The mean free path of an oxygen molecule is 2.0 × 10^-5 m, when the gas is at a pressure of 120 Pa and a temperature of 275 K. The molecular mass of oxygen is 32.0 g/mol and the Boltzmann constant is 1.38 × 10^-23J/K, Avogadro's number is 6.02 × 10²³molecules/mole, and the ideal gas constant is R = 8.314 J/mol•K = 0.0821 L ∙ atm/mol ∙ K. Assuming that the molecules are moving at their root-mean-square speeds, the average time interval between collisions of an oxygen molecule is closest to A) 20 ns. B) 43 ns. C) 95 ns. D) 200 ns. E) 420 ns.

Question

Quizplus · Accepted Answer

The average time interval between collisions, τ, can be calculated using the mean free path, λ, and the root-mean-square speed, u, of the oxygen molecule:
τ = λ/u
The root-mean-square speed, u, can be calculated using the formula:
u = sqrt(3RT/M)
where R is the gas constant, T is the temperature, and M is the molar mass.
u = sqrt(3RT/M)
= sqrt(3 x 8.314 x 275/32.0)
= 482.6 m/s
Therefore, τ = λ/u
= 2.0 x 10^-5 m / 482.6 m/s
= 41.4 x 10^-9 s
= 41.4 ns (nearest to 43 ns)

The Mean Free Path of an Oxygen Molecule Is 2