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

The volume of gas $A$ is twice that of gas $B$. The compressibility factor of gas $A$ is thrice that of gas $B$ at the same temperature. The ratio of the pressures of the gases for equal number of moles is:

Given van der Waals constant $a$ for $NH_{3}$,$H_{2}$,$O_{2}$ and $CO_{2}$ are respectively $4.17$,$0.244$,$1.36$ and $3.59$,which one of the following gases is most easily liquefied?

The van der Waals equation of state for a real gas is given. For $n$ moles of a real gas,the equation can be expressed as:

Derive the van der Waals equation.