[...] the real gas law (Van der Waal's gas equation) [...]
Van der Waals only provided the first equation with correction to the ideal gas law. His equation is by no means the
real gas law. It isn't even very accurate. Dozens of other equations were proposed that are less bad, in all circumstances, or in some domain of pressure and temperature, or for some gases.
Yes, Van der Waals forces attract molecules almost always, and this reduces the gas' volume since at any time, a fraction of the amount of molecules stick together. The effect should not be derived from a mean distance.
An example, for nitrogen, on page 8 therehttps://www.bnl.gov/magnets/Staff/Gupta/cryogenic-data-handbook/Section6.pdf