September 2017

Just take a breath

Robert Perkins, Quest University Canada (retired) Squamish BC

If you ask students in elementary grades to take a breath and then describe what they have taken in, they will likely simply reply “air”. There are a number of exploration exercises, many of them using balloons/ garbage bags, to allow students to

discover the relationship between pressure, temperature and volume of a gas — in a non-mathematical manner. One particularly useful exercise is to have the students construct a Cartesian Diver.1

Once a required topic in high school chemistry courses, discussion of the Gas Laws has been removed from several provincial syllabi. This has been unfortunate, as it was a wonderful topic to allow exploration of the concepts of inverse and direct proportionality, both mathematically and also with a number of very simple demonstrations. One can also find a number of YouTube videos on the various Gas Laws.

If you ask students in high school to take a breath and then describe what they have taken in, most of them will hopefully be able to reply with nitrogen and oxygen. Students who are more environmentally aware will likely be able to comment that there is also carbon dioxide, and that the amount of this greenhouse gas in the atmosphere has been steadily increasing. Depending upon which gas is being considered, a problem arises for some students, as the concentration of a particular gas may be expressed as a percentage (nitrogen and oxygen make up nearly 99% of the atmosphere), or as in the case of carbon dioxide, as ppmv (parts per million by volume).2 Many students are not comfortable with using ppmv, and some have difficulty using percentages in calculations.

Most instructors will set thought-provoking problems³ that will require information from a number of sources, and they will then often encourage their students to work in small groups to come up with a solution.
I would like to share a class exercise that has been very useful in addressing a number of concepts related to Ideal Gases.

Suppose that you have a room of dimensions 7.00 metres by 5.00 metres by 2.50 metres.

Part A

How many blocks of butter would it take to represent the mass of the air in the room? You may assume that the air in the room is perfectly dry; i.e., it contains no water vapour.

The volume of the air in the room is easily determined (87.5 m3). Students should realize that they will need to find the density of dry air from the Internet (1.204 g/L at 20 ^oC and 1 atm). By using the appropriate conversion factors, and keeping track of the units, they should arrive at a final answer of 105 kg for the mass of the air in the room. This will correspond to approximately 231 blocks of butter (1 block is 454 g or
1 pound).

Part B

Assuming ideal behaviour, what mass of helium gas would be contained in the room? Using the Internet, the students will find that the concentration of helium in dry air is 5.24 ppmv. They may assume ideal behaviour for all the gases in the room.

Method 1

Using the volume of the room as determined in part A, the volume of helium may be determined:

Using the Ideal Gas Law for 20 ^oC (students must be careful to convert this temperature to Kelvin), this represents a total of 0.0191 mol of He, or 76.4 mg of He.

Method 2

If we consider that all the components in the air exhibit ideal behaviour, then the volume ratio of He will be equal to the mole ratio of He. The number of moles of helium gas may be determined from the number of moles of gas in the room using the Ideal Gas Law. This gives a total of 3.64 x 10³ mol of gas, of which 5.24 ppm is helium gas, or 0.0191 mol of He (76.4 mg).

The students are generally surprised to find that there is “that much He” in the room, as to their way of thinking, He is a very rare gas. One can complete the analysis by asking them to determine the mass of carbon dioxide in the room, ignoring the amount that has been produced by the class while they have been struggling with the above calculations.

Using the value of 3.64 x 103 mol of gas obtained above, of which approximately 400 ppm is CO₂, one obtains a value of 1.46 mol of CO₂. This corresponds to 64.1 g of carbon dioxide, equal to only 0.14 blocks of butter.

I hope that other instructors may find this to be a useful exercise for their students.