Department of Chemical EngineeringUniversity of San Carlos – Technological Center

Nasipit, Talamban, Cebu City

ChE 323L

Physical Chemistry Laboratory 1

Colligative Properties: Freezing-Point Determination

Date(s) Performed: December 5, 2015

Date Submitted: December 19, 2015

A laboratory report submitted to

Dr. Alchris W. Go, PhD

Instructor, ChE 323L

Submitted by:

Bernard Kenneth A. Dela Cerna

BSChE-3

1. Introduction

This experiment deals with one of the colligative properties which is freezing-point

depression. Colligative properties are properties that depend only on the number of solute

particles in an ideal solution and not on the identity of the solute particles. Colligative

properties are important for characterizing the nature of a solute after it is dissolved in a

solvent and for determining molar masses of substances [Zumdahl & Zumdahl, 2012].

Colligative properties are governed by two laws, Raoult's law and Henry's law.

Raoult's law states that the relation between the ratio of the partial vapor pressure of each

component to its vapor pressure as a pure substance is approximately equal to its mole

fraction in a mixture. Mixtures obey Raoult's law when the components are structurally

similar. Henry's law states that for real dilute solutions, the vapor pressure of the solute is

proportional to its mole fraction, but the constant of proprtionality is not the vapor

pressure of the pure substance. Mixtures whose solute obeys Henry's law and whose

solvent obeys Raoult's law are called ideal-dilute solutions.

Freezing-point depression, a colligative property, is the lowering of a freezing point

of a solution due to the addition of a nonvolatile solute. The lowering of the freezing

point is due to the reduction of the chemical potential of the liquid solvent due to the

presence of solute [Atkins & de Paula, 2014].

Chemical potential is the partial molar Gibbs energy of a substance. The reduction in

chemical potential of the solvent means that the solid-liquid equilibrium takes place at a

lower temperature. The chemical potetial is lowered due to an entropy effect. The vapor

pressure of a pure liquid reflects the affinity of a solution towards greater entropy, which

can be achieved if the liquid changes to gas. When a solute is present, there is an

additional contribution to the entropy of the liquid. The solute's effect on the entropy is

reflected by the lowering of the vapor pressure, which lowers the freezing point of the

solvent. Because of the increase in entropy of the liquid, it reduces the tendency of the

liquid molecules to solidify/freeze which means that a lower temperature must be reached

before equilibrium between solid and solution is reached.

2

The difference between the freezing point of the pure solvent and the freezing point

of the solution is the freezing-point depression. This is shown in the following equation:

∆ T fp=T ps−T s

where Tps is the freezing point of the pure solvent, Ts is the freezing point of the

solution, and ΔTfp is the freezing point depression.

The freezing point depression is directly related to the molality of the solution. Their

relationship is expressed by the following equation:

∆ T fp=k f∗m∗i

where kf is the molal freezing-point depression constant of the solvent, m is the

molality of the solution, and i is the van't Hoff factor.

Non-electrolytes are substances that dissolve in water but does not dissociate into

ions. Electrolytes, especially the strong ones, break apart into ions when dissolved in

water [Zumdahl & Zumdahl, 2012]. The van't Hoff factor, i, tells us the relationship

between the moles of solute dissolved and the moles of particles in solution. The

theoretical van't Hoff factor of a strong electrolyte is the number of ions per formula unit.

For a non-electrolyte, its van't Hoff factor is 1 since it does not dissociate in water.

3

2. Objectives of the Experiment

2.1. To determine the freezing point depression of an electrolyte and a

nonelectrolyte using the Beckmann freezing point apparatus

2.2. To determine the van’t Hoff factor of an electrolyte and a nonelectrolyte

from the freezing point depression data

4

3. Methodology

3.1 Materials

Quantity Name of Material Chemical formula

200 mL Distilled water H2O

34.2 g Sucrose C12H22O11

5.8 g Salt NaCl

Rock Salt NaCl

Ice H2O

3.2 Equipment and Apparatus

Beckmann's freezing point apparatus Alcohol thermometer

Beaker Digital thermometer

Analytical balance

100-mL volumetric flask

3.3 Procedures

The group went to the counter to borrow the necessary materials and apparatus to be

used. The glasswares were then washed with water and detergent. After washing, the

glasswares were dried using lint-free tissues.

One of the members was then assigned to prepare the salt and sucrose solution. The

salt solution was prepared by placing a beaker in an analytical balance, pressing the tare

button, and adding salt to the beaker until about 5.8 grams was reached. A 100-mL

volumetric flask was placed in the analytical balance and weighed. This weight was

5

noted. The volumetric flask was then filled with distilled water up to its mark. It was then

weighed and the new weight was also recorded. The weight of the empty flask was

subtracted from the weight of the flask filled with water to obtain the weight of the 100-

mL of water to be used to make the solution. The weight of the water and the salt was

then recorded in the journal. The salt was then dissolved in the water and set aside. The

same was done with the sucrose solution with the sucrose used weighing about 34.2

grams. The sucrose solution was also set aside for later use.

