Van der Waals Equation Calculator

Calculate real gas behavior using the Van der Waals equation of state with intermolecular forces

Calculate Real Gas Properties

Gas Selection & Critical Point

mol
kPa
K
cm³/mol

Van der Waals Constants

Pa·m⁶/mol²

a = 3PcVc²

m³/mol

b = Vc/3

Van der Waals Results

0.000000
kPa
Van der Waals Result
0.000
kPa
Ideal Gas Pressure
0.000
kPa
Pressure Correction (an²/V²)
0.000
cm³
Volume Correction (nb)

Van der Waals equation: (P + an²/V²)(V - nb) = nRT

Gas: Custom Gas

Constants: a = 0.000e+0 Pa·m⁶/mol², b = 0.000e+0 m³/mol

Example Calculation

Carbon Dioxide Example

Gas: CO₂ (a = 0.364 Pa·m⁶/mol², b = 4.27×10⁻⁵ m³/mol)

Conditions: n = 1 mol, V = 0.001 m³, T = 300 K

Volume constraint: V > nb (0.001 > 4.27×10⁻⁵ ✓)

Calculation Steps

1. P = nRT/(V-nb) - an²/V²

2. P = (1×8.314×300)/(0.001-4.27×10⁻⁵) - (0.364×1²)/(0.001)²

3. P = 2594.2/(0.0009573) - 364000

4. P = 2,710,000 - 364,000 = 2,346,000 Pa

Result: 2,346 kPa (vs 2,594 kPa ideal gas)

Common Gas Constants

H₂ (Hydrogen)
a = 0.0244, b = 2.66×10⁻⁵
N₂ (Nitrogen)
a = 0.1408, b = 3.91×10⁻⁵
O₂ (Oxygen)
a = 0.1378, b = 3.18×10⁻⁵
CO₂ (Carbon Dioxide)
a = 0.364, b = 4.27×10⁻⁵
H₂O (Water)
a = 0.554, b = 3.05×10⁻⁵

Units: a in Pa·m⁶/mol², b in m³/mol

Van der Waals Tips

Parameter 'a' accounts for intermolecular attractions

Parameter 'b' accounts for molecular volume

Most accurate at high pressures and low temperatures

Volume must be greater than nb to avoid negative pressure

Understanding the Van der Waals Equation

Real Gas vs Ideal Gas

The Van der Waals equation corrects the ideal gas law to account for real gas behavior. It considers two factors: intermolecular attractions (parameter 'a') and molecular volume (parameter 'b') that the ideal gas law ignores.

When to Use Van der Waals

  • High pressure conditions
  • Low temperature conditions
  • Near critical point conditions
  • Gases with strong intermolecular forces

Van der Waals Equation

(P + an²/V²)(V - nb) = nRT

Pressure Correction

+ an²/V² accounts for intermolecular attractions

Volume Correction

- nb accounts for molecular volume

Van der Waals Constants

The constants 'a' and 'b' are calculated from critical point properties and are unique for each gas.

Attraction Parameter (a)

a = 3PcVc²

Larger 'a' means stronger intermolecular attractions

Repulsion Parameter (b)

b = Vc/3

Larger 'b' means larger molecular size

Critical Point Relation: 8PcVc = 3RTc, where Pc, Vc, and Tc are critical pressure, volume, and temperature respectively.