van der Waals, Johannes

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van der Waals, Johannes

DUTCH PHYSICIST
1837–1923

That atoms exist is a fact seemingly indisputable, but such was not always the case. In the early eighteenth century, when English chemist and physicist John Dalton made a case for his atomic theory , it was met with skepticism and spawned a vigorous debate that continued well into the twentieth century about whether or not atoms were real. Coming down squarely on the side of real atoms was van der Waals, the father of modern molecular science.

Johannes Diderik van der Waals was born in Leiden, the Netherlands, in 1837. The son of a carpenter, he was not afforded the advantages that some of his contemporaries enjoyed. Lacking knowledge of classical languages, he was barred from taking his academic examinations at the University of Leiden. Instead, he continued his studies in his spare time between

1862 and 1865, eventually obtaining teaching certificates in both mathematics and physics. In 1864 he was appointed as a teacher at a secondary school in Deventer. In 1866 he moved to the Hague, first as a teacher and then as a director of one of the secondary schools there.

When new legislation was introduced exempting science students from a classical education, van der Waals was finally allowed to sit for his university examinations. In 1873 he obtained his doctorate with a thesis titled, "On the Continuity of the Gas and Liquid State." His thesis proposed a correction to the equation of state for ideal gases that would allow the equation to be applied to real gases. That is, he proposed a modification of the formula PV = nRT to account for the fact that atoms are real and that they interact.

In his own words, his incentive to his life's work "came to me when, after my studies at university, I learned of a treatise by Clausius (1857) on the nature of the motion which we call heat. In this treatise … he showed how Boyle's law can very readily be derived on the assumption that a gas consists of material points which move at high velocity" (van der Waals, "The Equation of State of Gases and Liquids"). This treatise was a revelation, as it derived the ideal gas law from first principles and framed it in terms of atoms and molecules. Here was a theoretical rationalization for experimentally obtained data. But it also occurred to van der Waals that this treatise might not be complete. If the atoms of gases are in constant motion when a gas is dilute, then this must also be the case as the gas is compressed and, indeed, must still be the case down to maximum compression as the gas condenses to a liquid. This led to the idea of the continuity of matter and the notion that both the liquid and gaseous states can be described by a similar mathematical theory.

Further, van der Waals recognized that real gases take up volume and atoms do interact with one another. For the German mathematical physicist Rudolf Clausius to obtain his results, he had to ignore both of these factors. Van der Waals found experimentally derived constants that allowed him to modify the ideal gas law to take into account real atoms. His equation of state,

(P + a /V ²)(V − b ) = RT

has subsequently been modified to include Avogadro's number, but it was critical to scientists' first steps in understanding atoms and molecules. a arises from considering interatomic forces (collectively called "van der Waals forces" in his honor), and b recognizes that atoms have a real volume—that they actually exist.