Question

Given below are two statements :
Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the above statements, choose the correct answer from the option given below:

• A. Statement I is false but Statement II is true
• B. Statement I is true but Statement II is false
• C. Both Statement I and Statement II are false
• D. Both Statement I and Statement II are true

Answer 1

The Correct Option is D

The mean free path (\(\lambda\)) of gas molecules is given by:
\[\lambda = \frac{RT}{\sqrt{2} \pi d^2 N_A P}.\]
Here, \(\lambda \propto \frac{1}{d^2}\), verifying Statement (I).
The average kinetic energy of gas molecules is:
\[KE = \frac{f}{2} nRT,\]
where \(KE \propto T\), confirming Statement (II).
Thus, both Statement I and Statement II are correct.