The molecular (true) formula for a substance is not always the same as its empirical (simplest) formula. Both acetylene and benzene have the empirical formula CH. However, the molar mass for acetylene is 26 g/mol, while the molar mass of benzene is 78 g/mol. This is because the molecular formula for acetylene is C₂H₂ while the molecular formula for benzene is C₆H₆.

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To determine the molar mass of a gaseous substance and to use this value to find the molecular formula of the substance.

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Wear protective glasses and an apron at all times. Avoid skin contact with solids and solutions. There should be no flames in the laboratory during this laboratory activity. Dispose of all solutions in the containers provided by your teacher. Wash your hands before leaving the laboratory.

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Handle the flask at all times with a paper towel. Determine all masses to the nearest 0.01 g. You may develop your own data table or your teacher may provide you one.

1. Determine the mass of a stoppered 250 mL flask of air.
2. In an operating fume hood, place the tubing outlet from an unknown gas supply completely into the flask. Allow the gas to flow for at least 30 s to replace the air. Stopper tightly. If your teacher suggests the gas is less dense than air, invert the flask for filling.
3. Find the total mass of the flask, stopper, and unknown gas. Repeat Steps 2 and 3.
4. Place a mark on the outside of the flask neck at the bottom of the stopper. In an operating fume hood, fill the flask to the mark with water.
5. Measure the volume of water to the nearest milliliter with a graduated cylinder.
6. Determine the temperature and air pressure in the laboratory.
7. Wash hands thoroughly before leaving the laboratory.

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1. What is the volume (in liters) of air in the flask?
2. The density of air varies with changes in temperature and pressure. Refer to Table 1 below to find the density of air at your laboratory conditions. Use this density value (g/L) to calculate the mass of air in your flask.

   Temp\Pressure	730 mmHg	740 mmHg	750 mmHg	760 mmHg	770 mmHg
   30 oC	1.11	1.13	1.14	1.16	1.18
   25 oC	1.13	1.15	1.16	1.18	1.20
   20 oC	1.15	1.17	1.18	1.20	1.22
   15 oC	1.17	1.19	1.20	1.22	1.24

   Table 1 - Density of air (g/L) at various temperatures and pressures

3. What is the mass of the empty flask?
4. What is the mass of your sample of unknown gas?
5. Calculate the density of the unknown gas at the temperature and pressure of the laboratory.
6. The volume occupied by one mole of a gas (its molar volume) is the same for all gases at a given temperature and pressure. Refer to Table 2 for the proper molar volume of a gas at your experimental conditions. Use this value to calculate the experimental molar mass of your unknown gas.

   Temp\Pressure	730 mmHg	740 mmHg	750 mmHg	760 mmHg	770 mmHg
   30 oC	25.9	25.5	25.2	24.9	24.6
   25 oC	25.5	25.1	24.8	24.5	24.1
   20 oC	25.0	24.7	24.4	24.1	23.7
   15 oC	24.6	24.3	24.0	23.6	23.3

   Table 2 - Molar volume of ideal gas at various temperatures and pressures

   If your pressure or temperature is not shown, make estimates from the tables for density and molar volume.

7. (Data Check: Present the calculated value from Step 6 to your teacher to initial.) Obtain the empirical (simplest) formula for your unknown gas from your teacher. Determine its empirical formula mass.
8. The molecular formula is a whole-number multiple of the empirical formula.
   1. Is your molar mass the same as the empirical formula mass?
   2. If so, what is the molecular formula of your unknown gaseous substance? (If not, try doubling or tripling your empirical formula. Which multiple gives the closest molar mass to your experimental value?)
9. Using the molecular formula you found in Calculation 8, calculate the molar mass of your unknown gas. Report your molecular formula and molar mass to your teacher for verification.
10. Using the accepted value for molar mass from Calculation 9, find the error and percent error in the experimental value of the molar mass found in Calculation 6.
11. Which step(s) in the procedure do you believe contributed most to the total error found in this laboratory activity? Explain.

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1. Explain in your own words what you learned in this laboratory activity.
2. How would the density of the unknown gas affect how you hold the flask as you displaced the air with it?
3. Suppose that the empirical formula of your unknown gas were C₂H₄, and the experimental molar mass of your unknown gas were found to be twice that of the empirical formula mass. Explain why you would not write the molecular formula as 2C₂H₄.
4. Draw two pictures, one representing C₄H₈ and the other 2.C₂H₄. Use labeled circles to represent the units of each.
5. Challenge Item: Describe a possible modification of this procedure using Avogadro's Hypothesis to determine the molar mass of an unknown gas.

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Teachers Guide

Preparing for the Laboratory Activity

• Major Chemical Concept
• Level
• Expected Student Background
• Time
• Safety
• Materials
• Advance Preparation

Conducting the Laboratory Activity

• Pre-Lab Discussion
• Teacher/Student Interaction
• Anticipated Student Results
• Sample Data
• Sample Data Analysis
• Answers to Implications and Applications
• Possible Extensions

Assessing the Laboratory Learning

• Laboratory Practical Items
• Paper/Pencil Items
• Laboratory Practical Items (Teacher Notes)
• Paper/Pencil Items Answers

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Preparing for the Laboratory Activity

Major Chemical Concept

The molecular formula is a whole-number multiple of the empirical formula. When finding the mass of a gas sample, the mass of air in the air-filled flask must be taken into account.

