At low pressure,Vander Waal's equation is reduced to $\left[ P + \frac{a}{V^2} \right]V = RT$. The compressibility factor $(Z)$ can be given as

At $300 \, K$ temperature and $40 \, atm$ pressure,if one mole of $CO_2$ occupies $0.4 \, L$,then it is:

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

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: $CH_4, O_2, H_2$

For a gas,the deviation from ideal behavior is maximum at:

The van der Waals constants for $HCl$ gas are $a = 3.6 \ atm \ L^2 \ mol^{-2}$ and $b = 40 \ mL \ mol^{-1}$. The critical temperature of the gas is : ............. $K$ [ $R = 0.08 \ atm \ L \ K^{-1} \ mol^{-1}$ ]