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: $R = 0.082 \text{ dm}^3 \text{ atm K}^{-1} \text{ mol}^{-1}$]

Four gases $P, Q, R$ and $S$ have almost same values of $b$ but their $a$ values ($a, b$ are van der Waals' constants) are in the order $Q < R < S < P$. At a particular temperature among the four gases, the most liquefiable one is

The relation between pressure exerted by an ideal gas $(P_{ideal})$ and observed pressure $(P_{real})$ is given by the equation
$P_{ideal} = P_{real} + \frac{an^2}{V^2}$
$(i)$ If pressure is taken in $N \ m^{-2}$,number of moles in $mol$,and volume in $m^3$,calculate the unit of $a$.
$(ii)$ What will be the unit of $a$ when pressure is in atmosphere and volume in $dm^3$?

What are the values of $Z$ for $CO_2, CH_4$,and $O_2$ at $200 \ bar$ and $900 \ bar$ pressure?

The pressure exerted by $5 \, mol$ of a real gas in a $1 \, L$ container at $47 \, ^oC$ is ............. $atm$. $\left( a = 3.592 \, atm \, L^2 \, mol^{-2}, b = 0.0427 \, L \, mol^{-1} \right)$

For which of the following is the van der Waals equation valid?