# Why does pressure due to van der Waals' forces increase as the square of density?

1. Aug 14, 2011

### cyborg6060

In van der Waals' equation for real gases, the adaptation to account for intermolecular attractions in real gas is $a\frac{n^2}{V^2}$. This implies that the pressure due to the VDW forces on the container is proportional to the square of the density, $\rho^2 = \frac{n^2}{V^2}$.

When I do calculations following from $P_{VDW}=\frac{\pi \rho^2 \lambda}{H^3}$, I end up with a cubic dependence.

Is there a qualitative way to imagine why the pressure is proportional to the square of the molecular density, $\rho$?