van der Waals Equation of State

The Dutch physicist, Johannes Diderik van der Waals(1837-1923) received a 1910 Nobel Prize for his work on the equation of state for gases and liquids.  Johannes father was a carpenter so he could only afford to send Johannes to primary school.  Back then in the Netherlands, learning the classical languages was one of the prerequisites for entering university and Johannes had not learnt the languages.  Although Johannes was not allowed to take university classes, he studied at the Leiden University from 1862-1865 and he obtained teaching certificates in physics and math.  At the age of 36 van der Waals completed his Ph.D. when a new legislation passed that stated that science students could be enrolled in university without having the classical language requirement.  In van der Waals paper, “On the continuity of the gas and liquid state” he introduced the equation of state that has been used in physics and chemistry today.


Johannes van der Waals modified the ideal gas law, which assumes that molecules are very very very small and that they have no forces acting between them, which is the following equation:

PV = nRT

Where P is the pressure
V is the volume of the container
n is the number of moles of gases present in the container
R is the universal gas constant
T is the temperature

van der Waals came to the conclusion that the actual pressure felt by the container would be less if the molecules hitting the walls are pulled back due to the attraction by other molecules.  As well, that the actual volume available for the gas molecules would be less as the molecules have a finite size and occupy some volume. Therefore, the ideal gas law would have to work when P is increased and V is decreased.  He then introduced two constants a and b (van der Waals parameters) to make the following "van der Waals Equation of State":

The volume occupied by the gas molecules is directly proportional to the number of moles and the pressure depends on the square of n/V, the number of moles per unit volume.