Which expression correctly represents freezing point depression for a nonvolatile solute?

• A. ΔTf = Kf m
• B. ΔTf = i Kf m
• C. ΔTf = i Km
• D. ΔTf = Kb m

Answer: (B)

Freezing point depression scales with the number of solute particles in solution. The more particles present, the more the solvent’s freezing point is lowered. This is captured by the expression using the van’t Hoff factor, which counts how many particles result from the solute, times the freezing-point depression constant of the solvent, all multiplied by the molality of the solution. That gives ΔTf = i Kf m. If the solute does not dissociate, i equals 1, so it reduces to ΔTf = Kf m. The other forms don’t fit because they either omit the particle-counting factor, use a boiling-point constant instead of a freezing-point constant, or use a nonstandard symbol that doesn’t correspond to molality.