Question

A gas has a molecular diameter of 0.1 m. It also has a mean free path of 2.25 m. What is its density?

• A. ${10}^{-3}$
• B. ${10}^{-2}$
• C. ${10}^{-4}$
• D. ${10}^{-5}$

Answer 1

The correct option is A ${10}^{-3}$

Given :

Molecular diameter of a gas, $d=0.1m$.

Mean free path, $l=2.25m$.

The mean free path traversed by the molecules is given by

$l=\frac{1}{\sqrt{2}\pi d^2\rho }$

Therefor,

$\rho =\frac{1}{\sqrt{2}\pi d^{2}l}$

Using the given values we get,

$\rho =\frac{1}{\sqrt{2}\left(3.14\right)\left(0.1{)}^2\right(2.25)}$

$\rho =\frac{1}{0.0999}$

$\rho ={10}^{-3}$