# Worksheet: Root-Mean-Square Speed of Ideal Gas Particles

In this worksheet, we will practice determining the relationship between the absolute temperature of an ideal gas and the root-mean-square speed of its particles.

**Q1: **

A cloud of helium gas consists of helium atoms. The atoms have a root-mean-square speed of 652 m/s and the gas exerts a pressure of 45,250 Pa. Find the volume of the gas. Use a value of kg for the mass of a helium atom. Answer to three significant figures.

**Q2: **

A cloud of hydrogen gas with a volume of 1.05 m^{3}
consists of 4.22 moles of hydrogen atoms. The atoms have a root-mean-square
speed of 983 m/s. Find the pressure of the gas to the nearest kilopascal. Use a value
of 1.0079 g for the molar mass of hydrogen atom and a value of
for the molar gas constant.

**Q3: **

A particle of mass moves at a speed between opposite faces of an empty cubic container of side length and volume , as shown in the diagram, colliding elastically with the container’s walls. The particle changes its momentum by each time it collides with a wall and the particle collides with the wall shown being hit in the diagram once every seconds.

Which of the following correctly represents the average force exerted on the wall of the container that the particle is shown colliding with due to the particle’s collisions?

- A
- B
- C
- D

Which of the following correctly represents the average pressure exerted on the wall of the container that the particle is shown colliding with due to the particle’s collisions?

- A
- B
- C
- D
- E

**Q4: **

A particle of mass moves at a speed between opposite faces of an empty cubic container of side length , as shown in the diagram, colliding elastically with the walls of the container.

Which of the following correctly represents the change in the momentum of the particle in a collision with a wall of the container?

- A
- B0
- C
- D

Which of the following correctly represents the time interval between the particle’s collisions with the wall of the container that the particle is shown colliding with?

- A
- B
- C
- D

**Q5: **

The product of the pressure and volume of a gas is given by the formula , where is the number of particles in the gas, is the mass of a particle, and is the root-mean-square speed of the particles. Which of the following formulas can be combined with this formula to show that the kelvin temperature of a gas is given by , where is Boltzmann’s constant?

- A
- B
- C
- D

**Q6: **

A cloud of hydrogen gas with a volume of 2.56 m^{3}
consists of hydrogen atoms.
The atoms have a
root-mean-square speed of 776 m/s.
Give your answer to three significant figures.
Use a value of kg
for the mass of a hydrogen
atom.

**Q7: **

A cloud of helium gas consists of 1.28 moles of helium. The
atoms have a root-mean-square speed of 514 m/s and the gas exerts a pressure of
67,500 Pa. Find the volume of the gas. Use a value of 4.0026 g for the molar
mass of helium and a value of 8.31 m^{2}⋅kg/s^{2}⋅K⋅mol for the molar gas constant. Answer to three significant figures.

- A m
^{3} - B m
^{3} - C m
^{3} - D m
^{3} - E m
^{3}

**Q8: **

Nitrogen atoms in a container of volume 2.35 m^{3}
exert a pressure of 1,280 kPa. The nitrogen atoms have a root-mean-square speed
of 450 m/s. Find the number of moles of nitrogen atoms in the gas. Use a value
of 14.0067 g/mol for the molar mass of nitrogen and a value of 8.31 m^{2}⋅kg/s^{2}⋅K⋅mol
for the molar gas constant. Answer to three significant figures.

**Q9: **

Hydrogen atoms in a gas have a root-mean-square speed of
3,460 m/s. Find the temperature of the gas.
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.

**Q10: **

Nitrogen atoms having a root-mean-square speed of 1,250 m/s
exert a pressure of 115 kPa in a container of volume 0.145 m^{3}.
Find the number of atoms in the gas, giving your answer to three significant figures.
Use a value of kg for the mass of a nitrogen atom.

- A atoms
- B atoms
- C atoms
- D atoms
- E atoms

**Q11: **

Particles in a gas at a temperature of 355 K have a
root-mean-square speed of 775 m/s. Find the mass of the particles. Use m^{2}⋅kg/s^{2}⋅K for the value of Boltzmann’s constant. Give your answer to three significant figures.

- A kg
- B kg
- C kg
- D kg
- E kg