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 1.35×10 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 6.6465×10 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 m3 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 8.31/mkgsKmol for the molar gas constant.

Q3:

A particle of mass 𝑚 moves at a speed 𝑣 between opposite faces of an empty cubic container of side length 𝑑 and volume 𝑉, as shown in the diagram, colliding elastically with the container’s walls. The particle changes its momentum by 2𝑚𝑣 each time it collides with a wall and the particle collides with the wall shown being hit in the diagram once every 2𝑑𝑣 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?

  • A𝑚𝑣𝑑
  • B𝑚𝑣𝑑
  • C𝑚𝑑𝑣
  • D𝑚𝑑𝑣

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?

  • A𝑚𝑣2𝑑
  • B𝑑𝑚𝑣
  • C𝑚𝑣𝑑
  • D𝑚𝑑𝑣
  • E𝑚𝑑𝑣

Q4:

A particle of mass 𝑚 moves at a speed 𝑣 between opposite faces of an empty cubic container of side length 𝑑, 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?

  • A𝑚𝑣
  • B0
  • C2𝑚𝑣
  • D𝑚𝑣2

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?

  • A𝑑𝑣
  • B2𝑑𝑣
  • C2𝑑𝑣
  • D𝑑2𝑣

Q5:

The product of the pressure and volume of a gas is given by the formula 𝑃𝑉=23𝑛𝑚𝑣rms, where 𝑛 is the number of particles in the gas, 𝑚 is the mass of a particle, and 𝑣rms 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 𝑇=23𝑘𝑚𝑣rms, where 𝑘 is Boltzmann’s constant?

  • A𝑃𝑉𝑇=𝑃𝑉𝑇
  • B𝑃𝑉=𝑛𝑘𝑇
  • C𝑇=𝑇273KC
  • D𝑘=𝑅𝑁

Q6:

A cloud of hydrogen gas with a volume of 2.56 m3 consists of 3.25×10 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 1.6737×10 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 m2⋅kg/s2⋅K⋅mol for the molar gas constant. Answer to three significant figures.

  • A8.56×10 m3
  • B8.56×10 m3
  • C6.68×10 m3
  • D6.68×10 m3
  • E5.22×10 m3

Q8:

Nitrogen atoms in a container of volume 2.35 m3 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 m2⋅kg/s2⋅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 1.6737×10 kg for the mass of a hydrogen atom and use 1.3806×10 m2⋅kg/s2⋅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 m3. Find the number of atoms in the gas, giving your answer to three significant figures. Use a value of 2.32587×10 kg for the mass of a nitrogen atom.

  • A6.88×10 atoms
  • B6.88×10 atoms
  • C1.72×10 atoms
  • D2.75×10 atoms
  • E3.44×10 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 1.3806×10 m2⋅kg/s2⋅K for the value of Boltzmann’s constant. Give your answer to three significant figures.

  • A6.32×10 kg
  • B8.16×10 kg
  • C2.45×10 kg
  • D1.90×10 kg
  • E1.84×10 kg

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.