Dalton multiple proportions

According to chemical historian Ida Freund, the first instance of the law of multiple proportions can be found in a paper by John Dalton read in 1802 and published in 1805.[1] Dalton wrote:

If 100 measures of common air be put to 36 of pure nitrous gas ..., after a few minutes the whole will be reduced to 79 or 80 measures, and exhibit no signs of either oxygenous or nitrous gas. If 100 measures of common air be admitted to 72 of nitrous gas ..., there will, as before, be found 79 or 80 measures of pure azotic gas for a residuum. ... These facts clearly point out the theory of the process: the elements of oxygen may combine with a certain portion of nitrous gas, or with twice that portion, but with no intermediate quantity. ...

a) When Dalton says "measures" he is talking about volumes. Let us suppose that his measures were mL, and let us suppose further that he carried out this experiment at 20°C and 1.00 atm. How many moles of oxygen (O₂) and nitrous gas (NO) would have been used in these experiments? Note: "Common air" is about 20% oxygen by volume.
b) Write balanced equations for the two reactions. In both reactions, a water-soluble gas is produced, which "disappears" into the water over which the gases were collected. (Thus, in both experiments, the gas that is left is the nitrogen that does not take part in the reaction.) The product in the first experiment is NO₂; in the second experiment N₂O₃ is produced. Hint: to balance the first reaction, look at the mole ratios among the reactants, and in the second reaction, note that the NO:O₂ ratio is twice as great.

Reference

John Dalton, "Experimental Enquiry into the Proportion of the Several Gases or Elastic Fluids, Constituting the Atmosphere," Memoirs of the Literary and Philosophical Society of Manchester 1, 244-58 (1805)

[1]Ida Freund, The Study of Chemical Composition (New York: Dover, 1968) [first published in 1904], p. 155.

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