Question 1

Which of the following statements best describes the main improvement of the van der Waals equation over the ideal gas law?

Accepted Answer

It accounts for the attractive forces between molecules and the finite volume of molecules.

Question 2

A sample of gas at 300 K and 1 atm occupies a volume of 22.4 L. If the temperature is doubled at constant pressure, what will be the new volume?

Accepted Answer

$$44.8\ \mathrm{L}$$

Question 3

According to the kinetic theory, the pressure exerted by an ideal gas is given by:

Accepted Answer

$$p = \frac{2}{3} \left( \frac{N}{V} \right) \left( \frac{1}{2} m \overline{v^2$} \right)$$

Question 4

Which of the following is the correct expression for the root mean square (rms) speed of gas molecules?

Accepted Answer

$$v_{rms} = \sqrt{\frac{3k_B T}{m}}$$

Question 5

Dalton’s Law of Partial Pressures states that:

Accepted Answer

The total pressure of a mixture of gases is the sum of the partial pressures of the component gases.

Question 6

If the mean free path $$l of a $$gas molecule is given by $$l = \frac{1}{\sqrt{2} \pi d^2$ n_v}$$, what will happen to $$l if $$the number density $$n_v is $$doubled?

Accepted Answer

It will be halved.

Question 7

Which of the following best describes the relationship between temperature and the average kinetic energy of a gas molecule?

Accepted Answer

The average kinetic energy is directly proportional to the absolute temperature.

Question 8

A mixture contains 2 moles of oxygen and 3 moles of nitrogen at a total pressure of 5 atm. What is the partial pressure of nitrogen?

Accepted Answer

$$3\ \mathrm{atm}$$

Question 9

For a monoatomic ideal gas, what is the molar specific heat at constant volume $$C_v$$?

Accepted Answer

$$C_v = \frac{3}{2} R$$

Question 10

Which of the following is NOT an assumption of the molecular model of an ideal gas?

Accepted Answer

Molecules undergo inelastic collisions with each other.

Question 11

If the temperature of a gas is increased, what happens to the Maxwell-Boltzmann speed distribution?

Accepted Answer

The distribution shifts to higher speeds and broadens.

Question 12

A gas sample is compressed at constant temperature from 4.0 L to 2.0 L. According to Boyle’s Law, what happens to the pressure?

Accepted Answer

It doubles.

Question 13

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

Accepted Answer

$$\frac{1}{2} m \overline{v^2$} = \frac{3}{2} k_B T$$

Question 14

For a diatomic ideal gas at room temperature, what is the expected value of $$C_v$$?

Accepted Answer

$$C_v = \frac{5}{2} R$$

Question 15

Which of the following best explains why the mean free path of a gas molecule is much larger than its diameter?

Accepted Answer

The average separation between molecules is much larger than their size.

Question 16

If the molar mass of a gas is increased while keeping temperature constant, what happens to the rms speed of its molecules?

Accepted Answer

It decreases.

Question 17

Which of the following is the correct form of the ideal gas law using Boltzmann’s constant?

Accepted Answer

$$PV = Nk_B T$$

Question 18

A sealed container holds an ideal gas at constant volume. If the temperature is increased, what happens to the pressure?

Accepted Answer

It increases proportionally to the temperature.

Question 19

Which of the following is true about the specific heat at constant pressure ($$C_p) $$and at constant volume ($$C_v) $$for an ideal gas?

Accepted Answer

$$C_p \u003e C_v$$

Kinetic Theory of Gases: Study Notes

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