Question

Assertion :Mean free path of a gas molecules varies inversely as density of the gas Reason: Mean free path varies inversely as pressure of the gas

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

The mean free path of a gas molecule is the average distance between two successive collisions. It is represented by $\lambda$
$\lambda$ = $\frac{1}{\sqrt{2}}\frac{kT}{\pi {\sigma }^{2}P}$ and
$\lambda$ = $\frac{m}{\sqrt{2}.\pi {\sigma }^{2}d}$
Here, $\sigma$ = 0 diameter of molecule and
k= Boltzmann's constant
$\Rightarrow$ $\lambda$ $\propto$ $\frac{1}{d}$,
$\lambda$ $\propto$ $T$ and $\lambda$ $\propto$ $\frac{1}{p}$
Hence, mean free path varies inversely as density of the gas. It can easily proved that the mean free path varies directly as the temperature and inversely as the pressure of the gas.