EMF of a Cell

EMF OF A CELL

Definition

Electromotive force is defined as, "the difference of potential which causes flow of current from one electrode of higher potential to the other electrode of lower potential.

Thus, the emf of a galvanic cell can be calculated using the following relationship.

EMF = { Standard reduction potential of right hand side electrode } ‒ { Standard reduction potential of left hand side electrode }

E°_cell = E°_right ‒ E°_left

Example

Nernst equation for emf of a cell

The Daniel cell can be represented as

Zn(s)/Zn²⁺ (1M) // Cu²⁺(1M) / Cu

The cell reaction is

The Emf of the cell is given as

E_cell = E_Cu ‒ E_Zn                 ………... (1)

We know that,

the Nernst equation for reduction potential of Cu

E_Cu = E°_Cu + 0.0591/2  log [Cu²⁺]            ………….(2)

Similarly, the Nernst equation for reduction potential of Zn.

E_Zn = E°_Zn + 0.0591/2  log [Zn²⁺]            ………….(3)

Substituting equation 2 & 3 in 1, we get,

E_cell = ( E°Cu²⁺/Cu ‒ E°Zn²⁺/Zn ) + 0.0591/2 log ( [Cu²⁺]/[Zn²⁺] )

This is the Nernst equation for emf of a daniel cell

1. Measurement of emf of a cell

The potential difference or emf of a cell can be measured on the basis of poggendorff's compensation principle. Here the emf of the cell is just opposed or balanced by an emf of standard cell (external emf), so that no current flows in the circuit.

Fig. 3.7 Potentiometer for the measurement of emf

The potentiometer consists of a uniform wire AB (Fig. 3.7). A storage battery (K) is connected to the ends A and B of the wire through a rheostat (R). The cell of unknown emf (x) is connected in the circuit by connecting its positive pole to A and the negative pole is connected to a sliding contact (D) through a galvanometer G. The sliding contact is freely moved along the wire AB till no current flows through the galvanometer. Then the distance AD is measured. The emf of unknown cell is directly proportional to the distance AD.

E_x ∝ AD

Then the unknown cell (x) is replaced by a standard cell (s) in the circuit. The sliding contact is again moved till there is null deflection in the galvanometer. Then the distance AD' is measured.

The emf of standard cell E_s is directly proportional to the distance AD'.

 Es ∝ AD'

Then, the emf of the unknown cell can be calculated from the following equation.

Emf of the unknown cell x / Emf of the standard cell s = Length AD / Length AD'

Ex/ Es = AD / AD'

Emf of the unknown cell = Ex = [ AD / AD' ]× Ex 

2. Factors affecting emf of a cell

1. Nature of the electrolytes and electrodes.

2. Concentration and composition of the electrolytes.

3. pH and temperature of the solution. 

3. Applications of emf measurements

1. Determination of standard free energy change and equilibrium constant.

(i) The standard free energy change of a reaction can be calculated as follows

 ‒ΔG° = nFE°,

where,

n=Number of electrons involved;

F = 96,500 coulombs ;

E°= Standard emf of the cell.

(ii) The equilibrium constant of a reaction can be calculated as follows:

E° = (0.0591/n) log K

E° = Standardemf of the cell;

K = Equilibrium constant

2. Determination of pH by using a standard hydrogen electrode.

A hydrogen electrode is introduced into the solution, pH of which is to be determined. It is then coupled with a standard hydrogen electrode through the salt bridge and the emf of the cell is measured. If E is the emf of the cell,

E =  [ ‒2.303RT/nF  ]  log [H⁺]

E =   2.303RT/nF  .  pH

∴ ‒ log [H⁺] = pH

From the above equation the hydrogen ion concentration or the pH of the solution can be calculated.

3. Solubility of a sparingly soluble salt can be determined.

4. Valency of an ion can be determined.

5. Potentiometric titrations can be carried out.

6. Hydrolysis constant can also be determined,