Gay-Lussac combining ratios

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 this set of exercises.) Some of the results he reported also support the law of multiple proportions, the subject of another set of exercises.

1) He reported that "carbonic acid" (which we know as CO2) and ammonia combine in a ratio of 71.81:28.19 by mass. Thus we know that 71.81 g of CO2 would combine with 28.19 g of NH3.
a) Express these quantities in moles. What is the combining ratio by moles?
b) Suppose the reaction took place at 298 K with each gas at exactly 1 atm pressure; how many liters of each reactant are required? What is the combining ratio by volume?

2) He reported that "carbonic acid" (CO2) 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 CO2 would combine with 43.98 g of NH3.
a) Express these quantities in moles. What is the combining ratio by moles?
b) Suppose the reaction took place at 298 K with each gas at exactly 1 atm pressure; how many liters of each reactant are required? What is the combining ratio by volume?

3) He reported figures for the combination of "muriatic acid" (which we know as HCl) and ammonia, and he also reported different figures obtained by another investigator, Berthollet. We recognize Berthollet's numbers, 100 [grams] of ammonia to 213 [grams] of HCl, as correct.
a) Express these quantities in moles. What is the combining ratio by moles?
b) Suppose the reaction took place at 298 K with each gas at exactly 1 atm pressure; how many liters of each reactant are required? What is the combining ratio by volume?

4) He reported the combining ratios by mass of nitrogen and oxygen to form three distinct compounds. Consider the following numbers to represent grams of N2 and O2 respectively.
NitrogenOxygen
Nitrous oxide63.3036.70
Nitrous gas44.0555.95
Nitric acid29.5070.50
a) Express these numbers in moles. What is the combining ratio for each compound by moles?
b) Suppose the reaction between N2 and O2 takes place at 298 with each reactant at exactly 1 atm pressure; how many liters of each reactant are required? What is the combining ratio by volume?

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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