Question

(a) Define molar conductivity of a solution and explain how molar conductivity changes which change in concentration of solution for a weak and a strong electrolyte?

(b) The resistance of a conductivity cell containing $0.001M$ KCl solution at $298$ K is $1500$ $\Omega$. What is the cell constant if the conductivity of $0.001$ M KCl solution at 298 K is $0.146\times {10}^{-3}Sc{m}^{-1}$?

Answer 1

(a) Molar conductivity of a solution at a given concentration is the conductance of volume $V$ of a solution containing 1 mole the electrolyte kept between two electrodes with the area of cross-section $A$ and distance of unit length.

${\Lambda }_m=k\frac{A}{l}$

Now, $l=1$ and $A=V$ (volume containing 1 mole of the electrolyte).

$\therefore {\Lambda }_m=kV$

Molar conductivity increase with a decrease in concentration. This is because of the total volume $V$ of the solution containing mole of the electrolyte increases on dilution.

Variation of molar conductivities with dilution:

For strong electrolytes, molar conductivity slowly increases with dilution.

For weak electrolytes, molar conductivity increases steeply on dilution, especially near lower concentrations.

The variation of ${\Lambda }_m$ with $\sqrt{c}$ for strong and weak electrolytes are shown in the following plot: (ref. image)

(b) Given,

conductivity, $\sigma =0.146\times {10}^{-3}Sc{m}^{-1}$

Resistance, $R=1500\Omega$

$\therefore$ Cell constant $=\sigma \times R$

$=0.146\times {10}^{-3}\times 1500$

$=0.219c{m}^{-1}$