At $300 \ K$ and $760 \ torr$ pressure, the density of a mixture of $He$ and $O_2$ gases is $0.543 \ g \ L^{-1}$. The mass percent of oxygen is approximately $(R = 0.0821 \ L \ atm \ K^{-1} \ mol^{-1})$

Indicate the correct statement for a $1 \ L$ sample of $N_{2(g)}$ and $CO_{2(g)}$ at $298 \ K$ and $1 \ atm$ pressure.

$A$ $4 : 1$ molar mixture of $He$ and $CH_4$ is kept in a vessel at $20 \ bar$ pressure. Due to a hole in the vessel,the gas mixture leaks out. What is the composition of the mixture effusing out initially?

Identify the correct statements from the following:
$I$. For an ideal gas,the compressibility factor is $1.0$.
$II$. The kinetic energy of $NO_{(g)}$ (molar mass $= 30 \ g \ mol^{-1}$) at $T(K)$ is $x \ J \ mol^{-1}$. The kinetic energy of $N_2O_{4(g)}$ (molar mass $= 92 \ g \ mol^{-1}$) at $T(K)$ is $2x \ J \ mol^{-1}$.
$III$. The rate of diffusion of a gas is inversely proportional to the square root of its density.

At $100\,^\circ\text{C}$ and $1 \, \text{atm}$ pressure,if the density of liquid water is $1.0 \, \text{g cm}^{-3}$ and the density of water vapor is $0.0006 \, \text{g cm}^{-3}$,then the volume occupied by water molecules in $1 \, \text{L}$ of steam is ............. $\text{cm}^3$.

When $0.0168 \, mol$ of $O_2$ obtained from the decomposition of $KClO_3$ is collected over water at $25 \, ^\circ C$,the volume is $428 \, mL$ and the pressure is $754 \, mm$. What is the water vapor pressure at $25 \, ^\circ C$ in $mm$?