A 3.41 time 10 to the -6g sample is known to contain 4.67 times time 10 to the 16 molecules. what is this compound
The correct answer and explanation is:
To determine what compound the sample is, we can use the mass of the sample and the number of molecules to calculate its molar mass, then compare that to known molar masses of compounds.
Given:
- Mass of the sample = 3.41×10−63.41 \times 10^{-6} grams
- Number of molecules = 4.67×10164.67 \times 10^{16}
Step 1: Convert molecules to moles
Use Avogadro’s number: 6.022×1023 molecules/mol6.022 \times 10^{23} \text{ molecules/mol} Moles=4.67×1016 molecules6.022×1023 molecules/mol=7.76×10−8 mol\text{Moles} = \frac{4.67 \times 10^{16} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} = 7.76 \times 10^{-8} \text{ mol}
Step 2: Calculate Molar Mass
Molar Mass=MassMoles=3.41×10−6 g7.76×10−8 mol≈43.95 g/mol\text{Molar Mass} = \frac{\text{Mass}}{\text{Moles}} = \frac{3.41 \times 10^{-6} \text{ g}}{7.76 \times 10^{-8} \text{ mol}} \approx 43.95 \text{ g/mol}
Step 3: Identify the compound
A molar mass of approximately 44 g/mol suggests a few possibilities. The most common compound with a molar mass close to this is:
🔹 Carbon dioxide (CO₂) 12.01 (C)+2×16.00 (O)=44.01 g/mol12.01 \, \text{(C)} + 2 \times 16.00 \, \text{(O)} = 44.01 \text{ g/mol}
✅ Final Answer: The compound is Carbon Dioxide (CO₂)
Explanation:
This problem involves basic principles of chemistry — using mass, number of particles, and molar mass to identify a substance. By converting the given number of molecules to moles using Avogadro’s number, and then applying the definition of molar mass (mass per mole), we calculate a molar mass of approximately 44 g/mol. The only common compound that matches this molar mass is carbon dioxide (CO₂), making it the best and most accurate answer.