# UCO Colligative Properties of the Solution Freezing Point Depression Essay

E1Colligative Properties of Solutions:
Freezing Point Depression
PURPOSE
The experiment to be performed is divided into three sections:
(a) In part 1, the FP of the pure solvent, cyclohexane, is determined by constructing and/or observing a
cooling curve.
(b) In part 2 we determine the value of the molal freezing point depression constant, kf , of cyclohexane
by measuring the freezing point depression (relative to the FP of pure cyclohexane determined in
part 1 of a solution with a known molality of solute.
(c) In part 3 the molality of cyclohexane solution with an unknown solute is found. This makes possible
the calculation of the molar mass of the unknown.
Complete advanced study assignment (pre-lab) before coming to lab and hand it in before lab starts!
INTRODUCTION
Consider a hypothetical cooling curve which describes
the changes in phase of a pure substance in which heat
is lost at a steady rate at constant pressure (see figure 1).
The Freezing Point of Pure Liquid:
This experiment will focus on the region in which the
cooling liquid approaches and achieves the
freezing point (The boxed area on cooling curve in
Figure 1 is seen close up in Figure 2 below).
At the freezing point both liquid and solid are present. If the
system becomes thermally insulated from its surroundings,
that is, heat can neither enter or leave the system, a state of
equilibrium will be established. Here the number of molecules
moving from solid to liquid is the same as the number of
molecules moving from liquid to solid. This means that
the relative quantities of solid and liquid present will remain
constant and the temperature will remain constant until all of
the pure substance has solidified. Liquid ⇔ Solid + Heat (1)
The phenomenon of supercooling occurs when liquids do not
solidify even below their normal freezing point. In the non aqueous system used in this experiment
supercooling by the solvent is not expected.
The Freezing Point of a Solution:
Now consider the effect of a nonvolatile solute upon a freezing solution. Any added solute would
dissolve in the liquid phase but will be excluded from the solid crystal lattice. This means that, in effect,
the concentration of liquid solvent molecules has been diminished and the rate of liquid solvent
molecules moving to solid will decrease. On the other hand, the molecules of solid solvent (which
remains pure), continue to move from solid to liquid at the same rate. If the temperature is held at the
normal freezing point of the pure solvent, the system is thrown out of equilibrium and liquid phase is
formed at the expense of solid phase, to a point where only liquid solution is present. In order to
reestablish freezing, the temperature of the system needs to be lowered. This causes heat to be removed
from the system and restores an equilibrium in which solid is present. The solution, therefore, has a
lower freezing temperature than the pure solvent and the freezing point is said to be depressed.
Now as a solution freezes, solvent molecules are removed
from the liquid solution as they form the solid. This increases
the concentration of solute in the liquid solution and the
freezing point declines further. A solution therefore does not
have a sharply defined freezing point (FP). Usually the
freezing point of a solution is taken as the temperature at
which solid solvent crystals first begin to appear (Figure 3).
The FP depression is one of a set of physical properties of solutions (vapor pressure lowering, boiling
point elevation, and osmotic pressure) known collectively as colligative properties. These properties are
affected by the quantity of solute particles dissolved in the solution, regardless of their identity. The FP
depression (or the change in temperature of freezing) is described quantitatively by the following
equation:
∆Tf = -kf • m.
(2)
∆Tf = Tf,solution – T˚f,solvent . ∆Tf is negative because the temperature of the solution is lower than that of
the pure solvent.
Molality is moles of solute per kilogram of solvent. The concentration unit mol/kg is temperature
independent, unlike the mol/L concentration unit, because volume changes with temperature but mass
does not.
molality = m =
=
(3)
The magnitude of the freezing point change is proportional to the molality of the dissolved solute:
∆Tf ∝ [solute] = m. The proportionality constant, kf , is called the molal freezing point depression
constant. It is the property of the given solvent. The kf expresses the sensitivity of the solvent to having
its FP depressed by an added solute. The units are ˚C/m, which may be viewed as the number of degrees
the FP is depressed per one molal of solute concentration. As stated above each solvent has its own
unique value for kf.
So expanding equation 2:
Tf,solution – T˚f,solvent = ∆Tf = – kf
(4)
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The minus sign in the last expression in Eq. 4 is inserted because ∆Tf is always negative.
