Van der Waals Equation Calculator

One mole of CO₂ held in 1 L at 300 K exerts 22.4152 bar by van der Waals, about 10 % below the ideal-gas 24.9 bar.

Gas:

Amount n (mol):

Volume V (L):

Temperature T (K):

Pressure (van der Waals) P =

22.4151615994485 bar

Precision

Full answer, then cut to fewer decimals (not rounded):

22.4151615994485 bar
22.415161599448 bar
22.41516159944 bar
22.4151615994 bar
22.415161599 bar
22.41516159 bar
22.4151615 bar
22.415161 bar
22.41516 bar
22.4151 bar
22.415 bar
22.41 bar
22.4 bar

Ideal-gas pressure: 24.94338785 bar
Compressibility Z = PVm/RT: 0.8986414248
Critical temperature Tc = 8a/27Rb: 303.9980365 K
Critical pressure Pc = a/27b²: 74.04441969 bar
Critical volume Vc = 3b: 0.12801 L/mol

Step-by-step solution

P = RT/(Vm − b) − a/Vm² = 0.08314462618 × 300 ÷ (1 − 0.04267) − 3.64 ÷ 1²
P = 22.4151616 bar (ideal gas: 24.94338785 bar)

Van der Waals Equation Formula

P = RT/(Vm − b) − a/Vm²

Tc = 8a/(27Rb), Pc = a/(27b²), Vc = 3b

Worked Example

1 mol of CO₂ in 1 L at 300 K:

P = RT/(Vm − b) − a/Vm² = 0.08314462618 × 300 ÷ (1 − 0.04267) − 3.64 ÷ 1²
P = 22.4151616 bar (ideal gas: 24.94338785 bar)

Compressibility Z = PVm/RT: 0.8986414248 · Critical temperature Tc = 8a/27Rb: 303.9980365 K · Critical pressure Pc = a/27b²: 74.04441969 bar · Critical volume Vc = 3b: 0.12801 L/mol

GATE tip

Keep a in L²·bar/mol² and b in L/mol with R = 0.08314 L·bar/(mol·K); mixing SI and L·atm units is the usual slip.

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Frequently asked questions

What do a and b represent?

a corrects for intermolecular attraction (lowering pressure); b is the excluded volume of the molecules.

What compressibility does van der Waals predict at the critical point?

Zc = 3/8 = 0.375, higher than real gases (about 0.23–0.31).

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

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APA

Scientific Converters. (2026, October 15). Van der Waals Equation Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/van-der-waals-calculator/

IEEE

Scientific Converters, "Van der Waals Equation Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/van-der-waals-calculator/