Calculator Inputs
Formula Used
(P + a(n²/V²))(V − nb) = nRT
This is the standard Van der Waals form for a real gas with amount n, pressure P, temperature T, and volume V.
P = nRT/(V − nb) − a(n²/V²)
Use this rearranged form when you want pressure from temperature and total volume.
T = ((P + a(n²/V²))(V − nb)) / (nR)
Use this form when you know pressure and volume and need temperature.
Z = PV / (nRT)
The compressibility factor compares real-gas behavior with ideal-gas behavior. Ideal gases have Z = 1.
How to Use This Calculator
- Choose whether you want to solve pressure, temperature, or volume.
- Select a gas preset or enter custom a and b values manually.
- Enter the amount of gas in moles.
- Fill the known variables using bar, liters, and kelvin.
- Click Calculate Now to show the result above the form.
- Review the ideal-gas comparison, deviation percentage, and compressibility factor.
- Use the graph to compare the Van der Waals curve with the ideal-gas curve.
- Download the result area as CSV or PDF if you need a saved copy.
Van der Waals Equation a and b Values
The a constant measures intermolecular attraction. Larger a values usually mean stronger attractive forces. The b constant represents excluded volume, so larger b values usually mean larger effective molecular size. These constants change with the gas and the chosen unit system.
| Gas | a (L²·bar/mol²) | b (L/mol) | Meaningful note |
|---|---|---|---|
| Helium | 0.0341 | 0.02370 | Very weak attractions compared with larger molecules. |
| Nitrogen | 1.3900 | 0.03913 | Common reference gas for teaching thermodynamics. |
| Oxygen | 1.3600 | 0.03183 | Similar magnitude to nitrogen in many examples. |
| Carbon Dioxide | 3.5920 | 0.04267 | Stronger attractions than many diatomic gases. |
| Methane | 2.2830 | 0.04278 | Useful for real-gas fuel and process calculations. |
| Ammonia | 4.2250 | 0.03713 | Higher attraction constant due to stronger interactions. |
| Water Vapor | 5.4640 | 0.03049 | Very strong nonideal behavior in many conditions. |
Example Data Table
These sample rows use the same unit system as the calculator: bar, liters, moles, and kelvin.
| Case | Gas | n (mol) | T (K) | V (L) | a | b | Illustrative output |
|---|---|---|---|---|---|---|---|
| Example 1 | CO2 | 1.00 | 300 | 2.50 | 3.5920 | 0.04267 | Pressure mode shows real-gas pressure below the ideal estimate. |
| Example 2 | N2 | 1.20 | 320 | 3.20 | 1.3900 | 0.03913 | Pressure mode highlights moderate nonideal correction. |
| Example 3 | NH3 | 0.80 | 290 | 1.80 | 4.2250 | 0.03713 | Temperature or pressure can differ more from ideal values. |
Frequently Asked Questions
1) What does the Van der Waals equation improve?
It corrects ideal-gas behavior by adding attraction through a and finite molecular size through b. That usually improves predictions at higher pressure, lower temperature, and denser states.
2) What are Van der Waals equation a and b values?
a measures intermolecular attraction strength. b represents excluded volume per mole. Different gases have different values, and the numbers must match the unit system used in the equation.
3) Are a and b constants universal?
No. They depend on the gas and on the units used. This calculator expects a in L²·bar/mol² and b in L/mol, so coefficient tables must match that system.
4) Why must volume stay greater than n×b?
Because the free-volume term V − nb appears in the denominator. As volume approaches n×b, the corrected equation becomes singular and the calculation is not valid.
5) Why can the volume solution have multiple roots?
The volume form is cubic. In some nonideal regions, that cubic can produce several positive mathematical roots. This calculator reports them and selects the largest gas-like root.
6) When is the ideal gas equation usually close enough?
At low pressure and high temperature, molecules are farther apart. Attraction and size corrections become smaller, so ideal-gas and Van der Waals results often move closer together.
7) What does the compressibility factor Z mean?
Z = PV/(nRT) measures deviation from ideal behavior. Z = 1 matches ideal-gas behavior exactly. Values above or below one indicate repulsion-dominated or attraction-dominated effects.
8) Can I use preset gases and custom coefficients together?
Yes. Choose a preset for quick values, then edit a or b manually if needed. That is helpful for teaching examples, literature values, and custom datasets.