Question

The mean free path is the average distance traveled by a particle between collisions with other particles. Calculate the mean free path
of air at room temperature, =69.8 ∘F. Air is mostly nitrogen, so assume that the collisions are between moving N2 molecules. The diameter of N2 is =1.58×10−10 m and the gas is at atmospheric pressure, =101325 Pa

Answer 1

The mean free path of air at room temperature of 69.8 °F and an atmospheric pressure of 101325 Pa is 3.61 × 10⁻⁷ m.

What is the mean free path?

The mean free path (λ) is an average distance over which a moving particle substantially changes its direction or energy, typically as a result of one or more successive collisions with other particles.

Assuming air is mostly nitrogen, we can calculate the mean free path using the following formula derived from the kinetic theory.

λ = (R × T) / (√2 × π × d² × NA × P)

λ = [(8.314 J/mol.K) × 294.15 K] / [√2 × π × (1.58 × 10⁻¹⁰ m)² × (6.022 × 10²³ mol⁻¹) × 101325 Pa]

λ = 3.61 × 10⁻⁷ m

where,

• R is the ideal gas constant.

• T is the absolute temperature (room temperature).

• d is the diameter of nitrogen gas.

• NA is Avogadro's number.

• P is the atmospheric pressure.

The mean free path of air at room temperature of 69.8 °F and an atmospheric pressure of 101325 Pa is 3.61 × 10⁻⁷ m.

Learn more about the mean free path here: brainly.com/question/4595955