In the Van der Waal's equation in volume correction term, a given molecule is able to exclude 4 times of its volume from the volume of the container. Why is it so?
From the Wikipedia page on the topic, it says:
To see this, we must realize that a particle is surrounded by a sphere of radius 2r (two times the original radius) that is forbidden for the centers of the other particles. If the distance between two particle centers were to be smaller than 2r, it would mean that the two particles penetrate each other, which, by definition, hard spheres are unable to do.
Why is that volumetric region of radius 2r forbidden for other particles? I say so because clearly that region has enough space to accomodate at least two particles as whole (assuming them to be rigid).
Can someone provide a clear argument for that correction term?
The following are some previous posts on the given topic, but they don't answer my question well, so I am asking a new one:
The answer there is a complete cut and paste from Wikipedia, and since I have already explained my confusion regarding the explanation there, therefore it doesn't count.
Also, a comment there points out the same problem as mine but hasn't been clarified yet there.
