Van der Waals Equation Calculator (Real Gas Pressure)
Pick a gas, enter moles, volume and temperature to compare real and ideal gas pressure.
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Van der Waals Equation Calculator (Real Gas Pressure) by TheCalcTools
How the Van der Waals Equation Calculator (Real Gas Pressure) works
The van der Waals equation corrects the ideal gas law for two things: molecules take up space (constant b) and attract each other (constant a). The corrections matter most at high pressure and low temperature.
Constants are standard tabulated values in L²·bar/mol² and L/mol. With R = 0.08314462618 L·bar/(mol·K), pressure comes out in bar.
The formula
Worked example
Using the default values shown in the calculator:
| Gas | Carbon dioxide CO₂ (a 3.640, b 0.04267) |
|---|---|
| a (L²·bar/mol²) | 1 |
| b (L/mol) | 0.03 |
| Amount of gas (mol) | 1 |
| Volume (L) | 1 |
| Temperature (K) | 300 |
- 1 mol of CO₂ in 1 L at 300 K: ideal pressure 24.94 bar.
- Van der Waals gives 22.42 bar, -10.1% from ideal.
Result:
| Van der Waals pressure (bar) | 22.415 |
|---|---|
| Ideal gas pressure (bar) | 24.943 |
| Difference from ideal | -10.14% |
| Compressibility factor Z | 0.8986 |
Frequently asked questions
When does the ideal gas law fail?
When molecules are close together: high pressures, low temperatures, or gases near condensation such as CO₂ or water vapour.
Sources and further reading
- Wikipedia: Van der Waals equation
- Wikipedia: Van der Waals constants (data page)
- NIST: CODATA fundamental physical constants
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