The mass density of normal air at room temperature (293 K) is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$, and the average molecular mass of air is $29.0 \mathrm{u}$. If the mean free path of an air molecule at room temperature is measured to be $111 \mathrm{~nm}$, what is the average diameter of an air molecule?

Question

Quizplus · Accepted Answer

The mean free path $\lambda$ is related to the molecular diameter $d$ by the equation $\lambda = \frac{kT}{\sqrt{2}\pi d^2 P}$, where $P$ is the pressure, $T$ is the temperature, and $k$ is the Boltzmann constant. Using the given density and molecular mass, we can find $P$ and solve for $d$, resulting in approximately $0.28 \mathrm{~nm}$.

The Mass Density of Normal Air at Room Temperature (293 1.29 kg/m31.29 \mathrm{~kg} / \mathrm{m}^{3}1.29 kg/m3

The Mass Density of Normal Air at Room Temperature (293 $1.29 \mathrm{~kg} / \mathrm{m}^{3}$