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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.
