November 2015

# A different way to do gas laws — Part 3: Pressure-amount relationship

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John Eix (retired), Oakville ON

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This last article of a three-part series describes how to use syringes, pressure gauges and Mason jars to do the gas laws: Boyle’s Law (pV), Gay-Lussac’s Law (pT) and Avogadro’s Experiment (pn). The huge advantage of using a Mason jar for the pressure vs amount relationship is that the stopper and ring combination produce a sealed container that can withstand a pressure inside of 2 atm without fear of the stopper popping or the glass breaking.

A 500 mL Mason jar is used (see Fig. 1) with two different gases: air, plus one of oxygen, nitrogen, carbon dioxide, methane or propane. Depending on time, aliquots of 20 or 40 mL of the first gas are added to the Mason jar through the injection port using stopcock B. After each aliquot is added, measure the pressure by opening and closing stopcock A (pressure port). Cease adding gas once the pressure is greater than 550 mm of Hg or 73 kPa. You should have 8 to 17 readings depending on the volume of aliquot used. Let the gas inside the jar escape by opening stopcock B. Repeat for the second gas.

Fig. 1. S17 Science Gas Kit. The apparatus is called EQ 888 S17 Science Gas Kit apparatus is available at S17 Science for $90 US or CAN $108.00. Kits with other gas equipment to do more gas investigations can also be purchased. See www.s17science.com.

A sample set of data is shown in Fig. 2. A plot of pressure vs number of aliquots yields a straight line that passes through the origin as shown in Fig. 3. The amazing part of this graph for students is that both gases (air and CO2) follow the same straight line. To help students account for the trend ask the following questions:

- What variables have we found that alter the pressure of a gas? Temperature, volume of a sealed container and now the number of aliquots.
- If we compare two syringes containing 40 mL of CO2 at atmospheric pressure and room temperature, what is the simplest assumption we can make about the number of CO2 molecules in each of those syringes? Given p, T, V and # of aliquots are the same, the simplest assumption is that each syringe has the same number of CO2 molecules.
- Based on this assumption when we plot aliquots on the horizontal axis, what are we really plotting? Number of molecules.

Based on the graph and assumption, if we compare 40 mL of air with 40 mL of CO2 in a syringe at atmospheric pressure and room temperature, what can we conclude about the number of molecules in these two syringes? Since both 40 mL of air and 40 mL of CO2 fall on the same point on the graph then they must have the same number of molecules in each syringe assuming that two syringes of 40 mL of CO2 at atmospheric pressure and room temperature contain the same number of molecules — Avogadro’s principle.

Fig. 2. Sample data for air and carbon dioxide
Aliquot | mL added | Air gauge p. (mm of Hg) ± 2 | CO2 gauge p (mm of Hg) ± 2 | Difference ±4
0 | 0 | 0 | 0 | 0
1 | 20 | 20 | 20 | 0
2 | 40 | 52 | 52 | 0
3 | 60 | 90 | 95 | 5
4 | 80 | 130 | 130 | 0
5 | 100 | 168 | 170 | 2
6 | 120 | 202 | 200 | 2
7 | 140 | 245 | 240 | 5
8 | 160 | 278 | 280 | 2
9 | 180 | 315 | 315 | 0
10 | 200 | 352 | 350 | 2
11 | 220 | 383 | 387 | 4
12 | 240 | 422 | 422 | 0
13 | 260 | 460 | 458 | 2
14 | 280 | 488 | 495 | 7
15 | 300 | 528 | 525 | 3
16 | 320 | 560 | 552 | 8

Fig 3. Pressure vs aliquot for air and carbon dioxide.

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