$CH_4$ gas is behaving non-ideally. The compressibility factor for the gas is $1.5$ at $2 \ atm$ and $400 \ K$. Calculate the molar volume for the gas in $litre$. [Given $R = 0.08 \ L \ atm \ K^{-1} \ mol^{-1}$]

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

Calculate the compressibility factor for $SO_2$,if $1 \ mol$ of it occupies $0.35 \ L$ at $300 \ K$ and $50 \ atm$ pressure.

Consider the equation $Z = \frac{pV}{RT}$. Which of the following statements is correct?

$A$ gas is said to behave like an ideal gas when the relation $PV/T = \text{constant}$. When do you expect a real gas to behave like an ideal gas?

For real gases,the relation between $p$,$V$,and $T$ is given by the van der Waals equation:
$(p + \frac{an^2}{V^2})(V - nb) = nRT$
Where $a$ and $b$ are van der Waals constants,$nb$ is approximately equal to the total volume of the molecules of a gas,and $a$ is the measure of the magnitude of intermolecular attraction.
$(i)$ Arrange the following gases in the increasing order of $b$. Give reason: $O_2, CO_2, H_2, He$
$(ii)$ Arrange the following gases in the decreasing order of magnitude of $a$. Give reason: $CH_4, O_2, H_2$