Rayleigh nitrogen contaminants

The discovery of the element argon by Lord Rayleigh and William Ramsay had its origins in Rayleigh's measurements of the density of nitrogen with an eye toward accurate determination of its molar mass. Rayleigh prepared some samples of nitrogen by chemical reaction of nitrogen-containing compounds; under his standard conditions, a glass globe filled with this "chemical nitrogen" had a mass of 2.2990 g. He prepared other samples by removing oxygen, carbon dioxide, and water vapor from atmospheric air; under the same conditions, this "atmospheric nitrogen" had a mass of 2.3102 g.

a) One possibility Rayleigh investigated was that "atmospheric nitrogen" was pure and "chemical nitrogen" contaminated with a lighter gas. Assume that "chemical nitrogen" was really a mixture of H₂ and N₂; compute the mole fraction of H₂ needed to account for the difference with "atmopheric nitrogen." Now assume instead that "chemical nitrogen" was a mixture of atomic and molecular nitrogen; compute the mole fraction of atomic N that would account for the observed measurements.
b) With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in "atmospheric nitrogen" on the assumption that it was a mixture of nitrogen and argon and "chemical nitrogen" was pure nitrogen.

Reference

Lord Rayleigh, "Argon," Royal Institution Proceedings 14, 524-538 (1895).

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