A Guide To Solved Examples of Nernst Equation

Nernst Equation is one of the most vital equations when it comes to understanding electrochemistry. Nernst equation is the tool that is applied in calculating the electric point of the half-cells in an electrochemical cell at non-ordinary conditions such as at different temperatures, concentrations and pressures. This equation has a great contribution in establishing a direct relationship between the reduction potential of any cell when it is kept under different physical conditions to the reduction potential of that cell measured at standard room conditions which means 1 molar concentration, 298 Kelvin temperature, and 1 atmospheric pressure. In this informative article, you will know what is electrochemistry, what is electrochemical cell, and a few nernst equation examples in the end.

What Is an Electrochemical Cell?

An electrochemical cell is a type of apparatus capable of producing electric current from chemical change caused due to chemical reactions and further releasing this energy by a spontaneous redox reaction. Electric current is the transfer of free electrons from one species to the other. An electrochemical cell consists of two half-cells. Each half-cell has one electrode and one electrolyte; it can be of the same element or different as well. 

The components of an electrochemical cell are:

• Electrodes – Electrodes are cylindrical-shaped conducting solids that are made up of metals. They are of two types:

The Anode – In an electrochemical cell, oxidation takes place at the anode. 

The Cathode – In electrochemical cells, reduction takes place at the cathode.

• Electrolyte – An electrolyte is a solution made up of compounds mixed with polar solvents like water that can produce free ions responsible for producing electricity.

• Salt Bridge – A salt bridge is responsible for completing the electrochemical circuit because it acts as a bridge by connecting the reduction half of the cell to the corresponding oxidation half. A salt bridge consists of saturated salt solution such as potassium chloride (KCl).

What Is the Nernst Equation?

Nernst Equation has many applications such as it is used in finding ionic concentrations of the ions like Zn, Cu etc. It is also used in comparing the reduction and oxidation capacity of the agents. Nernst Equation also determines the oxidation and reduction potential in one cell reaction.

Ecell = E0 + (RT/nF)*lnQ

Ecell = Electrochemical potential of the cell

E0 = Electrochemical potential of the cell under standard

T = Temperature in the cell

n = The number of free electrons transmitted from one half-cell to another.

F = Faraday’s constant 

Q = Reaction Quotient

R = Gas constant 8.314 J/(mol*K)

Nernst Equation Examples

1. To calculate the standard chemical potential of M3+/M electrode, the following cell is constituted:

Pt | M | M3+ (0.00178 L/mol) || Ag+ (0.012L/mol) | Ag

The EMF of this electrochemical cell was found to be 0.43 volts. Calculate the standard potential in this electrochemical cell for the half-cell reaction.

M3+ + 3e- ——————> M

Given E0Ag+/Ag = 0.82 volts.

Solution. The cell reaction will be written as M + 3Ag+ ——————> 3Ag + M3+

Applying the Nernst equation on this cell reaction,

Ecell = E0cell – 0.0591/3 * log [M3+]/[Ag+]3 

0.43 = E0cell – 0.0591/3 * log{(0.00178)/(0.012)} 

0.43 = E0cell – 0.0639

E0cell = 0.43 + 0.064 = 0.485 volts

And we know 

E0cell = E0cathode – E0anode

E0cell = 0.82 volts – 0.485 volts = 0.335 volts.

1. Calculate the quantity of the current produced by a Daniel cell that was carrying 1 litre electrolytic solutions of 1 molar Cu2+ ions and 1 molar Zn2+, the cell is operated till the potential drops to 1 volt. 

Given E0Zn2+/Zn = -0.75 volts; E0Cu2+/Cu = 0.35 volts

Solution: 

The half-cell reaction at the anode electrode, Zn ——————> Zn2+ + 2e-

The half cell reaction at the cathode electrode, Cu2+ + 2e- ——————> Cu

Since, by reading the question we can make sense that the current is getting drawn from the cell, hence the concentration of Cu2+ will decrease and the concentration of Zn2+ will increase.

Ecell = E0cell – 0.059/n*log([Zn2+]/[Cu2+])

1 = 1.102 – 0.059/2*log([Zn2+]/[Cu2+])

([Zn2+]/[Cu2+]) = 3042

Suppose x moles/litre amount of copper ion (Cu2+) is getting converted into copper atom (Cu), when the potential drop was 1 volt, then

([Zn2+]/[Cu2+]) = (1 + x)/(1 – x) = 3042 

x = 3041/3043 = 0.99934

This means that three electrons were involved in the process of the conversion of Cu2+ to Cu and Zn to Zn2+. Hence, the amount of current withdrawn from the daniel cell is equal to 

2 * 0.999934 * 96500 = 192987.262 = 1.929 * 105 Columb.

Conclusion

Nernst Equation is one of the most vital equations when it comes to understanding electrochemistry. Nernst equation is the tool that is applied in calculating the electric point of the half-cells in an electrochemical cell at non-ordinary conditions such as at different temperatures, concentrations and pressures. With the application of Nernst Equation, the cell potential can be calculated at any concentration of reactant, temperature and pressure for an electrochemical cell. We covered what is an electrochemical cell, some nernst equation examples.