# Worksheet: Particle Speed Distributions in Gases

In this worksheet, we will practice describing how the distribution of particle speeds in a gas and their root-mean-square speed vary with temperature.

**Q1: **

The diagram shows three distributions of particle speeds in a gas when the gas is at three different temperatures. Which of the following most correctly expresses the relationship between the temperatures?

- A
- B
- C
- D
- E

**Q2: **

The distribution of the speed of particles in two different gases is shown in the diagram. Gas I is shown in blue and gas II is shown without any color. In which gas are the individual particles with the highest speed found?

- AGas I
- BGas II

**Q3: **

The distribution of the speed of particles in two different gases is shown in the diagram. Gas I is shown in blue and gas II is shown in orange. Particle speeds to the left of the distributions’ approximate centers are considered lower speeds and particle speeds to the right of the distributions’ approximate centers are considered higher speeds. The value is the difference between the number of particles moving at lower speeds in gas I and gas II. The value is the difference between the number of particles moving at higher speeds in gas I and gas II. Which is greater, or ?

- A
- B

**Q4: **

The distribution of the speed of particles in two different gases is shown in the diagram. Gas I is shown in blue and gas II is shown in orange. Which of the gases contains more particles?

- AGas I
- BGas II

**Q5: **

A distribution of particle speeds in a gas is shown in diagram (a). Diagram (b) shows a distribution of particle speeds in a gas where the particles’ speed distribution has been changed in one specific way. In diagram (b), the original distribution is shown by the faded line. Which of the following statements most correctly describes the change made to the distribution?

- AThe number of particles moving at each speed has been divided by the same value.
- BAll the particles in the gas have had their speeds divided by the same value.
- CThe number of particles moving at each speed has been decreased by the same value.
- DAll the particles in the gas have had their speeds decreased by the same value.

**Q6: **

A distribution of particle speeds in a gas is shown in diagram (a). Diagram (b) shows a distribution of particle speeds in a gas where the particles' speed distribution has been changed in one specific way. In diagram (b), the original distribution is shown by the faded line. Which of the following statements most correctly describes the change made to the distribution?

- AThe number of particles moving at each speed has been increased by the same value.
- BAll the particles in the gas have had their speeds increased by the same value.
- CAll the particles in the gas have had their speeds multiplied by the same value.
- DThe number of particles moving at each speed has been multiplied by the same value.

**Q7: **

A distribution of particle speeds in a gas is shown in diagram (a). Diagram (b) shows a distribution of particle speeds in a gas where the particles’ speed distribution has been changed in one specific way. In diagram (b), the original distribution is shown by the faded line. Which of the following statements most correctly describes the change made to the distribution?

- AAll the particles in the gas have had their speeds decreased by the same value.
- BThe number of particles moving at each speed has been decreased by the same value.
- CThe number of particles moving at each speed has been divided by the same value.
- DAll the particles in the gas have had their speeds divided by the same value.

**Q8: **

A group of molecules in a gas have the following speeds: 125 m/s, 175 m/s, 155 m/s, 220 m/s, 120 m/s, and 200 m/s.

What is the root-mean-square speed of the particles to the nearest meter per second?

- A170 m/s
- B88 m/s
- C166 m/s
- D69 m/s
- E164 m/s

What is the difference between the root-mean-square speed of the particles and the average speed of the particles, rounding to the nearest meter per second?

- A0 m/s
- B97 m/s
- C78 m/s
- D2 m/s
- E4 m/s

What is the difference between the root-mean-square speed of the particles and the average speed of the particles if all the particle speeds are increased by a factor of ten? Round to the nearest meter per second.

- A20 m/s
- B780 m/s
- C970 m/s
- D40 m/s
- E0 m/s

**Q9: **

Diagrams (a) and (b) show distributions of particle speeds in two different gases.

For diagram (a), in which of the following regions of the distribution is the particle speed value that is equal to the root-mean-square speed of particles in the gas?

- ARegion I
- BRegion II
- CThe boundary of region I and region II

For diagram (b), in which of the following regions of the distribution is the particle speed value that is equal to the root-mean-square speed of particles in the gas?

- AThe boundary of region I and region II
- BRegion II
- CRegion I

**Q10: **

A distribution of particle speeds in a gas is shown in diagram (a). Diagram (b) shows a distribution of particle speeds in a gas where the particles’ speed distribution has been changed in one specific way. In diagram (b), the original distribution is shown by the faded line. Which of the following statements most correctly describes the change made to the distribution?

- AThe number of particles moving at each speed has been decreased by the same value.
- BAll the particles in the gas have had their speeds divided by the same value.
- CAll the particles in the gas have had their speeds decreased by the same value.
- DThe number of particles moving at each speed has been divided by the same value.

**Q11: **

- AAll the particles in the gas have had their speeds decreased by the same value.
- BAll the particles in the gas have had their speeds divided by the same value.
- CThe number of particles moving at each speed has been decreased by the same value.
- DThe number of particles moving at each speed has been divided by the same value.

**Q12: **

A distribution of particle speeds in a gas is shown in diagram (a). Diagram (b) shows a distribution of particle speeds in a gas where the particles’ speeds distribution has been changed in one specific way. In diagram (b), the original distribution is shown by the faded line. Which of the following statements most correctly describes the change made to the distribution?

- AThe number of particles moving at each speed has been multiplied by the same value.
- BAll the particles in the gas have had their speeds multiplied by the same value.
- CThe number of particles moving at each speed has been increased by the same value.
- DAll the particles in the gas have had their speeds increased by different values.

**Q13: **

Two distributions are shown in the diagram. Which of the distributions has a greater root-mean-square value?

- ADistribution II
- BDistribution I

**Q14: **

The diagram shows a group of particles that move independently of each other. The direction of a particle’s motion is shown by the arrow drawn from its center.

What is the ratio of the number of particles moving horizontally to the number of particles moving vertically?

What is the difference between the number of particles moving upward and the number of particles moving downward?

What is the difference between the number of particles moving to the left and the number of particles moving to the right?

Which of the following distribution charts correctly represents how the motions of the particles are distributed?

- A
- B
- C
- D

**Q15: **

Hydrogen atoms form part of the atmosphere of a planet that
has a gravitational field strength of 14.6 N/kg. Modeling the planet’s
atmosphere as having a uniform temperature of 128 K, find the maximum height
above the planet’s surface that a hydrogen atom would rise to because of the
internal energy of the hydrogen gas. Assume that variation in the planet’s gravitational field strength over this height is negligible. Use a value of kg
for the mass of a hydrogen atom and use m^{2}⋅kg/s^{2}⋅K
for the value of Boltzmann’s constant. Give your answer to three significant figures.

**Q16: **

- AAll the particles in the gas have had their speeds decreased by different values.
- BThe number of particles moving at each speed has been multiplied by the same value.
- CAll the particles in the gas have had their speeds multiplied by the same value.
- DAll the particles in the gas have had their speeds increased by the same value.

**Q17: **

A container of volume
0.00425 m^{3} contains
0.121 mol
of oxygen at a pressure of
628 kPa.
Find the root-mean-square speed of the
atoms. Use a value of
16 g/mol
for the molar mass of oxygen and use a value of
8.31 m^{2}⋅kg/s^{2}⋅K⋅mol
for the molar gas constant. Give your answer to
three significant figures.