Avogadro's number Original Scenario-Based Practice

Questions

1. 1.

   A deep-space exploration probe relies on an electrochemical ion-drive powered by the complete dissociation of molten magnesium chloride ($\text{MgCl}_2$) into free ions. During an acceleration burn, the propulsion injector vaporizes and completely ionizes exactly 0.750 moles of pure magnesium chloride. Taking Avogadro's number as $6.022 \times 10^{23}\text{ entities/mol}$, what is the total number of individual ions (cations and anions combined) released into the drive chamber?

   • A) $1.355 \times 10^{24}$ ions
   • B) $4.517 \times 10^{23}$ ions
   • C) $9.033 \times 10^{23}$ ions
   • D) $1.807 \times 10^{24}$ ions
2. 2.

   During an atmospheric survey of an uncharted exoplanet, a planetary rover's high-resolution spectrometer isolates a single molecule of an unknown gaseous compound. The sensor determines the absolute mass of this individual molecule to be $7.64 \times 10^{-23}\text{ g}$. Taking Avogadro's number as $6.022 \times 10^{23}\text{ molecules/mol}$, what is the molar mass of this gaseous compound?

   • A) $23.0\text{ g/mol}$
   • B) $32.0\text{ g/mol}$
   • C) $46.0\text{ g/mol}$
   • D) $92.0\text{ g/mol}$
3. 3.

   A subterranean archaeological outpost uncovers an ancient chronometer powered by pure crystalline silicon nanofilaments. The clockwork mechanism consumes exactly $2.4088 \times 10^{22}$ individual silicon atoms to complete one full chronometric pulse. If researchers insert a micro-capsule containing $0.200\text{ moles}$ of pure silicon, how many complete pulses can the chronometer execute before the fuel is exhausted? (Assume Avogadro's number is $6.022 \times 10^{23}\text{ atoms/mol}$.)

   • A) 2 pulses
   • B) 8 pulses
   • C) 50 pulses
   • D) 5 pulses
4. 4.

   In an off-world terraforming module, an automated catalytic reactor synthesizes methane ($\text{CH}_4$) fuel by capturing volatile atmospheric gases. The telemetry log reports that precisely $1.8066 \times 10^{24}$ individual hydrogen atoms have been incorporated into newly formed methane molecules. Taking Avogadro's number as $6.022 \times 10^{23}\text{ entities/mol}$, what is the total quantity of methane gas, in moles, produced by this reaction?

   • A) $12.0\text{ mol}$
   • B) $3.0\text{ mol}$
   • C) $1.5\text{ mol}$
   • D) $0.75\text{ mol}$
5. 5.

   During an interstellar survey mission, an automated synthesis unit prepares four sealed fuel canisters containing different pure gases: 1.5 moles of argon ($\text{Ar}$), 1.0 mole of carbon monoxide ($\text{CO}$), 0.50 moles of water vapor ($\text{H}_2\text{O}$), and 0.50 moles of methane ($\text{CH}_4$). The vessel's diagnostic computer must identify the canister that contains the largest absolute number of individual constituent atoms to calibrate its atomic particle beam. Based on Avogadro's number and molecular chemical formulas, which sample delivers the highest total count of atoms?

   • A) 1.5 moles of argon gas
   • B) 1.0 mole of carbon monoxide gas
   • C) 0.50 moles of water vapor
   • D) 0.50 moles of methane gas

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