Avogadro's number Original Scenario-Based Download PDF

Questions

1. 1.

   A subterranean research outpost powers its atmospheric scrubber using a sealed canister containing a mixture of helium ($\text{He}$) and neon ($\text{Ne}$) gases. Diagnostic monitors confirm that the canister holds a total of 1.50 mol of noble gas atoms, of which exactly $3.011 \times 10^{23}$ are neon atoms. Taking Avogadro's number to be $6.022 \times 10^{23}\text{ atoms/mol}$, how many helium atoms are present in the canister?

   • A) $3.011 \times 10^{23}\text{ atoms}$
   • B) $6.022 \times 10^{23}\text{ atoms}$
   • C) $9.033 \times 10^{23}\text{ atoms}$
   • D) $1.2044 \times 10^{24}\text{ atoms}$
2. 2.

   On an orbital research station, a quantum containment trap isolates a sealed sample of gaseous dinitrogen monoxide ($\text{N}_2\text{O}$). Diagnostic sensors scan the vessel and report that the trapped gas contains a total of $3.6132 \times 10^{24}$ atoms combined. Taking Avogadro's number to be $6.022 \times 10^{23}\text{ atoms/mol}$, how many moles of $\text{N}_2\text{O}$ molecules are held within the trap?

   • A) $0.667\text{ mol}$
   • B) $6.00\text{ mol}$
   • C) $18.0\text{ mol}$
   • D) $2.00\text{ mol}$
3. 3.

   In a subterranean crystal cavern, a robotic survey unit uses an optical trap to isolate a single molecule of a synthesized propellant vapor known as ignis-9. Diagnostic telemetry establishes that this substance has a molar mass of 180.66 g/mol. Taking Avogadro's number to be $6.022 \times 10^{23}$ particles/mol, what is the mass of this single isolated molecule in grams?

   • A) $3.000 \times 10^{-24}$ g
   • B) $3.000 \times 10^{-22}$ g
   • C) $1.088 \times 10^{26}$ g
   • D) $3.333 \times 10^{-25}$ g
4. 4.

   A terraforming drone on an arid exoplanet releases a sealed canister containing 0.500 mol of pure methane gas ($CH_4$) to jumpstart atmospheric synthesis. Given that Avogadro's number is $6.022 \times 10^{23}\text{ particles/mol}$, what is the total number of hydrogen atoms contained within this released gas sample?

   • A) $3.011 \times 10^{23}$ hydrogen atoms
   • B) $6.022 \times 10^{23}$ hydrogen atoms
   • C) $1.506 \times 10^{24}$ hydrogen atoms
   • D) $1.204 \times 10^{24}$ hydrogen atoms
5. 5.

   An automated deep-space fabricator synthesizes ultra-pure silicon heat shields one atom at a time. During a precision calibration run, the fabricator logs that it has laid down exactly $1.8066 \times 10^{24}$ individual silicon atoms onto a collector plate. Given that Avogadro's number is $6.022 \times 10^{23}\text{ atoms/mol}$, how many moles of silicon atoms were deposited during this calibration run?

   • A) 3.00 mol
   • B) 0.333 mol
   • C) 1.09 mol
   • D) 10.9 mol