Molecular Weight of a Condensable Vapor

Name: Andrew Yaksic

Purpose: To experimentally determine the molecular weight of a condensable vapor.

Equipment: 6-cm-square thin aluminum foil, barometer, 200-mL graduated cylinder, 125-mL flask, rubber band, Bunsen burner, iron ring, wire gauze, ring stand, pin, analytical balance, 600-mL beaker, iron clamp, cooling pad, boiling chips

Materials: 1,2-dichloroethane, water

Introduction: There are several important laws pertaining to gas behavior. The core of all gas equations is the ideal gas equation, PV=nRT, where P represents pressure, V represents volume, n represents the number of moles of gas present, R represents the universal gas constant (62.4 torr-L/mol-K), and T represents the absolute temperature in degrees Kelvin. This law can be used to calculate any of the variables, so long as the other four are known.

Boyle's Law was formulated in 1662 by Robert Boyle. It states that pressure times volume is a constant. Thus, pressure and volume are inversely proportional. Charles's Law states the direct relationship between pressure and temperature. These two laws merge to form the combined gas law, which states that P1V1/T1=P2V2/T2. This law can be used to determine the condition of a gas, so long as five of the six variables are known.

An important concept in this experiment is dynamic equilibrium. This occurs when the rate of condensation equals the rate of evaporation. Dynamic equilibrium is responsible for the concept of vapor pressure, which is necessary in calculating the partial pressure of the vapor contained in the flask. Dalton's Law of Partial Pressures states that two gases contained in a flask will exert a pressure equal to the sum of the pressures that they would exert if they were not together in the same container. The partial pressures in this case arise from the vapor pressure from the liquid in a state of dynamic equilibrium and the air contained in the flask.

The volatile liquid used in this experiment is 1,2-dichloroethane. This is a molecule that looks like this:

This experiment will involve heating the liquid so that it evaporates completely, then waiting for it to condense so that it reaches dynamic equilibrium at room temperature. The number of moles will be calculated using the gas laws explained above. The weight of the 1,2-dichloroethane will be determined analytically.

Procedure:

1. A square of aluminum foil, about 6 cm on a side, was placed on the mouth of a 125- mL flask. The sides were folded down to fit securely over the mouth. The foil cap was secured to the flask using a rubber band. A pin was used to poke a hole in the center of the foil over the mouth of the flask. The hole was made to be as small as possible. The flask and cap were weighed and the mass was recorded.

2. The cap was removed and 3 mL of 1,2-dichloroethane was poured into the flask. The cap was replaced.

3. A 600-mL beaker was two-thirds filled. Several boiling chips were placed into the beaker. The beaker was placed onto a ring stand. The flask was secured using an iron clamp and suspended in the beaker as shown below. The beaker was then heated.

4. The temperature of the boiling water and the barometric pressure were measured and recorded.

5. The flask was heated until the liquid was gone. The flask was removed from the beaker and set aside on a cooling board.

6. Once cool, the cap was examined to ensure that no water drops were on the outside surface of the aluminum. The flask, cap, and condensed liquid were weighed. The mass was recorded.

7. The flask was filled completely with water. The water was poured into a 200-mL graduated cylinder. The volume of the water was measured and recorded.

Observations:

Mass of flask plus cap: 53.1162 ± .0001 g
Mass of flask plus cap plus liquid: 53.5713 ± .0001 g Temperature of boiling water: 100.0 ± .2°C Barometric pressure: 744 ± 1 torr
Volume of the flask: 138 ± 2 mL
Temperature of air: 23.0 ± .2°C 

Results:

The observations above need to be adjusted for the air that was inside the flask. In order to do this, the following steps are necessary.

1. The mass of the air originally contained within the flask must be calculated. To do this, first the number of moles of air must be calculated using PV=nRT, and then that must be multiplied by the molecular weight of air, which is given as 28.95 grams per mole.

This means that the flask contained .161 grams of air when weighed “empty.”

In order to determine how many moles of air were in the air once the volatile liquid and vapor reach dynamic equilibrium, the combined gas law must be applied to determine what the volume of the vapor would have been at room temperature.

This means that .138 L - .110 L, or .028 L, of air remained in the flask with the vapor and liquid. In order to determine the mass of this air, PV=nRT must be used, as shown below.

