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.

  • A 1 . 7 3 × 1 0 m
  • B 2 . 4 0 × 1 0 m
  • C 1 . 9 4 × 1 0 m
  • D 1 . 2 5 × 1 0 m
  • E 9 . 2 3 × 1 0 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 2.10×107 m . Use a value of 1.10×1011 m for the radius of a helium atom.

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

  • A 2 . 3 3 × 1 0 2 7 molecules/m3
  • B 2 . 3 7 × 1 0 2 7 molecules/m3
  • C 2 . 3 0 × 1 0 2 7 molecules/m3
  • D 2 . 2 5 × 1 0 2 7 molecules/m3
  • E 2 . 2 1 × 1 0 2 7 molecules/m3

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

  • A 3 . 3 1 × 1 0 3 mol/m3
  • B 3 . 5 7 × 1 0 3 mol/m3
  • C 3 . 7 3 × 1 0 3 mol/m3
  • D 3 . 6 7 × 1 0 3 mol/m3
  • E 3 . 4 4 × 1 0 3 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.

  • A 2 . 7 3 × 1 0
  • B 1 . 2 2 × 1 0
  • C 1 . 2 4 × 1 0
  • D 1 . 0 5 × 1 0
  • E 1 . 8 0 × 1 0

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