03 determination of molar mass by vapor density · adapted from advanced chemistry with vernier...

Adapted from Advanced Chemistry with Vernier & Laboratory Experiments for Advanced Placement Chemistry by Sally Ann Vonderbrink, Ph. D.

Determination of Molar Mass by Vapor Density

One of the properties that helps characterize a substance is its molar mass. If the substance in question is a volatile liquid, a common method to determine its molar mass is to vaporize it and apply the ideal gas law, PV = nRT to the data collected. Because the liquid is volatile, it can easily be converted to a vapor. Volatile substances are usually composed of nonpolar molecules. As a result the molecules have primarily London dispersion forces and very little thermal energy is required to overcome these attractive forces since the molecules are relatively small. Therefore, the liquid vaporizes easily and quickly at temperatures less than 100°C. While the substance is in the vapor phase, you can measure its volume, pressure, and temperature. You can then use the ideal gas law to calculate the number of moles of the substance. Finally, you can use the number of moles of the gas to calculate molar mass.

OBJECTIVES In this experiment, you will

• Evaporate a sample of a liquid substance and measure certain physical properties of the substance as it condenses.

• Determine the molar mass of an unknown liquid.

Figure 1

MATERIALS Data Collection Mechanism unknown volatile liquidTemperature Probe fume hoodGas Pressure Sensor or barometer test tube, 13 × 100 mm, and holderring stand two 400 mL beakers (or larger)two utility clamps hot platealuminum foil analytical balanceice needle tissues or paper towels

Best results are obtained when the test tube containing the sample is submerged in the water bath to just below the foil cap. Consider using tall form beakers for your water baths.



PROCEDURE Before beginning the experiment, make sure that you have a means of measuring the barometric pressure in the room. A conventional barometer or a Gas Pressure Sensor may be used.

1. Obtain and wear goggles. Conduct this experiment in a fume hood or well-ventilated area.

2. Trim a piece of aluminum foil so that it just covers the top of a small, 13 × 100 mm, test tube. Use a needle to make a small hole in the center of the foil. Measure and record the mass of the test tube and foil.

3. Prepare a hot-water bath by warming about 300 mL of tap water in a 400 mL beaker. Keep the beaker on a hot plate once the water is warm. You want it to boil by Step 8.

4. Use a second 400 mL beaker to prepare an ice-water bath.

5. Set up the data collection system.

a. Connect a Temperature Probe to the interface. b. Start the data collection program. Be sure the program shows the correct readings for the probe. c. There is no need to store and graph the data for this experiment.

6. Obtain a liquid sample of an unknown volatile compound. Pour about 0.5 mL of the liquid into the test tube and quickly cover the test tube with the aluminum foil. Use your fingernail to make an air-tight seal with the foil just under the lip of the test tube. Place the test tube in the hot water bath. Make sure that the foil is above the water level, but submerge your test tube as far as possible without making contact with the bottom of the beaker (see Figure 1).

7. Immerse the Temperature Probe in the hot-water bath (see Figure 1). Do not allow the tip of the probe to touch the beaker.

8. Heat the hot-water bath to boiling and maintain the boiling as your sample of liquid vaporizes. Note that some of your sample will escape the test tube through the needle hole in the foil. This process also serves to flush the air out of the test tube.

9. Keep the test tube in the boiling-water bath for at least three minutes after all of the liquid in the test tube has vaporized. Watch the temperature readings and record the temperature of the boiling water bath, which will be used in the ideal gas law calculations.

10. Use a test-tube holder to quickly transfer the test tube to the ice water bath. Cool the test tube for about one minute, then remove it and dry it completely. Measure and record the mass of the test tube and the aluminum foil top.

11. Record the room’s barometric pressure.

12. Rinse out the test tube and fill it to the top with tap water. Cover the test tube with the aluminum foil. Measure and record the mass of the test tube, water, and foil.



DATA TABLE

Trial 1 Trial 2

Mass of test tube and foil cover (g)

Temperature of hot water bath (ºC)

Mass of test tube and foil and gas sample (g)

Barometric pressure (atm)

Mass of test tube and foil and water (g)

PRE-LAB QUESTIONS 1. What is the difference between a vapor and a gas?

2. A student performs an experiment designed to determine the molar mass of a sample of an unknown volatile liquid. The following data was collected:

Trial 1

Mass of test tube and foil cover (g) 7.5228 g

Temperature of water bath (ºC) 99°C

Mass of test tube and foil and condensed gas (g) 7.5387 g

Barometric pressure (atm) 0.987 atm

Mass of test tube and foil and water (g) 16.1228 g

(a) Determine the mass of the condensed unknown. (b) Assuming the density of water to be 1.00 g/mL, determine the total volume of the test tube.

(c) Starting with the ideal gas law, substitute the fact that n is equal to grams/molar mass and derive an

expression for calculating the experimental molar mass of the student’s volatile liquid sample.

(d) Calculate the molar mass for this student’s sample.

(e) Calculate the percent error for this student’s experimental determination of the molar mass assuming the unknown liquid was methyl alcohol (CH3OH).



