The mean free path for a nitrogen molecule in a tank of dry nitrogen at $273 \mathrm{~K}$ is $0.15 \mu \mathrm{m}$. If the diameter of a nitrogen molecule is $0.29 \mathrm{~nm}$, what is the pressure in the tank?
A) $67.2 \mathrm{kPa}$
B) $211 \mathrm{kPa}$
C) $95.1 \mathrm{kPa}$
D) $48.0 \mathrm{kPa}$
E) $299 \mathrm{kPa}$

Question

Quizplus · Accepted Answer

The mean free path ($\lambda$) is related to the pressure ($P$), temperature ($T$), and diameter of the molecule ($d$) by the equation $\lambda = \frac{kT}{\sqrt{2}\pi d^2 P}$, where $k$ is the Boltzmann constant. Rearranging for $P$ and substituting the given values (converting units where necessary), we find that the pressure is closest to $67.2 \mathrm{kPa}$.

The Mean Free Path for a Nitrogen Molecule in a Tank