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Van Der Waals Equation Calculator

Work out van der waals equation instantly with clear inputs, formula shown and shareable results.

About Van Der Waals Equation Calculator

The van der Waals equation corrects the ideal gas law twice: b removes the volume the molecules themselves occupy, and a accounts for their mutual attraction. One mole of a nitrogen-like gas in 0.5 L at 300 K gives 48.6 bar against the ideal 49.9 bar, a compressibility factor just under one because attraction dominates at this density.

Formulas

van der Waals equation

(P + a n^2 / V^2)(V - n b) = n R T

Compressibility factor

Z = P V / (n R T)

Worked example

With the default values below, Van Der Waals Equation Calculator returns van der Waals Pressure of 47.8790. Change any input above and every figure here is recalculated in your browser.

Inputs used

Amount of gasminimum 0 mol
1 mol
Container volumeminimum 0 L
0.5 L
Temperatureminimum 0 K
300 K
van der Waals constant aminimum 0 L2 bar/mol2
1.355 L2 bar/mol2

Results

van der Waals Pressure
47.8790 bar
Ideal Gas Pressure For Comparison
49.8868 bar
Deviation From Ideal
-4.02%
Compressibility Factor Z
0.9598

Step by step

  1. 1Values used
  2. 2van der Waals equation
  3. 3Compressibility factor
  4. 4van der Waals Pressure= 47.8790 bar
  5. 5Ideal Gas Pressure For Comparison= 49.8868 bar
  6. 6Deviation From Ideal= -4.02
  7. 7Compressibility Factor Z= 0.9598

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What do a and b mean physically?

a measures intermolecular attraction, which lowers pressure; b is the excluded volume of the molecules, which raises it by reducing free space.

When does the ideal gas law fail?

Near condensation - high pressure or low temperature. Above the critical temperature and below a few bar the ideal law is within a percent.

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