# Relationship between freezing point depression and molar mass

### Determining Molar Mass

The freezing point depression is the difference in the freezing points of the . and freezing point depression, we can see similarities between the two. Ratios: molar mass of $$\ce{NaCl}$$, $$\: \text{g} = 1 \: \text{kg}$$. The equilibrium of a component (A) between a pure solid (S) phase and a Molar Mass of a solute by Freezing Point Depression: giving the relationship. The difference between these two temperatures allows for the calculation of the The molality, m, of a solution can be expressed in terms of the molar mass of.

Fill a mL beaker about one-third full of water, and add ice until the beaker is three-fourths full. Start the data collection. The computer acquires a temperature reading every second. Move the test tube into the ice-water bath and hold it so the level of liquid in the test tube is below the level of water in the bath. Immediately begin stirring the liquid with the wire stirrer, continuously and at a constant rate. Once freezing begins, as long as liquid and solid are both present, the temperature remains constant until the entire mass has solidified.

Allow the computer to continue recording the temperature until the plot has leveled off at a constant temperature. Note that once the cyclohexane has frozen solid, the temperature starts to decrease again. When a sufficient number of data points have been collected, stop the data collection.

Remove the test tube from the ice-water bath and let it warm up to room temperature. Adjust the y-axis limits so the plot fills the page. Title the graph, and then print it. Preparing a Solution of the Unknown Compound Accurately weigh 0. Check to be sure the cyclohexane contained in the test tube has melted.

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Remove the stopper from the test tube and carefully add the unknown solid to the cyclohexane, avoiding the loss of any compound adhering to the sides of the test tube or stopper. Replace the stopper and re-weigh the paper to account for any crystals that remain on it. Stir the solution in order to completely dissolve the solid. It is important that no crystals remain. Make a new ice-water bath. Measuring the Freezing Point of the Unknown Compound Prepare the computer to collect a second set of data.

Move the test tube that contains the solution into the ice-water bath. Immediately begin stirring the solution continuously and at a constant rate. Collect the data for — s in order to clearly see the change in slope that occurs as the solution freezes.

Stop the data collection. Save the data, adjust the limits of the y-axis, title the graph, and print it. Do not throw any cyclohexane or unknown compound down the sink. Pour the liquid mixture into the "Laboratory Waste" jar. Rinse the test tube and temperature probe with acetone to remove the last traces of any crystals, pouring the rinses in the waste jar.

Freezing-point depression is the phenomenon that is observed when the freezing point of a solution is lower than that of the pure solvent. This phenomenon results from interactions between the solute and solvent molecules. The difference in freezing temperatures is directly proportional to the number of solute particles dissolved in the solvent.

The molar mass of a non-volatile solute can be calculated from the difference in freezing temperatures if the masses of the solvent and the solute in the solution are known.

This video will introduce the relationship between freezing-point depression and the molar mass of the solute, a procedure for determining molar mass of an unknown solute, and some real world applications of inducing and observing changes in freezing temperature. Freezing point depression is a colligative property, meaning it is only affected by the ratio of solute to solvent particles, and not their identity.

At the freezing point of a pure substance, the rates of melting and freezing are equal. When a solution is cooled to the freezing point of its solvent, the solvent molecules begin to form a solid. It is less energetically favorable to form a mixed lattice of solvent and solute particles.

The solute particles remain in the solution phase. Only solvent-solvent interactions contribute to lattice formation, so solvent-solute interactions reduce the rate of freezing compared to that of the pure solvent. The temperature at which freezing begins is the freezing point of the solution. The solution continues cooling as it freezes, but this continued decrease in temperature reflects the increasing concentration of solute in the solution phase. Eventually, the solution temperature is so low and so little solvent remains in the liquid phase that it becomes favorable for the solute particles to form a lattice.

Once this point is reached, the temperature remains approximately constant until the mixture has frozen solid. The molar mass of the solute, and therefore the identify of the solute, can be determined from the relationship between the freezing point of the pure solvent, the freezing point of the solution, and the molality of the solution.

Molality, or m, is a measure of concentration in moles of the solute per kilogram of the solvent. This relationship depends on the the freezing point depression constant of the solvent and the number of solute particles produced per formula unit that dissolves. Molality can be expressed in terms of molar mass, so the equation can be rearranged to solve for the molar mass of the solute.

Plugging this into the freezing point equation allows the elucidation of the molar mass, once the temperature difference is known.

