Molar mass Original Scenario-Based Download PDF

Questions

1. 1.

   In a subterranean geothermal cavern, an autonomous exploration drone analyzes a newly discovered crystalline mineral with the chemical formula $\text{Z}_2\text{Q}_3$. The diagnostic module measures that a pure $0.125\text{ mol}$ sample of this mineral has a total mass of $27.50\text{ g}$, with element Q accounting for exactly $12.00\text{ g}$ of the sample. Based on these analytical measurements, what is the molar mass of the compound $\text{Z}_2\text{Q}_3$ and what is the molar mass of element Z?

   • A) $220.0\text{ g/mol}$ for $\text{Z}_2\text{Q}_3$ and $62.0\text{ g/mol}$ for Z
   • B) $220.0\text{ g/mol}$ for $\text{Z}_2\text{Q}_3$ and $124.0\text{ g/mol}$ for Z
   • C) $220.0\text{ g/mol}$ for $\text{Z}_2\text{Q}_3$ and $32.0\text{ g/mol}$ for Z
   • D) $110.0\text{ g/mol}$ for $\text{Z}_2\text{Q}_3$ and $31.0\text{ g/mol}$ for Z
2. 2.

   An environmental control module inside an underwater biosphere regulates an artificial atmosphere composed exclusively of oxygen ($\text{O}_2$, molar mass 32.00 g/mol) and helium (He, molar mass 4.00 g/mol) to prevent nitrogen narcosis during deep-sea operations. The diagnostic monitoring array reports that helium accounts for exactly 80.0% of the total gas molecules in the living quarters, while oxygen comprises the remaining 20.0%. Based on these atmospheric telemetry data, what is the average molar mass of this breathing gas mixture, and what total mass of this gas mixture is contained in a 25.0-mol emergency reserve canister?

   • A) 18.00 g/mol and 450 g
   • B) 9.60 g/mol and 240 g
   • C) 26.40 g/mol and 660 g
   • D) 6.40 g/mol and 160 g
3. 3.

   In an atmospheric regulation bay on an exploratory starship, automated sensors monitor two distinct synthetic fire-suppressant gases, Gas Alpha and Gas Beta. A diagnostic pod measures that a pure $0.350\text{ mol}$ sample of Gas Alpha has a mass of $22.4\text{ g}$, while a separate detector determines that a chamber holding $1.806 \times 10^{23}$ molecules of pure Gas Beta has a mass of $19.2\text{ g}$. Taking Avogadro's constant as $N_A = 6.02 \times 10^{23}\text{ mol}^{-1}$, how do the molar masses of Gas Alpha and Gas Beta compare?

   • A) Both gases have the same molar mass of $64.0\text{ g/mol}$.
   • B) Gas Alpha has a molar mass of $64.0\text{ g/mol}$, while Gas Beta has a molar mass of $10.6\text{ g/mol}$.
   • C) Gas Alpha has a molar mass of $7.84\text{ g/mol}$, while Gas Beta has a molar mass of $64.0\text{ g/mol}$.
   • D) Gas Alpha has a molar mass of $64.0\text{ g/mol}$, while Gas Beta has a molar mass of $32.0\text{ g/mol}$.
4. 4.

   In an orbital bio-foundry, engineers synthesize an artificial membrane stabilizer containing an unidentified element X. A precision dispenser measures a 0.0450 mol sample of this pure compound, recording its mass as 38.34 g. In an alternate derivative where exactly one atom of element X per molecule is replaced by one sulfur atom (molar mass 32.07 g/mol), the overall molar mass increases by 16.07 g/mol. What are the molar mass of the original compound and the atomic mass of element X?

   • A) 852 g/mol and 48.14 g/mol
   • B) 868 g/mol and 32.07 g/mol
   • C) 852 g/mol and 16.00 g/mol
   • D) 868 g/mol and 16.00 g/mol
5. 5.

   During an orbital survey of a frozen exoplanet, an automated probe extracts a pure 0.250-mol sample of an unknown greenhouse gas trapped inside geothermal ice cores. Analytical instruments determine that the sample has a mass of 16.52 g, and mass spectrometry establishes its molecular formula as $\text{C}_2\text{H}_4\text{F}_x$. Given atomic masses of $12.01\text{ g/mol}$ for carbon, $1.01\text{ g/mol}$ for hydrogen, and $19.00\text{ g/mol}$ for fluorine, what is the molar mass of the gas and the integer value of $x$?

   • A) $66.08\text{ g/mol}$ with $x = 2$
   • B) $66.08\text{ g/mol}$ with $x = 1$
   • C) $33.04\text{ g/mol}$ with $x = 1$
   • D) $4.13\text{ g/mol}$ with $x = 2$