Question

Discrepancies in the experimental values of the molar mass of nitrogen provided some of the first evidence for the existence of the noble gases. If pure nitrogen is collected from the decomposition of ammonium nitrite,

NH4NO2(s) Heat N2(g) + 2H2O(g)
its measured molar mass is 28.01. If O2,CO2 and H2O are removed from air, the remaining gas has an average molar mass of 28.15. Assuming this discrepancy is solely a result of contamination with argon (atomic mass 39.95). calculate the ratio of moles of Ar to moles of N2 in air.

Answer 1

The discrepancy in the molar mass of nitrogen when collected from air is due to contamination with argon. The ratio of moles of Ar to moles of N2 in air is approximately 0.0053:1, indicating the presence of argon for every mole of nitrogen.

Step-by-step explanation:

The question involves the identification of discrepancies in the experimental molar mass of nitrogen, which provided evidence for the existence of noble gases. To find the ratio of moles of Ar to moles of N2 in air, we can use the given molar masses:

• Molar mass of pure nitrogen (N2): 28.01 g/mol
• Average molar mass of nitrogen in air (after removing O2, CO2, and H2O): 28.15 g/mol
• Molar mass of argon (Ar): 39.95 g/mol

Assuming the only contamination in the collected nitrogen is argon, the difference in the molar mass measurements from air indicates the presence of argon.

Calculate the mass difference:
28.15 g/mol - 28.01 g/mol = 0.14 g/mol

The mass difference per mole, attributed to argon, suggests a combination of both nitrogen and argon. By defining the mole ratio of argon to nitrogen as x, we can set up the following equation based on the average molar mass:

28.01 + x(39.95 - 28.01) = 28.15

Solving for x gives:

x = (28.15 - 28.01) / (39.95 - 28.01)

x ≈ 0.0053

Therefore, the ratio of moles of Ar to moles of N2 in the air is approximately 0.0053:1, which means that for every mole of nitrogen, there is approximately 0.0053 moles of argon.