Question

use the references to access important values if needed for this question.
a 1.06 mol sample of kr gas is confined in a 25.1 liter container at 16.1 °c.
if the volume of the gas sample is decreased to 12.6 l, holding the temperature constant, the pressure will increase. which of the following kinetic theory ideas apply?
(select all that apply.)
□ with less available volume, the molecules hit the walls of the container more often.
□ at lower volumes molecules have higher average speeds.
□ with higher average speeds, on average the molecules hit the walls of the container with more force.
□ for a given gas at constant temperature, the force per collision is constant. some other factor must cause the pressure increase.
□ none of the above.

Explanation:

• According to kinetic molecular theory, when the volume of a gas is decreased at constant temperature:
• The average speed of gas molecules (\(v_{rms}=\sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is temperature and \(M\) is molar mass) depends only on temperature. Since \(T\) is constant, the average speed of molecules is constant. So, the statement “At lower volumes molecules have higher average speeds” and “With higher average speeds, on average the molecules hit the walls of the container with more force” are incorrect.
• When volume \(V\) decreases, the number of molecules per unit volume (\(n/V\)) increases. Molecules have to travel a shorter distance to collide with the walls of the container. So, with less available volume, the molecules hit the walls of the container more often.
• For a given gas at constant temperature, the average kinetic energy (\(KE=\frac{3}{2}RT\)) and thus the force per collision (related to the change in momentum during collision, which is related to kinetic energy) is constant. The increase in pressure is due to the increased frequency of collisions (because of decreased volume), not a change in force per collision.

Answer:

• With less available volume, the molecules hit the walls of the container more often.
• For a given gas at constant temperature, the force per collision is constant. Some other factor must cause the pressure increase.