Purpose

Determine the molar mass of a non-electrolyte using freezing point depression.

Theoretical Background

Textbook Reference

• Tro, Chemistry: A Molecular Approach, 5th Ed., Ch. 14.6.
• Tro, Chemistry: Structures and Properties, 2nd Ed., Ch. 13.6.

Colligative Properties

Several properties of solutions are colligative properties; these include:

• Vapor Pressure Lowering: In accordance with Raoult’s Law, the vapor pressure of a solution is decreased when a non-volatile solute is dissolved into a solvent.
• Freezing Point Depression: The freezing point of a solvent is lowered when a solute is dissolved in water.
• Boiling Point Elevation: The boiling point of a solution is higher than that of the pure solvent.
• Osmotic Pressure: Higher concentrations of solute would lead to greater amounts of water flowing into it through a semi-permeable membrane from a solution with lower concentration.

These colligative properties are similar in that they depend only on

• The concentration of solute particles^[1] present.
• The identity of the solvent (but not the solute).

Freezing Point Depression

When a solute is added to a solvent, the freezing point of the solute decreases by [latex]\Delta T_f[/latex] such that^[2]

[latex]T_{\mbox{f,soln}} = T_{\mbox{f,pure solvent}} - \Delta T_f[/latex]

The freezing point depression, in turn, is related to the molality of the solution [latex]m[/latex] by

[latex]\Delta T_f = K_f \times m[/latex]

where [latex]K_f[/latex] is the freezing point depression constant (in °C/m)^[3], and the molality of a solution is given by

[latex]?\mbox{ molal} = \frac{\mbox{moles solute}}{\mbox{kg solvent}}[/latex]

Given the freezing point depression constant [latex]K_f[/latex] and the freezing point of the solution as well as the pure solvent, you will be able to determine the molality of the solution. With the molality of the solution and the mass of solvent, you can figure out the number of moles of solute in the solution.  This, and the mass of solute added into the solution, will give you the molar mass of the solute.

Laboratory Procedures

In this experiment, you will measure the freezing point of cyclohexane and three solutions of cyclohexane with an unknown compound. Given the freezing point depression constant of cyclohexane (K_f = 20.8°C/m) and the experimental data, you can then find the molar mass of your unknown.

Supplies and Equipment

Equipment

• Large test tube
• Spatula
• Pipet bulb
• 10.00 mL volumetric pipet
• Digital thermometer
• 600 mL beaker
• 50 mL beaker
• test tube rack

Chemicals/Consumables

• Weighing Paper
• Cyclohexane
• Acetone
• Unknown solid
• Ice
• Salt (non-chemical grade)

Procedure

While we know that the freezing point of cyclohexane is 6.59°C (CRC Handbook of Chemistry and Physics), in practice it is not a good idea to rely on this since your thermometer may not be perfectly calibrated. It is often more accurate to measure the difference between two measurements than their respective absolute values.  As a result, we will start by measuring the freezing point of pure cyclohexane.  In this way, any systematic error associated with the thermometer would hopefully cancel out through the procedure.

Hints and Safety Rules

• Handle the test tube and the solution gently; it is important that you do not break the test tube during the course of the experiment.
• You will need to add salt to the ice bath to sufficiently lower the temperature of the solution.  As mentioned above, this is another example of freezing point depression in action.
• As cyclohexane is flammable, you should not use a Bunsen flame or a hot plate to warm up the solution – it is unnecessary and dangerous. Also, you’re more likely to boil off some of the cyclohexane which would make later steps inaccurate as it will change the amount of solvent present.
• On the report form, you will just report the average freezing point for each solution. However, in your lab notebook, you must report the freezing point measured for each trial.
• There is no reason to warm the solution back up to room temperature between trials. Proceed with the experiment by refreezing the cyclohexane/solution once you have observed the last crystal of cyclohexane melt.

Freezing Point of Pure Cyclohexane

1. Rinse with acetone and air dry a large test tube provided for this experiment.
2. Obtain a small amount of cyclohexane in a small beaker (not the beaker that contains your test tube). Using a volumetric pipet, measure accurately 10.00 mL of cyclohexane and dispense that into the test tube.  Place the test tube in a test tube rack.
3. Add salt and ice to the 600 mL beaker into which the test tube will be placed, to prepare an ice/salt bath.
4. Place the test tube into the ice/salt bath and gently stir the contents of the test tube with the digital thermometer until its contents have partially (~10-20%) frozen.
   A good rule of thumb is that, at this point, you will find it difficult to move the thermometer in the solution.
5. Take the test tube out of the beaker and, stirring, allow the test tube to warm up at room temperature.  As the cyclohexane melts, the temperature of the mixture should remain relatively constant.
6. Watch the cyclohexane carefully. At the instant that the very last crystal of cyclohexane melts, record the temperature. This is the melting/freezing point for the cyclohexane.
7. Repeat steps 4 to 6 two more times until you have three trials that are no more than 0.1°C apart from each other.

Freezing Point of Solutions of Cyclohexane with an Unknown Solute

In this part, you will make an unknown solution by dissolving the unknown compound into the cyclohexane into the test tube you used in the previous part, and measure the freezing point of this solution.

8. Write down the number for your assigned unknown.
9. Weigh accurately approximately 0.1 g of your assigned unknown compound and add all of it into the test tube containing cyclohexane. You may find it easier to dissolve it by stirring it with a glass rod, warming up the solution where necessary using your hand (not a hot plate).  If you are having difficulties dissolving the solution, consult your instructor for advice.
10. When the solute has completely dissolved, repeat steps 4-7 above with this solution.
11. Repeat steps 8 to 10 two more times (for a total of 0.2 g and 0.3 g approximately of unknown).

Waste Management

All chemicals from this experiment must be placed in the beaker labeled for hazardous waste for disposal.

Data Analysis

First, determine the masses of the solute and solvent present.

• For the solute, for each step you will have increasing masses of solute present.
• For the solvent, you will do this using the volume of cyclohexane dispensed.  The density of cyclohexane at room temperature is 0.7781 g/mL (Merck index, as indexed in PubChem).

Also, for each solution, you must determine the average freezing point for each solution (as well as the pure cyclohexane).

For each of the three solutions, you can determine the freezing point depression for each of these solutions.  Given that K_f = 20.8°C/m for cyclohexane, you can find the molality in each of these solutions using the formula

[latex]m = \frac{\Delta T_f}{K_f}[/latex]

Given the definition of the molality, the number of moles of solute in the solution is

[latex]\mbox{mol solute} = \mbox{molality} \times \mbox{kg solvent}[/latex]

and, since you know the mass of solute in each solution, you can find the molar mass of the solute from each trial.