# math probs by ashrafp

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```									I have a special, ideal balloon. This balloon does not exert any pressure on the gas inside
it. I start by taking the balloon and inflating it to 4 L in Wilmington DE last night. The
weather channel said that the temperature was 45.0 °F, and the pressure was 30.27 inches
of Hg.

1. First I take this balloon scuba diving and go down to a depth of 100 ft where the
pressure is 7 atm. and the temperature is 54.2 °F. What is the volume of the
balloon?
2. Next I take the ballon out to Colorado. In Denver when I arrive at the airport the
temperature is 68.4 °F and the barometric pressure is 640 mmHg. Now what size
is the balloon?
3. Next on my trip is a hike up to the top of Longs Peak (14,256 ft) where the
pressure is 470 torr and the temperature is -20°C. Now what size is the balloon?
4. Finally I take the balloon on the airplane for the trip home and let it out the
window. The 747 is flying at 40,000 ft where the pressure is about 80.0 torr and
the temperature is -60.0 °C. What is the volume of the balloon here?
5. And last of all the balloon soars up into the stratosphere where the pressure has
dropped to 0.8 torr and the temperature is 0°C, what size is it just before it pops?
GAS LAW MATH PROBLEMS

1. Helium takes up 5.71 liters at O°C and 3.95 atmospheres. What is the volume of the same
helium at 32°F and 800 mmHg?

2. 257 mL of oxygen in a gas tube goes from 17°C to 42°C from being out in the sun. The
pressure in the tube is 39 N/in2, but it does not change as the temperature increases. What is the
volume of the tube after it has heated?

3. An enormous (57,400 cubic meter) expandable helium balloon at 22°C is heated up by a fire
under it and the action of the sun on the dark plastic covering on top. There will be a small
increase in pressure from 785 mmHg to 790 mmHg, but the major effect wanted is an increase in
volume so the balloon can lift its cargo. To what temperature must the balloon get in order to fill
out to 60,500 cubic meters?

4. A constant pressure tank of gas at 1.01 atm has propane in it at 15°C when it is at 255 cubic
meters. What is its volume at 48°C?

5. A SCUBA tank is filled with air at 16.7 atm at 24°C, but someone leaves it out in the sun to
warm to 65°C. What is the tank pressure?

6. What is the mass of neon in a 625 mL neon tube at 357 mmHg & 25°C?

7. What is the mass of 15 liters of chlorine gas at STP?

8. How many liters of ammonia at STP are produced when 10 g of hydrogen is combined with
nitrogen?

9. What is the mass of 25 liters of fluorine gas at 2.85 atm, 450°C?

10. A 250 kg tank of liquid butane (C4H1O) burns to produce carbon dioxide at 120°C. What
volume of carbon dioxide is produced at 1 atm?

11. Five grams of octane (C8H18) and enough oxygen to burn it are in an automobile cylinder
compressed to 20 atm at 28°C. The mixture explodes and heats the cylinder to 150°C. What is the
pressure in the (same sized) cylinder after the explosion?

12. If 0.515g of magnesium is added to HCl, it makes hydrogen gas and magnesium chloride. The
hydrogen is collected at 23°C and 735mmHg. What is the volume of hydrogen?

13. The dirigible Hindenberg had 3.7 x 106 m3 of hydrogen in its gas bags at 1.1 atm and 7°C.
What was the weight of the hydrogen in pounds?
ANSWERS TO GAS LAW MATH PROBLEMS
1. 21.4 L            2. 279 ml          3. 39.9°C          4. 174 ft3

5. 73.9 g            6. 284 cubic meters 7. 19.0 Atm       8a. 15,000 ft. MSL

9. Ammonia diffuses 3.16 times faster (Wouldn't you
8b. 27,000 ft. MSL
KNOW it?)

10. 0.242 g          11. 47.5 g         12. 74.7 L         13. 7.51 L

14. 45.6 g           15. 8.76 Kg        16. 5.56 E5 L      17. 33.5 L

18. 35.4 Atm.        19. 532 ml         20. 2.12 Kg        21. 209 KL

22. 1.17 KL          23. 7.80 E5 L

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