[sharbeldam]

My try to this question in the picture:

[P + a(n/V)2] (V/n - b) = RT

P(V/n-b)=RT
pv/n-Pb=RT

PV-Pbn=RTn

V-bn=RTn/P
V=nRT/P + bn
Pressure according to ideal gas law is V=nRT/P

so non ideal volume is larger, correct?

[Borek]

[P + a(n/V)2] (V/n - b) = RT

Looks broken to me. Please try to format equations using LaTeX, as explained here, at the moment it is very difficult to follow and guess what you mean.

so non ideal volume is larger, correct?

Always. In ideal gas all molecules are pointlike, they have no volume at all. That's not true for the real gases, and the more they are compressed the more important is the fact molecules do have finite size/volume.

[Enthalpy]

At very high pressure, the volume of a real gas is larger. Putting it simply, the molecules have a volume, which vaguely resembles the volume of the liquid substance. This is the b in the Van der Waals formula.

Note that pressures (few kbar) accessible to usual technology do compress liquids and solids, not just be reducing the movements, but also by reducing the distances between the nuclei. A diamond anvil does this much more strongly.

A real gas can also take less volume than an ideal one, because molecules attract an other. This is the b in the formula. It happens when the gas nearly condenses into a liquid. So to say, several molecules stick to an other for a limited time and take as much volume as one, but then heat suffices to separate them. Only when they group in large numbers do they form a liquid.

Van der Waals' formula was a first attempt. It's very far from perfect or even from good, but it's the simplest one. Many others exist because none works nicely with all substances. Especially hydrogen and helium tend to resist modelling.