Molar Mass Determination by Depression of the
Freezing Point
February 7, 2012
Adrienne Oxley
Lab Partner: Everett Spell
Title page includes the name of the
experiment, the date, your name and
your lab partner’s name.
Introduction:
This experiment focused on colligative properties, properties
that are based on the concentration of solute particles present and not
In text references are
shown as superscripts
which correspond to a
numbered reference
found at the end of the
report (in the reference
section)
the chemical identity of the solute. Freezing point depression was used
to study the molar mass of a substance.1 This colligative property is
based on the idea that a solution freezes at a lower temperature than
the pure solvent.1,2 By adding unknown impurities to a solution of
water and studying the effects this solute “impurity” has on the freezing
point, valuable information about the identity of the substance can be
obtained. The following equation describes the idea of freezing point
depression:
ΔTf = iKfm
The ΔTf term indicates the change in temperature observed for the
Introduction includes
explanation of concepts
found in key equations.
All variables used are
clearly defined (see
highlighted portion)
solution relative to that of the pure substance (the freezing point
depression), kf is a term specific to the identity of the solvent being used
(in this case water is used and kf is 1.86 ⁰C/m), and m is the molality of
particles in the solution (a measure of moles of solute per kg of solvent).
By measuring a change in temperature,
the molality of an aqueous solution can
be calculated and this information can
Use figures whenever
possible to illustrate
points (Note: if you use a
figure, you need to
reference it and refer to
it in the text – there
should be explanation of
the figure).
subsequently be used to determine
molar mass (provide the initial mass of
sample was recorded).
Figure 1 shows a typical phase
diagram for a pure solvent (the smaller
line inside) and the effects on the
phase diagram when a solute is added
to make a solution (outer line). The
equilibrium lines present in this phase
diagram are shifted in the presence of a
3
Figure 1. Phase diagram illustrating fp depression
solute and the new diagram indicates a lower freezing point for the
solution. Solvent is the only thing that freezes, not the solute
“impurity” and so the solute molecules are left behind.2 The
freezing/melting point of a solution is the phase change between solid
and liquid substances (equilibrium state). Molecules must leave and
enter the solid phase at the same rate, which occurs at a lower
temperature for the solution based on the lowering of the vapor
pressure. This phenomenon is the basis for “salting” roads in the
winter. The salt, solute particles, lower the freezing point of water (in
the form of snow/rain) so that it takes lower temperatures for roads to
freeze over.
Purpose:
This experiment has three separate, yet related purposes: (1) to
determine the freezing point of water, (2) to find the freezing point of a
solution (both liquid and solid unknown), and (3) to use this information
to determine the molar mass of an unknown substance.
Usually in undergraduate
laboratory sessions,
experimental procedures
are taken directly from
or adapted from
laboratory texts. This
information needs to be
referenced.
Purpose is clearly stated
and to the point.
Purpose makes
connections between
steps of the experiment
(sometimes the purpose
will include info as to the
methods being used to
obtain the desired
information)
Procedures:1
First the freezing point of water was determined by preparing a
water-ice mixture and recording, with a thermometer, the lowest
temperature observed. This measurement was performed in an
insulated cup to minimize heat loss to the surroundings and prevents
uncalibrated thermometers from interfering with results.
Second, the freezing point of a solution of water and an
unknown liquid was obtained. A water-ice mixture was prepared as in
the first part of the experiment and a calculated amount of liquid
unknown was added to this solution by weighing the sample on the
balance. The amount added, 10 g, was determined by assuming the
In the formal laboratory
report, procedures
should be in past tense.
Also, avoid the use of
“you”, “I”, “we”, etc.
molality of the resulting solution to be approximately 2 m and the molar
mass to be 50 g. The liquid solution was stirred until a temperature
decrease of at least 4 degrees was observed (in the event that a 4
degree decrease was not observed, more solute was added). The
solution was thoroughly stirred and the lowest temperature recorded.
The solution was strained to remove ice and then weighed. This data
was then used to determine the freezing point depression and molar
mass (see Data and Calculations section). These procedures were
repeated for a second trial.
