Let’s learn to apply the preceding equation. Determine the freezing point of an aque-
ous solution containing 10.50 g of magnesium bromide in 200.0 g of water.
The most common mistake is to forget to subtract the ΔTvalue from the normal freezing
point.
The freezing-point depression technique is also commonly used to calculate the molar
mass of a solute.
For example, a solution is prepared by dissolving 0.490 g of an unknown compound in
50.00 mL of water. The freezing point of the solution is –0.201°C. Assuming the com-
pound is a nonelectrolyte, what is the molecular mass of the compound? Use 1.00 g/mL as
the density of water.
m=ΔT/Kf=0.201 K/(1.86 K kg mol−^1 ) =0.108 mol/kg
50.00 mL (1.00 g/mL) (1 kg/1000 g) =0.0500 kg
(0.108 mol/kg) (0.0500 kg) =0.00540 mol
0.490 g/0.00540 mol =90.7 g/mol
Many students make the mistake of stopping before they complete this problem.
Boiling-Point Elevation
Just as the freezing point of a solution of a nonvolatile solute is always lower than that of
the pure solvent, the boiling point of a solution is always higher than the solvent’s. Again,
only the number of solute particles affects the boiling point. The mathematical relationship
is similar to the one for the freezing-point depression above and is
ΔTb=iKbmolality
where ΔTbis the number of degrees the boiling point has been elevated (the difference
between the boiling point of the pure solvent and the solution); Kbis the boiling-point ele-
vation constant; the molalityis the molality of the solute; and iis the van’t Hoff factor. You
can calculate a solution’s boiling point if you know the molality of the solution. If you know
the amount of the boiling-point elevation and the molality of the solution, you can calcu-
late the value of the van’t Hoff factor, i.
For example, determine the boiling point of a solution prepared by adding 15.00 g of
NaCl to 250.0 g water. (Kb=0.512 K kg mol−^1 )
Δ= =TiKm 1 3(1.86K kg mol−^1 )
(1mole Mg Br
(gMgBr)1
2
2
)
10 50. 8 84.113g MgBr
g)
2
(.200 0
1
100
kg
0 0g
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ = =
1.59K
Tfp (27 3 3.15 1.59)K 271.56K (−−==°1.59 C)
Solutions and Colligative Properties 185
KEY IDEA
STRATEGY