Cell Potential And Nernst Equation

Electrochemistry of Class 12

Cell Potential And Nernst Equation

Nernst equation is used to relate either half−cell potential or emf of a cell with the concentration of the related species. Let us first consider a redox change occuring in a electrochemical cell,

Cell Potential And Nernst Equation

where A, B, C and D are the reagents whose concentrations varies i.e. they are either gases or in solution phase. For reagent A, the free energy per mole of A may be given thermodynamically as

GA = Cell Potential And Nernst Equation + RT ln [A]

For m1 moles of A, Cell Potential And Nernst Equation

Similarly, for all other reagents,

Cell Potential And Nernst Equation

Now, the free energy change for the overall cell reaction can be deduced as

ΔG = ΔG° + RT ln Cell Potential And Nernst Equation …(i)

where ΔG° is the free energy change when all the reactants and products are present at concentrations equal to 1 M.

Any spontaneous reaction occuring in a cell, occurs with a decrease in free energy. This decrease in free energy brings in an equivalent amount of electrical work obtainable from a given system over and above any PdV energy that can be delivered to the surrounding. This can be calculated by the total charge driven through cell and the potential difference. Thus

−ΔG = Total charge × EMF of cell

−ΔG = nF × Ecell

[Negative sign indicates decrease of free energy and it implies that as Ecell becomes more and more positive, the ΔG will become more and more negative, making the reaction spontaneous]

Similarly, −ΔG° = nFCell Potential And Nernst Equation

Therefore, equation (i) can be written as

−nFEcell = −nFCell Potential And Nernst Equation + RT ln Cell Potential And Nernst Equation

or nFEcell = Cell Potential And Nernst Equation − RT ln Cell Potential And Nernst Equation

Dividing both the sides by nF gives,

Ecell = Cell Potential And Nernst EquationCell Potential And Nernst Equation ln Cell Potential And Nernst Equation

Putting T = 298 K, R = 8.314 J/mol K, F = 96500 C, we get

Ecell = Cell Potential And Nernst Equation …(ii)

The equation (ii) is called Nernst equation, which is applicable to half cell reaction as well as to complete cell reactions.

Daniel cell represented as Zn(s)⏐ Cell Potential And Nernst Equation (c1)⏐⏐ Cell Potential And Nernst Equation (c2)⏐Cu(s) assumes that Zn is the anode and Cu is the cathode. Such an assumption would be true only if the cell potential (Ecell) is positive. The cell potential is given in the following three ways of which we would choose the first one in all our problems.

ERP(Cathode) is the reduction potential of the cathode while ERP(Anode) is reduction potential of the anode, EOP(Cathode) is the oxidation potential of the cathode while EOP(Anode) is the oxidation potential of the anode.

Now, let us see, how to find the EMF of Daniel cell using Nernst equation. Since we need to represent the reduction potential of cathode and anode, we first need to write the relevant reduction reactions.

For cathode: Cell Potential And Nernst Equation+ 2e– → Cu

Cell Potential And Nernst Equation

Cell Potential And Nernst Equation is the standard reduction potential of the given half reaction, R is the universal gas constant T is the absolute temperature at which the cell works, F is the faraday constant and n is the number of moles of electrons as seen in the reaction. The expression in the log term should be that of Kc or Kpc. This means that if reaction involves no gases, then the expression in the log term should be that of Kc while if a gas is involved then the expression in the log term should be that of Kpc. In these expressions, the concentration should be always in moles per liter while the partial pressures in atmosphere units.

Note: Since Ecell  has been defined as Cell Potential And Nernst Equation, the Nernst expression holds good even if the number of moles of electrons of the two half reactions are different.

For example, consider the cell,

Cell Potential And Nernst Equation

It is also possible to balance the electrons in both the half cell reactions and then subtract Cell Potential And Nernst EquationfromCell Potential And Nernst Equation. That is,

Further Reading : 

  1. Concentration Cells
  2. Type of Half Cells 
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