Level: introductory
Reference: Amedeo Avogadro, "Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in Which They Enter into These Compounds," Journal de Physique 73, 58-76 (1811)
Notes: Amedeo Avogadro's (1776-1856) principal contribution to chemistry was a paper in which he advanced two hypotheses: (1) that equal volumes of gas contain equal numbers of molecules and (2) that elementary gases such as hydrogen, nitrogen, and oxygen were composed of two atoms. This set of exercises takes students through some of the data Avogadro presented in his paper. They use the atomic model of matter and the concept of a molecular formula that describes molecular composition in terms of definite numbers of atoms of definite mass. They also show how Avogadro's hypotheses made sense of the observations available to him (and to Dalton and Gay-Lussac). Students do not need a modern table of atomic masses to do these exercises; indeed, they should not use one. Having said that the exercises use data and ideas from Avogadro's paper and do not rely on later chemical knowledge, I ought to make it clear that the exercises do not recap Avogadro's logic. His hypotheses sprang from his attempt to reconcile Dalton's theory and Gay-Lussac's observations (as detailed below); in the exercises, the hypotheses come first and the student applies them to Dalton's model to arrive at Gay-Lussac's observations as "predictions".
Avogadro's famous paper was an attempt to reconcile Dalton's atomic hypothesis with Gay-Lussac's results on combining volumes. He could see something that seems obvious to our eyes, even if Dalton and Gay-Lussac could not see it: Dalton's atomic model and Gay-Lussac's observations on combining volumes would be mutually consistent if there were a simple relationship between atoms and volumes. In particular, Dalton's atomic model would provide an excellent explanation of Gay-Lussac's observations if every one of Gay-Lussac's volumes contained the same number of Dalton's atoms. Avogadro made this reasonable hypothesis (the "volumes" hypothesis), which is now sometimes called Avogadro's law.
There was just one problem: reactions involving gaseous elements produced twice as much product (twice as many volumes) as expected under the simple model in which gaseous elements exist as atoms. (For example, one atom of oxygen combines with two of hydrogen to produce one molecule of water; however, one volume of oxygen was observed to combine with two of hydrogen to produce two volumes of water vapor.) Avogadro saw how to fix this problem: suppose that the gaseous elements existed not as atoms but as pairs of atoms (or higher multiples of two). So Avogadro made this second hypothesis (the "diatomic" hypothesis), which we also recognize as correct.
The diatomic hypothesis was the real stumbling block for Avogadro's contemporaries. To be fair, there was no independent evidence for this hypothesis--no evidence at all except that it was required to reconcile Dalton's atoms with Gay-Lussac's volumes. Furthermore, contemporary chemical notions of bonding (i.e., between electrical opposites) provided a good reason to doubt that identical atoms would bind to each other. Avogadro was right, but it would take about 50 years and the clear exposition of Cannizzaro before the chemical world realized it.
Footnote: Avogadro's name is best known to today's students of chemistry because of the Avogadro constant, also known as Avogadro's number. Jean Perrin named the number of molecules in a mole (or gram-mole as it was called at the time) in honor of Avogadro early in the 20th century. Avogadro did not determine this number.
Further information: A detailed summary of key primary literature on multiple proportions, the atomic hypothesis, and atomic weights, including some quantitative treatment of data may be found in Leonard Nash, "The Atomic-Molecular Theory," in James Bryant Conant, ed., Harvard Case Histories in Experimental Science, vol. 1 (Cambridge, MA: Harvard, 1957), pp. 215-321.
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/avogadro.doc
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