Question

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

Options

• 124 × 10⁻⁴ S m² mol⁻¹

• 1240 × 10⁻⁴ S m² mol⁻¹

• 1.24 × 10⁻⁴ S m² mol⁻¹

• 12.4 × 10⁻⁴ S m² mol⁻¹

Answer 1

Resistance of a conductivity cell filled with a solution of an electrolyte of concentration 0.1 M is 100 Ω. The conductivity of this solution is 1.29 S m⁻¹. Resistance of the same cell when filled with 0.02 M of the same solution is 520 Ω. The molar conductivity of 0.02 M solution of the electrolyte will be 124 × 10⁻⁴ S m² mol⁻¹.

Explanation:

We know that

`kappa = 1/R xx "cell constant"`

∴ Cell constant = κ × R

= 1.29 × 100

= 129 m⁻¹

For 0.02 M solution,

`kappa = 1/R xx "cell constant"`

= `1/520 xx 129` S m⁻¹

Conc. (c) = 0.02 mol L⁻¹

= 0.02 × 10³ mol m⁻³

`Lambda_m = kappa/c`

= `(129//520 (Sm^-1))/(0.02 xx 10^3 (mol//m^-3))`

= 124 × 10⁻⁴ S m² mol⁻¹