Level: introductory
Reference: Vannoccio Biringuccio, De La Pirotechnia (1540), translation by Cyril Stanley Smith & Martha Teach Gnudi (New York: Basic Books, 1959) Book I, chapter 4, p. 58.
Notes: Vannoccio Biringuccio's (1480-1539) De La Pirotechnia treated many of the applied arts and practical knowledge from which the science of chemistry evolved, particularly mining and metallurgy. I must credit Arthur Greenberg's book The Art of Chemistry (New York: Wiley, 2003), p. 60 for this exercise. Greenberg's book includes the passage on which this exercise is based and several illustrations from the Pirotechnia.
Pedagogical note: Teachers may or may not wish to emphasize significant figures in this problem. Standard rules of thumb for significant figures would hold that the ratio has only one significant figure. That makes the formula PbO seemingly straightforwardly. A more careful examination of uncertainties would make the O:Pb ratio 1.2:1.0. (If we regard the uncertainty in oxygen content as +/- one part in nine, then one decimal place in the ratio better represents that uncertainty: that is, +/- one part in 12 as opposed to no decimal places with an implicit uncertainty of +/- one part in one.)
The fact that the ratio works out to be significantly greater than 1:1 is no cause for concern, although it means that this problem does not offer support for simple whole number ratios in inorganic compounds. Biringuccio's observation can hardly be considered a meticulous chemical analysis, so his numbers cannot be taken to be very precise. Furthermore, more oxygen than lead can be easily explained by the formation of higher oxides to a small but not negligible extent (contrary to what the exercise assumed).
Solutions: To download solutions, go to:
http://web.lemoyne.edu/giunta/classicalcs/biringuccio.doc
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