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MMLU-Pro / 3834 / The discovery of the element argon by Lord Rayleigh and Sir William Ramsay had…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The discovery of the element argon by Lord Rayleigh and Sir 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 nitrogencontaining compounds; under his standard conditions, a glass globe filled with this 'chemical nitrogen' had a mass of $2.2990 \mathrm{~g}$. He prepared other samples by removing oxygen, carbon dioxide, and water vapour from atmospheric air; under the same conditions, this 'atmospheric nitrogen' had a mass of $2.3102 \mathrm{~g}$ (Lord Rayleigh, Royal Institution Proceedings 14, 524 (1895)). With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in the latter sample on the assumption that the former was pure nitrogen and the latter a mixture of nitrogen and argon.
Plain-text mathematical notation (without MathML)
The discovery of the element argon by Lord Rayleigh and Sir 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 nitrogencontaining compounds; under his standard conditions, a glass globe filled with this 'chemical nitrogen' had a mass of $2.2990 \mathrm{~g}$. He prepared other samples by removing oxygen, carbon dioxide, and water vapour from atmospheric air; under the same conditions, this 'atmospheric nitrogen' had a mass of $2.3102 \mathrm{~g}$ (Lord Rayleigh, Royal Institution Proceedings 14, 524 (1895)). With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in the latter sample on the assumption that the former was pure nitrogen and the latter a mixture of nitrogen and argon.
Original LaTeX notation
The discovery of the element argon by Lord Rayleigh and Sir 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 nitrogencontaining compounds; under his standard conditions, a glass globe filled with this 'chemical nitrogen' had a mass of $2.2990 \mathrm{~g}$. He prepared other samples by removing oxygen, carbon dioxide, and water vapour from atmospheric air; under the same conditions, this 'atmospheric nitrogen' had a mass of $2.3102 \mathrm{~g}$ (Lord Rayleigh, Royal Institution Proceedings 14, 524 (1895)). With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in the latter sample on the assumption that the former was pure nitrogen and the latter a mixture of nitrogen and argon.

category

chemistry

options

  1. 0.022
  2. 0.011
  3. 0.003
  4. 0.030
  5. 0.008
  6. 0.025
  7. 0.040
  8. 0.015
  9. 0.018
  10. 0.005

src

scibench-atkins

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Source and history

upstream_id / Original problem ID
3834
task_id
8ceb5cf9-9af4-58f4-beae-b8d254384675
task_key
default--test--3834
task_revision_id
1
config / split
default / test

Official source

initial import