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

Questions

1. 1.

   In a subterranean crystal foundry, an alchemist captures a glowing vapor canister containing $1.204 \times 10^{23}$ molecules of pure sulfur trioxide gas ($\text{SO}_3$). Assuming ideal gas behavior at standard temperature and pressure (STP), what are the total mass and the volume occupied by this sulfur trioxide sample at STP? (Molar mass of $\text{SO}_3 = 80.0\text{ g/mol}$; standard molar volume at STP = 22.4 L/mol; Avogadro's constant $N_A = 6.02 \times 10^{23}\text{ molecules/mol}$)

   • A) 160 g and 44.8 L
   • B) 6.40 g and 4.48 L
   • C) 40.0 g and 11.2 L
   • D) 16.0 g and 4.48 L
2. 2.

   In a floating sky-citadel, an alchemical engineer inflates a primary levitation ballast with 11.2 L of pure helium gas ($\text{He}$) at standard temperature and pressure (STP). An auxiliary stabilizing cell is then charged with pure methane gas ($\text{CH}_4$) such that it contains the exact same total number of atoms as the helium ballast. Assuming ideal gas behavior at STP, what are the mass and the volume of the methane gas inside the auxiliary cell? (Molar masses: $\text{He} = 4.0\text{ g/mol}$, $\text{CH}_4 = 16.0\text{ g/mol}$; standard molar volume at STP = $22.4\text{ L/mol}$; Avogadro's constant $N_A = 6.02 \times 10^{23}\text{ particles/mol}$)

   • A) 8.00 g and 11.2 L
   • B) 40.0 g and 56.0 L
   • C) 1.60 g and 2.24 L
   • D) 3.20 g and 4.48 L
3. 3.

   In an enchanted clockwork sky-haven, an alchemical glider relies on a sealed fuel cell containing pure propane gas ($\text{C}_3\text{H}_8$). Diagnostic crystal monitors indicate that the cell currently holds $2.408 \times 10^{24}$ individual hydrogen atoms bound entirely within the gas molecules. Assuming ideal gas behavior at standard temperature and pressure (STP), what are the total mass and the volume of the propane sample? (Molar mass of $\text{C}_3\text{H}_8 = 44.0\text{ g/mol}$; standard molar volume at STP = $22.4\text{ L/mol}$; Avogadro's constant $N_A = 6.02 \times 10^{23}\text{ atoms/mol}$)

   • A) 22.0 g and 11.2 L
   • B) 44.0 g and 22.4 L
   • C) 88.0 g and 44.8 L
   • D) 176 g and 89.6 L
4. 4.

   On an exploratory void-cruiser, an atmospheric reclamation unit isolates $66.0\text{ g}$ of pure dinitrogen monoxide gas ($\text{N}_2\text{O}$) from an auxiliary stasis vault. To safely route the sample into a neutralization chamber operated at standard temperature and pressure (STP), the ship's computer must determine both its STP volume and the absolute quantity of nitrogen atoms present. What are the volume at STP and the total number of nitrogen atoms contained in this gas sample? (Molar mass of $\text{N}_2\text{O} = 44.0\text{ g/mol}$; molar volume at STP = $22.4\text{ L/mol}$; Avogadro's constant $N_A = 6.02 \times 10^{23}\text{ particles/mol}$)

   • A) $33.6\text{ L}$ and $1.81 \times 10^{24}$ nitrogen atoms
   • B) $33.6\text{ L}$ and $9.03 \times 10^{23}$ nitrogen atoms
   • C) $14.9\text{ L}$ and $8.03 \times 10^{23}$ nitrogen atoms
   • D) $22.4\text{ L}$ and $1.20 \times 10^{24}$ nitrogen atoms
5. 5.

   An automated terraforming drone releases a bio-containment sphere containing exactly 16.8 L of pure carbon monoxide gas ($\text{CO}$) at standard temperature and pressure (STP). To configure the thermal neutralization matrix, the drone's navigation computer must verify the physical parameters of the gas payload. What are the mass and the total number of gas molecules present in this containment sphere? (Molar mass of $\text{CO} = 28.0\text{ g/mol}$; standard molar volume at STP $= 22.4\text{ L/mol}$; Avogadro's constant $N_A = 6.02 \times 10^{23}\text{ molecules/mol}$)

   • A) 14.0 g and $3.01 \times 10^{23}$ molecules
   • B) 28.0 g and $6.02 \times 10^{23}$ molecules
   • C) 21.0 g and $4.52 \times 10^{23}$ molecules
   • D) 42.0 g and $9.03 \times 10^{23}$ molecules

Answers and step-by-step solutions appear after you finish the test.