POST-LAB QUESTIONS AND DATA ANALYSIS

1. Determine the mass of the condensed unknown.

2. Use the mass and density of the water in the test tube from Step 12 of the procedure to calculate the volume of the test tube.

3. Use the expression you derived for Pre-Lab Question # 2 part (c) along with the data collected to calculate the molar mass of your unknown compound.

4. Use your experimentally determined molar mass and reference material to identify the unknown volatile liquid you tested.

5. A student failed to vaporize the entire sample prior to placing the test tube in the ice bath. How did this error affect the calculated molar mass? Justify your answer using calculations.

6. A different student failed to dry the outside of the test tube prior to massing it in Step 12. How did this error affect the calculated molar mass? Justify your answer using calculations.

7. How would your calculated molar mass have been affected if you had used twice the initial amount of the unknown compound?



TEACHER INFORMATION 1. This experiment conforms to the guidelines for the third laboratory experiment listed in the College

Board AP Chemistry guide (the Acorn book). A thermometer (preferably digital) can be substituted for the temperature probe.

2. Before beginning the experiment, make sure that you have a means of measuring the barometric pressure in the room. A conventional barometer or a Gas Pressure Sensor may be used.

3. For best results your students should use a balance with at least 0.001 g accuracy and tall beakers for the hot water baths.

4. The experiment should be carried out in a fume hood and the liquid should be heated with a hot plate.

5. Your students must have the following skills to successfully complete this experiment. • Handle the equipment precisely and carefully so that the liquid evaporates and condenses

according to the procedure. • Use an analytical balance. • Understand the ideal gas law and its mathematical applications.

6. Your students should use a volatile liquid that vaporizes below 100°C and has a low toxicity.

Recommended liquids are listed below. It is best to have small containers with approximately 1 mL of a volatile liquid pre-labeled with a KEY. It is best to use at least three from the following list and repeat them again and again in a random pattern to create 12 or so “unknowns”. Anhydrous reagents are required to achieve good precision.

• Acetone (b.p. 56.2°C, molar mass = 58.08 g/mol) • Cyclohexane (b.p. 80.7°C, molar mass = 84.16 g/mol) • Ethyl acetate (b.p. 77.2°C, molar mass = 88.105 g/mol) • Ethyl alcohol, anhydrous (b.p. 78.4°C, molar mass = 46.07 g/mol) • Methyl alcohol, anhydrous (b.p. 64.7°C, molar mass = 32.05 g/mol)

7. Each student lab team will use 0.5 mL of a volatile liquid. The small volumes improve the safety of this experiment. Demonstrate how to use your fingernail to scrape down the foil cap just under the lip of the test tube to improve the seal.

8. Students are directed to measure the mass of a test tube filled with tap water, covered by their piece of aluminum foil. We suggest that students place an Erlenmeyer flask on a balance, tare it, and then add the test tube to the flask to determine the mass of the test tube, water, and foil (since the foil will already have a pinhole in it).

HAZARD ALERTS Acetone: Dangerous fire risk; flammable; slightly toxic by ingestion and inhalation. Hazard Code: C—Somewhat hazardous. Cyc1ohexane: Dangerous fire risk; flammable liquid; slightly toxic by ingestion, inhalation, and skin contact; store in a dedicated flammables cabinet. Hazard Code: B—Hazardous.



Ethyl acetate: Dangerous fire hazard and explosion risk; irritating to skin and eyes; slightly toxic by ingestion, inhalation, and skin absorption; store in a dedicated flammables cabinet. Hazard Code: B—Hazardous. Ethyl alcohol (ethanol): Dangerous fire risk; flammable; addition of denaturant makes the product poisonous-it cannot be made non-poisonous; store in a dedicated flammables cabinet. Hazard Code: C—Somewhat hazardous. Methyl alcohol (methanol): Dangerous fire risk; flammable; toxic by ingestion (ingestion may cause blindness); store in a dedicated flammables cabinet. Hazard Code: B—Hazardous. The hazard information reference is: Flinn Scientific, Inc., Chemical and Biological Catalog Reference Manual, P.O. Box 219, Batavia, IL 60510, (800) 452-1261, www.flinnsci.com

SAMPLE DATA TABLE (same as that given in Pre-Lab Question 2)

Trial 1






Answers to PRE-LAB QUESTIONS Before beginning the experiment, make sure that you have a means of measuring the barometric pressure in the room. A conventional barometer or a Vernier Gas Pressure Sensor may be used.

1. What is the difference between a vapor and a gas? A gas is a gas at room temperature and pressure while a vapor describes the “gas” of a substance that is a liquid or solid at room temperature. Therefore, in a given room with an open container of ethanol there is nitrogen gas, oxygen gas, carbon dioxide gas, etc. present along with water vapor and ethanol vapor.



2. A student performs an experiment designed to determine the molar mass of a sample of unknown volatile liquid. The following data was collected.

Trial 1






(a) Determine the mass of the condensed unknown.

