A nitrogen molecule has a diameter of about 0.29 nm. The mean free path of a nitrogen molecule in a tank of dry nitrogen at room temperature (293 K) and standard pressure (1 atm) is about 0.10 µm. A tank containing nitrogen at standard temperature (273 K) and pressure has volume V. If the tank is compressed by means of a piston to 20% of its original volume, what is the mean free path for a nitrogen molecule under the new conditions?
A) 0.020 µm
B) 0.125 µm
C) 0.080 µm
D) 0.112 µm

Question

Quizplus · Accepted Answer

The mean free path is inversely proportional to the pressure. Compressing the tank to 20% of its original volume increases the pressure by a factor of 5 (since pressure is inversely proportional to volume). Therefore, the mean free path decreases by a factor of 5, resulting in 0.10 µm / 5 = 0.020 µm.

A Nitrogen Molecule Has a Diameter of About 0