Freezing point depression provides a convenient way to determine the molar mass of an unknown
substance. A solution containing a known mass of solute per mass of solvent is prepared and its freezing
point is measured. The number of moles of solute can be determined by rearranging Eq. 4 to solve for
moles of solute, nsolute:
∆Tf = – kf

(5)
nsolute =
Because the mass of unknown solute is known (previously measured on the balance) and the number of
moles has been calculated (Eq. 5), you can determine the molar mass of the unknown solute
using the equation 6 below.
Mm =
(6)
A schematic of the freezing point apparatus on top of a magnetic stirrer is shown in Figure 4 below.
Setting up the Apparatus
You will be provided with a short 15×150 mm test tube, a split
rubber stopper, a short sealed mercury or alcohol
thermometer, and a Spinvane magnetic stir bar. A 250 mL
beaker is recommended for a temperature-bath, with ice, and a
magnetic stirrer unit.
1. Carefully adjust the thermometer within the split rubber
stopper so that graduations on the thermometer are visible
through the split. Now adjust the thermometer up or down
within the rubber stopper such that when thermometer
assembly is inserted into the mouth of the test tube, the
thermometer bulb will be approximately in the middle of the
solvent volume that you will use in the test tube at the
beginning of the procedure. {The liquid height will be
approximately 4-5 cm from the bottom of the test tube.}
2. Prepare an ice-water slurry. To minimize the amount of icewater required it is suggested that you use a 250-mL beaker.
Fill the beaker about 2/3 full with ice, add just enough water
to fill the spaces between the ice pieces. Now using your glass
stirring rod, stir the ice-H2O mixture until the temperature
reaches approximately ±0.2 ˚C.
Figure 4. Set up to monitor temperature.
Procedure Part 1. Freezing point of pure cyclohexane:
3. Remove the split rubber stopper thermometer assembly from the 15×150 mm test tube. To mass the liquid
solvent, place the clean, dry 15 x 150 mm test tube into a dry 250 mL Erlenmeyer flask, in order to hold the tube
up-right when you place it on the balance. Place the test-tube and flask assembly on a top loading centigram
balance and tare it (this sets the balance to read 0.00 g).
4. Pour about 20 mL of cyclohexane into the test tube and record the mass to the nearest ±0.01 g in your notebook
(information may be transferred to your report form, later).
5. Put one spinvane magnetic stir bar into the test tube with the solvent. Re-assemble your apparatus. During the
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data collection, you may hold the apparatus by the split rubber stopper or with a utility clamp without transferring
heat to the solution.
6. We will construct one cooling curve to observe the equilibrium between the liquid and solid solvent at the
experimentally determined freezing (melting) point and record the temperature at which this occurs. Transfer the
re-assembled freezing point apparatus to the beaker containing the ice-water bath on top of a magnetic stirrer unit.
Make sure that the cyclohexane level in the test tube is below the surface of the ice-water bath. Add more ice if
needed. Turn the magnetic stirrer ON and adjust the speed so it will stir the pure cyclohexane solvent smoothly.
When the temperature of the solvent is approximately 14-12˚C begin to take time-temperature readings and record
them in the table every 15 seconds.
When the thermometer reading has reached a plateau (recorded temperature remains constant) collect 5 or 6 data
points more to record this event and data collection can be discontinued. You may remove the apparatus from the
ice-H2O bath and allow the solvent to warm up and liquefy completely to be used in part 2. Plot the data using
Excel and record the experimental temperature of freezing of the pure solvent, Tf˚, in your notebook. This
temperature corresponds to the last few constant temperature readings you recorded.
