Question 1

According to the kinetic-molecular theory, which of the following statements is TRUE about the average kinetic energy of a gas at a given temperature?

Accepted Answer

It is the same for all gases at the same temperature.

Question 2

Which equation correctly gives the root mean square (rms) velocity $u_{\mathrm{rms}}$ of a gas molecule?

Accepted Answer

$u_{\mathrm{rms}} = \sqrt{\dfrac{3RT}{M}}$

Question 3

A sample of nitrogen gas ($N_2$) at 25°C has an rms speed of 515 m/s. Why does the smell of ammonia (NH$_3$) take much longer to travel across a room than this speed would suggest?

Accepted Answer

Because gas molecules undergo frequent collisions, resulting in a much slower net movement (diffusion) across the room.

Question 4

Which of the following best describes effusion?

Accepted Answer

The leakage of a gas through a small aperture into a vacuum.

Question 5

According to Graham's Law, what is the ratio of the rate of effusion of helium (He, $M = 4.00$ g/mol) to methane (CH$_4$, $M = 16.0$ g/mol)?

Accepted Answer

2.0

Question 6

Which of the following is an assumption of the ideal gas law that is NOT true for real gases at high pressures?

Accepted Answer

Gas molecules have negligible volume compared to the container.

Question 7

Which correction is made in the van der Waals equation to account for the finite volume of gas molecules?

Accepted Answer

Subtract $nb$ from the volume: $[V - nb]$

Question 8

A real gas deviates from ideal behavior at low temperatures because:

Accepted Answer

Intermolecular attractions become significant, causing the pressure to be lower than predicted.

Question 9

Which of the following best explains why the rate of effusion is directly proportional to the rms velocity of gas molecules?

Accepted Answer

Faster molecules are more likely to hit the aperture and escape.

Question 10

If the molar mass of gas A is four times that of gas B, what is the ratio of the rate of effusion of gas B to gas A?

Accepted Answer

2:1

Question 11

Which of the following is the correct form of the van der Waals equation for a real gas?

Accepted Answer

$\left[P + a\left(\dfrac{n}{V}\right)^2\right][V - nb] = nRT$

Question 12

Which of the following statements about mean free path is correct?

Accepted Answer

It is the average distance a molecule travels before colliding with another molecule.

Question 13

A gas sample behaves ideally at low pressure because:

Accepted Answer

The volume of the gas molecules is negligible compared to the container volume.

Question 14

Which of the following would cause a real gas to deviate most from ideal behavior?

Accepted Answer

High pressure and low temperature.

Question 15

If the temperature of a gas is doubled (in Kelvin), what happens to the average kinetic energy of its molecules?

Accepted Answer

It doubles.

Question 16

Which of the following is a direct consequence of the kinetic-molecular theory for gases?

Accepted Answer

At a given temperature, all gases have the same average kinetic energy.

Question 17

A balloon filled with hydrogen gas will deflate faster than one filled with oxygen gas because:

Accepted Answer

Hydrogen molecules have a higher rms velocity and effuse more rapidly through the balloon material.

Question 18

Which of the following best explains why real gases require a pressure correction in the van der Waals equation?

Accepted Answer

Intermolecular attractions reduce the observed pressure compared to the ideal gas prediction.

Question 19

Which of the following would increase the mean free path of gas molecules in a container?

Accepted Answer

Decreasing the pressure of the gas.

Question 20

A real-world example: In a hospital, helium is sometimes used in breathing mixtures for patients with respiratory issues. Why is helium preferred over nitrogen in these cases, based on kinetic-molecular theory?

Accepted Answer

Helium has a lower molar mass, resulting in higher rms velocity and easier diffusion through airways.

Gases: Kinetic Molecular Theory, Effusion & Diffusion, and Real Gas Behavior

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