In the empirical demonstration of the Van der Waals equation at Khan Academy, they made a demonstration of the real volume, for example, it was said that it has to be larger than the ideal volume, since the size of the molecules is not disregarded, hence it would be:
$$ V_{\text{ideal}} = V_{\text{real}} + nb $$
Where, $ b $ was said to be related to the size of the molecule.
But why don't I also include intermolecular interaction? Depending on it, the volume may even be smaller.