Mole conversions (mass, particles, gas volume at STP) Original Scenario-Based Download PDF

Questions

1. 1.

   In an atmospheric sky-harvester floating above the clouds of a terraformed planet, an automated blending unit combines 0.75 mol of diatomic oxygen gas ($\text{O}_2$) with an ozone gas ($\text{O}_3$) stream that occupies 11.2 L at standard temperature and pressure (STP). The resulting gas mixture is directed into a sealed reaction chamber for water synthesis. Assuming ideal gas behavior, what are the total mass of the gas mixture and the total number of oxygen atoms present in the chamber? (Molar mass of O = 16.0 g/mol; molar volume of an ideal gas at STP = 22.4 L/mol; Avogadro's constant = $6.02 \times 10^{23}\text{ atoms/mol}$)

   • A) 48.0 g and $1.806 \times 10^{24}$ atoms
   • B) 48.0 g and $1.204 \times 10^{24}$ atoms
   • C) 72.0 g and $2.709 \times 10^{24}$ atoms
   • D) 36.0 g and $1.355 \times 10^{24}$ atoms
2. 2.

   During an atmospheric survey of a volcanic exoplanet, an autonomous exploration drone traps a 4.40 g sample of an unknown gaseous fluorocarbon that occupies 1.12 L at standard temperature and pressure (STP). Onboard spectroscopic sensors detect a total of $1.204 \times 10^{23}$ fluorine atoms within this isolated gas volume. Assuming the gas behaves ideally, what are the molar mass of the compound and the number of fluorine atoms present in each individual molecule? (Molar volume at STP = 22.4 L/mol; Avogadro's constant = $6.02 \times 10^{23}\text{ particles/mol}$)

   • A) 88.0 g/mol and 4 fluorine atoms
   • B) 44.0 g/mol and 2 fluorine atoms
   • C) 88.0 g/mol and 2 fluorine atoms
   • D) 176.0 g/mol and 4 fluorine atoms
3. 3.

   In the life-support recycling module of a deep-space orbital station, an automated emergency scrubber discharges 3.36 L of carbon monoxide gas ($\text{CO}$) at standard temperature and pressure (STP) into a neutralizing chamber. To calibrate the neutralization catalyst, the environmental computer must determine both the mass of the gas and the total count of constituent atoms present in the chamber. Given that the molar mass of $\text{CO}$ is 28.0 g/mol, the molar volume of an ideal gas at STP is 22.4 L/mol, and Avogadro's constant is $6.02 \times 10^{23}\text{ particles/mol}$, which pair of values correctly represents the contents of the chamber?

   • A) 1.80 g of $\text{CO}$ and $1.81 \times 10^{23}$ atoms
   • B) 4.20 g of $\text{CO}$ and $9.03 \times 10^{22}$ atoms
   • C) 8.40 g of $\text{CO}$ and $3.61 \times 10^{23}$ atoms
   • D) 4.20 g of $\text{CO}$ and $1.81 \times 10^{23}$ atoms
4. 4.

   During an atmospheric skimming maneuver over an alien gas giant, an autonomous research drone sequesters $1.806 \times 10^{24}$ molecules of dinitrogen monoxide ($\text{N}_2\text{O}$) inside an analytical containment cell. Assuming the gas behaves ideally at standard temperature and pressure (STP), what are the total mass of the collected sample and the volume it occupies under these conditions? (Atomic masses: N = 14.0 g/mol, O = 16.0 g/mol; molar volume at STP = 22.4 L/mol; Avogadro's constant = $6.02 \times 10^{23}\text{ mol}^{-1}$)

   • A) 44.0 g and 22.4 L
   • B) 132 g and 67.2 L
   • C) 88.0 g and 44.8 L
   • D) 132 g and 22.4 L
5. 5.

   A subterranean bio-dome on an icy moon generates methane gas ($\text{CH}_4$) as an emergency thermal fuel. During an automated calibration cycle, the synthesizer deposits exactly 8.0 g of pure methane into a sealed expansion vessel maintained at standard temperature and pressure (STP). Given that the molar mass of methane is 16.0 g/mol and Avogadro's constant is $6.02 \times 10^{23}$ particles/mol, which pair of values correctly represents the volume occupied by the gas and the total number of hydrogen atoms present in the vessel?

   • A) 5.6 L and $6.02 \times 10^{23}$ hydrogen atoms
   • B) 11.2 L and $1.20 \times 10^{24}$ hydrogen atoms
   • C) 11.2 L and $3.01 \times 10^{23}$ hydrogen atoms
   • D) 22.4 L and $2.41 \times 10^{24}$ hydrogen atoms