Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at $STP$. Take the diameter of an oxygen molecule to be $3 \mathring A$.

The mean free path and the average speed of oxygen molecules at $300 \ K$ and $1 \ atm$ are $3 \times 10^{-7} \ m$ and $600 \ m/s$,respectively. Find the frequency of its collisions.

Under which of the following conditions is the law $PV = RT$ obeyed most closely by a real gas?

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.

$A$ system consists of two types of gas molecules $A$ and $B$ having the same number density $2 \times 10^{25} \, /m^3$. The diameters of $A$ and $B$ are $10 \, \mathring{A}$ and $5 \, \mathring{A}$ respectively. They undergo collisions at room temperature. The ratio of the average distance covered by molecule $A$ to that of $B$ between two successive collisions is $..... \times 10^{-2}$.

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.