The procedures used in determining the freezing point of a
solution of unknown liquid were repeated using an unknown solid. The
appropriate amount of solid solute was weighed on a balance and
added to a small amount (approximately 20 mL) of water. The solid
solution was then added to the water-ice mixture, which was stirred
thoroughly and the lowest temperature recorded. Freezing point
depression was calculated and used to determine molality, which was
subsequently used to determine molar mass (again, see Data and
Calculations section). Again, these procedures were repeated for a
second trial.
In the event that the calculated molar mass was less than the
actual molar mass for the solid unknown, the substance was identified
as ionic and the van’t Hoff factor was determined. The i value is a ratio
of true molar mass to calculated molar mass.
Data and Calculations:
The following data tables summarize the experimental data.
Temperature values were observed, other data was determined
through calculations. Sample calculations are shown below.
Table 1. Freezing Point Data and Molality Calculations
Data is tabulated and
organized. All values
have units associated
with them and calculated
values are reported to
the appropriate number
of significant figures.
Substance
Freezing
Freezing Point
Calculated
Mass of
Mass of
Mass of
Point (⁰C)
Depression *
Molality**
unknown
solution
Solvent
(⁰C)
(mol/kg)
Solute (g)
(g)
(g)
Pure water
0.2
---
---
---
---
w/Liquid
-3.8
4.0
2.2
10.21
120.29
110.08
-3.9
4.1
2.2
9.69
156.17
146.48
-4.6
4.8
2.6
10.07
105.11
95.04
-4.3
4.5
2.4
11.21
132.35
121.14
(Trial 1)
w/Liquid
(Trial 2)
w/Solid
(Trial 1)
w/Solid
(Trial 2)
Table 2. Calculated and Actual Molar Mass Values*** (g/mol) (Note: values in
parentheses indicate numbers to appropriate significant figures)
Tables are clearly
labeled and described.
Unknown
Trial 1
Trial 2
Average
Actual
Percent
Error****
Liquid
43.13
30.07
(Methanol)
(43)
(30)
Solid (NaCl)
41.07
38.24
(41)
(38)
36.60 (37)
32
14.38 %
(14%)
39.66 (40)
58.5
32.21%
(32%)
Finding Change in Temperature:
*∆Tliquid = Tfinal – Tinitial = -3.8°C – 0.2°C = -4.0 °C (Note: the negative sign
indicates that the temperature decreased but does not need to be
carried through the calculations)
Using ∆T to find molality (note: assuming i = 1):
**∆Tf = Kfm
Clearly labeled example
calculations are shown for
each type of calculation
performed (including
units).
m = ∆T/Kf = 4.0 °C/1.86 °C/m = 2.15 m = 2.15 mol/kg = 2.2
mol/kg
***Using mass of solvent and unknown in conjunction with molality to
find molar mass:
Mass of solution: 121.19 g
Mass of liquid unknown added: 10.21 g
Mass of solvent (water): 121.19 g – 10.21 g = 110.98 g
= Molar Mass(MM) x molality
= MM x 2.2 mol/kg
MM = 43 g/mol  molar mass of liquid unknown
****Percent Error Reported for Molar Masses:
=
x 100 = 14.38 % =
14 %
Van’t Hoff factor Calculations (for solid):
i = Actual molar mass/average molar mass = 58.5/39.66 = 1.4
Discussion:
The freezing point depression is a colligative property of
solution, meaning it depends only on the amount of substance and not
on the chemical properties of the substance. In order to ensure
accuracy, a freezing point depression of at least 4.0 °C was to be
observed. Any values less than this would have indicated insufficient
solute particles to impact the freezing point by an amount that would
have allowed for accurate calculation of molar mass. The freezing point
of pure water was determined in part A of the experiment. Freezing
point values obtained in parts B and C were compared to this value to
determine the depression. The unknown liquid resulted in a freezing
point depression of 4 °C and the solid unknown yielded a depression of
4.8 °C. Both values fell within the required depression of 4.0 °C and so
no additional solute needed to be added to the water/ice mixture.
Discussion presents the
data obtained and
compares this data to
various trials and to
expected data.