Part 2. Determination of kf for Cyclohexane
Descriptive Introduction
In this part of the experiment, the molal freezing point depression constant, kf , of cyclohexane will be determined
experimentally. The freezing temperature will be found for a solution using a known mass of cyclohexane (from
part 1) as the solvent and a measured mass of para-dichlorobenzene as the solute. The freezing point depression,
∆Tf, of the solution is found by determining the difference between the freezing temperature of the solution and
the freezing temperature of the pure solvent found in part 1. The molality of the solution, m , is calculated from
the known masses of solute and solvent. The freezing point depression constant of the solvent, kf, may be found
by solving equation 2 for kf = ∆Tf/ m
Procedure Part 2: Freezing point of known solution
7. Do not mass solute out until you are ready to make the solution since it will sublime rapidly resulting in a
preventable error! When ready, use a square plastic weighing boat, mass out approximately 0.5 g (±0.01 g) of
para-dichlorobenzene (Mm=147.01 g/mol). Remove the stopper/thermometer assembly just far enough to add the
sample of p-dichlorobenzene and avoid loss of cyclohexane solvent. Re-assemble your freezing point apparatus
(FPA) and insert it into a 250 mL Erlenmyer flask to hold-it upright. Place the Erlenmyer flask and FPA on the
magnetic stirrer unit, turn the stirrer ON and stir to dissolve the solute completely to form a solution. While the
solute is being dissolved, add about (3-6 g) of NaCl to your ice-water bath, in the 250 mL beaker, and stir to
dissolve. Check the temperature of the ice-water-NaCl solution with another thermometer. We are looking for a
temperature below 0˚C but no more than -1 to -2 ˚C.
8. Place your FPA into the ice-water bath over the magnetic stirrer and turn it ON. Bring your FPA to the front
wall of your beaker so that you may observe the changes taking place inside the FPA. Observe the solution to see
if solid (freezing) does occur and note the approximate temperature. Remove your FPA from the ice-water bath
and allow to warm and form a solution again. Prepare for time-temperature data collection. Re-insert your FPA
into the ice-water bath, and when the temperature inside your FPA is ~12-10˚C, start taking temperature-time data
and record it every 15 seconds until you have collected ~5-8 data points beyond the first sign of solid formation,
or freezing. Remove your FPA from the Ice-bath.
9. Allow solid-liquid solution to warm and repeat the process in step 8, using the same solution for a second
determination. When you have finished the measurement, remove the magnetic stir bar, wipe the thermometer and
magnetic stir bar with a paper towel place it carefully on your desk. Take the test tube and pour the solution into
the waste cyclohexane bottle located under the fume hood for the waste disposal. Do not pour it into the sink!
Remove the last trace of solution by rinsing the test tube with 1-2 mL cyclohexane, dispose of the wash into the
waste container and warm the test-tube in your hand to evaporate the last traces of liquid and dry the test tube.
When a solute is added to the solvent the shape of the cooling curve changes from what is observed in Figure 1
(pure solvent) to that shown in Figure 5. When the solvent begins to freezes we see the temperature begin to
decrease rather than remain constant as observed with the pure solvent.
-4-
For both known and unknown solutions we must split our
time-temperature data into two parts, one that represents
the cooling of the solution and the other that represents
the freezing of the solvent. From our time-temperature
data we select the first few data points that correspond to
a straight line and represent the cooling of the liquid.
Using Excel we draw a least-squares straight line (Exceltrendline) through the data points selected (1st trendline).
We also draw another trendline through the remaining
data points(2nd trendline) that correspond to the freezing
of the solvent. The temperature at the point where these
two lines intersect is the freezing point of the solution.
Figure 5. Time vs. temperature data for solution
This temperature can be obtained algebraically from the intersection of the two Excel trendlines.
Part 3. The Molar Mass of an Unknown Solid
Descriptive Introduction
In this section, a measured mass of an unknown solute will be added to a fresh sample of cyclohexane solvent.
Both solvent and solute masses will be determined before mixing. The freezing point depression, ∆Tf, of this new
solution will then determined. Since kf has already been obtained in part 2, the molality of the solution, m,
containing the unknown can be calculated from equation 2 as follows: m = -∆Tf/kf. The molality, which is in
units of moles solute per kg of solvent, may now be used to find the number of moles of unknown solute present.
Since the mass of the unknown is measured at the beginning of part 3, the molar mass may now be calculated.
Watch your units, they insure a proper sequence of calculations.
Procedure Part 3: Freezing point of unknown solution
10. Use your clean dry 15×150 mm test tube from step 9 and obtain a fresh sample of ~20 mL of cyclohexane,
mass it to a precision of (±0.01 g) and record it in your notebook.
11. Use a plastic weighing boat, mass out approximately 0.5 g (±0.01 g) of one of the unknown solutes provided
(there are three available) and add it to the solvent in the test tube. Insert the magnetic stirrer, thermometer/rubber
stopper assembly into your test tube to re-assemble your FPA. As in step 7, stir the mixture to dissolve the solute
completely. Position your FPA at the inner wall of the beaker closest to you so you may observe the formation of
solid as the temperature decreases.
