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Question:

Calculate the mass of compound (molar mass=256 g/mol) to be dissolved in 75 g of benzene to lower its freezing point by 0.48 K (Kf=5.12 K kg/mol).

Solution:

Let W g of compound is to be dissolved.
Number of moles of compound, n = mass/molar mass = W/256
Mass of benzene = 75 g = 75/1000 kg = 0.075 kg
Molality of solution, m = number of moles of solute/mass of solvent in kg
m = W/256 × 0.075 = W/19.2 m
The depression in the freezing point, ΔTf = 0.48 K
The molal depression in freezing point constant = Kf = 5.12 K kg/mol
ΔTf = Kf m
0.48 = 5.12 × W/19.2
W = 0.48 × 19.2/5.12 = 1.8
Hence, 1.8 g of solute is to be dissolved.