Ideal gas have no volume and IMF, while real gas would have a finite volume and IMF. The following will illustrate one of the consequences of IMF on the behavior of real gases using the van der Waals equation: where the value of a and b account for the intermolecular forces between gas molecules and the finite volume of a gas molecule, respectively.  As concentration, c, is substitution into the preceding equation followed by rearrangement yields .

To examine the importance of intermolecular force in the behavior of real gases, while ignoring the effect of the volume of a gas molecule, let b = 0, thus the equation simplifies to

P = - a c 2 + (RT) c

where the derivative is .

The derivative shows that at (i.e. at a low [gas], an increase in [gas] would increase the pressure in the system)

while at (i.e. at a high [gas], an increase in [gas] would decrease the pressure in the system).

The rationale of the behavior at low [gas] is straight-forward:

↑ gas molecules  --> ↑ [gas]  --> ↑ frequency of gas collision into container's wall --> ↑ force exerted on container's wall due to gas molecule collisions  --> ↑ pressure

while the behavior at high [gas] is somewhat counter-intuitive, i.e. the preceding argument is invalid - rather it is due to IMF, which would be less likely to occur at a low [gas], but be more likely to occur at a high [gas].

↑ gas molecules  --> ↑ IMF among gas molecules  -->  ↓ effective [gas]  --> ↓ gas collision frequency into container's wall  --> ↓ force on container's wall  --> ↓  pressure

At [gas] = RT / 2a, an increase in the concentration of pressure produces no change in the pressure in the system means that the preceding factors cancell each other's effect.

source:  originally pointed-out to me by: L. Izu.