Behaviour of Real Gases — Core Principles

Core Principles

Real gases are actual gases that deviate from the theoretical ideal gas model. The ideal gas model assumes negligible molecular volume and no intermolecular forces. Real gases, however, possess finite molecular volume and experience attractive and repulsive forces.

These deviations are most pronounced at high pressures and low temperatures. At high pressures, the finite volume of molecules becomes significant, reducing the available free space. At low temperatures, intermolecular attractive forces become dominant, reducing the pressure exerted by the gas.

The compressibility factor, $Z = PV/nRT$, quantifies this deviation; $Z=1$ for ideal gases, $Z<1$ when attractive forces dominate, and $Z>1$ when molecular volume dominates. The van der Waals equation, $(P + an^2/V^2)(V - nb) = nRT$, corrects the ideal gas law by introducing 'a' for intermolecular attractions and 'b' for molecular volume.

Understanding critical temperature ($T_c$), critical pressure ($P_c$), and critical volume ($V_c$) is essential for gas liquefaction, as $T_c$ defines the maximum temperature at which a gas can be liquefied.

Important Differences

vs Ideal Gas

Aspect	This Topic	Ideal Gas
Molecular Volume	Negligible (point masses)	Finite and non-zero
Intermolecular Forces	Absent (no attraction or repulsion)	Present (attractive and repulsive forces)
Obey Gas Laws	Strictly obeys ideal gas law ($PV=nRT$) under all conditions	Obeys ideal gas law only at high temperature and low pressure; deviates at high pressure and low temperature
Compressibility Factor (Z)	Always $Z=1$	Can be $Z<1$ (attractive forces dominant) or $Z>1$ (molecular volume dominant)
Liquefaction	Cannot be liquefied	Can be liquefied below its critical temperature
Equation of State	$PV=nRT$	Van der Waals equation: $(P + an^2/V^2)(V - nb) = nRT$ (or other real gas equations)

The fundamental distinction between ideal and real gases lies in their molecular properties and interactions. Ideal gases are theoretical constructs with negligible molecular volume and no intermolecular forces, perfectly adhering to $PV=nRT$. Real gases, the actual gases around us, have finite molecular volumes and experience intermolecular forces, causing them to deviate from ideal behavior, especially under extreme conditions. This deviation is quantified by the compressibility factor (Z) and addressed by more complex equations of state like the van der Waals equation, which incorporates corrections for these real-world imperfections. Unlike ideal gases, real gases can be liquefied.