# The resistance of a conductivity cell when filled with 0.05 M

#1

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

#2

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}}\$