Question

Identify the correct statement(s).

• A. For a gas in a rigid container, mean free path is independent of pressure and temperature
• B. Translational kinetic energy of a given amount of an ideal gas is independent of pressure
• C. All the molecules of a gas at a given temperature have the same kinetic energy
• D. The average kinetic energy of $1\text{mol}$ of gas molecules at a given temperature is proportional to ${}^{\prime }{M}^{\prime }$. (where '$M$' is molar mass of gas)

Answer 1

Answer: (A), (B)

The correct options are
A For a gas in a rigid container, mean free path is independent of pressure and temperature
B Translational kinetic energy of a given amount of an ideal gas is independent of pressure

(a) Mean free path $=\frac{1}{\sqrt{2}\pi {\sigma }^2\left(\frac{N}{V}\right)}$
where $\pi {\sigma }^2=\text{areas of cross of section}$
$\frac{N}{V}=$ Number of molecules per unit volume so mean free path is independent of "$P$" and "$T$" as $N$ and $V$ are fixed for rigid container.
$\therefore$ (a) is correct.

(b) $KE\left(\text{translational}\right)=\left(\frac{3}{2}nRT\right)$
translational K.E. depends only only temperature.

(c) As the kinetic energy depends upon the velocity of molecules, $KE=\frac{1}{2}m{v}^2$
and from Maxwell's distribution curve, it can be seen that molecules of all gases have a wide range of speeds so they have different kinetic energies.

(d) $KE\left(\text{average per mole}\right)=\left(\frac{3}{2}RT\right)$
It depends only on temperature.