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Poutnik
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If $V=Nb$, then container volume is 4 times total volume of molecules, according to the geometry used in the reasoning of van der Waals real gas model.

$$b'_2 = 4\pi d^3/3 = 8\times (4\pi r^3/3)$$ $$b' = b'_2/2 \quad \rightarrow \quad b'=4\times (4\pi r^3/3),$$ $$b = N_A b' .$$

Molecules at such a state are not able to freely move anymore, forming for each other not passable obstacles. Therefore the statistical pressure model breaks down.

Note that this and similar states are far, unjustified extrapolations of applicability of the van der Waals model. As this model breaks physically much sooner than mathematically.

Poutnik
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