Gas Law

Complete ALL problems under each heading in your packer. SHOW ALL WORK AND LABELS!

Bolye’s Law Problems

Example: If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be? • Read the problem and determine what is given and what is unknown? • Decide which law to use. • Substitute the values (given numbers) from the problem into the equation Given: P1 = 1.5 atm Unknown or find: P2 = ? = X V1 = 5.6 L V2 = 4.8 L
Note: Since this problem involves two pressures and two volumes we will use Boyle’s law equation to solve it: P1V1 = P2V2

(1.5) (5.6) = X (4.8) Now solve for X

8.4 = 4.8 X 4.8 4.8

1.75 atm = X = P2 The new pressure inside the piston is 1.75 atm.

1. I have added 15 L of air to a balloon at sea level (1.0 atm). If I take the balloon with me to Denver, where the air pressure is 0.85 atm, what will the new volume of the balloon be?

2. I’ve got a car with an internal volume of 12,000 L. If I drive my car into the river and it implodes, what will be the volume of the gas when the pressure goes from 1.0 atm to 1.4 atm?

3. 1.0 L of a gas at standard temperature and standard pressure is compressed to 473 mL. What is the new pressure of the gas?

4. In a thermonuclear device, the pressure of 0.050 liters of gas within the bomb casing reaches 4.0 x 106 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion?

5. Synthetic diamonds can be manufactured at pressures of 6.00 x 104 atm. If we took 2.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 104 atm, what would the volume of that gas be?

6. The highest pressure ever produced in a laboratory setting was about 2.0 x 106 atm. If we have a 1.0 x 10-5 liter sample of a gas at that pressure, then release the pressure until it is equal to 0.275 atm, what would the new volume of that gas be?

7. Atmospheric pressure on the peak of Mt. Everest can be as low as 150 mm Hg, which is why climbers need to bring oxygen tanks for the last part of the climb. If the climbers carry 10.0 liter tanks with an internal gas pressure of 3.04 x 104 mm Hg, what will be the volume of the gas when it is released from the tanks? (hint: convert pressure into atm)

8. While using explosives to knock down a building, the shock wave can be so strong that 12 liters of gas will reach a pressure of 3.8 x 104 mm Hg. When the shock wave passes and the gas returns to a pressure of 760 mm Hg, what will the volume of that gas be? (hint: convert pressure into atm)

9. An experimental research submarine with a volume of 15,000 liters has an internal pressure of 1.2 atm. If the pressure of the ocean breaks the submarine forming a bubble with a pressure of 250 atm pushing on it, how big will that bubble be?

10. Divers get “the bends” if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has 0.05 L of gas in his blood under a pressure of 250 atm, then rises instantaneously to a depth where his blood has a pressure of 50.0 atm, what will the volume of gas in his blood be? Do you think this will harm the diver?

Charles’ Law Problems

Example: If I have 45 liters of helium in a balloon at 250 C and increase the temperature of the balloon to 550 C, what will the new volume of the balloon be? • Read the problem and determine what is given and what is unknown? (Convert temperature into Kelvin) • Decide which law to use. • Substitute the values (given numbers) from the problem into the equation Given: V1 = 45 L T1 = 25 oC = 25 + 273 = 298 k T2 = 55oC = 55 + 273 = 328 k V2 = ? = X
Note: Since this problem involves two volumes and two temperatures we will use Charles law equation to solve it: V1 = V2 T1 T2

45 = X 298. 328 Now cross multiply divide to find X

(45) (328) = 298 X 298 298

49.53 L = X = T2 The new volume of the balloon is 49.53 L

1. Calcium carbonate decomposes at 12000 C to form carbon dioxide and calcium oxide. If 25 liters of carbon dioxide are collected at 12000 C, what will the volume of this gas be after it cools to 250 C?

2. I have 130 liters of gas in a piston at a temperature of 2500 C. If I cool the gas until the volume decreases to 85 liters, what will temperature of the gas be?

3. The temperature inside my refrigerator is about 40 Celsius. If I place a balloon in my fridge that initially has a temperature of 220 C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator?

4. A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a temperature of 20 0C, what will the volume of the balloon be after he heats it to a temperature of 250 0C?

5. On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250 mL bag at a temperature of 19 0C, and I leave it in my car which has a temperature of 600 C, what will the new volume of the bag be?

6. A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty soda bottle (volume of 2 L) at room temperature (25 0C), what will the new volume be if you put it in your freezer (-4 0C)?

7. Some students believe that teachers are full of hot air. If I inhale 2.2 liters of gas at a temperature of 180 C and it heats to a temperature of 380 C in my lungs, what is the new volume of the gas?