To prepare the freezing mixture, ice cubes were taken from the refrigerator of the

lab. It was then placed in the large vessel of the Beckmann's freezing point set-up in

layers, alternating with rock salt, to create a freezing mixture whose temperature, which

was measured with the alcohol thermometer, was more or less than -10 °C. The first

substance whose freezing point was measured was distilled water. It was added to the

main test tube via the side inlet which was then covered with a rubber cork after adding.

The digital thermometer was inserted to the main test tube through a hole in the top cork

of the main test tube. The main test tube was then placed in a larger test tube that would

serve as an air jacket. They were then placed in the larger vesser containing the freezing

mixture.

One of the members was assigned to stir the water inside the main test tube to make

sure that the temperature was evenly distributed inside. Another member was assigned to

stir the freezing mixture to ensure that the test tube would always be in constant contact

with the freezing mixture and to make sure that the salt and ice would mix. The last

member was assigned to checking the solution for the formation of ice crystals and

reading the temperature in the digital thermometer. When the first ice crystals formed,

one of the members took note of the temperature reading and wrote it down in the lab

journal. The main test tube was then washed with water and detergent and dried. The

used freezing mixture was disposed and replaced with a new batch of ice and salt. 2 trials

were done for the determination of the freezing point of water. The same procedures were

done for the determination of the freezing point of the salt solution and the sucrose

solution with 2 trials being done for each. After all the data had been gathered, all the

equipment and apparatus were washed and dried and returned to the counter. The work

place was also cleaned after the experiment was done.

6

4. Results and Discussion

Distilled Water Salt solution Sucrose solution

Freez

ing

Point

Depr

essio

n

Trial 1

(°C)

-0.105 -4.144 -2.105

Trial 2 (°C) -0.005 -4.279 -2.064

Average (°C) -0.055 -4.2115 -2.0845

Std. dev. (°C) 0.071 0.09546 0.02899

Van't Hoff

Factor

Experimental -- 2.230 1.084

Theoretical -- 2 1

% Error -- 11.5 % 8.4%

Table 1: Freezing Point Depression of Solutions with their respective Van't Hoff Factors

As observed in the table above, the salt solution had a larger freezing point

depression compared to that of sucrose. It can also be seen that the calculated

van't Hoff factor of the salt solution is larger than that of sucrose. This confirms

the relationship of the van't Hoff factor to a solute's identity as an electrolyte or

non-electrolyte. An electrolyte, such as salt, dissociates into more ions than a non-

electrolyte, such as sucrose, which does not dissociate at all. This means that the

salt solution has a greater freezing point depression than sucrose as seen in the

data because the van't Hoff factor of salt is also greater than that of sucrose.

As observed in the calculations above, the van't Hoff factor for salt and

sucrose exceeded the theoretical value. This should not be since the theoretical

value is the highest possible value that the solute could obtain. Since salt only has

2 ions that can deionize in a solution, it cannot achieve a van't Hoff factor greater

than 2. The same reasoning applies to the van't Hoff factor for sucrose.

One of the possible reasons why the group obtained an erroneous data may

be the recording of the temperature when the first ice crystals formed. It was

observed during the experiment that the crystals formed only after the stirrer and

thermometer were not in contact with the solution. We also observed that the

temperature of the solutions kept on decreasing and when we remove the

7

thermometer and stirrer, the ice crystals then appear and when we return the

thermometer, the temperature reading is higher than the reading before the

thermometer was removed.

7

Using the calculated molality from the experiment and the theoretical van't

Hoff factor, the freezing point of the solutions should have been:

Solution Molality of

Solution (m)

Theoretical

van’t Hoff

Factor

Theoretical

Freezing Point of

Solution (°C)

Average

Experimental

Freezing Point (°C)

Salt 1.0019 2 -3.727 -4.2115

Sucrose 1.0069 1 -1.873 -2.0845

Table 3: Calculated Freezing Point of Solution from Molality of Solution and Theoretical

van’t Hoff Factor vs Experimental Freezing Point of Solution

With the prior knowledge that ∆ T f =k f ∙msolution ∙ i and ∆ T f =T f solvent−T f solution, and we can

manipulate both equations to compute for the theoretical freezing point of the solution:

(Given kf for water is 1.86 °C/m and freezing point of water is 0°C.)

T fsolution=T fsolvent−∆ T f

T fsolution=T fsolvent−(k f ∙ msolution∙ i)

T fsalt=0∘C−(1.86∘Cm

∙1.0019 ∙ 2)=−3.727∘C

T fsalt=0∘C−(1.86∘Cm

∙1.0069 ∙1)=−1.873∘C

As observed in the table above, our experimental freezing point temperature of the

solution is lower compared to the theoretical freezing point. This caused our calculated

van’t Hoff Factor to exceed the maximum possible factor.

8

5. Conclusion

The freezing point depression found from doing the experiment shows that an

electrolyte has a greater freezing point depression than a non-electrolyte. The van't Hoff

factor of an electrolyte is also greater than that of a non-electrolyte. Both statements are

true due to the fact that electrolytes dissociate into more ions than non-electrolytes.

