A conductivity cell is filled with a 0.01 M solution of an electrolyte and its resistance is found to be 250 . When the same cell is filled with a 0.05 M solution of the same electrolyte, the ratio of the molar conductivity of the first solution to that of the second solution is found to be 2 . The resistance of the 0.05 M solution is ________ .

Step-by-step solution

Let the cell constant be G^* . For the first solution: Concentration, C₁ = 0.01 M Resistance, R₁ = 250 Molar conductivity, ₁ = G^* 1000 R₁ C₁ For the second solution: Concentration, C₂ = 0.05 M Resistance, R₂ Molar conductivity, ₂ = G^* 1000 R₂ C₂ Given that ₁ ₂ = 2 ₁ ₂ = R₂ C₂ R₁ C₁ 2 = R₂ 0.05 250 0.01 2 = R₂ 5 250 2 = R₂ 50 R₂ = 100 Answer: 100