Nernst Equation and Its Applications

The Nernst equation formula establishes a relationship between the reaction quotient, electrochemical cell potential, temperature, and the standard cell potential.

E_cell = E₀ – (RT/nF) lnQ

Nernst distribution law can be used to calculate the electrochemical cells’ potential under non-standard situations. The Nernst equation is frequently used to compute an electrochemical cell’s cell potential for any given pressure, reactant concentration, and temperature. A German chemist, Walther Hermann Nernst, proposed the equation. The Nernst equation connects the electrochemical cell’s cell potential, temperature, standard cell potential, and the “Q” reaction quotient.

Nonetheless, the cell potential fluctuates due to concentration, temperature, and pressure. Since it is responsible for the change in cell potential, the Nernst equation is frequently used to calculate the electrochemical cell’s potential under any situation, such as pressure, temperature, and reactant concentration.

The expression for the Nernst equation is E_cell = E₀ – (RT/nF) lnQ

Where,

• E₀ denotes the cell potential under normal circumstances
• E_cell is the cell potential of a cell
• T is for temperature
• R denotes the universal gas constant
• n represents the number of electrons transferred during the redox reaction
• Q denotes the reaction quotient
• F is the Faraday constant

According to the Nernst Equation, the reaction quotient affects the overall potential of an electrochemical cell. The consumption of reactants and the formation of products throughout the reaction cause the cell potential to decrease slowly.

When the Nernst reaction reaches chemical equilibrium, the reaction quotient equals the (Kc) equilibrium constant. At this time, the cell potential of an electrochemical cell is zero as 𝞓 G = 0 at equilibrium, in addition to G = -nFE_cell

Nernst equation at 250C:

The Nernst equation may be stated as follows for observations taken at 298 K.

E_cell = (E₀ – 0.0591/n )logQ

As a result, according to the Nernst equation, the reaction quotient determines the overall potential of an electrochemical cell.

Application of Nernst Equation

• It is used to calculate ion concentration
• The equation is also used in the marine environment
• Helpful in figuring the potential of an ion with the charge “z” over the membrane
• It is used in pH measurements
• It can be used in potentiometric titrations and solubility products.

To Determine the Products’ Solubility

When sufficiently low concentrations of ions are in equilibrium with a sparingly soluble salt, the Nernst equation can be used with minimal error. Instead of directly determining the attention of the relevant ions, the more prevalent and more straightforward method would be to set up a cell with one of the electrodes containing the insoluble salt, which has a net cell reaction as the salt dissolves.

For example, we could calculate the Ksp for silver chloride using the cell’s silver-silver chloride electrode: The question mark represents the silver ion molarity concentration.

Titrations by Potentiometry

Because of the presence of other ions and a lack of information on their activity coefficients, precise estimation of an ion concentration via direct measurement of the cell’s potential is not possible. As a result, in such cases, the ion concentration is determined indirectly by titration with some ion.

| Pt(s) | Fe₂+, Fe₃+ || Reference Electrode

Initially, only Fe₂+ was present in the left cell. As the titrant Ce₄+ is added, the ferrous ion is oxidised to Fe₃+ ions, bringing the reaction to an end: Fe₂+ Ce₄+ ((Fe₃+ Ce₃+). The cell power is calculated as tiny amounts/drops of Ce₄+ are added. The Nernst equation ratio of oxidised iron ion concentrations determines the left half-cell potential.

E = 0.68 – 0.059 logarithm[Fe₂+]/[Fe₃+]

pH measurement

The pH of a solution is defined by the activity of the hydrogen ion rather than its concentration. A hydrogen electrode measures hydrogen ion activity (aH+) directly, so pH = -logH+. A question mark represents the H+ ion molarity, which is also a measure of the hydrogen ion concentration.

H₂ (1 atm) | Pt | H+ (? M) || Reference Electrode

Limitation of Nernst Equation

Because the activity of an ion in a very dilute solution approaches infinity, it can be defined in terms of ion concentration. But even so, in very high concentration solutions, the ion concentration does not equal the ion activity. In such cases, the Nernst equation must be used in conjunction with experimental measurements to determine the actual movement of the ion.

Another limitation of this equation is that it cannot calculate cell potential when a current is flowing through the anode. This is because the progression of current affects the activity of the particles on the anode’s surface. At the point when a current move through the anode, additional factors like resistive misfortune and overpotential should be thought of.

Conclusion

Potentiometric titrations are commonly used to determine the amounts of easily oxidised or reduced species. The reaction must be quick and have a high equilibrium constant. The equivalence point is identified by the rapid change in potential that happens when control of the cell potential shifts from the analyte’s redox system to the titrant. The pH is measured using an electrode consisting of a thin glass membrane that exchanges Na+ ions for H+ ions.

Membrane (Donnan) potentials form when an ion’s passage through a semipermeable membrane is selectively facilitated or impeded. A famous example is a sodium proteinate solution in which the protein anion is too big to enter through the membrane. Ion-specific channels or “pumps” have a comparable effect in organisms.