Which expression correctly represents freezing-point depression ΔTf?

Which expression correctly represents freezing-point depression ΔTf?

• A. ΔTf = i Kf / m
• B. ΔTf = i^2 Kf m
• C. ΔTf = Kf m / i
• D. ΔTf = i Kf m

Answer: (D)

Freezing-point depression is a colligative property: how much the freezing point lowers depends on the number of solute particles in solution, not their identity. The extent of lowering is proportional to the molality of the solution (m), the solvent’s freezing-point-depression constant (Kf), and the van't Hoff factor (i), which counts how many particles the solute forms in solution. Put together, the correct relationship is ΔTf = i Kf m. This means each mole of solute that yields i particles lowers the freezing point by i times Kf per mole of solute per kilogram of solvent. For a non-electrolyte, i is about 1; for electrolytes, i is greater than 1 depending on dissociation. The other forms misplace these factors or use them incorrectly (inverting m, squaring i, or dividing by i), so they don’t match how freezing-point depression actually behaves.

Freezing-point depression is a colligative property: how much the freezing point lowers depends on the number of solute particles in solution, not their identity. The extent of lowering is proportional to the molality of the solution (m), the solvent’s freezing-point-depression constant (Kf), and the van't Hoff factor (i), which counts how many particles the solute forms in solution. Put together, the correct relationship is ΔTf = i Kf m. This means each mole of solute that yields i particles lowers the freezing point by i times Kf per mole of solute per kilogram of solvent. For a non-electrolyte, i is about 1; for electrolytes, i is greater than 1 depending on dissociation. The other forms misplace these factors or use them incorrectly (inverting m, squaring i, or dividing by i), so they don’t match how freezing-point depression actually behaves.