Van der Waals Gas Calculator
Calculate real gas pressure, temperature, or volume using the Van der Waals equation.
Presets for CO2, N2, H2O, O2, CH4, and other common gases.
Result
Van der Waals Equation
The Van der Waals equation corrects the ideal gas law to account for two real-gas effects:
- Intermolecular attractions (pressure correction, constant a)
- Finite molecular volume (volume correction, constant b)
The equation:
( P + an^2/V^2 ) * ( V - nb ) = nRT
Rearranged to solve for pressure:
P = nRT / (V - nb) - an^2 / V^2
Variables:
| Symbol | Meaning | Units |
|---|---|---|
| P | Pressure | atm |
| V | Volume | litres (L) |
| T | Temperature | Kelvin (K) |
| n | Amount of gas | moles |
| a | Attraction constant | L^2 atm/mol^2 |
| b | Volume constant (co-volume) | L/mol |
| R | Gas constant | 0.08206 L·atm/(mol·K) |
What do a and b represent?
- a is larger for polar molecules with strong intermolecular attractions (water has a = 5.536, CO2 has a = 3.640)
- b approximates the volume excluded per mole due to the finite size of molecules
- Ideal gas: a = 0, b = 0 (no attractions, point particles)
Common gas constants:
| Gas | a (L^2·atm/mol^2) | b (L/mol) |
|---|---|---|
| Ideal Gas | 0 | 0 |
| Helium (He) | 0.0346 | 0.0238 |
| Hydrogen (H2) | 0.2453 | 0.0265 |
| Nitrogen (N2) | 1.390 | 0.0391 |
| Oxygen (O2) | 1.360 | 0.0318 |
| Methane (CH4) | 2.253 | 0.0428 |
| CO2 | 3.640 | 0.0427 |
| Water (H2O) | 5.536 | 0.0305 |
| Ammonia (NH3) | 4.169 | 0.0371 |
At low pressures and high temperatures, real gases approach ideal behavior and the two equations give similar results. Near the critical point (high pressure, near condensation), real-gas corrections become significant.