Level: introductory
Reference: Joseph-Louis Proust, "Researches on Copper," Ann. chim. 32, 26-54 (1799).
Notes: Joseph-Louis Proust (1754-1826) analyzed a great many compounds and minerals in the late 18th and early 19th century. He is usually credited with establishing the law of constant composition, that is, that chemical compounds have the same elements in the same proportions no matter what the source. This exercise asks the student to derive the formula of a mixed inorganic salt from composition data reported by Prout. The paper on which this problem is based predates the concept of atomic weights and formulas, so we are putting the data to a different use than did (or could) Proust. What Proust did with these data was show that this synthetic copper carbonate had the same composition as copper carbonates derived from natural mineral sources (i.e., the data were evidence for constant composition).
Pedagogical note: Note, in the answer to part a, that the mole ratio looks a lot better when all the moles are divided by moles of copper than by moles of water. An instructor may or may not wish to point out this fact and some causes for it. If any one of the measurements is inaccurate, that measurement may appear somewhat "out of line" with the others; however, if one divides through by the inaccurate measurement, it will cause all of the other measurements to be similarly "out of line." It appears that the water measurement is less accurate than the others, so the ratios don't look good (i.e., don't look so much like small integers) when all quantities are divided by the quantity of water. When the quantities are divided through by a quantity other than water, then only water appears to be a bit off.
Dividing quantities of moles by the smallest number of moles in an analysis is often a convenient first step in trying to express molar ratios in terms of small integers. But, the smallest measurement is usually the measurement that has the greatest relative uncertainty. (Without knowing details of Proust's experiments, we might surmise that the uncertainty in the water measurement was one part in 10, in carbon dioxide one part in 46, and in copper one part in 100.) No wonder the data look better when divided through by moles of copper (the measurement with the least relative uncertainty) than when divided through by moles of water (the measurement with the most).
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/proust.doc
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