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

For real gases,the relation between $P$,$V$ and $T$ is given by the van der Waals equation,$(P + \frac{an^2}{V^2})(V - nb) = nRT$. For the following gases $CH_4, CO_2, O_2, H_2$,which gas will have $(i)$ highest value of $'a'$ $(ii)$ lowest value of $'b'$?

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: $CH_4, O_2, H_2$

Consider the following table:

Gas	$a / (kPa \cdot dm^6 \cdot mol^{-2})$	$b / (dm^3 \cdot mol^{-1})$
$A$	$642.32$	$0.05196$
$B$	$155.21$	$0.04136$
$C$	$431.91$	$0.05196$
$D$	$155.21$	$0.4382$

$a$ and $b$ are van der Waals constants. The correct statement about the gases is:

Compressibility factor,$Z$,of a gas is given as $Z = \frac{pV}{nRT}$.
$(i)$ What is the value of $Z$ for an ideal gas?
$(ii)$ For a real gas,what will be the effect on the value of $Z$ above Boyle's temperature?

What is the compressibility factor $(Z)$ for the deviation of real gases from ideal behavior?