Deviation from Ideal Gas Behaviour — Core Principles

Core Principles

Real gases deviate from the ideal gas law ($PV=nRT$) because they do not perfectly adhere to the ideal gas assumptions. The two main reasons for this deviation are: (1) gas molecules possess a finite volume, and (2) intermolecular forces (attractive and repulsive) exist between gas molecules.

These deviations are most pronounced at high pressures and low temperatures. The compressibility factor ($Z = \frac{PV}{nRT}$) is used to quantify this deviation. For an ideal gas, $Z=1$. For real gases, $Z<1$ indicates dominant attractive forces, making the gas more compressible, while $Z>1$ indicates dominant repulsive forces (due to molecular volume), making the gas less compressible.

The van der Waals equation, $(P + \frac{an^2}{V^2})(V - nb) = nRT$, introduces correction terms for these factors: 'a' for attractive forces and 'b' for molecular volume, providing a more accurate model for real gas behavior.

Important Differences

vs Ideal Gas

Aspect	This Topic	Ideal Gas
Molecular Volume	Negligible compared to container volume.	Finite and non-negligible, especially at high pressure.
Intermolecular Forces	Absent (no attraction or repulsion).	Present (attractive and repulsive forces exist).
Compressibility Factor (Z)	$Z=1$ under all conditions.	$Z \neq 1$ (can be $<1$ or $>1$) for most conditions.
Equation of State	Obeys $PV=nRT$.	Obeys van der Waals equation $(P + \frac{an^2}{V^2})(V - nb) = nRT$ or other real gas equations.
Liquefaction	Cannot be liquefied.	Can be liquefied below its critical temperature ($T_c$).
Conditions for Behavior	Hypothetical, a theoretical construct.	Approaches ideal behavior at high temperature and low pressure.

The fundamental distinction between ideal and real gases lies in their adherence to the assumptions of the Kinetic Molecular Theory. Ideal gases are theoretical constructs assuming point masses with no intermolecular interactions, leading to perfect obedience of $PV=nRT$ and a constant compressibility factor of 1. Real gases, however, are composed of actual molecules with finite volume and inherent intermolecular forces, causing them to deviate from ideal behavior. These deviations are quantified by the compressibility factor $Z \neq 1$ and are most pronounced under high pressure and low temperature conditions, necessitating more complex equations like the van der Waals equation for accurate description.