Question

The electrical resistance of a column of 1000 cm length and 0.5 cm radius filled with 0.1 mol L\(^{-1}\) KOH solution is \(5 \times 10^3\) ohm. Calculate the molar conductivity of the solution.

Hint:

Molar conductivity increases with dilution because ion mobility increases in a dilute solution.

Answer 1

Step 1: Given Data \[ R = 5 \times 10^3 \text{ ohm}, \quad c = 0.1 \text{ mol L}^{-1} \] Step 2: Finding Conductivity (\( \kappa \)) Conductivity is given by: \[ \kappa = \frac{1}{R} \times \frac{l}{A} \] where: \[ A = \pi r^2 = \pi (0.5)^2 = 0.785 \text{ cm}^2, \quad l = 1000 \text{ cm} \] \[ \kappa = \frac{1}{5 \times 10^3} \times \frac{1000}{0.785} = 0.000255 \text{ S cm}^{-1} \] Step 3: Finding Molar Conductivity (\( \Lambda_m \)) \[ \Lambda_m = \frac{\kappa \times 1000}{c} = \frac{0.000255 \times 1000}{0.1} = 2.55 \text{ S cm}^2 \text{ mol}^{-1} \]