Explain real gases showing deviations from ideal gas with correction of pressure and volume and derive van der Waals equation.

(N/A) Real gases deviate from ideal behavior at high pressure and low temperature. The ideal gas equation $PV = nRT$ is based on two assumptions of the kinetic theory of gases which do not hold true for real gases:
$1.$ The volume occupied by gas molecules is negligible compared to the total volume of the gas.
$2.$ There are no forces of attraction between gas molecules.
Van der Waals introduced corrections for these:
Volume Correction: The effective volume available for the movement of molecules is $(V - nb)$,where $b$ is the excluded volume per mole.
Pressure Correction: The observed pressure $P$ is less than the ideal pressure due to intermolecular attraction. $P_{\text{ideal}} = P + \frac{an^2}{V^2}$,where $a$ is the attraction constant.
Substituting these into the ideal gas law $PV = nRT$,we get the van der Waals equation:
$(P + \frac{an^2}{V^2})(V - nb) = nRT$.