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 $dm^3$?

(N/A) Given the equation: $P_{ideal} = P_{real} + \frac{an^2}{V^2}$
$(i)$ Rearranging for $a$: $a = \frac{(P_{ideal} - P_{real}) \cdot V^2}{n^2}$
Since the term $\frac{an^2}{V^2}$ must have the same units as pressure $(P)$:
Units of $a = \frac{\text{Units of } P \cdot (\text{Units of } V)^2}{(\text{Units of } n)^2}$
Given $P = N \ m^{-2}$,$V = m^3$,and $n = mol$:
Units of $a = \frac{N \ m^{-2} \cdot (m^3)^2}{(mol)^2} = N \ m^4 \ mol^{-2}$
$(ii)$ Given $P = atm$,$V = dm^3$,and $n = mol$:
Units of $a = \frac{atm \cdot (dm^3)^2}{(mol)^2} = atm \ dm^6 \ mol^{-2}$