Van der Waals Equation Calculator
Pressure of a real gas from the Van der Waals equation, compared with the ideal gas value.
Results
What this tool does
The ideal gas law assumes molecules are points that never notice each other. Johannes van der Waals fixed both assumptions in 1873 with two constants: one for the space molecules take up, one for the attraction between them. The correction matters most where it is least convenient — at high pressure and near condensation — and it earned him the 1910 Nobel Prize. Default values here are carbon dioxide.
Formula
(p + a n²/V²)(V - n b) = n R T
Variables
| Symbol | Meaning | Unit |
|---|---|---|
nn | Amount of substance | mol |
vv | Volume | L |
tt | Temperature | K |
aa | Van der Waals a | L²·atm/mol² |
bb | Van der Waals b | L/mol |
PP | Pressure | atm |
PB | Pressure | bar |
PI | Ideal gas pressure | atm |
DV | Deviation from ideal | % |
Worked example
- Amount of substance1 mol
- Volume1 L
- Temperature300 K
- Van der Waals a3.592 L²·atm/mol²
- Van der Waals b0.04267 L/mol
- Pressure22.12245 atm
- Pressure22.41557 bar
- Ideal gas pressure24.61721 atm
- Deviation from ideal-10.134 %
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
Frequently asked questions
What do a and b actually represent?
b is the volume the molecules themselves occupy, so the gas has less room to move in than the container suggests — it pushes the pressure up. a accounts for the attraction between molecules, which pulls them inwards and softens their impact on the walls — it pulls the pressure down. Both are measured constants specific to each gas, and you must look them up rather than guess them.