Question

Resistance of 0.2 M solution of an electrolyte is 50 Ω. The specific conductance of the solution is 1.4 S m⁻¹. The resistance of 0.5 M solution of the same electrolyte is 280 Ω. The molar conductivity of 0.5 M solution of the electrolyte in S mol⁻¹ is ______.

Options

• 5 × 10⁻⁴

• 5 × 10⁻³

• 5 × 10³

• 5 × 10²

Answer 1

Resistance of 0.2 M solution of an electrolyte is 50 Ω. The specific conductance of the solution is 1.4 sm⁻¹. The resistance of 0.5 M solution of the same electrolyte is 280 Ω. The molar conductivity of 0.5 M solution of the electrolyte in S mol⁻¹ is 5 × 10⁻³.

Explanation:

For 0.2 M solution,

Resistance (R₁) = 50 Ω

Specific conductance (κ) = 1.4 S m⁻¹

So, cell constant = κ × R = 1.4 × 50 = 70 m⁻¹

Now, for 0.5 M solution,

Resistance (R₂) = 280 Ω

Use the same cell constant:

`kappa_2 = "cell constant"/R_2`

= `70/280`

= 0.25 S m⁻¹

Now calculate molar conductivity:

`Lambda_m = (kappa xx 1000)/C`

= `(0.25 xx 1000)/0.5`

= 500 S cm² mol⁻¹

Convert to S m² mol⁻¹.

500 S cm²/mol = 5 × 10⁻³ S m²/mol