Van der Waals Pressure Calculator

Calculator Inputs

Amount of gas (n)

Amount unit

Total volume (V)

Volume unit

Temperature (T)

Temperature unit

Van der Waals constant a

Use L²·bar/mol².

Van der Waals constant b

Use L/mol.

Output pressure unit

Graph points

Reset

Formula Used

Van der Waals equation for pressure:

P = (nRT / (V - nb)) - (a n² / V²)

Ideal gas comparison: P_ideal = nRT / V

Where:

P = pressure
n = amount of gas
R = gas constant, 0.08314462618 L·bar·mol⁻¹·K⁻¹
T = absolute temperature in kelvin
V = total gas volume
a = attraction correction constant
b = excluded-volume correction constant

The first term increases pressure because usable volume becomes smaller than the container volume. The second term lowers pressure because molecular attraction reduces wall collisions.

How to Use This Calculator

Enter the gas amount, total volume, and temperature.
Select the matching input units for amount, volume, and temperature.
Enter the Van der Waals constants a and b in L²·bar/mol² and L/mol.
Choose the output pressure unit you want to display.
Click Calculate Pressure to show the result above the form.
Review the advanced metrics, comparison with ideal pressure, and the Plotly curve.
Use the CSV or PDF buttons to export your result summary.

Example Data Table

Sample Gas	n (mol)	V (L)	T (K)	a (L²·bar/mol²)	b (L/mol)	Van der Waals Pressure (bar)	Ideal Pressure (bar)	Z
CO₂ Example	1.50	10.00	320.00	3.592	0.04267	3.9358	3.9909	0.9862
NH₃ Example	2.00	8.00	350.00	4.225	0.03710	7.0792	7.2752	0.9731
N₂ Example	1.20	6.50	300.00	1.390	0.03910	4.5910	4.6049	0.9970

FAQs

1) What does the Van der Waals pressure equation improve?

It corrects the ideal gas model for molecular attraction and finite molecular size. That makes it more realistic for dense gases, lower temperatures, and higher pressures.

2) Why must volume be greater than n × b?

The term V - nb represents usable free volume. If it becomes zero or negative, the equation loses physical meaning for that state and the calculation cannot proceed.

3) What units should I use for a and b?

This calculator expects a in L²·bar/mol² and b in L/mol. The other input units are converted internally to stay consistent with that constant set.

4) Why is the real-gas pressure sometimes lower than ideal pressure?

Attractive intermolecular forces reduce the effective force of collisions against the container wall. That often lowers pressure compared with the ideal gas prediction.

5) What does the compressibility factor Z show?

Z compares real-gas behavior with the ideal model. A value near 1 means nearly ideal behavior. Values below or above 1 indicate nonideal effects.

6) Can I use Celsius or Fahrenheit here?

Yes. The calculator converts Celsius and Fahrenheit to kelvin internally before applying the Van der Waals equation, which requires absolute temperature.

7) What does the graph represent?

It plots pressure versus total volume while holding amount, temperature, and constants fixed. It also compares the real-gas curve with the ideal gas curve.

8) When should I prefer this over the ideal gas equation?

Use it when gases are dense, compressed, strongly interacting, or near conditions where ideal assumptions fail. It is especially helpful for engineering and thermodynamics checks.