Colligative Property Problems
Vapor pressure lowering (Raoult's law)
The vapor pressure of pure benzene (C6H6) is 100. torr at 26.1 oC. Calculate the vapor
pressure of a solution containing 24.6 g of camphor (C10H16O) dissolved in 100. mL of
benzene. The density of benzene is 0.877 g/mL.
Xben = nben/(nben + ncam)
nben = 100. mL x (0.877 g/mL) x (1 mol/78.1 g) = 1.12 mol
ncam = 24.6 g x (1 mol/152.2 g) = 0.162 mol
Xben = 1.12 mol/(1.12 mol + 0.162 mol) = 0.874
Pben = (Xben)(Poben) = (0.874)(100. torr) = 87.4 torr
Freezing point depression and boiling point elevation
Ethylene glycol (EG), CH2(OH)CH2(OH), is a common automobile antifreeze. Calculate
the freezing point of a solution containing 651 g of EG in 2505 g of water. Would you
keep the substance in your car radiator during the summer? The molar mass of EG is
62.01 g/mol. Kf = 1.86 oC/m and Kb = 0.52 oC for water.
mol of EG = 651 g x (1 mol/62.10 g) = 10.5 mol
molality of solution = 10.5 mol EG/2.505 kg of H2O = 4.19 m
∆T = Kf m = (1.86 oC/m)(4.19 m) = 7.79 oC
Since pure water freezes at 0 oC, the solution will freeze at -7.79 oC.
The boiling point elevation can be calculated in the same way.
∆T = Kb m = (0.52 oC/m)(4.19 m) = 2.2 oC
Because the solution will boil at 102.2 oC, it would be preferable to leave the antifreeze in
the car radiator in summer to prevent the solution from boiling.
A 7.85 g sample of a compound with empirical formula C5H4 is dissolved in 301 g of
benzene. The freezing point of the solution is 1.05 oC below that of the pure benzene.
What are the molar mass and molecular formula of this compound? Kf for benzene is
5.12 oC/m.
molality = ∆T/Kf = 1.05 oC/(5.12 oC/m) = 0.205 m
The number of moles of solute in 301 g or 0.301 kg of solvent is given by
(0.205 mol/1 kg solvent) x 0.310 kg solvent = 0.0617 mol
Molar mass of solute = 7.85 g/0.0617 mol = 127 g/mol
Empirical formula mass of solute = 64 g/mol
Molar mass of solute/ Empirical formula mass of solute = (127 g/mol)/(64 g/mol) ≈ 2
Empirical formula is 2 x C5H4 = C10H8 (naphthalene)
Osmotic Pressure
Calculate the concentration of urea (NH2CONH2) that has an osmotic pressure of 30.0
atm at 25 oC.
π = MRT !
M = π/RT = (30.0 atm)/[(0.08206 L atm mol-1 K-1)(25 + 273.15 K)]
M = 1.23 mol/L = 1.23 M
Make sure you do the colligative property problems in the text for more
practice.
If you want your quiz, they will be outside my door in a folder starting
Monday morning.