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In this lesson, we will learn how to calculate 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 . 2 2 Γ 1 0 5 Pa is 4 . 6 2 Γ 1 0 β 8 m. Find the effective radius π of the methane molecule.

Q2:

The mean free path for helium at a certain temperature and pressure is 2 . 1 0 Γ 1 0 β 7 m . Use a value of 1 . 1 0 Γ 1 0 β 1 1 m for the radius of a helium atom.

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

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

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 β π d 1 / 3 , where d π 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 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 β 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 β C and at a pressure of 1.00 atm. Use 2 . 1 2 Γ 1 0 β 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 collides with a molecule π during a time interval, the collision of either molecule π or molecule π is counted, but not both.

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