9

6. Answers to Questions

6.1 Define an ideal solution and a nonvolatile solute

An ideal solution is a solution that obeys Raoul's law. A solution that obeys Raoult's

law have components that are structurally similar. They obey this law throughout the

composition range from one pure component to another. A nonvolatile solute is a solute

that when dissolved, has no tendency to escape from the solution into the vapor phase.

6.2 Enumerate and explain the assumptions made in formulating the

equation used in freezing point depression. When is the equation∆ T fp=kf∗m

applicable?

One of the assumptions is that the solutions behave ideally(obey Raoult's

law) and have low concentrations. Colligative properties depend only on the

number of solute particles and not on their identity. This statement is mostly true

for dilute solutions since they are closer to the ideal behavior than the more

concentrated solutions. Another assumption made is that the solute is nonvolatile

and will not contribute to the vapor pressure of the solution. If the solute is

volatile, it would add up to the vapor pressure of the solution, which in turn would

give us a result that would deviate from the expected value. This equation is

applicable to non-electrolyte solutions whose ideal van't Hoff factor is one. The

equation used in this experiment contained the van't Hoff factor to account for the

dissocation of the solute into ions. Since it is no longer placed in the equation in

the question, the van't Hoff factor for solutions using this equation must be one.

6.3 If there is a difference between the calculated values and the ideal values,

explain why.

Our calculated values were higher than the ideal values. As explained in the

discussion, one of the possible reasons is the erroneous recording of the

temperature due to the crystallization occurring only when the stirrer and

thermometer were removed. Another reason may be that the solution was super

cooled, causing the ice crystals to form at a temperature lower than the expected

freezing point.

10

6.4 Explain why a covalent compound has an ideal van't Hoff factor of one.

10

Covalent compounds are generally non-electrolytes. Non-electrolytes do not

dissociate into ions in aqueous solution. Since the van't Hoff factor tells us the

relationship between the moles of solute dissolved and the moles of particles it

forms in a solution, the ideal van't Hoff factor for covalent compounds, which are

non-polar in general and are insoluble in the polar solvent water, would be one.

6.5 Explain why a reduction in chemical potential leads to freezing point depression

and boiling point elevation.

The reduction in chemical potential of the solvent means that the solid-liquid

equilibrium takes place at a lower temperature. The chemical potential is lowered due to

an entropy effect. The vapor pressure of a pure liquid reflects the affinity of a solution

towards greater entropy, which means that the lower the vapor pressure, the greater the

entropy of a solution and the lower the chemical potential. When a solute is present, there

is an additional contribution to the entropy of the liquid. The solute's effect on the

entropy is reflected by the lowering of the vapor pressure, which lowers the freezing

point of the solvent and elevates the boiling point. Because of the increase in entropy of

the liquid, it reduces the tendency of the liquid molecules to solidify/freeze which means

that a lower temperature must be reached before equilibrium between solid and solution

is reached. The increase in entropy of the liquid weakens the tendency of the liquid to

form gas and thus a higher boiling point must be reached for the liquid to evaporate.

6.6 Explain why, for identification of compounds with very large molecular weight

like proteins, the rise of osmotic pressure is more frequently used rather than the freezing

point depression and boiling point elevation.

Compounds with very large molecular weight like proteins are scarcely soluble in

most solvents. Due to this condition, the concentrations of their solutions would be too

low for a significant change in the freezing or boiling point to be determined. Osmotic

pressure, on the other hand, would be better to use because even a small amount of solute

would create a bigger change compared to the change it would do to boiling and freezing

points. This is the reason why the rise of osmotic pressure is used for these types of

compounds.

11

6.7 Mention at least three common industrial applications where the freezing point

depression is used.

Freezing point depression is being used by automobile industries by to

estimate how much anti-freeze they need to add to make sure that fuels don't

freeze in cars during winter.

Dirty ice cream or ice cream being sold by street vendors are placed in

containers that have a mixture of ice and salt surrounding it as a cooling

mixture. The ice and salt mixture is colder than regular ice due to the

depression of the freezing point of water brought about by the presence of

salt.

In countries where the winters are so cold that the snow becomes too thick on

the roads for cars to pass through, salts are placed on the snow for them to

melt easily and make the road accesible again. When the temperature is lower

than what NaCl can handle, CaCl2 is sometimes used instead since it

dissociates into more ions than NaCl.

12

7. References

Atkins, P., & de Paula, J. (2014). Atkins' Physical Chemistry (Tenth Edition ed.). Oxford: Oxford University Press.

Echipare, L., & Harju, Z. (n.d.). Freezing Point Depression. Retrieved December 18, 2015, from UCDavis ChemWiki: http://chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/Solutions_and_Mixtures/Colligative_Properties/Freezing_Point_Depression#Contributors

Lower, S. (n.d.). 7b.4: Osmosis and Osmotic Pressure. Retrieved December 18, 2015, from UCDavis ChemWiki: http://chemwiki.ucdavis.edu/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A_Lower's_Chem1/07b._Solution_Chemistry/7b.4%3A_Osmosis_and_Osmotic_Pressure

Zumdahl, S. S., & Zumdahl, S. A. (2012). Chemistry: An Atoms First Approach, International Edition. Brooks/Cole, Cengage Learning.

13

8. Appendices

14