The resistance of a conductivity cell when filled with 0.05 M solution of an electrolyte x is 100 Ω at 40°C. The same conductivity cell filled with 0.01 M solution of electrolyte y has a resistance of 50 Ω. The conductivity of 0.05 M solution of

electrolyte x is 1.0 x ${{10}^{-4}}$ S ${{cm}^{-1}}$.

Calculate

(i) cell constant.

(ii) conductivity of 0.01 M y solution

(iii) molar conductivity of 0.01 M y solution

Given, for electrolyte x, molarity = 0.05 M, resistance = 100 Ω and conductivity = 1.0X${{10}^{-4}}$ S${{cm}^{-1}}$

For electrolyte y, molarity = 0.01 M, resistance = 50 Ω and conductivity = ?

(i) Cell constant, G = Resistance ® X Conductivity (K) = 100X 1.0X ${{10}^{-4}}$ =${{10}^{-2}}$ ${{cm}^{-1}}$

(ii) Conductivity of solution y,

k= Cell constant/Resistance = ${{10}^{-2}}$/50 = 2 x ${{10}^{-4}}$ S ${{cm}^{-1}}$

(iii) Molar conductivity,

$A_{ m }$ = k x 1000/ Molarity = 2 x ${{10}^{-4}}$ x 1000 / 0.01

=20 S ${{cm}^{2}}$${{mol}^{-1}}$