Determine the Mass

Question

Determine the mass (in units of grams) of a nonvolatile, nonionizing compound that must be added to 4.79 kg of water to lower the freezing point to -1.3°C if the molar mass of the compound is 50.0 g/mol.

*ΔT_f = K_fC_mi, K_f = -1.86^°C/m

Answer 1

Colligative properties:

∆T = imK

∆T = change in freezing point = 1.3º

i = van't Hoff factor = 1 since it is a non ionizing compound

m = molality = moles solute / kg solvent = ?

K = freezing constant = 1.86º/m

Solving for m (molality) we have ..

m = ∆T / (i)(K) = 1.3 / (1)(1.86)

m = 0.6989 moles / kg

There are 4.79 kg so we have 0.6989 mols / kg x 4.79 kg = 3.347 moles

The molar mass = 50.0 g/mol

Mass of unknown (in grams) = 3.347 moles x 50.0 g / mol = 167 g (3 sig. figs.)