12. Make sure your cold temperature bath (ice-water-NaCl) is still able to go down to approximately -2˚C. If not
add more ice. Place your apparatus into your ice-bath with the magnetic stirrer ON, and check to see by cooling if
a solid forms and note the approximate temperature. Warm back up and start collecting time-temperature data in
15 s intervals when the temperature in the FPA reaches approximately12-10˚C. Continue collecting data until you
have obtained ~5-6 data points past the temperature at which the first sign of a solid was observed. Record your
data in your notebook. Allow solid to melt completely by warming the test tube and contents in your hand.
13. Collect time-temperature data as in step 12 for a second determination of the freezing temperature of your
unknown solution. When you have finished the measurement, remove thermometer/rubber stopper assembly,
magnetic stir bar and wipe them off with paper towel and return it to the cart. Pour the solution in the test tube
into the waste cyclohexane container located under the fume hood. Clean out your test tube with a little soap,
water, and a test tube brush and place it on the equipment cart.
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__
E1
Colligative Properties
of Solutions: ∆Tf
Name __________________Date _________
Section: __________MW/TTH/M-TH (circle)
Partner’s Name (if any)________________
Instructor: __________________________
1. National Fire Protection Association (NFPA) labeling for hazardous materials.
Do a short internet search for an NFPA 704 Fire Diamond for cyclohexane and p-dichlorobenzene
(aka 1,4 para-dichlorobenzene).
(a) Where is the location of the diamond (Left, Top, Right, Bottom) for flammability? ____________
(b) What is the color of the diamond for flammability? _______________________
(c) What is the Degree of Hazard for flammability of cyclohexane? _____
What does this mean? ___________________________________________________________
(d) What is the Degree of Hazard for flammability of para-dichlorobenzene? _____
What does this mean? ___________________________________________________________
2. (a) A given pure solvent has a freezing point of 6.00 °C. Show the cooling curve for this solvent starting from
approximately 12˚C to its freezing point.
(b) If the freezing point of a pure solvent is 6.00 °C, will the
solvent which is contaminated with a soluble material (impure)
have a freezing point higher than, lower than, or same as, circle
(d) Show the cooling curve below for this contaminated solvent in (b) from approximately 12˚C to slightly
beyond the freezing point. Indicate on the plot where the freezing point occurs.
3. The freezing point of a cyclohexane sample is 6.20 °C. A solution is prepared by dissolving 0.4660 g of an
unknown solute in 36.0 g cyclohexane. The freezing point of the solution is 4.11 °C.
(a) Calculate the molar mass, Mm, of the unknown solute below. [kf for cyclohexane is 20.0 °C·kg/mole]
(b) The freezing point depression constant, kf, depends on the solvent, solute or both. [circle your answer]
(c) The relationship between ∆Tf and molar mass of a solute is such that as ∆Tf increases, the molar mass
-6-
E1
Colligative Properties
of Solutions: ∆Tf
Name __________________Date _________
Section: MW/TTH/M-TH (circle)
Partner’s Name (if any)________________
Report Form
Instructor: __________________________
DATA
Part 1. Temperature of freezing of the pure solvent, ∆Tf˚.
Mass of (~20 mL) of cyclohexane used here in part 1, and Trial 1 and 2 in part 2. _______________ g
Time(s) / Temperature (˚C) data for pure solvent:
0 s________ 15 s________ 30 s________ 45 s________ 60 s________ 75 s________
90 s________ 105 s________ 120 s________ 135 s________ 150 s________ 165 s________
180 s________ 195 s________ 210 s________ 225 s________ 240 s________ 255 s________
270 s________ 285 s________ 300 s________ 315 s________ 330 s________ 345 s________
Part 2. Determination of known solution, Tf(soln).