8. How hot will a 2.3 L balloon have to get to expand to a volume of 400 L? Assume that the initial temperature of the balloon is 25 0C.

9. I have made a thermometer that measures temperature by the compressing and expanding of gas in a piston. I have measured that at 1000 C the volume of the piston is 20 L. What is the temperature outside if the piston has a volume of 15 L? What would be appropriate clothing for the weather?

10. 100 ml of a gas is collected at a temperature of 25 deg C. What would be the volume of the gas at standard temperature?

Combined Gas Law Problems

Example: A toy balloon has an internal pressure of 1.05 atm and a volume of 5.0 L. If the temperature where the balloon is released is 200 C, what will happen to the volume when the balloon rises to an altitude where the pressure is 0.65 atm and the temperature is –150 C? • Read the problem and determine the given and the unknown variables? (Convert temperature into Kelvin if necessary) • Decide which law to use. • Substitute the values (given numbers) from the problem into the equation Given: P1 = 1.05 atm V1 = 5.0 L T1 = 20 o C = 20 + 273 = 293 k P2 = 0.65 atm T2 = -15oC = -15 + 273 = 258 k V2 = ? = X

Note: Since this problem involves two pressures, two volumes and two temperatures we will use Combined Gas law equation to solve it: P1V1 = P2V2 T1 T2

(1.05) (5) = (0.65) X 293. 258 Now cross multiply divide to find X

(1.05) (5) (258) = 0.65 X (293) (0.65) 0.65

7.11 L = X = V2 The volume of the balloon will increase to 7.11L

1. A small research submarine with a volume of 1.2 x 105 L has an internal pressure of 1.0 atm and an internal temperature of 150 C. If the submarine descends to a depth where the pressure is 150 atm and the temperature is 30 C, what will the volume of the gas inside be if the hull of the submarine breaks?

2. People who are angry sometimes say that they feel as if they’ll explode. If a calm person with a lung capacity of 3.5 liters and a body temperature of 360 C gets angry, what will the volume of the person’s lungs be if their temperature rises to 390 C. Based on this, do you think it’s likely they will explode?

3. If I initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a temperature of 200 K, and then I raise the pressure to 14 atm and increase the temperature to 300 K, what is the new volume of the gas?

4. A gas takes up a volume of 17 liters, has a pressure of 2.3 atm, and a temperature of 299 K. If I raise the temperature to 350 K and lower the pressure to 1.5 atm, what is the new volume of the gas?

5. A gas that has a volume of 28 liters, a temperature of 45 0C, and an unknown pressure has its volume increased to 34 liters and its temperature decreased to 35 0C. If I measure the pressure after the change to be 2.0 atm, what was the original pressure of the gas?

6. A gas has a temperature of 14 0C, and a volume of 4.5 liters. If the temperature is raised to 29 0C and the pressure is not changed, what is the new volume of the gas?

7. If I have 17 liters of gas at a temperature of 67 0C and a pressure of 88.89 atm, what will be the pressure of the gas if I raise the temperature to 94 0C and decrease the volume to 12 liters?

8. I have an unknown volume of gas at a pressure of 0.5 atm and a temperature of 325 K. If I raise the pressure to 1.2 atm, decrease the temperature to 320 K, and measure the final volume to be 48 liters, what was the initial volume of the gas?

9. If I have 21 liters of gas held at a pressure of 78 atm and a temperature of 900 K, what will be the volume of the gas if I decrease the pressure to 45 atm and decrease the temperature to 750 K?

10. If I have 2.9 L of gas at a pressure of 5 atm and a temperature of 50 0C, what will be the temperature of the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3 atm?
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P1V1 = P2V2

V1 = V2
T1 T2

P1V1 = P2V2 T1 T2

Unit – 5 Gas Laws Trivedi Page 1 of 6

Answers: 1) 1.75 L 2) 8571.42L 3) 2.11 atm 4) 2.0 x 105 L 5) 3.33 x 10-5 L 6) 72.7 L 7) 2.0 x 103 L 8) 600 L 9) 72 L 10) 0.25 L, yes

Answers: 1) 5.05 L 2) 342 K 3) 0.47 L 4) 0.71 L 5) 0.285L or 285 mL 6) 1.81 L 7) 2.35 L 8) 51,826 K 9) The temperature is 280 K, which corresponds to 70 C. A jacket would be appropriate clothing for this weather. 10) 0.091L or 91.61 mL

Answers :1) 767 L 2) 3.53 L it seems unlikely that this very small increase in lung volume would cause somebody to explode, though you never know 3) 29.36 L 4) 30.5 L 5) 2.51 atm 6) 4.74 L 7) 136 atm 8) 117 L 9) 30.3 L 10) 160 K