# Why is excluded volume in van der Waals equation divided by 2?

Source: Physics Stack Exchange

The excluded volume calculated based on the diagram is 8 times the volume of a molecule. The volume is then divided by 2 to give the so-called excluded volume per molecule. Why divided by 2 only?

Obviously more than two molecules can come close together, and their assigned excluded volumes can overlap with each other, giving a smaller $$b$$. Is $$b$$ just an upper limit of excluded volume?

Collision is predominantly a bimolecular act. The probability of three gas molecules simultaneously colliding is incredibly low, therefore it quite accurate to say that the excluded molar volume $$b$$ is overcounted by a factor of 2.