Which of the following aqueous solutions would have the greatest freezing-point depression? (A) 0.10 m (NH₄)₂SO₄
(B) 0.10 m MnSO₄
(C) 0.10 m NaF
(D) 0.10 m KCI
(E) 0.10 m CH₃OH

A) 0.10 m (NH₄)₂SO₄ has the greatest freezing-point depression

Given

The aqueous solutions

Required

The greatest freezing-point depression

Solution

Colligative freezing point

for electrolyte :

ΔTf = Kf x m x i

i (van't Hoff factor ) = 1 + (n-1) α

All solutions in the problem have a molal concentration (0.1 m) and the same solvent ⇒ assuming water (The same Kf) so that what affects the value of  ΔTf is the value of i (For methanol which is not an electrolyte, we put it aside )

Assuming the degree of electrolyte ionization α= 1, the magnitude i is determined by the number of ions produced by the electrolyte (n)

(NH₄)₂SO₄ ⇒ 2NH₄⁺ + SO₄²⁻ : 3 ions

MnSO₄ ⇒ Mn²⁺ + SO₄²⁻ : 2 ions

NaF ⇒ Na⁺ + F⁻ : 2 ions

KCl ⇒ K⁺ + Cl⁻ : 2 ions

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