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

decreasethe 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.