Worksheet: Mean Free Path of Gas Molecules

In this worksheet, we will practice applying the mean free path of a particle in an ideal gas given the pressure and temperature of the gas.

Q1:

The mean free path for methane at a temperature of 273 K and a pressure of 1.22×10 Pa is 4.62×10 m. Find the effective radius 𝑟 of the methane molecule.

  • A1.73×10 m
  • B2.40×10 m
  • C1.94×10 m
  • D1.25×10 m
  • E9.23×10 m

Q2:

For the equations of hydrodynamics to apply to a highly compressible fluid, the mean free path must be much less than the linear size of a volume 𝑎𝑉d/, where d𝑉 is a small volume of fluid. For air in the stratosphere at a temperature of 220 K and a pressure of 5.8 kPa, determine the value of 𝑎 that is 100 times greater than the mean free path of molecules in the air. Use a value of 1.88×10 m as the effective radius of the molecules in air.

Q3:

The mean free path for helium at a certain temperature and pressure is 2.10×10 m. Use a value of 1.10×10 m for the radius of a helium atom.

What is the density of helium under these conditions in molecules per cubic meter?

  • A2.30×10 molecules/m3
  • B2.37×10 molecules/m3
  • C2.25×10 molecules/m3
  • D2.21×10 molecules/m3
  • E2.33×10 molecules/m3

What is the density of helium under these conditions in moles per cubic meter?

  • A3.31×10 mol/m3
  • B3.57×10 mol/m3
  • C3.73×10 mol/m3
  • D3.44×10 mol/m3
  • E3.67×10 mol/m3

Q4:

Find the total number of collisions between molecules in 1.70 s interval within 1.25 L of nitrogen gas that is at a temperature of 0C and at a pressure of 1.00 atm. Use 2.12×10 m as the effective radius of a nitrogen molecule and use a value of 28.0 g/mol for the molar mass of nitrogen. Consider that each collision involves two molecules, therefore if a molecule 𝑎 collides with a molecule 𝑏 during a time interval, the collision of either molecule 𝑎 or molecule 𝑏 is counted, but not both.

  • A2.73×10
  • B1.22×10
  • C1.24×10
  • D1.05×10
  • E1.80×10

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