Experiment 21
Determination of Molar Mass by Freezing Point Depression
Introduction
The colligative properties are properties of solutions that depend only on the
concentration of solute particles in solution, not the identity of the solute. A typical example of
this is freezing point depression, the lowering of the freezing point of a solution compared to the
freezing point of the pure solvent. The equation is:
f = kf m (i)
(1)
(Change in the freezing point) = (solvent constant) x (molality)
For water the value of kf is 1.86°C/m. This means that a solution that is 1.00 m in solute
particles in water will have its freezing point lowered by 1.86°C from the normal freezing point
of pure water (at 0°C) to -1.86°C. The molality is the moles of solute per kg solvent:
m=
moles solute
kg solvent
(2)
Since the molar mass is the number of grams for every mole of a substance, the molar
mass can be determined by measuring the freezing point depression for a solution where the
mass of solute and solvent are known.
m=
Tf
kf
Molar Mass =
(3)
g solute
m x (kg solvent)
(4)
By carefully measuring the freezing point lowering, the mass of solute, and the mass of
solvent the molar mass can be determined. Care must be taken that all of the solute remains
dissolved at the temperatures where measurements are taken or results will not be accurate.
An interesting difference can be observed between ionic and covalent solutes. Because
the freezing point depression depends on the number of solute particles in solution, ionic
compounds usually show a greater depression of the freezing point than expected based on the
solution molality. This is due to the ionization of these compounds in water forming than one
particle, for example:
H2O
NaCl(s)  Na+(aq) + Cl-(aq)
Sodium chloride dissolves in water to form more than one particle. For the freezing point
depression for ionic compounds an “i” factor is multiplied to the molality, where the “i” factor is
the relative number of ions acting as solute particles. This factor can be experimentally
calculated from
i=
nTf
m (1.86)
Procedure
1.
Preparation of a low temperature bath.
Prepare a bath in a 250 ml beaker by thoroughly mixing approximately 100 mL of ice, 50
mL of rock salt, and 20 mL of water. Keep it mixed during the experiments. Also, use
the thermometer to stir with.
2.
Measuring the freezing point of the pure solvent.
Measure out 10 mL of pure deionized water into a large test tube. Place the digital
thermometer in the test tube sitting in the temperature bath. You may stir with the metal
thermometer. Also, frequently stir the ice bath with the test tube to keep it cold. Record
the temperature to the nearest 0.1 degree C in the test tube every 30 seconds for about
five minutes. If necessary, make a graph (see Figure 1) from which the freezing
temperature for pure water can be determined. NOTE: IT IS NOT NECESSARY TO
FREEZE THE ENTIRE LIQUID. LET THE SOLID MELT BEFORE YOU PULL THE
THERMOMETER OUT OF THE TEST TUBE. OTHERWISE YOU MAY PULL THE
TIP OFF OF THE THERMOMETER. To keep the bath cold, refresh your salt-water-ice
bath by pouring off excess water, adding more ice, and stirring with the test tube.
3.
Measuring the freezing point of a 1.00 m KCl solution.
Accurately measure about 10 g of pure H2O into a large test tube, and dissolve enough
salt in it to make a 1.00 m KCl solution. Place the thermometer into the test tube. Then,
(5)
place the test tube in the low temperature bath and take the measurements as you did in
part 2. Make certain the solution is well-mixed when the readings are made. This data
will be used to make a graph similar to Figure 2 from which the freezing point of the 1.00
m salt solution can be determined. Repeat for a 2.00 m salt solution.
Calculate the i factor, using equation (5).
4.
Determining the molar mass of sucrose from the freezing point depression.
Dissolve completely 2 to 3 g of sucrose (sugar) in 10 g of pure water. Record the exact
masses used. Repeat the procedure above, recording the temperature every 30 seconds
for 10 minutes. Draw the cooling curve and determine the freezing point depression.
Use the measured freezing point depression to determine the molar mass of
sucrose. Calculate the % error based on the formula C12H22O11. If the error is
unreasonable, thaw the sugar water and repeat the freezing process. What is the “i”
factor for sucrose? Why?
5.
Obtain an unknown covalent compound from the stockroom, and repeat Step 4. Use
equations (3) and (4) to calculate a formula weight for the unknown. Thaw the mixture,
and repeat the freezing for precision, if needed.
(NOTE: If you check out a different thermometer from before, you should calibrate it
[Step 2] for accuracy.)
Name
Lab day and time
Experiment 21: Freezing Point Depression
Pure water (solvent)
Tf °C (from graph) =
KCl
1 mKCl
Mass H2O, g
Mass NaCl, g
Molality NaCl
Tf °C (from graph)
∆Tf °C
i = ∆Tf /(m · kf)
2 mKCl
Sucrose solutions
Trial 1
Mass H2O, g
Mass sucrose, g
Tf °C (from graph)
∆Tf °C
Molality sucrose
m = ∆Tf / kf
Molar mass sucrose
Average molar mass
% error in molar mass
i factor for sucrose
Unknown letter_______________
Mass unknown ________________
∆T unknown solution ___________
m unknown solution ________________
molar mass unknown _________________
Trial 2