Highest Freezing Point in Aqueous Solutions: Freezing Point Depression

Freezing point depression represents a colligative property where adding a solute lowers the solvent’s freezing point, with the extent depending on the solute particle count (van’t Hoff factor i times molarity for dilute solutions). Under ideal conditions (complete dissociation, no ion pairing), the depression ΔT_f = i × m × K_f is smallest for the solution with the lowest i × [concentration], yielding the highest freezing point closest to pure water’s 0°C. This MCQ tests electrolyte dissociation: Cu(NO₃)₂ → 3 ions, K₂Cr₂O₇ → 3 ions, NaCl → 2 ions, MgCl₂ → 3 ions.

Freezing Point Formula

The freezing point of the solution is T_f = 0°C – ΔT_f, where ΔT_f = i × C × K_f (C = molarity ≈ molality for dilute aqueous solutions, K_f = 1.86 K kg/mol for water). Highest T_f means smallest ΔT_f, so compare i × C values.

Option Analysis

• (A) 0.002 M Cu(NO₃)₂: Dissociates as Cu(NO₃)₂ → Cu²⁺ + 2NO₃⁻ (i=3), so i×C=3×0.002=0.006 M effective
• (B) 0.001 M K₂Cr₂O₇: Dissociates as K₂Cr₂O₇ → 2K⁺ + Cr₂O₇²⁻ (i=3), so i×C=3×0.001=0.003 M effective
• (C) 0.001 M NaCl: Dissociates as NaCl → Na⁺ + Cl⁻ (i=2), so i×C=2×0.001=0.002 M effective—the smallest
• (D) 0.002 M MgCl₂: Dissociates as MgCl₂ → Mg²⁺ + 2Cl⁻ (i=3), so i×C=3×0.002=0.006 M effective

Correct Answer

Option (C) has the smallest i×C=0.002, thus minimal ΔT_f and highest freezing point. Options (A) and (D) tie for largest depression; (B) falls between.

Comparison Table

Option	Compound	i (ions)	C (M)	i×C (effective)	Relative Freezing Point
A	Cu(NO₃)₂	3	0.002	0.006	Lowest (tied)
B	K₂Cr₂O₇	3	0.001	0.003	Middle
C	NaCl	2	0.001	0.002	Highest
D	MgCl₂	3	0.002	0.006	Lowest (tied)

Real-World Application

This principle applies in real life, like salt on icy roads lowering water’s freezing point.