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
Van der Waals Constants
a = 3PcVc²
b = Vc/3
Van der Waals Results
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
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.