1 : 1 : 1
2 : 4 : 3
1 : 1 : 1.5
1 : 2 : 3
ΔTf = iKfm
where:
ΔTf = depression in freezing point
i = van't Hoff factor (number of particles produced per formula unit)
Kf = cryoscopic constant (molal depression constant)
m = molality of the solution
For 0.1 M aqueous solutions, we can assume molality ≈ molarity.
HCl → H⁺ + Cl⁻ (i = 2)
CuSO₄ → Cu²⁺ + SO₄²⁻ (i = 2)
K₂SO₄ → 2K⁺ + SO₄²⁻ (i = 3)
Since Kf and m are the same for all three solutions, the ratio of the depression in freezing points is determined by the ratio of the van't Hoff factors:
Ratio of ΔTf = i(HCl) : i(CuSO₄) : i(K₂SO₄) = 2 : 2 : 3
However, if we consider the activity of ions this might slightly change. If we account for the activity of ions, we expect the ratio to be closer to 1:1.5:3, but this is still an approximation since it is affected by the ionic strength of the solution. If the solution was ideal, we would expect the ratio 2:2:3, however due to ion-pairing effects it may vary slightly.
Therefore, the closest option is 1 : 1 : 1.5 although an ideal solution would yield 2:2:3 and real-world values would depend on many factors and would likely be in between these two ratios.