Q: Which of the following correctly expresses Graham's Law of Effusion for two gases, A and B?

$$ \frac{\text{Rate}_A}{\text{Rate}_B} = \sqrt{\frac{M_B}{M_A}} $$

Question 1

According to the Kinetic Molecular Theory, which of the following statements is NOT an assumption made about ideal gases?

Accepted Answer

Gas particles experience significant attractive and repulsive forces between each other.

Question 2

Which equation correctly relates the average kinetic energy of a gas particle to temperature?

Accepted Answer

$$ KE = \frac{1}{2}mv^2$ = \frac{3}{2}k_B T $$

Question 3

If the temperature of a gas is decreased, what happens to the average kinetic energy and the velocity of the gas particles?

Accepted Answer

Both average kinetic energy and velocity decrease.

Question 4

A balloon filled with helium is released into the atmosphere. As it rises and the temperature drops, what happens to the pressure inside the balloon according to the Kinetic Molecular Theory?

Accepted Answer

The pressure decreases due to lower kinetic energy and fewer collisions with the balloon walls.

Question 5

Graham's Law of Effusion can be derived from which fundamental principle of the Kinetic Molecular Theory?

Accepted Answer

The average kinetic energy of all gases at the same temperature is the same.

Question 6

Which of the following correctly expresses Graham's Law of Effusion for two gases, A and B?

Accepted Answer

$$ \frac{	ext{Rate}_A}{	ext{Rate}_B} = \sqrt{\frac{M_B}{M_A}} $$

Question 7

If equal moles of hydrogen (H$$_2) $$and oxygen (O$$_2) $$are at the same temperature, which gas will have a higher average velocity and why?

Accepted Answer

Hydrogen, because it has a lower molar mass.

Question 8

A sample of neon gas is heated from 300 K to 600 K. What happens to the most probable speed of the neon atoms?

Accepted Answer

It increases by a factor of $$ \sqrt{2} .$$

Question 9

Which of the following best explains why lighter gases effuse faster than heavier gases?

Accepted Answer

Lighter gases have higher average velocities at the same temperature.

Question 10

A rigid container holds a mixture of nitrogen and argon gases at the same temperature. Which statement is true about the average kinetic energy of the two gases?

Accepted Answer

Both gases have the same average kinetic energy.

Question 11

If the temperature of a gas is doubled, what happens to the root mean square speed ($$u_{rms}) of $$its molecules?

Accepted Answer

$$ u_{rms} $$ increases by a factor of $$ \sqrt{2} .$$

Question 12

Which of the following is a real-world application of Graham's Law of Effusion?

Accepted Answer

Separating uranium isotopes for nuclear fuel.

Question 13

A gas sample in a closed container is cooled at constant volume. What happens to the pressure and why?

Accepted Answer

Pressure decreases because the particles move slower and collide less frequently with the walls.

Question 14

Which of the following best describes the relationship between molar mass and the most probable speed of a gas at a given temperature?

Accepted Answer

The most probable speed is inversely proportional to the square root of the molar mass.

Question 15

Which of the following equations gives the root mean square speed ($$u_{rms}) of a $$gas molecule?

Accepted Answer

$$ u_{rms} = \sqrt{\frac{3RT}{M}} $$

Question 16

A mixture of gases is at the same temperature. Which gas will have the greatest average velocity?

Accepted Answer

The gas with the smallest molar mass.

Question 17

Which of the following is NOT a prediction of the Kinetic Molecular Theory for ideal gases?

Accepted Answer

Gas particles exert attractive forces on each other.

Question 18

If a gas sample is compressed to half its original volume at constant temperature, what happens to the frequency of collisions with the container walls?

Accepted Answer

The frequency of collisions doubles.

Question 19

Which of the following best explains why the pressure of a gas increases when it is heated at constant volume?

Accepted Answer

The particles move faster and collide more frequently and forcefully with the walls.

Question 20

A sample of CO$$_2$$ and a sample of O$$_2$$ are at the same temperature. Which statement is true about their average kinetic energies and velocities?

Accepted Answer

They have the same average kinetic energy, but CO$$_2$$ molecules move slower.

Kinetic Molecular Theory, Graham’s Law of Effusion, and Gas Particle Velocities

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