Trial 1
Mass of (~20 mL) of cyclohexane {from part 1? insert} __________ g
Mass of para-dichlorobenzene
__________ g
Trial 2
← _same as T1__ g
← _same as T1__ g
Time(s) / Temperature (˚C) data Trial 1:
0 s________ 15 s________ 30 s________ 45 s________ 60 s________ 75 s________
90 s________ 105 s________ 120 s________ 135 s________ 150 s________ 165 s________
180 s________ 195 s________ 210 s________ 225 s________ 240 s________ 255 s________
270 s________ 285 s________ 300 s________ 315 s________ 330 s________ 345 s________
Time(s) / Temperature (˚C) data Trial 2:
0 s________ 15 s________ 30 s________ 45 s________ 60 s________ 75 s________
90 s________ 105 s________ 120 s________ 135 s________ 150 s________ 165 s________
180 s________ 195 s________ 210 s________ 225 s________ 240 s________ 255 s________
270 s________ 285 s________ 300 s________ 315 s________ 330 s________ 345 s________
Part 3. Determination of unknown solution, Tf(soln). Unknown# ______
Trial 1
__________ g
__________ g
Mass of (~20 mL) of cyclohexane
Mass of unknown solute
Trial 2
← _same as T1__ g
← _same as T1__ g
Time(s) / Temperature (˚C) data Trial 1:
0 s________ 15 s________ 30 s________ 45 s________ 60 s________ 75 s________
90 s________ 105 s________ 120 s________ 135 s________ 150 s________ 165 s________
180 s________ 195 s________ 210 s________ 225 s________ 240 s________ 255 s________
270 s________ 285 s________ 300 s________ 315 s________ 330 s________ 345 s________
-7-
Time(s) / Temperature (˚C) data Trial 2:
0 s________ 15 s________ 30 s________ 45 s________ 60 s________ 75 s________
90 s________ 105 s________ 120 s________ 135 s________ 150 s________ 165 s________
180 s________ 195 s________ 210 s________ 225 s________ 240 s________ 255 s________
270 s________ 285 s________ 300 s________ 315 s________ 330 s________ 345 s________
Calculations and Results
Part 1.
Temperature of freezing of cyclohexane, Tf˚ (from Excel plot, attach to your report) ___________ t˚C
Part 2. Determination of kf
Temperature of freezing of known
cyclohexane/para-dichlorobenzene solution, Tf(sol’n)
Trial 1
Trial 2
__________ ˚C
__________ ˚C
(Attach Excel data and calculations.)
Avg Tf(sol’n) = __________˚C
∆Tf = Tf,solution – T˚f,solvent =
__________ ˚C (show calculation)
Molality of known solution
Molality =
n solute
m solvent (kg)
__________ m (show calculation)
=
Average kf = -∆Tf/ m =

Avg kf = __________˚/molal
Part 3. Determination of the Mmass of unknown solute
Temperature of freezing of unknown solution, Tf(sol’n)
(Attach Excel data and calculations.)
Trial 1
__________ ˚C
Trial 2
__________ ˚C
Avg Tf(sol’n) = __________˚C
∆Tf = Tf,solution – T˚f,solvent =
__________ ˚C (show calculation)
molality = -∆Tf/kf =
__________ m (show calculation)
nsolute = m (molality)(mass solvent (kg)) =
Mmass =
____________ mol solute
=
____________ g/mol Unk# _______
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Questions/Problems
Problems
1. Cyclohexanol, C6H11OH, is sometimes used as the solvent in molecular weight determinations
by freezing point depression. If 0.253 g of benzoic acid, C6H5COOH, dissolved in 12.45 g of
cyclohexanol, lowered the freezing-point of pure cyclohexanol by 6.55 ˚C, what is the molal
freezing-point constant, kf, of this solvent? (show calculation below, pay attention to significant
figures.)
_________________˚/ m
2. Since the freezing point of a solution depends on the relative number of particles, what would
you calculate to be the freezing point of 0.1 m solutions in water of
(a) NaCl, and (b) BaCl2?
Assume that these salts are 100% ionized in solution. {Compare your answers with the actual
respective freezing points: -0.348 ˚C and -0.470 ˚C. The difference is due to the decreased
activity of the ions (discussed in lecture). Because of the attractive forces between the positively
and negatively charged ions, they do not move completely independently of one another.}
(show calculation below, pay attention to significant figures.)
(a) __________ ˚C
(b) __________ ˚C
3. How many grams of each of the following per kilogram of water in your car radiator are needed
to give equal protection against freezing down to -10.0 ˚C? (show calculation below)
(a) Methyl alcohol, CH3OH, b.p. 64.6 ˚C.
__________ g
(b) Ethylene glycol, C2H4(OH)2, b.p. 197.2 ˚C.
__________ g
(c) In spite of higher cost, what advantage does ethylene glycol possess over methyl
alcohol as a winter antifreeze and/or summer coolant?
-9-

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