Thus, there were .033 ± .002 grams of air in the flask with the vapor. This can be subtracted from the observed amount to find out the actual amount of liquid condensed.

• 53.5713 ± .0001 g - .033 ± .002 g = 53.538 ± .002 g
• 53.538 ± .002 g – 53.1162 ± .0001 g = .422 ± .002 g

There were .422 grams of 1,2-dichloroethane in the flask, taking the air in the flask into account.

The number of moles of vapor is shown by the calculation below. The calculation is done at 373 K because this is the temperature at which all of the 1,2-dichloroethane is in the
gaseous state, fully occupying the .138 L flask.

Thus, the molecular weight of 1,2-dichloroethane can be calculated as follows:

Molecular weight of 1,2-dichloroethane. (Grams of 1,2-dichloroethane divided by moles of 1,2-dichloroethane.)
= .422 ± .002 g / .00441 ± .00007 mol
= .422 ± .47% g / .00441 ± 1.59% mol
= 95.7 ± 2.06% g/mol
= 96 ± 2 g/mol

Discussion: The known value of the molecular weight of 1,2-dichloroethane is 99.0 grams per mole. A percent error calculation can be performed comparing the known value to the experimentally obtained value.

(observed – true) / true x 100
= (96 – 99) / 99 x 100
= -3.03% error.

This is a very reasonable amount of error. It is caused by several sources of error that present themselves throughout the course of the experiment. Since the result was too low, the results could have overcompensated for the amount of air present in the flask. In addition, during one of the final procedural steps, the cap was removed to wipe away excess liquid from the cap. It is possible that some of the liquid removed was condensed vapor, not water. Additionally, other sources of error exist. The limitations of crucial measuring devices, such as the barometer and the thermometer, caused slight error in an experiment that had to be precise. This explains the plus/minus allowance of 2, which would have brought the empirically obtained molecular weight to within 1 amu of the actual value.

The theory associated with this experiment is the atomic theory. Phase changes tie into the atomic theory of elements. The number of molecules of 1,2-dichloroethane does not change, whether in liquid or gaseous form, which enables the calculations from this experiment to successfully determine the number of moles of 1,2-dichloroethane. In addition, the kinetic theory of gases allowed calculations about different pressures and temperatures to take place according to the laws associated with the theory, as outlined in the Introduction.

There are several ramifications to this experiment. Primarily, it enables a scientist to determine the MW of any volatile liquid that is also a condensable vapor. The volumes of gases can be predicted at different temperatures, or at any different conditions. The volatile liquids used in this experiment must be large enough not to effuse from the pinhole created, so the mean free path of the vapor must be considered.

Questions:

1. a. Before adding the volatile liquid, the flask contains air.
b. At the point when the volatile liquid has completely vaporized, the flask contains some vapor and some air.
c. At the end of the experiment, at the final weighing, the flask contains some liquid, some vapor, and some air.

2. The temperature of boiling water is used for measuring the volume of the vapor instead of the temperature of the liquid after it has cooled to room temperature because the 1,2- dichloroethane is completely vaporized at the temperature of boiling water. At room temperature, the 1,2-dichloroethane is partially condensed, so some of the moles of the substance would be in liquid form. At the boiling point of water, the total number of moles is spread out throughout the total volume of the flask, making the calculation much simpler.

3. The deviations from ideal behavior should tend toward a smaller PV product than usual. This would make the calculated molecular weight too large, as the calculated number of moles calculated would be too small.

4. The volatile liquid used must have a high enough molecular weight not to be able to escape through the pinhole. It must also be able to condense at room temperature.

5. The error arising from neglect of the missing air is in the same direction as neglect of the vapor. The missing air represents mass that should be included in the final mass reading, but is not; the vapor also represents mass that should be included in the final mass reading, but is not.

6. The flask had a volume of .125 L. There were temperatures of 373 K and 298 K. If the gas had a volume of .125 L at 373 K, then it would have had a volume of .100 L at 298 K. The additional .25 L of air at 298 K would equal .010 mol of air by a PV=nRT calculation, assuming a pressure of 760 torr. .010 mol of air is equal to .2895 grams of air. The vapor pressure of the liquid must be enough to cause an error of 8 g/mol. Without more specific data about atmospheric pressure at the time of the experiment, the vapor pressure cannot be calculated.

Conclusion: The experiment was successful to a reasonable degree of accuracy. The purpose of the experiment was achieved.