Molar Mass Determination
By Depression of the Freezing Point
CH 510
Dr. Berg
June 19 th
, 2007
Sarah Wascura

Abstract: The objective of this experiment was to study the equilibria that can exist between pure water and aqueous solutions. To achieve this, we measured the freezing point of pure water using a water and ice mixture. After a temperature was found, we added a known mass of an “unknown,” in this case our trials included 2-propanol and urea, to the ice water solution. This depressed the freezing point and allowed us to find the molality of the solution, which in turn will lead us to the molar mass through a series of calculations that will be included later in this report.
The depression of the freezing point occurs because the vapor pressure of a solution at 0 o
C is less than that of the pure liquid. The vapor pressure of ice at 0 o
C is higher than that of the solution, and some ice melts. This requires heat and therefore causes the temperature to fall. The vapor pressures of both the ice and solution fall, but the ice vapor pressure falls faster and the new freezing point is established at some temperature below the known freezing point of pure water, 0 o
C.
Figure 1: An indication of the temperature change that will occur at the freezing point when a solvent is introduced into a pure liquid.

Data and Observations: To begin, we measured the freezing point of a pure ice-water mixture. This temperature was recorded at 0.13 o C. Since we know the freezing point of water is 0.00 o
C, our depression temperature readings were corrected by using this measurement. A known mass of 2-propanol and urea was added to our ice-water mixture and a new temperature was recorded. Two trials were conducted using the 2-propanol as the solute and one trial was conducted using the urea as the solute in the ice-water solution.
FP water (solvent)
FP water with solute
Temp Change
Mass of liquid used
Mass of cup and liquids
Mass of cup
Mass of solution
Mass of water only
Trial 1 2-
Propanol
0.13 o
C
-4.3
4.43
10.072
69.729
1.691
68.038
57.966 o
C o C g g g g g
Trial 2 2propanol
0.13
-4.58
4.71
9.524
64.763
2.189
62.574
53.05 o o o
C
C
Trial 3
Urea
0.13
C -4.61
4.74 o
C o
C o C g 10.102 g g 70.921 g g 2.118 g g 68.803 g g 58.701 g
Figure 2: Data collection of temperature and mass data used to calculate molar mass.
The above data can be manipulated to yield the molality of the solutions. From that information, the molar mass of the solute can be determined by using the following molality and freezing point depression equations.
Molality = moles dissolved/kilograms solvent

T f
= k f m where k f
is a characteristic of the solvent used (water = 1.86) and m is molality

Calculated Results: The calculations used to calculate the molar mass of the
“unknown” solutions used in the experiment stem from the equations listed previously in the report. Below are some sample calculations used to find the results listed in Trial 1 in
Figure 3.
To find the molality from the temperature change:

T f
= k f m
4.43 o C = 1.86 (m) m = 2.38 mol/kg
To find the moles of solute:
Moles = (Molality)*(kilograms of solvent)
Moles = (2.38 m/kg) * (0.0579 kg)
Moles = 0.138 moles
To find molar mass of solute:
Molar Mass = (Grams used in experiment / Moles solute)
Molar Mass = (10.072g / 0.138 moles)
Molar Mass = 72.95 g/mol
To find percent error:
% Error = (Actual – Theoretical) / Actual
% Error = [(60.1 – 72.95) / 60.1] * 100
% Error = 21.39%

Molality from equation
Moles 2-propanol
Trial 1 2-
Propanol
2.38
0.138 mol/kg
Trial 2 2propanol
2.53 mol/kg mol 0.134 mol
Trial 3
Urea
2.54 mol/kg
0.150 mol
Molar mass 72.95 g/mol 70.90 g/mol 67.53 g/mol
% error 21.39 % 17.96 % 12.36 %
Figure 3: Results calculated from the molality and freezing point depression equations
From Trials 1 and 2, the average molar mass was calculated to be 71.93 g/mol. The average error associated with this calculation is 19.68%.
Comments and Conclusions: Through the experiment, we followed the procedure and each calculation step, however we ended up with molar masses that were not in line with the actual masses of our compounds. Our percent errors were high even though it seemed as if our calculations were correct. The positive aspects of the experiment included the ease of the procedure and the discussion behind it.
This experiment could easily be done in a high school setting when teaching about colligative properties. The materials involved in this lab are common and the calculations involve given equations that can be applied easily. Students would enjoy this experiment because it shows them that adding different things to pure water will change the freezing point. A fun application of this that I use in class is to have the kids make ice cream. They lower the freezing point of ice water by adding salt and the colder water will help to freeze a milk-sugar-vanilla mixture.