Van der Waals equation is given as $\left(P+\frac{a{n}^2}{V^2}\right)\left(V-nb\right)=nRT$, here $P$ is pressure, $V$ is volume, $T$ is temperature, $n$ is the number of moles, and $R$ is the universal gas constant.

The dimensional formula of pressure is$P=\frac{\mathrm{Force}}{\mathrm{Area}}=\frac{{\displaystyle \left[{\mathrm{MLT}}^{-2}\right]}}{\left[L^2\right]}=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$ 

The dimensional formula of the volume is $\left[L^3\right]$

As we know, the quantities with the same dimensions are added or subtracted. Thus, the dimension of $P=$the dimension of $\frac{a{n}^2}{V^2}$.

Therefore, $a=\frac{P{V}^2}{n^2}=\frac{\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]{\left[{\mathrm{L}}^3\right]}^2}{{\left[\mathrm{mol}\right]}^2}=\left[{\mathrm{ML}}^5{\mathrm{T}}^{-2}{\mathrm{mol}}^{-2}\right]$

Thus, the unit of constant $\mathrm{a}$ is $\mathrm{N} {\mathrm{m}}^4 {\mathrm{mol}}^{-2}$.