Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters $1\,\mathring{A}$ and $2\,\mathring{A}$. The gases may be considered under identical conditions of temperature,pressure,and volume.

Statement-$1$: Real gas approaches ideal gas behaviour for low pressures and high temperatures.
Statement-$2$: At low pressure,the density of a gas is very low.

$A$ $25 \times 10^{-3} \, m^3$ volume cylinder is filled with $1 \, mol$ of $O_2$ gas at room temperature $(300 \, K)$. The molecular diameter of $O_2$ is $0.3 \, nm$ and its root mean square speed is $200 \, m/s$. What is the average collision rate (per second) for an $O_2$ molecule?

The change in volume $V$ with respect to an increase in pressure $P$ has been shown in the figure for a non-ideal gas at four different temperatures ${T_1}, {T_2}, {T_3}$ and ${T_4}$. The critical temperature of the gas is

For a molecule of an ideal gas,the number density is $2 \sqrt{2} \times 10^8 \text{ cm}^{-3}$ and the mean free path is $\frac{10^{-2}}{\pi} \text{ cm}$. The diameter of the gas molecule is

The mean free path of molecules of a certain gas at $STP$ is $1500\,d$,where $d$ is the diameter of the gas molecules. While maintaining the standard pressure,the mean free path of the molecules at $373\,K$ is approximately $..........\,d$