Kinetic Molecular Theory of Gases Problem Set
1. Two moles of nitrogen gas are kept in a glass container. The temperature of the gas is 400K.
What is the average kinetic energy of the molecules in this system?
a.
b.
c.
d.
e.
9.98kJ
98.4J
4.99kJ
16.4kJ
49.2J
2. Which of the following is not an assumption of the kinetic molecular theory of gases?
a. Gas particles are in random, continuous motion
b. The volumes of the particles of a gas are negligible
c. Collisions between gas particles are elastic
d. The kinetic energy of gas particles are different for all gases at a certain temperature
e. Gas particles do not experience attractions/repulsions to other particles
3. What will happen to the average kinetic energy of a system if you increase the temperature?
a. Average kinetic energy will increase exponentially with the temperature
b. Average kinetic energy will increase directly with the temperature
c. Average kinetic energy will not change
d. Average kinetic energy will decrease directly with the temperature
e. Average kinetic energy will decrease exponentially with the temperature
4. Which factors will affect the average velocity of the molecules in a gas? Choose all that apply.
a. Temperature
b. Volume
c. Pressure
d. Number of moles
e. Molar mass
5. Do all molecules in a 1-mole sample of CH4 gas have the same kinetic energy at 273 K? Explain.
6. Consider a sample of ideal gas.
a. How is the average kinetic energy of the molecules related to temperature?
b. How is the average velocity of the gas molecules related to temperature?
c. How is the average velocity of the gas molecules related to the molar mass of the gas at a
constant temperature?
7. Which of the following statements are true?
a. At constant temperature, the lighter the gas molecules, the faster the average velocity of
the gas molecules.
b. At constant temperature, the heavier the gas molecules, the larger the average kinetic
energy of the gas molecules.
c. A real gas behaves most ideally when the container volume is relatively large and the
molecules are moving relatively quickly.
d. As temperature increases, the effect of interparticle interactions on gas behavior is
increased.
e. At constant V and T, as gas molecules are added into a container, the number of
collisions per unit area increases, resulting in a higher pressure.
f. The kinetic molecular theory predicts that pressure is inversely proportional to
temperature at constant volume and moles of gas.
8. Calculate the average kinetic energies and root mean square velocities of CH4 and NH3 at 273 K
and 546 K.
9. Consider a 1.0-L container of neon gas at STP. Will the properties listed in the table increase
decrease or remain the same under each of the following conditions?
Average KE
Increase temp to 100 °C
Decrease temp to -50 °C
Decrease volume to 0.5 L
Double moles
Average velocity
Frequency of collisions
10. Consider three identical flasks filled with different gasses.
Flask A: CO at 760 torr and 0 °C
Flask B: N2 at 250 torr and 0 °C
Flask C: H2 at 100 torr and 0 °C
a. In which flask will the molecules have the greatest average KE?
b. In which flask will the molecules have the greatest average velocity?
11. Each scenario below has three flasks containing different gas samples. Which flask in each group
will behave least like an ideal gas.
Variable:
Constant
a. Hydrogen, Neon, Butane (C4H10)
T = 200 K; P = 1.000 atm
b. T = 100 K, 250 K, 400 K
Oxygen gas, P = 1.000 atm
c. P = 5 atm, 50 atm, 500 atm
CO2 gas, T = 273 K
Answers
1.
2.
3.
4.
5.
C
D
B
A, E
No. The particles have a distribution of different velocities. 273 K represents the average kinetic
energy of the molecules in the sample.
6. A. Average kinetic energy increases with temperature
B. Velocity increases with temperature
C. Velocity decreases as molar mass increases
7. A, C, E are true
B. particle mass has no relationship to KE
C. Intermolecular interactions are stronger at low temperatures
F. P and T are directly proportional
8. CH4: 3.40 kJ, 20.3 m/s (@ 273 K); 6.81 kJ, 29.1 m/s (@ 546 K)
NH3: 3.40 kJ, 20.0 m/s (@ 273 K); 6.81 kJ; 28.3 m/s (@ 546 K)
9.
Average KE
Average velocity
Increase temp to 100 °C
Increase
Increase
Decrease temp to -50 °C
Decrease
Decrease
Decrease volume to 0.5 L Same
Same
Double moles
Same
Same
10. A. KE is constant between the 3 flasks
B. Flask C (H2) has the highest average velocity
11. A. Butane
B. 100 K
C. 500 atm
Frequency of collisions
Increase
Decrease
Increase
Increase