Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is 100 . The conductivity of this solution is 1.29 ~S ~m ⁻¹ . Resistance of the same cell when filled with 0.2 M of the same solution is 520 . The molar conductivity of 0.02 M solution of the electrolyte will be

Step-by-step solution

There is one mistake in Question paper. Assuming concentration of solution is 0.2 M instead of 0.02 M . Since resistance of 0.2 M is 520 . aligned R & =100 K & = 1 R ( a ) 1.29 & = 1 100 ( a ) ( a ) & =129 ~m ⁻¹ R & =520 , C =0.2 M K & = 1 R ( a )= 1 520 (129) ⁻¹ ~m ⁻¹ & = K V _ in cm & = 1 520 129 1000 0.2 10⁻⁶ ~m ^3 & = 129 520 1000 0.2 10⁻⁶ & =1.24 10⁻³ & =12.4 10⁻⁴ aligned