These values were used to determine the molality of solution for a
liquid unknown and a solid unknown.
In the case of the liquid unknown (later identified as methanol),
the calculations shown above indicated an average molality of 2.2 mol
of methanol per kg of water (2.15 for trial 1 and 2.20 for trial 2). This
value was compared to the original mass of unknown added to the
water/ice mixture. The liquid unknown, methanol, should have had a
molar mass of 32 g/mol, however the observed molar mass was an
average of 37g/mol (43.13 g/mol for trial 1 and 30.07 g/mol for trial 2).
When taking only the average into consideration, the percent error was
calculated to be approximately 14%. While the values appeared to be
relatively close to one another, the error is significant (typically an error
of less than 5% is desired). This error may have been the result of a
number of experimental errors. While recording temperature of the
water/ice mixture upon addition of unknown liquid, the sample was not
Possible sources of
experimental error are
outlined in the discussion.
An explanation of error is
given rather than a blanket
statement of “human
error”. There is also
mention as to how the
source of error would
influence the data.
vigorously stirred and so the value may have been invalid. Constant
stirring of solution would have assured even mixing of solute particles
and a more accurate determination of freezing point. Also, upon
measuring the mass of decanted solution for trial 1, some of the liquid
spilled onto the bench top. This would have resulted in a lower mass
and thus the higher observed molar mass value. Variations in calculated
values between trials were most likely the result of inconsistent
measurements – more solutions was present in trail 2 and a different
mass of solute was introduced.
The same procedures were followed for solid unknown (later
identified as NaCl). The calculations indicated an average molality of 2.5
mol of NaCl per kg of water (2.58 for trial 1 and 2.42 for trial 2). The
molar mass was again determined by comparing this value to the
original mass of unknown added to the water/ice mixture. The molar
Percent errors are
calculated and discussed.
This allows the
experimenter to comment
on the accuracy of the data.
mass of NaCl should have been 58.5 g/mol, however an average value
of 40 g/mol was calculated (41.07g/mol for trial 1 and 38.24 g/mol for
trial 2). This gave a percent error of approximately 32%. The solid
produced an even greater error than the liquid unknown. This may be
due to the fact that the solid unknown was actually an ionic compound
and so the van’t Hoff factor was necessary to account for the presence
of multiple ions per unit of NaCl. This may also be due to a lack of
stirring the water/ice mixture upon addition of the unknown, as was the
case in the liquid unknown. Another source of error may have been the
solid unknown not completely dissolving in water prior to addition to
the water/ice mixture.
The experimentally determined molar mass of the solid sample
was less than the actual molar mass of NaCl. This indicated an ionic
solid and the van’t Hoff factor, i, was therefore calculated. The van’t
Hoff factor was determined to be 1.4 which is less than the “ideal” value
of 2 for NaCl (which dissociates into two ions). This deviation for the
ideal value may be due to ion pairing at this relatively high
concentration of NaCl.
Conclusions:
The experiment allowed for the determination of freezing point
Conclusions should refer
back to purpose. Here you
are answering the question
“Was the experiment
successful?”
of water based on uncalibrated thermometers. Freezing point
depressions were observed for both the introduction of unknown liquid
and unknown solid. Using experimental measurements, the molar mass
was also calculated for an unknown liquid and an unknown solid. Based
on percent error calculations for the observed data, accurate molar
mass values were not obtained (indicated by a percent error greater
than 5%).
References:
1. Slowinski, Emil J.; Wolsey, Wayne C.; Rossi, Robert C. Chemical
Principles in the Laboratory – Tenth Edition. Brooks/Cole.
References follow ACS
formatting. Information on
how to adhere to ACS
guidelines can be found in
the ACS Style Guide.
Belmont. CA. 2012.
2. Silberberg, Martin S. Chemistry: The Molecular Nature of
Matter and Change. McGraw Hill. New York, NY. 2012.
3. Mombourquette, Michael J. “Collegative Properties,
Introduction”.
http://www.queensu.ca/people/faculty/mombourquette/firstyr
chem/collegative/index.htm.