The compressibility factor for a definite amount of van der Waal’s gas at $0^{\mathrm{o}}\mathrm{C}$ and 100 atm is found to be 0.5. Assuming the volume of gas molecules negligible, the van der Waals’ constant 'a'  for the gas is $\mathrm{x} {\mathrm{L}}^2{\mathrm{mol}}^{-2}\mathrm{atm}$. Then the value of $10\mathrm{x}$ is (nearest integer)

A gas has a compressibility factor of $0.5$ and a molar volume of $0.4 {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ at a temperature of $800 \mathrm{K}$ and pressure $\mathrm{x} \mathrm{atm}$. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be  $\mathrm{y} {\mathrm{dm}}^3 {\mathrm{mol}}^{-1}$ . The value of$\mathrm{x}/\mathrm{y}$ is _________

[Use: Gas constant, $\mathrm{R}=8\times {10}^{-2} \mathrm{L} \mathrm{atm} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ ]

Among the gases $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}$ and $\mathrm{f}$, the gases that show only positive deviation from ideal behavior at all pressures in the graph are

The isotherms of a gas are shown below :

Among the following,

(i) At ${\mathrm{T}}_1$, the gas cannot be liquefied

(ii) At point $\mathrm{B}$, liquid starts to appear at ${\mathrm{T}}_2$

(ii) ${\mathrm{T}}_{\mathrm{C}}$ is the highest temperature at which the gas can be liquefied

(iv) At point $\mathrm{A}$, a small increase in pressure condenses the whole system to a liquid

The correct statements are :

The variation of the compressibility factor$\left(\mathrm{Z}\right)$with pressure $(\mathrm{P} \mathrm{in} \mathrm{bar})$ for some gases, are shown in the figure below. Identify the gases $\left(\mathrm{A}\right),\left(\mathrm{B}\right)$ and $\left(\mathrm{C}\right)$.