Application of the Ideal Gas Law and Avogadro’s Hypothesis

I teach the Gas Laws as the final topic in students’ first Chemistry course.¹ The KMT, Avogadro’s Hypothesis, the Combined Gas Law, and the Ideal Gas Law take three 70-minute class periods at most.

I’m not a fan of the usual verification labs regarding Boyle’s, Charles’ or Gay-Lussac’s Law.² These can be recipe-driven; students don’t find them all that engaging.

That said, the application of the Ideal Gas Law presents golden opportunities for learning.

This is such an opportunity.

The accompanying supplemental material outlines a ca. 40-minute activity in which students use the Ideal Gas Law, the composition of air—78% N₂(v/v), 21%O₂(v/v), and 1% Ar(v/v)³—and Avogadro’s Hypothesis, to determine the molar mass of two gases, presented as unknowns—CO₂ and CH₄.⁴

Students don’t need to get their hands dirty; you can do the work before class. Or students can do the whole shebang, depending on how much time you have, and how much challenge you want to give.

Materials

• Four empty, preferably clear, 2-L soda bottles each with its cap. We assume that each bottle & lid has the same mass. Feel free to check. You could also use 2-L Erlenmeyer flasks with stoppers.
• Centigram balance
• Large graduated cylinder—500-mL or 1000-mL would make it easy
• Natural gas, CH₄, from the gas tap in your lab, delivered with a rubber hose
• Dry ice (ca 8 g)
• Other gases as you may have: This could include propane, C₃H₈, from a camping cylinder, or butane, C₄H₁₀, from a portable stove . . .

Procedure

1. Determine the volume of one of the bottles by filling it to the rim with water, and decanting the water into a large graduated cylinder. Record this volume; it will be the volume of each 2-L bottle used. Since this bottle is now wet, set it aside.
2. Record the temperature and barometric pressure in the laboratory. If you don’t have a barometer, “borrow” the one in the Physics lab, or check the local weather network.
3. To fill a bottle with CO₂, add about 8 g of dry ice. When it has sublimated, cap the bottle and weigh it. This bottle contains CO₂(g), obtained by upward displacement of air. I have not tried generating CO₂ by reacting, say, vinegar, CH₃COOH(aq) and baking soda, NaHCO₃, and filling the bottle with CO₂. Carbon dioxide gas obtained in this manner will likely be saturated with water vapor, for which we can correct in the calculations.⁵
4. To another bottle, attach a hose to the natural gas tap and fill the bottle by downward displacement of air. When you detect a strong odor of natural gas, all of the air has been displaced. Cap the bottle and weigh it, recording the mass on the bottle. This bottle contains pretty much pure CH₄(g).
5. Collect any other gases that you have as appropriate. I think that two “unknowns” in the activity is sufficient. If you have other gases, you could save these for your laboratory exam.

What students need to do:

Given the percent composition of air, students calculate the average molar mass of air. Thanks to Avogadro’s hypothesis⁶, they know that each bottle, filled with any gas at the same temperature and at pressure, will contain the same quantity of moles. They can now determine the quantity of moles of air in the bottle, and hence its mass. The mass of air is subtracted it from the mass of the bottle & air—the so-called “empty bottle”, to determine the mass of the bottle containing a vacuum.

This vacuum-containing bottle mass is then used to determine the mass of the “unknown” gas. Since students know the volume, temperature and pressure of the gas⁷—and the quantity of moles of gas in the bottle, they can determine the molar mass, g·mol^-1, of each unknown.

The supplemental material is a student-ready handout, which also contains clues to help students determine the identity of the gas after they calculate its molar mass.

Bonuses:

A. This activity gives—to two significant digits—extremely accurate results.

B. Teachers can give as much or as little direction as they like, catering the challenge-level to their students.