Freezing point depression for a solute is given by which relation?

• A. ΔTf = i Kf m
• B. ΔTf = Kf m / i
• C. ΔTf = i Kb m
• D. ΔTf = m / (i Kf)

Answer: (A)

Freezing point depression is a colligative property: the extent to which a solvent’s freezing point lowers depends on how many solute particles are present, not on their identity. The decrease in freezing point is proportional to the solute’s concentration in molality (m) and to a solvent-dependent constant (Kf), and it scales with the van’t Hoff factor (i), which counts how many particles the solute forms in solution. Put together, the change in freezing point is ΔTf ≈ i Kf m. This means non-electrolytes (which don’t dissociate) have i ≈ 1, while electrolytes have i equal to the number of ions produced per formula unit (for example, NaCl gives i ≈ 2). The constants: Kf is the freezing-point depression constant with units °C·kg/mol, and m is molality (moles of solute per kilogram of solvent). The other expressions don’t fit because they either divide by i, use the boiling-point constant (Kb) which relates to boiling-point elevation, or place m in the denominator, all of which misrepresent how the number of dissolved particles drives the freezing-point change.