Mass of test tube, foil and condensed gas Mass of test tube and foil cover = Mass of condensed gas7.5387g 7.5228g 0.0159 g

−∴ − =

(b) Assuming the density of water to be 1.00 g/mL, determine the total volume of the test tube.

Mass of test tube, foil and water Mass of test tube and foil cover = Mass of water

16.1228g 7.5228g 8.6000 g assuming a density of 1.00g/mL, the volume of the test tube (and volume of the vapor) i

−∴ − = ∴

s equal to 8.60 mL

(c) Starting with the ideal gas law, substitute the fact that n is equal to grams/molar mass and derive an expression for calculating the experimental molar mass of the student’s volatile liquid sample.

( )

PV nRTgPV RT

MMgRTMM PV gRT MMPV

=

∴ =

∴ = ∴ =

(d) Calculate the molar mass for this student’s sample.

( ) L0.0159 g 0.0821=gRTMM

PV=

• atmmol• K

99 273 K⎛ ⎞

+⎜ ⎟⎝ ⎠

( )0.987 atm( ) 0.00860 L( )

g= 57.093 mol



(e) Calculate the percent error for this student’s experimental molar mass assuming the unknown volatile liquid was ethyl alcohol (C2H5OH).

2 5g of C H OH 46.08

mol57.093 46.08 100% percent error = 23.90%

46.08

MM =

−∴ × =

Answers to POST-LAB QUESTIONS AND DATA ANALYSIS (Answers are based on the sample data given in the Pre-Lab section. Actual student values will vary based on the unknowns used.)

1. Determine the mass of the condensed unknown. Mass of test tube, foil and condensed gas Mass of test tube and foil cover = Mass of condensed gas

7.5387g 7.5228g 0.0159 g−

∴ − = 2. Use the mass and density of the water in the test tube from Step 12 of the procedure to calculate the

volume of the test tube. Mass of test tube, foil and water Mass of test tube and foil cover = Mass of water

16.1228g 7.5228g 8.6000 g assuming a density of 1.00g/mL, the volume of the test tube (and volume of the vapor) i

−∴ − = ∴

s equal to 8.60 mL

3. Use the expression you derived for Pre-Lab Question # 2 part iii. along with the data collected to calculate the molar mass of your unknown compound.

( ) L0.0159 g 0.0821=gRTMM

PV=

• atmmol• K

99 273 K⎛ ⎞

+⎜ ⎟⎝ ⎠

( )0.987 atm( ) 0.00860 L( )

g= 57.093 mol

4. Use your experimentally determined molar mass and reference material to identify the unknown volatile liquid you tested. Answers will vary based on the unknowns used. Item 6 of the TEACHER INFORMATION section lists appropriate unknowns. You may either refer students to reference material or simply post the possible unknowns so that students can look up the correct chemical formulas. Students should use the molar mass calculated from the unknown’s chemical formula as a basis for comparison.

5. A student failed to vaporize the entire sample prior to placing the test tube in the ice bath. How did this error affect the calculated molar mass? Justify your answer using calculations. If some of the original liquid sample remained in the test tube, two factors are at work. Credit should be given for either of the justifications given below:

The molar mass would be reported as too small. The volume of the vapor would be reported as too high since some of the “space” in the test tube was actually occupied by liquid rather than

vapor. Therefore the V term in the expression gRTMMPV

= is too large (and in the denominator),



thus the calculated molar mass is too small. OR The molar mass would be reported as too large. The mass of the vapor is reported as too large since the unvaporized liquid is more dense than the vapor alone would be. Therefore, the g or

mass term in the expression gRTMMPV

= is too large (and in the numerator), thus the calculated

molar mass is too large.

6. A different student failed to dry the outside of the test tube prior to massing it in Step 12. How did this error affect the calculated molar mass? Justify your answer using calculations. The molar mass would be reported as too small. Failing to dry the outside of the test tube at the conclusion of the experiment affects the following calculation which ultimately becomes the volume of the gas. Mass of test tube, foil and water Mass of test tube and foil cover = Mass of water−

Therefore, the V term in the expression gRTMMPV

= is too large (and in the denominator), thus the

calculated molar mass is too small. 7. How would your calculated molar mass have been affected if you had used twice the initial amount of

the unknown compound? The calculated molar mass of the liquid would be the same. It would simply take longer for the sample to vaporize completely.

T h e r m o m e t e r

B o i l i n g W a t e r

P i n H o l e

R u b b e r B a n d

A l u m i n u m F o i l

V o l a t i l e L i q u i d

An experiment is to be performed to determine the molecular mass of a volatile liquid by the vapor density method. The equipment shown above is to be used for the experiment. A barometer is also available.

(a) What data are needed to calculate the molecular mass of the liquid? (b) What procedures are needed to obtain these data?

(c) List the calculations necessary to determine the molecular mass. (d) If the volatile liquid contains non-volatile impurities, how would the calculated value of the

molecular mass be affected? Explain your reasoning.

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Note that all parts a-d are worth 2 points each. Some of the [1] pieces are cut off

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03 determination of molar mass by vapor density · adapted from advanced chemistry with vernier...

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