Alexander Fufaev
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Van der Waals Equation: How to Describe Real Gas

Important Formula

Formula: Van der Waals Equation
What do the formula symbols mean?


Pressure of the (real) gas. With the real gas - in contrast to the ideal gas - the gas pressure may be very high.


Temperature of the (real) gas. With the real gas - in contrast to the ideal gas - the temperature of the gas may be low.


Volume of the (real) gas. Molar volume: \( V_{\text m} ~=~ \frac{V}{n} \).

Amount of substance

Amount of substance indirectly indicates the number of particles of the gas.


Covolume is the material-dependent intrinsic volume of the particles of the real gas. It reduces the volume \( V \) available for the motion of the particles to \( (V ~-~ n\,V_{\text b}) \). For the ideal gas, the following holds: \( V_{\text b} ~=~ 0 \). The unit of covolume is \( \mathrm{m}^3 / \mathrm{mol} \).

Cohesion parameter

Cohesion parameter is a material-dependent quantity that indicates the force between the particles of the gas. In the case of an ideal gas, the following holds true: \( a ~=~ 0 \). The term \( \frac{n^2 \, a}{V^2} \) is called internal pressure. The unit of the cohesion parameter is \( \mathrm{Pa}\,\mathrm{m}^6 / \mathrm{mol}^2 \).

Gas constant

Molar gas constant (also called universal gas constant) is a physical constant from thermodynamics and has the following exact value: $$ R ~=~ 8.314 \, 462 \, 618 \, 153 \, 24 \, \frac{\mathrm J}{\mathrm{mol} \, \mathrm{K}} $$

The Van der Waals equation is designed for real gases and introduces corrections to the ideal gas equation in order to describe the behavior of real gases more precisely.

The equation thus modifies the volume \( V \) and the pressure \( \mathit{\Pi} \) compared to the ideal gas equation to take into account the effects of molecular size and attractive forces.