Van der Waals Calculator Formula

Understand the math behind the van der waals calculator. Each variable explained with a worked example.

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Formulas Used

Pressure (Van der Waals)

pressure_vdw = ((n * 0.08206 * temp) / (volume - n * b)) - (a * pow(n, 2) / pow(volume, 2))

Pressure (Ideal Gas)

pressure_ideal = (n * 0.08206 * temp) / volume

Variables

VariableDescriptionDefault
nMoles of Gas (n)(mol)1
tempTemperature (T)(K)300
volumeVolume (V)(L)1
aVan der Waals a(L²·atm/mol²)1.36
bVan der Waals b(L/mol)0.0318

How It Works

Van der Waals Equation

Formula

[P + a(n/V)²] × [V - nb] = nRT

Solving for P: P = nRT/(V - nb) − a(n/V)²

Where:

  • a = correction for intermolecular attraction (L²·atm/mol²)
  • b = correction for molecular volume (L/mol)
  • Other variables as in the ideal gas law

    • The a term reduces pressure (attraction pulls molecules inward). The b term reduces available volume.

    Worked Example

    1 mol of N₂ (a = 1.36, b = 0.0318) at 300 K in 1 L.

    n = 1temp = 300volume = 1a = 1.36b = 0.0318
    1. 01P = nRT/(V - nb) - a(n/V)²
    2. 02P = (1)(0.08206)(300)/(1 - 1×0.0318) - 1.36(1/1)²
    3. 03P = 24.618/0.9682 - 1.36
    4. 04P = 25.42 - 1.36
    5. 05P = 24.06 atm

    Frequently Asked Questions

    What do the Van der Waals constants represent?

    The constant a accounts for attractive forces between molecules (larger a = stronger attractions). The constant b accounts for the finite volume of molecules (larger b = bigger molecules).

    Where do I find a and b values?

    They are tabulated for common gases. For example, CO₂: a = 3.59, b = 0.0427; H₂O: a = 5.46, b = 0.0305.

    When is the Van der Waals equation needed?

    Use it at high pressures (above ~10 atm) or low temperatures where intermolecular forces become significant and ideal gas behavior breaks down.

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