A 1 L container contains O₂ gas at STP. If the diameter of the O₂ molecule is 3.75 $\times$ 10 ^-10m, the mean free path of the O₂ molecule is A) 5.96 $\times$ 10 ^-8 m B) 6.53 $\times$ 10 ^-8 m C) 4.57 $\times$ 10 ^-8 m D) 6.89 $\times$ 10 ^-8 m E) 7.67 $\times$ 10 ^-8 m

Question

Quizplus · Accepted Answer

The mean free path, λ, of a gas molecule is given by
λ = (1/√2πd^2n) where d is the diameter of the gas molecule, n is the number density of the gas (mol/m^3) and π is the constant pi.
At STP, the number density of a perfect gas is 2.69 x 10^25 m^-3. Substituting the values given, we get
λ = (1/√2π(3.75 x 10^-10)^2(2.69 x 10^25)) = 5.96 x 10^-8 m
Therefore, the best choice is A.

A 1 L Container Contains O2 Gas at STP ×\times× 10 -10m, the Mean Free Path of the O2 Molecule

A 1 L Container Contains O₂ Gas at STP $\times$ 10 ^-10m, the Mean Free Path of the O₂ Molecule