Step 1: Van der Waals Equation.
The ideal gas equation is:
Van der Waals modified it to account for:
1. Finite volume of gas molecules
2. Intermolecular attraction
The van der Waals equation is:
Where:
= measure of intermolecular attraction
= excluded volume of gas molecules
Step 2: Explanation of Corrections.
Pressure correction:
The term corrects for intermolecular attraction.
Volume correction:
The term accounts for finite molecular volume.
Step 3: Van der Waals Isotherm (P–V Curve).
When plotting pressure vs volume at constant temperature:
1. At high temperature ( ):
Curve resembles ideal gas behaviour (smooth decrease).
2. At critical temperature ( ):
Curve shows a point of inflection (critical point).
3. At low temperature ( ):
Curve shows a characteristic S-shaped region.
This region represents liquid–gas phase transition.
The flat portion after Maxwell correction represents coexistence of liquid and vapour phases.
Step 4: Critical Constants.
At critical point:
Critical constants are:
Final Answer:
The van der Waals equation is:
and its P–V curve shows deviation from ideal behaviour with a characteristic S-shaped isotherm below critical temperature.