Gay-Lussac multiple proportions

Joseph Gay-Lussac reported the combining proportions of several compounds, concluding that gases combine in simple ratios by volume. (This conclusion is the subject of another set of exercises.) Some of the results he reported also support the law of multiple proportions, the subject of this set of exercises.

1) He reported that "carbonic gas" is composed of 27.38 [grams] of carbon to 72.62 [grams] of oxygen, and that a different compound, "carbonic oxide," is 42.99 [grams] of carbon and 57.01 [grams] of oxygen.
a) How much oxygen would combine with 100. g of carbon to make "carbonic gas?"
b) How much oxygen would combine with 100. g of carbon to make "carbonic oxide?"
c) Is there a simple relationship between the answers to (a) and (b)? If so, what is it?

2) He reported the combining ratios by mass of nitrogen and oxygen to form three distinct compounds. We can take the following numbers as representing grams of oxygen and nitrogen in these compounds.
NitrogenOxygen
Nitrous oxide63.3036.70
"Nitrous gas"44.0555.95
"Nitric acid"29.5070.50

a) How much oxygen would it take to combine with 100. g of nitrogen to form each of these compounds?
b) Is there a simple relationship among the answers to part (a)? If so, what is it?

3) He reported that "carbonic acid" and ammonia combine in a ratio of 71.81:28.19 by mass. Thus we know that 71.81 g of "carbonic acid" would combine with 28.19 g of ammonia.
a) How much ammonia (in grams) would be needed to combine with 100.0 g of "carbonic acid?"
b) He reported that "carbonic acid" and ammonia combine in a ratio of 56.02:43.98 by mass to form a different compound, a "sub-carbonate." Thus we know that 56.02 g of "carbonic acid" would combine with 43.98 g of ammonia. How much ammonia (in grams) would be needed to combine with 100. g of "carbonic acid" to make this compound?
c) Is there a simple relationship between the answers to (a) and (b)? If so, what is it?

Reference

Joseph Louis Gay-Lussac, "Memoir on the Combination of Gaseous Substances with Each Other," Mémoires de la Société d'Arcueil 2, 207ff (1809)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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