5.1.4 The Combined Gas Law

Question 1

The Combined Gas Law

Answer 1

• The combined gas law states that for a fixed amount of gas the pressure of a gas times its volume and divided by its temperature is a constant.

Question 2

note

Answer 2

• Boyle’s law states that the pressure of a gas times its volume is a constant at constant temperature
  (PV = constant).
• Charles’s law states that the volume of a gas divided by its Kelvin temperature is a constant at constant pressure (V/T = constant).
• The combined gas law is a combination of Boyle’s law and Charles’s law. The combined gas law states that the pressure of a fixed amount of gas times its volume and divided by it temperature is a constant.
• A 2.37 L sample of gas at 25.0 ̊C and 1.00 atm is heated to 297.0 ̊C and simultaneously compressed to a pressure of 10.0 atm. What is the final volume?
• First, convert the temperatures to kelvins by adding 273.15. Plugging the known values into the combined gas law yields the final volume, 0.453 L.

Question 3

Suppose you have a sample of gas. You simultaneously decrease the volume and raise the temperature. What happens to the pressure?

Answer 3

the pressure goes up

Question 4

Suppose that you have a 2.0 L sample of hydrogen at 1.00 atm and 59°C. If you heat the sample to 84°C and compress it to 2.2 atm, what will the final volume be?

Answer 4

0.98L

Question 5

Suppose that a 4.0 L sample of gas at 1.0 atm is heated from 44°C to 53°C, and during this process the volume doubles. What will the final pressure of the gas sample be?

Answer 5

0.51 atm

Question 6

3.8 L of argon gas at 83°C and 4.25 atm will occupy how much volume at 52°C and 1.75 atm?

Answer 6

8.4 L

Question 7

An airplane takes off from the ground at 1.00 atm. There is a 2.0 L bottle in the baggage compartment. The bottle is filled with a mixture of nitrogen, oxygen, and carbon dioxide gases. From takeoff to 30,000 ft, the temperature drops from 27°C to −80°C. The plane then descends to 10,000 ft. What is the change in the pressure of the bottle from 30,000 ft to 10,000 ft if the temperature at the final altitude is −50°C?

Answer 7

0.100 atm increase

Question 8

Propane (C3H8 ) is a volatile gas. A propane tank can hold 32 L of propane. The tank is filled on a winter day when the temperature is −10°C and the resulting pressure is 1,620 torr. The propane tank is a closed system and remains so. Assume no propane is added or escapes. During the summer, the temperature will rise to 40°C. The maximum amount of pressure that the propane tank can endure under these conditions is 1,880 torr.

Is the following statement true or false? The tank will explode before the propane in the tank reaches 40°C.

Answer 8

true

Question 9

Suppose that 2.3 L of gas at 35°C and 1.0 atm is expanded to 4.5 L at 42°C. What will the final pressure of the gas be?

Answer 9

0.52 atm

Question 10

The following equation is based on the Combined Gas Law: (PiVi / Ti ) = (PfVf / Tf ) Based on this equation, predict what would happen to the volume of a gas if the temperature of the gas increased and if Pf = Pi . Which law does this equation become if Pf = Pi?

Answer 10

The volume would increase. Charles’ Law

Question 11

3.8 L of argon gas at 83°C and 4.25 atm is expanded to a volume of 4.2 L at 72°C, what will the final pressure be?

Answer 11

3.7 atm

Question 12

The Combined Gas Law states that (PiVi / Ti ) = (PfVf  / Tf ). Which statement best explains how this law also includes Boyle’s Law?

Answer 12

When the temperature is constant, the pressure and volume are inversely proportional.