Gas Law Homework Problem Set

1. The volume of a bicycle tire is 1.35 liters and the manufacturer recommends a tire pressure of 125 PSI.
   1. If you want the bicycle tire to have the correct pressure at 20.0 °C, what volume of air is required at STP?
   2. If you fill the tire with nitrogen, what is the mass of the gas?
   3. If you fill the tire with compressed gas from a 100.0 mL cylinder at 1.50x10⁷ Pa, what is the final pressure in the tire? Will it explode?
   4. You fill the bicycle tire to 125 PSI on a cold december day (-22 °F), and leave it until a hot day in July (101 °F). What is the pressure of the tire (assuming that it does not leak and it does not change volume or burst).

2. A fire extinguisher with a volume of 3.0 liters is filled with 150.0 grams of CO₂. Assuming that it is an ideal gas, what is the pressure at 20.0 °C?

   What is the volume of the CO₂ at 1.0 atm and 25 °C after the CO₂ is released from the fire extinguisher?

3. A diver is using a NITROX mixture (oxygen enriched air to reduce risk of decompression illness and increase bottom time) to breath underwater. If the mixture is 36% O₂ and 64% N₂) what is the partial pressure of oxygen (Pa) when the diver is at
   1. sea level (1.0 atm)
   2. 33.9 ft (2.0 atm)
   3. 100 ft (3.9 atm)
   4. 500 ft (15.8 atm). (The high partial pressure of nitrogen at this depth would cause the diver to suffer from severe nitrogen narcossis. This is far deeper than a diver can go , even with NITROX.)

4. A ballon used for sampling stratospheric ozone is filled with 150.0 kg of He. What is the volume of the balloon when,
   1. The balloon starts from a research station in Antartica at sea level where the barrometric pressure is 755 mmHg and the temperature is -25.0 °C.
   2. The balloon rises to 10,000 ft (3048 m, the height of a medium size mountain) where the instruments report that the temperature is -50 °C and the pressure is 6.368x10⁴ Pa.
   3. The balloon continues to rise, at 29,028 ft (8,848 m, the height of Mt Everest and about typical crusing altitude for a jet aircraft) the temperature is -70 °C and the pressure is 2.30x10⁴ Pa.
   4. The balloon enters the stratosphere, at 65000 ft (20,000 m, crusing altutude for a U2 spy plane) the temperature is -70 °C and the pressure is 3.68x10³ Pa.
   5. The balloon reaches its maximum altitude of 100000 ft (30500 m) the temperature is -3°C and the pressure is 616 Pa.

5. I recieved the following question from Larry Stratton (larstrat@centurytel.net), a retired civil engineer. Assume a blocked length of pipe with a contained volume of 10 ft^3. Assume air is injected until a pressure gauge reading of 3.5 psi is stabilized. Then assume an air leak at the rate of 0.003 ft^3/min. How long will it take for the air pressure to drop to 2.5 psi gauge reading? In the real world of low pressure air testing for sewer pipes, there are factors not considered here, i.e., type of pipe etc., but this will do as an exercise. larstrat@centurytel.net

Scott Van Bramer
Department of Chemistry
Widener University
Chester, PA 19013

© copyright 1996, S.E. Van Bramer
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Last Updated: Saturday, May 18, 1996