Compressibility factor and deviation from ideal gas behaviour I have recently started to study the deviation of ideal gas behavior. The source from which I am reading doesn't give me an intuitive understanding of the compressibility factor.
I dont understand how the ratio PV/nRT relates to compressibility and why Z<1 means the gas is more compressible and Z>1 means the gas is less compressible.
My textbook simply states this without explaining and I would like to know how we arrive at this conclusion.
 A: I think there may be some confusion as to terminology: compressibility is defined as  $$ -\frac 1V \frac{\partial V}{\partial p}$$ where something like temperature or entropy is held constant, whereas the compressibility factor is defined as a certain ratio.
(ref: https://en.wikipedia.org/wiki/Compressibility)
In the ideal gas, particles do not interact with each other. The intuition behind the compressibility factor is that when particles do interact this causes a deviation from the ideal gas law. 
The virial expansion is a convenient mathematical construct that looks like the ideal gas law, but with correction factors. It looks like this $$ \frac {PV}{nRT} = 1 + \frac BV + \frac {C}{V^2}+...$$
(ref: https://en.wikipedia.org/wiki/Compressibility_factor#Theoretical_models)
And it turns out that B depends on two-particle interactions, C depends on three particle interactions, etc. 
So this virial expansion looks a lot like the compressibility factor, but it has these other terms in it.  
So the intuition is that if two body and three body interactions are important, then B and C become larger, and this causes the compressibility factor to be different from 1. 
The question as to whether the factor is smaller or larger than 1 should mainly depend on the effect of two body interactions, as they are logically more important in a gas than three or more body interactions. If there is a short range repulsive force between particles, then one would expect B > 0 and compressibility > 0.  And vice versa for the case of an attractive short range force (like the van der Waals force).
A: The compressibility factor was originally derived from empirical testing of gases to correct for the observed non-ideal behavior at more extreme pressures and temperatures. Although it cannot be derived from first principles in the kinetic theory of gases, the experimentally derived factors can be reconciled using Van Der Waal's equation that deals with the interactive forces between molecules.
