When 0.1 ~mol ~L ⁻¹ of KCl was filled in a Conductivity cell the resistance was 80 ohms at 298 K . (Conductivity of 0.1 M KCl at 298 K is 1.29 ~S ~m ⁻¹ . The same cell when filled with an unknown electrolyte of concentration 0.025 M , had a resistance of 92 ohms. What is the Molar conductivity of the electrolyte at the given concentration?

Step-by-step solution

The cell constant G^ * is given by the product of conductivity and resistance R . For the KCl solution, _ KCl = 1.29 S m ⁻¹ = 1.29 10⁻² S cm ⁻¹ . G^ * = _ KCl R_ KCl = 1.29 10⁻² S cm ⁻¹ 80 = 1.032 cm ⁻¹ . For the unknown electrolyte, the conductivity _ unk is calculated using the cell constant and the measured resistance R_ unk = 92 . _ unk = G^ * R_ unk = 1.032 cm ⁻¹ 92 0.011217 S cm ⁻¹ . The molar conductivity _ m is defined as _ m = 1000 C , where C is the concentration in mol L ⁻¹ . Given C = 0.025 M , we have: