Question

A cell with N/50 KCl solution showed a resistance of 550 ohms at 25°C. The specific conductivity of N/50 KCl at 25°C is 0.002768 ohm⁻¹,cm⁻¹. The cell filled with N/10 ZnSO₄ solution at 25°C shows a resistance of 72.18 ohms. Calculate the cell constant and molar conductivity of ZnSO₄ solution.

Answer 1

Given:

Resistance with `N/50`​ KCl = R₁ = 550 Ω

Specific conductivity of `N/50` KCl = κ₁ = 0.002768 ohm cm⁻¹

Resistance with `N/10` ZnSO₄ = R₂ = 72.18 Ω

Molarity of ZnSO₄ = 0.1 mol/L

`"Cell constant" = kappa_1 xx R_1`

= 0.002768 × 550

= 1.5224 cm⁻¹

Specific conductance of ZnSO₄

`kappa_2 = "Cell constant"/R_2`

= `1.5224/72.18`

= 1.55224 cm⁻¹

Molar conductivity of ZnSO₄

`Lambda_m = (kappa_2 xx 1000)/C`

= `(0.02108 xx 1000)/0.1`

= 210.8 ohm cm² mol⁻¹