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)


   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.