Calculate the compressibility factor $(Z)$ of $1 \text{ mole}$ of a certain real gas if it occupies $0.4 \text{ dm}^3$ at $300 \text{ K}$ and $40 \text{ atm}$. [Given: $R = 0.082 \text{ dm}^3 \text{ atm K}^{-1} \text{ mol}^{-1}$]

Pressure exerted by $1 \, mole$ of methane in a $0.25 \, L$ container at $300 \, K$ using van der Waals equation is ............... $atm$ (given $a = 2.253 \, atm \, L^2 \, mol^{-2}, b = 0.0428 \, L \, mol^{-1}$):

Which among the following statements is/are incorrect regarding real gases?
$(i)$ Their compressibility factor is never equal to unity $(Z \neq 1)$.
$(ii)$ The deviations from ideal behavior are less at low pressures and high temperatures.
$(iii)$ Intermolecular forces among gas molecules are equal to zero.
$(iv)$ They obey Van der Waals equation,$PV = nRT$.

The unit of the Van der Waals constant '$a$' is .......

The deviation from the ideal gas equation $PV = nRT$ is maximum under which of the following conditions?

For one mole of a van der Waals' gas,the compressibility factor $Z = (pV/RT)$ at a fixed volume will certainly decrease,if
[Given : $a$ and $b$ are standard parameters for van der Waals' gas]