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Worksheet: Mean Free Path of Gas Molecules

Q1:

The mean free path for methane at a temperature of 273 K and a pressure of 1 . 2 2 Γ— 1 0 5 Pa is 4 . 6 2 Γ— 1 0 βˆ’ 8 m. Find the effective radius π‘Ÿ of the methane molecule.

  • A 1 . 2 5 Γ— 1 0 βˆ’ 1 0 m
  • B 2 . 4 0 Γ— 1 0 βˆ’ 1 0 m
  • C 1 . 7 3 Γ— 1 0 βˆ’ 1 0 m
  • D 1 . 9 4 Γ— 1 0 βˆ’ 1 0 m
  • E 9 . 2 3 Γ— 1 0 βˆ’ 1 0 m

Q2:

The mean free path for helium at a certain temperature and pressure is 2 . 1 0 Γ— 1 0 βˆ’ 7 m . Use a value of 1 . 1 0 Γ— 1 0 βˆ’ 1 1 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 0 Γ— 1 0 2 7 molecules/m3
  • B 2 . 2 5 Γ— 1 0 2 7 molecules/m3
  • C 2 . 3 3 Γ— 1 0 2 7 molecules/m3
  • D 2 . 2 1 Γ— 1 0 2 7 molecules/m3
  • E 2 . 3 7 Γ— 1 0 2 7 molecules/m3

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

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

Q3:

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 π‘Ž β‰ˆ 𝑉 d 1 / 3 , where d 𝑉 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 π‘Ž that is 100 times greater than the mean free path of molecules in the air. Use a value of 1 . 8 8 Γ— 1 0 βˆ’ 1 1 m as the effective radius of the molecules in air.

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 0 ∘ C and at a pressure of 1.00 atm. Use 2 . 1 2 Γ— 1 0 βˆ’ 1 0 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 π‘Ž collides with a molecule 𝑏 during a time interval, the collision of either molecule π‘Ž or molecule 𝑏 is counted, but not both.

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