States of Matter · JEE Advanced previous year questions

Molar volume $(V_{\mathrm{m}})$ of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with $V_{\mathrm{m}}$ as the variable. The ratio (in $\mathrm{mol}\mathrm{d}{\mathrm{m}}^{-3}$) of the coefficient of $V_{\mathrm{m}}^2$ to the coefficient of $V_{\mathrm{m}}$ for a gas having van der Waals constants $a=6.0\mathrm{d}{\mathrm{m}}^6\mathrm{atm}\mathrm{mo}{\mathrm{l}}^{-2}$ and $b=0.060\mathrm{d}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$ at 300 K and 300 atm is ____. $\text{Use}$: Universal gas constant (R) = $0.082\mathrm{d}{\mathrm{m}}^3\mathrm{atm}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is ____. $\text{Use}$: Universal gas constant (R) = $8.3\mathrm{J}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}$; Atomic mass (in amu): H = 1, O = 16

A closed vessel contains $10\mathrm{g}$ of an ideal gas $\mathbf{X}$ at $300\mathrm{K}$, which exerts $2\mathrm{atm}$ pressure. At the same temperature, $80\mathrm{g}$ of another ideal gas $\mathbf{Y}$ is added to it and the pressure becomes $6\mathrm{atm}$. The ratio of root mean square velocities of $\mathbf{X}$ and $\mathbf{Y}$ at $300\mathrm{K}$ is

1. A.$2\sqrt{2}:\sqrt{3}$
2. B.$2\sqrt{2}:1$
3. C.$1:2$
4. D.$2:1$

A gas has a compressibility factor of 0.5 and a molar volume of $0.4\mathrm{d}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$ at a temperature of $800\mathrm{K}$ and pressure $\mathbf{x}\mathrm{atm}$. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be $\mathbf{y}\mathrm{d}{\mathrm{m}}^3\mathrm{mo}{\mathrm{l}}^{-1}$. The value of $\mathbf{x}/\mathbf{y}$ is ____. $[\text{Use: Gas constant, }\mathrm{R}=8\times 10^{-2}\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}\mathrm{mo}{\mathrm{l}}^{-1}]$