 # How do you calculate freezing point depression?

Freezing point depression is one of the colligative properties of matter, which means it is affected by the number of particles, not the chemical identity of the particles or their mass. Freezing point depression is calculated using Raoult’s Law and the Clausius-Clapeyron Equation to write an equation called Blagden’s Law. In an ideal solution, freezing point depression only depends on solute concentration.

Example: 1.60 g of naphthalene (C10H8) is dissolved in 20.0 g of benzene. The freezing point of pure benzene is 5.5 oC, and the freezing point of the mixture is 2.8 oC. What is the molal freezing point depression constant, Kf of benzene?

Solution:

Calculate the freezing point depression of benzene.

ΔTf= (Freezing point of pure solvent) – (Freezing point of solution)
(5.5 oC) – (2.8 oC) = 2.7 oC

Calculate the molal concentration of the solution.

molality = moles of solute / kg of solvent
moles of naphthalene = (1.60 g) (1 mol / 128 g) = 0.0125 mol naphthalene
molality of solution = (0.0125 mol) / (0.0200 kg) = 0.625 m

Calculate Kf of the solution.

ΔTf = (Kf) (m)

(2.7 oC) = (Kf) (0.625 m)

Kf = 4.3 oC/m