Table of Contents
The Van der Waals Equation
The Van der Waals equation modifies the ideal gas law to account for the finite size of molecules and attractive forces between them. The ideal gas law PV=nRT assumes point particles with no interactions, becoming inaccurate at high pressures and low temperatures.
Johannes van der Waals proposed this equation in 1873, earning him the 1910 Nobel Prize. Constant 'a' corrects for intermolecular attractions (reducing pressure), and constant 'b' corrects for molecular volume.
Formula
Van der Waals Constants
| Gas | a (L²·atm/mol²) | b (L/mol) |
|---|---|---|
| Helium | 0.0346 | 0.0238 |
| Nitrogen | 1.370 | 0.0387 |
| CO&sub2; | 3.658 | 0.0429 |
| Water Vapor | 5.537 | 0.0305 |
Frequently Asked Questions
When does the ideal gas law fail?
The ideal gas law breaks down at high pressures (above ~10 atm), low temperatures near the boiling point, or for gases with strong intermolecular forces like water vapor or ammonia.
What does Z tell us?
The compressibility factor Z=PV/(nRT) equals 1 for an ideal gas. Z less than 1 means dominant attractive forces; Z greater than 1 means dominant repulsive forces.
Are there better equations?
Yes, the Peng-Robinson and Soave-Redlich-Kwong equations are more accurate for engineering, especially near the critical point. The Van der Waals equation remains valuable for its conceptual clarity.