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. Both Assertion and Reason are incorrect

Answer 1

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

The distance travelled by a gas molecule between two successive collisions is known as free path
i.e $\lambda =\frac{1}{\sqrt{2}}\frac{kT}{\pi d^{2}P}$
where $d=$ Diameter of the molecule
$k=$Boltzmann constant
$P=$ Pressure and
$T=$ Tmeperature of as molecules
From the above equation, we can see that $\lambda$ varies inversely as the pressure of the gas
Also $\lambda =\frac{m}{\sqrt{2}\pi d^2\rho }$ i.e $\lambda \propto \frac{1}{\rho }$
where $m=$ mass of each molecules
$\rho =$ density of gas molecule