Johannes van der Waals

**Van der Waals Equation
(Johannes van der Waals)**

The behavior of real gases usually agrees with the predictions of the ideal gas equation to within ±5% at normal temperatures and pressures. At low temperatures or high pressures, real gases deviate significantly from ideal gas behavior. In 1873, while searching for a way to link the behavior of liquids and gases, the Dutch physicist Johannes van der Waals developed an explanation for these deviations and an equation that was able to fit the behavior of real gases over a much wider range of pressures.

Van der Waals realized that two of the assumptions of the kinetic molecular theory were questionable. The kinetic theory assumes that gas particles occupy a negligible fraction of the total volume of the gas. It also assumes that the force of attraction between gas molecules is zero.

The first assumption works at pressures close to 1 atm. But something happens to the validity of this assumption as the gas is compressed. Imagine for the moment that the atoms or molecules in a gas were all clustered in one corner of a cylinder, as shown below. At normal pressures, the volume occupied by these particles is a negligibly small fraction of the total volume of the gas. But at high pressures, this is no longer true. As a result, real gases are not as compressible at high pressures as an ideal gas. The volume of a real gas is therefore larger than expected from the ideal gas equation at high pressures.

The volume actually occupied by the particles in a gas is relatively small at low pressures, but it can be a significant fraction of the total volume at high pressure. In O2, for example, the gas molecules occupy 0.13% of the total volume at 1.00 atm but 17% of the volume at 100 atm. |

Van der Waals proposed that we correct for the fact that the volume of a real gas is
too large at high pressures by *subtracting* a term from the volume of the real gas
before we substitute it into the ideal gas equation. He therefore introduced a constant
constant (*b*) into the ideal gas equation that was equal to the volume actually
occupied by a mole of gas particles. Because the volume of the gas particles depends on
the number of moles of gas in the container, the term that is subtracted from the real
volume of the gas is equal to the number of moles of gas times *b*.

*P*(*V* - *nb*) = *nRT*

When the pressure is relatively small, and the volume is reasonably large, the *nb*
term is too small to make any difference in the calculation. But at high pressures, when
the volume of the gas is small, the *nb* term corrects for the fact that the volume
of a real gas is larger than expected from the ideal gas equation.

The assumption that there is no force of attraction between gas particles cannot be true. If it was, gases would never condense to form liquids. In reality, there is a small force of attraction between gas molecules that tends to hold the molecules together. This force of attraction has two consequences: (1) gases condense to form liquids at low temperatures and (2) the pressure of a real gas is sometimes smaller than expected for an ideal gas.

To correct for the fact that the pressure of a real gas is smaller than expected from
the ideal gas equation, van der Waals *added* a term to the pressure in this
equation. This term contained a second constant (*a*) and has the form: *an*^{2}/*V*^{2}.
The complete van der Waals equation is therefore written as follows.

History of Chemistry |

Experiments Index |

Scientists Index |