Now that you understand the phenomenon of freezing point depression, let's go through a procedure for determining the molar mass of an unknown solute from freezing point temperatures. The solute is a non-ionic, non-volatile organic molecule that produces one particle per formula unit dissolved, and the solvent is cyclohexane.

### Freezing Point Depression and its use to find molecular mass

To begin this experiment, connect the temperature probe to the computer for data collection. Insert the temperature probe and a stirrer into the sample container. Set the length of data collection and the rate of sampling. Allow sufficient time in the data collection for the sample to freeze. Set upper and lower limits of the temperature range to sample. Add 12 mL of cyclohexane to a clean, dry test tube. Wipe the temperature probe with a Kimwipe. Insert the stopper assembly into the test tube such that the tip of the temperature probe is centered in the liquid and does not touch the sides or bottom.

In a beaker, prepare an ice water bath. Para-dichlorobenzene is used in mothballs and urinal cakes, and so it may have a familiar smell, however direct inhalation of its vapors may be harmful or even toxic.

Students should avoid skin contact with para-dichlorobenzene and direct inhalation of its vapors. All heating of para-dichlorobenzene must be done under a fume hood. Waste Disposal All chemicals used must be disposed of in the proper waste container. The acetone and para-dichlorobenzene must not go down the sink!

Place a Bunsen burner below the wire gauze adjusting the height so that the flame will be in direct contact with the center of the wire gauze. Fill a mL beaker with tap water to just a few centimeters below the brim.

Place the beaker of water onto the wire gauze. This will serve as a hot water bath for the experiment. Use a thermometer to monitor the temperature of the water bath. Weigh a clean dry large test tube using an electronic balance, and record its mass. Add about 30 grams of para-dichlorobenzene PDB to the test tube. Reweigh and record the mass of the test tube and the PDB.

Calculate the mass of PDB in the test tube by difference. Use your utility clamp to clamp the large test tube containing the PDB to the ring stand as shown in Figure 4 we shall add the thermometer and stirrer presently.

Figure 4 Insert your thermometer into the split rubber stopper by prying apart the stopper and carefully sliding it over the middle of the thermometer. You should not have to force the thermometer at any time during this process.

Insert the stirring rod into the smaller hole in the stopper so that the loop at the end surrounds the thermometer as shown in Figure 4. As the temperature of the water bath reaches the melting point of the PDB, it will begin to melt. Support these by clamping the split rubber stopper to the ring stand as shown in Figure 4. Adjust the bottom of the thermometer bulb so that it is about 1 cm above the bottom of the large test tube.

Stir the contents of the large test tube by raising the glass loop up and down slowly to melt any remaining solid PDB. Turn off the Bunsen burner and carefully lower the iron ring and water bath. Using your beaker tongs, place the beaker of hot water onto the lab bench well away from the test tube.

Dry off the outside of the test tube using a paper towel. Monitor the temperature of the PDB as it cools. Stir the liquid slowly but continuously to help minimize supercooling. Continue for at least 4 minutes after the first solid starts to appear, or until the liquid has solidified to a point that you are no longer able to stir it.

## 10: Determination of the Molar Mass by Freezing Point Depression (Experiment)

Near the melting point you will observe crystals of PDB in the liquid, and these will increase in amount as the cooling proceeds. Note the temperature at which these crystals first start to appear.

Determining the Freezing Point of PBD with about 2 g Unknown Solute Weigh your unknown sample and its container on the electronic balance and record this mass on your data sheet. Carefully transfer about 2 grams of the unknown solid into the large test tube, taking great care that none of the unknown sample is spilled during this process.

If you do spill some you will need to start this step over with a fresh sample of weighed PDB. After transferring some of the unknown, reweigh the remaining unknown sample and its container.

Calculate the mass of unknown sample transferred to the test tube by difference. The amount you added should be between 1 and 3 grams. If you transferred less than 1 gram of unknown, you will need to add more unknown to the large test tube and reweigh before proceeding. Raise the hot water bath around the large test tube and heat the PDB-unknown mixture until it is completely melted. Stir well to mix the unknown with the PDB thoroughly. Remove the hot water bath as before, and dry off the outside of the test tube with a paper towel.

Monitor the temperature of the PBD-unknown mixture as it cools. Continue for at least 4 minutes after the first solid starts to appear, or until the mixture has solidified to a point that you are no longer able to stir it.