What is the mean free path for the molecules in an ideal gas when the pressure is 100 kpa and the temperature is 300 k given that the collision cross-section for the molecules of that gas is 2.0 × 10-20 m2? boltzmann's constant is k = 1.38 × 10-23 j/k.

The mean free path = 2.16*10^-6 m

Explanation:

Given:

Pressure of gas P = 100 kPa

Temperature T = 300 K

collision cross section, σ = 2.0*10^-20 m2

Boltzmann constant, k = 1.38*10^-23 J/K

To determine:

The mean free path, λ

Calculation:

The mean free path is related to the collision cross section by the following equation:

where n = number density

Substituting for P, k and T in equation (2) gives:

Next, substituting for n and σ in equation (1) gives:

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