelvin, the temperature is called T.

In Eqn, adding the value of G and G0 to it (3),

we get the following: 

–nFE=–nFE0+RTlnQ

When we divide the two sides by nF, we get

It is also possible to write Eqn(4) in the form of log10 as-

A temperature of 298K means that 2.303RTF = 0.0592.

It says that the electrical potential can change based on the reaction quotient Q of the reaction, which is shown in equation 6. During the process, reactants are used up, and products are made. As a result, the concentration of reactants decreases while the concentration of products rises. It then takes a long time for the cell potential to go down until the reaction is steady.

How to determine the equilibrium constant using Nernst Equation?

When the electrochemical cell’s reactants and products approach equilibrium, the value of G becomes 0. The reaction quotient and the equilibrium constant (Kc) are the same. Because G = -nFE, the equilibrium cell potential is also 0.

The following equation is generated by substituting the values of Q and E into the Nernst equation.

E0cell – (RT/nF) ln Kc = 0

The following diagram depicts the link between the Nernst equation, the equilibrium constant, and the Gibbs energy change.

The Relationship Between the Nernst Equation, the Equilibrium Constant, and the Gibbs Energy Change

The Nernst equation vs. the equilibrium constant vs. the Gibbs energy change

The equation is converted by converting the natural logarithm to base-10 logarithm and inserting T=298K (standard temperature).

(0.0592V/n) log Kc E0cell

The following equation may be produced by rearranging this equation.

(nE0cell)/0.0592V log Kc

As a result, the connection between the standard cell potential and the equilibrium constant may be calculated. When Kc exceeds one, the value of E0cell exceeds zero, indicating that the balance favors the forward reaction. Similarly, when Kc is less than one, E0cell will be negative, indicating that the opposite reaction will be preferred.

Applications of the Nernst Equation

To compute the following, the Nernst equation must be used:

• When under any conditions, the potential of a single electrode can be either reduced or oxidized
• Electrode potentials that are considered standard
• A comparison of a substance’s relative capacity to reduce or oxidize other substances is performed.
• Determine the possibility of combining single electrodes to generate an electric potential by experimenting with different combinations of electrodes.
• A cell’s electrochemical potential (emf).
• Concentrations of ions that are unknown
• When using the Nernst equation, you may determine the pH of solutions and the solubility of sparingly soluble salts.
• Equilibrium constants are accurately determined.
• Using an electrochemical cell to determine the voltage and concentration of a component,
• Calculating the potential that a concentration cell generates (in corrosion)
• A Pourbaix diagram is constructed to depict the equilibrium potential between a metal and its numerous oxidized species as a function of pH.

Limitations

• It is possible to describe the activity of an ion in a very dilute solution in terms of its concentration because the action of an ion is near to infinity when it is incredibly dilute. 
• However, if the ion concentration is exceptionally high, the relationship between engagement and activity is no longer valid.
• To use the Nernst equation in these situations, it is necessary to undertake experimental observations to determine the actual movement of the ion.

This equation also has the disadvantage of determining cell potential while there is currently flowing through the electrode. This is because the current flowing through the electrode affects the activity of the ions on its surface. Therefore, when a current runs through the electrode, it is necessary to consider additional considerations such as resistive loss and overpotential.

Summary

In a nutshell, electrical work is the inverse of the product of total charge (Q) and cell potential (P) (Ecell). You get complete control when you multiply the number of electrons (n) moles by the Faraday constant (F = 96,485 C/mole e). Electrical work is the most significant amount of work that the system can produce and, as such, is equal to the change in available energy. The Nernst equation is used to calculate an electrochemical reaction’s cell potential. It relates the cell potential to the response quotient. This equation applies to both individual electrode potentials and potential variations between half-cells. It is easier to use the Nernst equation to one electrode at a time. This article taught us the Nernst equation expression, derivation, and relationship to the equilibrium constant. We also learned the Nernst equation for Daniel’s cell.