Friday, October 23, 2015

Avogadro's Number Part 1: A History of the Mole with Very Little about Avogadro

Happy Mole Day! I thought that it would be appropriate to recognize the day with a post about Avogadro's Number and the associated Mole.  Avogadro's Number, which denotes the number of objects in a mole (6.022*1023), has a certain fascination for people, particularly, in my experience, among chemistry students.  There is even a website (and foundation) dedicated to Mole Day and the mole. While I have been trying to make these posts about people, to get to the bottom of Avogadro's number, one has to dig a lot deeper than Avogadro.  He does, however, make a good starting place.

Amedeo Avogadro (1776-1856)
Lorenzo Romano Amedeo Carlo Avogadro of Quaregna and Cerreto (phew, that's long) was by training a lawyer. He became interested in math and physics around 1800 and started working with electricity and metallic salts. Despite his lack of formal training, he did end up with a post as the chair of theoretical physics at the University of Turin. One of his projects was determining the electronegativity of various elements. He is best known for, and has the mole name after him because of, his "molecular hypothesis", first suggested in an essay in 1811. He suggested that molecules in a gas are scattered such that the average distance is constant when the temperature and pressure are constant. That is, that at the same temperature and pressure, there are the same number of molecules in a set volume of one gas as of another gas. By using this hypothesis, he was able to calculate the molecular weight of gases by using their densities.This, however, put Avogadro in opposition to John Dalton (1766-1844), who had rejected this idea (see page 555 onwards of A New System of Chemistry, 1810). This was in part because Dalton and others believed that all gases contained only one atom of an element--for instance, that a molecule of water was HO rather than H2O. Since Avogadro kept to himself and tended to cite himself, his hypothesis did not gain much credibility, though André-Marie Ampère (1775-1836) came to the same conclusion in 1814. This additional support doesn't seem to have helped any, so it was a while before his hypothesis was accepted.

Stanislao Cannizzaro (1826-1910)
By the middle of the 19th century, scientists were still debating about the nature of atoms, molecules, and their divisibility, and to make matters worse, they were starting to write formulas, diagrams, and calculate masses without a standard system. They could not agree on notations and other conventions, such as how to write chemical formulas or what the standard weight for describing an atom would be. In order to deal with these problems, August Kekulé (1829-1896) organized what came to be known as the Karlsruhe Congress, which met in September 1860 in Karlsruhe, Germany. The hero of the day was Stanislao Cannizzaro, who had written an article in 1858 that was based on Avogadro's hypothesis. This paper was circulated at the conference, and in it Cannizzaro suggested that the weight of hydrogen be taken as 1.0. He also suggested that oxygen be assumed to be diatomic as a gas, such that the formula for water would be H2O and the mass is 16.0. Cannizzaro clearly stated a theory in which atoms, molecules, and multiple identical atoms in the same molecule are distinguished. His argument and explanation influenced Lothar Meyer and Dimitri Mendeleev to both accept Avogadro's hypothesis, and after the conference it gained a wider popularity.

Few scientists, however, were concerned with how many molecules were actually in that volume of gas. They were more concerned with the hypothesis itself and what that meant for being able to determine other properties of matter, such as how big atoms and molecules actually are. The next step in determining Avogadro's number takes us from Avogadro and Cannizzaro in Italy to Austria, where Johann Josef Loschmidt (1821-1895) was working.
Johann Josef Loschmidt (1821-1895)
(image from Wikimedia commons)

Loschmidt wanted to find out what the actual size of a molecule of a gas was, and used current theories of gases to determine this. Rudolph Clausius had derived in 1859 the mean free path of molecules in a gas in terms of the cross-sectional area, and James Maxwell derived his own expression the following year. Loschmidt then calculated what fraction of the gas was occupied by the molecules themselves based on the mean free path and then assumed that when the gas is liquefied, the volume is only slightly larger than that of the molecules themselves. The problem then was the air had not been liquefied, so he used the work of Hermann Kopp to estimate the density of liquid air. He determined that the size of a nitrogen molecule was 9.69*10-10 m, or about three times too big. But not bad. However, despite knowing how big molecules were, no one seemed particularly concerned about how many molecules were in a region of space. A following paper in 1865, ostensibly by Loschmidt, states that a cubic millimeter of gas contains 866 billion molecules, but that wasn't the point of the article.

Studies of gasses over the course of the rest of the century and into the 20th century would help to elucidate the question of how many molecules are in a given volume, but I will leave that for another day! Check back soon (or subscribe to the emails) for more information about the definition and calculation of Avogadro's number and where the name mole came from.

Original Papers in order of publication