Dumas vapor density

Level: introductory

Reference: J. Dumas, "Memoire sur quelques Points de la Théorie atomistique," Ann. Chim. Phys. 33, 337-391 (1826) [exercises 1-3]; J. Dumas, "Dissertation sur la Densité de la Vapeur de quelques corps simples," Ann. Chim. Phys. 50, 170-8 (1832) [exercise 4]

Notes: Jean-Baptiste Dumas (1800-1884) devised a method of determining the molar mass of substances that can conveniently be turned into vapors. The Dumas method is still the subject of laboratory exercises in chemistry courses. It involves finding the mass, volume, temperature, and pressure of a substance in the vapor phase. The determination of molar mass in a modern Dumas method experiment uses the ideal gas law; that is the kind of analysis involved in the exercises. The concept of the mole had not yet been developed in Dumas' day. He computed molar masses (or rather relative molecular weights) on the basis of relative gas densities. The molar mass of a vapor relative to, say hydrogen, was equal to the density of the vapor divided by that of hydrogen under comparable conditions. The method depends on Avogadro's hypothesis, namely that gases under comparable conditions contain the same number of molecules.[1] Dumas did know how to adjust a measured density to refer to a different pressure (namely by using Boyle's law) and he knew how to adjust to a different temperature (namely by using Charles' law).

Exercise 4 deals with Dumas' data on sulfur. Elements that do not form diatomic molecules in the gas phase (such as sulfur) and compounds with anomalous vapor pressures (such as NH₄Cl and PCl₅) made Dumas question his method and the hypothesis it was based on. Dumas (and Avogadro) believed that the molecules of elements in the gas phase were made up of two atoms. Many other chemists believed that gaseous elements were single atoms, that like atoms would repel each other rather than bond to each other. Whether they expected monatomic or diatomic molecules, no one expected or accepted hexatomic molecules such as Dumas' results for sulfur implied. The vapors associated with ammonium chloride and the like we now recognize as "dissociation vapor pressures" that vary with temperature and pressure not as ideal gases but as dissociation equilibrium constants. In any event, the work of Dumas was one of the few attempts to integrate Avogadro's hypothesis with the chemical knowledge of the time. Complete integration would wait for the work of Cannizzaro after another 30 years. (Classic Calculations includes exercises based on the work of Avogadro, Boyle, and Cannizzaro.)

Now, of course, armed with a better understanding of bonding and a whole arsenal of structure-determination tools, we realize that there is no single state of aggregation for gas-phase elements. Most of the common elements that are gases under normal conditions are diatomic (e.g., N₂, O₂, H₂, Cl₂). The noble gases (unknown in Dumas' day) are monatomic. An important form of oxygen is triatomic, O₃. As for sulfur, the most stable forms of crystalline sulfur have S₈ molecules. In the gas phase, S₈ and other cyclic structures exist in a temperature-dependent equilibrium that includes S₂ and isolated sulfur atoms (particularly at very high temperatures). Interestingly, Dumas' experiments on sulfur all yielded results that suggested S₆ as the average size, but there was some scatter with temperature.

Pedagogical note: Notice the large number of digits reported, particularly in exercise 2. Quantitative error analysis was not well developed in the early 19^th century, nor was the use of significant figures to express precision.

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/dumas.doc

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