GAS / Molar Mass
Argon / 0.04 kg/mol
Helium / 0.004 kg/mol
Oxygen / 0.032 kg/mol
  1. (I) A cylinder contains a mixture of helium and argon gas in equilibrium at a temperature of 124o C.
  1. What is the average kinetic energy of each type of molecule?
  2. What is the rms speed of helium?
  3. What is the rms speed of argon?
  1. (I) Determine the temperature at which rms speed of a helium atom equals 860 m/s.
  2. (I) What is the rms speed of helium on the surface of a star, where the temperature is 4151 K?
  3. (II) A water droplet with a 6.5 µm diameter is in equilibrium with air molecules (density of 1000 kg/m3) in a room where the temperature is 295 K. What is the rms speed of the droplet?
  4. (I) If both temperature and volume of an ideal gas are halved, how does the pressure change?
  5. (I) One mole of xenon gas at 19o C occupies a container with a volume of 0.258 m3. What is the pressure exerted by the xenon atoms on the walls of the container?
  6. (II) A cylinder with a moveable piston contains a gas at a temperature of 15.9o C, a volume of 1.73 m3, and an absolute pressure of 31500 Pa. What will be the final temperature of the gas if it is compressed to 0.37 m3 and the absolute pressure increases to 1.82 x 105 Pa?
  7. (II) An air bubble originating from a diver has a radius of 5 mm at some depth h. When the bubble reaches the surface of the water, it has a radius of 6 mm.
  1. Assuming the temperature of the air bubble remains constant; determine the depth of the diver.
  2. Determine the absolute pressure at this depth.
  1. (II) A sealed glass bottle at 27o C contains air at a pressure of 1.01 x 105 Pa and has a volume of 28.5 cm3. The bottle is tossed into an open fire. When the air temperature inside the bottle reaches 231o C, what is the air pressure inside the bottle?
  2. (III) Gas confined in a tank at pressure 1.09 x 108 Pa and a temperature of 10.9o C. Half of the gas is withdrawn and the temperature is raised to 67o C. What is the new pressure in the tank?
  3. (III) Determine the density of oxygen gas at 1.9 atm and 10o C.

1a. 8.22x10-21 J
1b. 1570 m/s
1c. 497 m/s / 2. 119 K / 3. 5088 m/s / 4. 2.92x10-4 m/s
5. Remains constant. / 6. 9410 Pa / 7. 84.6o C / 8a. 7.50 m
8b. 175,000 Pa
9. 1.70x105 Pa / 10. 6.53x107 Pa / 11. 2.62 kg/m3

ADDITIONAL PROBLEMS (Answers are included)

1) A car starts out when the air temperature is 288 K. The air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming the volume remains constant?

A) 483 kPa

B) 507 kPa

C) 517 kPa

D) 532 kPa

Answer: C

2) An automobile tire has a volume of 0.0185 m3. If the pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire?

A) 2.25 × 1023

B) 2.25 × 1024

C) 3.25 × 1023

D) 3.25 × 1024

Answer: B

3) Your lungs hold 4.2 L of air at a pressure of 101.3 kPa. If you are holding your breath and dive into a pool to a depth of 5.0 m below the surface of the water, what is the volume of the air in your lungs assuming that the temperature remains the same?

A) 2.8 L

B) 2.9 L

C) 3.2 L

D) 3.3 L

Answer: A

4) What is the temperature of 3.0 moles of gas at a pressure of 250 kPa held in a volume of 15 L?

A) 150 K

B) 200 K

C) 250 K

D) 300 K

Answer: A

5) If you double the absolute temperature of an ideal gas, the rms value of the speed of the molecules

A) doubles.

B) quadruples.

C) is multiplied by.

D) is multiplied by .

Answer: C

6) The air in a room is composed principally of nitrogen, oxygen, and carbon dioxide. These have molecular weights of approximately 28, 32, and 44 g/mol, respectively. If the three gases coexist in thermal equilibrium,

A) therms speeds of their molecules are equal.

B) the average kinetic energies of their molecules are equal.

C) therms speeds, in increasing order are nitrogen, oxygen, and carbon.

D) the kinetic energies, in increasing order are nitrogen, oxygen, and carbon.

Answer: B

7) The molecular weight of nitrogen is 28 g/mol. What is the rms speed of nitrogen molecules at 8.0°C?

A) 450 m/s

B) 500 m/s

C) 550 m/s

D) 600 m/s

Answer: B

8) At what temperature is the rms speed of hydrogen molecules, which have a molecular weight of 2.02 g/mol equal to 2000 m/s?

A) 17.0ºC

B) 34.0ºC

C) 51.0ºC

D) 68.0ºC

Answer: C

9) What is the internal energy in 2.7 moles of hydrogen at 300 K? As an approximation, treat the hydrogen gas as if it was monatomic.

A) 10 kJ

B) 12 kJ

C) 14 kJ

D) 18 kJ

Answer: A

10) The molecular weight of carbon dioxide is 44.0 g/mol. What is the internal energy in 3.00 kg of carbon dioxide at 300 K? As an approximation, treat the carbon dioxide gas as if it was monatomic.

A) 2.55 × 105 J

B) 1.70 × 105 J

C) 2.55 × 104 J

D) 1.70 × 104 J

Answer: A