Answer:
The correct answer is AlCl₃ 0.5 M
Explanation:
Freezing-point point depression is a colligative property and it is directly proportional to the number of particles in which the solute dissociates in solution:
ΔTf= Kf x m x i
Where ΔTf is the freezing-point depression (fusion temperature of pure solvent - fusion temperature of solvent in solution), Kf is the cryoscopic constant, m is the molality of solution and i is the van't Hoff factor. The van't Hoff factor indicates the number of particles in which the solute dissociates per individual solute molecule. As more the van't Hoff factor, more the freezing point depression, and lower the freezing point.
As all the solutes has the same concentration (0.5 M), the solution with the lowest freezing point will be one whose solute dissociates into the largest amount of particles:
NaCl → Na⁺ + Cl⁻ ⇒ i= 2
CaCl₂→ Ca⁺ + 2 Cl⁻ ⇒ i= 3
AlCl₃→ Al³⁺ + 3 Cl⁻ ⇒ i= 4
C₁₂H₂₂O₁ ⇒ i= 1
Thus, the AlCl₃ 0.5 M solution will be the one with lowest freezing point.