Question

Consider the following statements for air molecules in an air tight container.
(I) The average speed of molecules is larger than root mean square speed.
(II) Mean free path of molecules is larger than the mean distance between molecules.
(III) Mean free path of molecules increases with temperature.
(IV) The rms speed of nitrogen molecule is smaller than oxygen molecule. The true statements are.

• A. Only II
• B. II & III
• C. II & IV
• D. I, II & IV

Answer 1

The correct option is A Only II

(I)

$v_{avg}=\sqrt{\frac{8kT}{m\pi }}$

$v_{rms}=\sqrt{\frac{3kT}{m}}$

$v_{avg}>v_{rms}$

so (I) is correct.

(II)

The mean free path of a molecule is smaller than the distance between molecules.

( II ) is wrong.

(III)

Mean free path is directly prop to temp T.

$\lambda =\frac{RT}{\sqrt{2}\pi d^2{N}_{A}P}$

so (III) is correct.

(IV)

$v_{rms}=\sqrt{\frac{3kT}{m}}$

Since $m_{N_2}<m_{O_2}$, rms speed of nitrogen is more than rms speed of oxygen molecule.

so (IV) is wrong.