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

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

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 $dm^3$?

If $Z$ is a compressibility factor,the van der Waals equation at low pressure can be written as:

One mole of a monoatomic real gas satisfies the equation $p(V-b)=RT$ where $b$ is a constant. The relationship of interatomic potential $V(r)$ and interatomic distance $r$ for the gas is given by

What is the value of $Z$ for an ideal gas and a real gas?