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Appropriate for all levels.

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Students should be able to:

• Calculate density
• Find formula masses
• Use a balance
• Read a graduated cylinder
• Read a thermometer
• Read a barometer
• Select appropriate information from tables
• Calculate percent error

This laboratory activity is not intended to be used as part of a gas unit. It should follow the development of the mole concept and empirical and molecular formulas.

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30 - 40 min

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• No flames should be allowed if flammable gases are used.
• Use fume hood for filling and venting gases from flask.

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Consumables (per class)

• Unknown gas candidates are:

Butane (pressurized cans of lighter fluid)

Helium (where balloons are sold)

Oxygen (school shop, welding supply or pharmacy)

Burner gas (mostly methane, but may contain some ethane)

• See Advance Preparation below.

Non-Consumables (per lab team)

• 1 Balance
• 1 Erlenmeyer or Florence flask, 250 mL
• 1 Graduated cylinder, 500 mL (preferred)
• 1 Rubber stopper or cork, solid, wrapped with plastic wrap
• 1 Thermometer

Non-Consumable (for class)

• Barometer

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Pressurized cans should be fitted with rubber tubing. You can also dispense gases from an automobile inner tube. Remove the inner valve, and attach a clamped rubber tubing to valve. Fill the inner tube from pressurized source of gas.

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Conducting the Laboratory Activity

Pre-Lab Discussion

Using a flask of water, lead students to develop a method for determining the volume and mass of water in the flask. Pour out the water and ask if an empty flask is truly empty. Allow sufficient wait-time so that students realize that the "empty" flask contains air. Discussion will provide a method for determining the mass of air in the flask, a necessary step in this activity. Make sure that students know how to read a barometer. Emphasize the need for very careful measurements, recorded to the proper number of significant figures, since masses of the unknown gases will be small. Demonstrate filling the flask upright for gases more dense than air and inverted for gases less dense than air.

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Make suggestions and ask questions about reading measurements precisely, the type unknown gas, the design of the data table, whether to hold the flask upright or upside down to fill. (The density of air is about 1.3 g/L at STP.) Remind students to touch the flask as little as possible, to use a dry flask, and not to measure the volume of the flask with water until the second run is completed. Encourage students curiosity about the colorless gas.

Discuss how to use tables of air density and molar volume. Emphasize the importance of following rules for carrying significant figures carefully throughout the calculations. All supporting setups of calculations should be shown.

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Sample Data

1. Mass of flask, stopper, and air 96.29 g
2. Mass of flask, stopper, and unknown gas 96.58 g
3. Volume of flask to bottom of stopper 265 mL
4. Temperature 20 °C
5. Pressure 759 mmHg

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Student responses will vary. Mass is small and is probably the greatest contributor to error. Another error is caused by inadequate displacement of air while collecting the unknown gas.

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1. Student responses will vary: ⁺ 4-8% is acceptable. Gives chance for teacher to correct misconceptions - a form of student self-assessment; non-threatening and ungraded except for extra credit.
2. Less than density of air: hold flask mouth down so gas "falls up."
3. 2 C₂H₄ represents two molecules of C₂H₄ . C₄H₈ represents one molecule of C₄H₈ .
4. Answers will vary, but students should show two unattached "units" of C₂H₄ and one "unit" of C₄H₈. These units are, of course, molecules.
5. Requires higher-order thinking skills. Not all students will be able to answer this. The only difference in procedure is that the mass of a known gas is compared to an unknown gas. This method does not require the use of molar volume. This modification could be used for an extra credit activity, or for the class to do as a second activity to confirm the results of the first.

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1. The same activity could be treated as a gas-law problem without the molar volume table being provided.
2. Molecular formulas can also be determined using a volatile liquid in a warm flask as a demonstration for advanced students.

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Assessing the Laboratory Learning

Laboratory Practical Items

1. Go to Stations 1 through 6 and examine the models of different molecules. Indicate on your quiz paper the number(s) of all molecules that (has/have) the empirical formula C₂H₆O.
2. Go to Station 7 and determine the mass of the flask containing the unknown gas, using the balance at the station. You should also know that the flask, stopper and air had a total mass of _____. The temperature and pressure were _____ and _____. The volume of the flask was _____mL. Find the molar mass of unknown gas in the flask.

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1. Find the molar mass of this compound:

   Mass of empty flask and stopper	104.57 g
   Mass of flask, stopper and sample gas	105.03 g
   Volume of flask	256 mL
   Temperature	20 oC
   Barometer reading	750 mmHg

2. What is the apparent molecular formula of a compound if its empirical formula is CH₂O and a student found its experimental molar mass to be 59 g/mol?
3. What is the percent error in the mass obtained in Question 2 ?

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1. Construct six models. Three or four could be correct.
2. Prepare a sample of gas in a tightly stoppered flask. Fill in blanks in question for mass of flask, stopper and air; temperature and pressure; volume of flask up to bottom of stopper. Provide Tables 1 and 2. (You may also decide to allow students to use their lab write-ups for reference.)

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1. Student will need molar volume table for this calculation. Results:

   Mass of gas:	0.45 g
   Molar volume:	24.4 L
   Calculated molar mass:	44 g

2. Nearest molecular formula = C₂H₄O₂ or HC₂H₃O₂ (acetic acid)
3. Percent error = 1/60 x 100 = 1.67 %

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