What mass (in g) of carbon is in a sample of acetone (CH3COCH3) that contains 6.02 x 10^23 atoms of hydrogen?

• A. 48 g
• B. 36 g
• C. 24 g
• D. 12 g

Answer: (C)

Verified step by step guidance

1. First, identify the molecular formula of acetone, which is \( \text{CH}_3\text{COCH}_3 \). This indicates that one molecule of acetone contains 6 hydrogen atoms.
2. Next, determine the number of acetone molecules in the sample. Since there are \( 6.02 \times 10^{23} \) hydrogen atoms and each acetone molecule contains 6 hydrogen atoms, divide the number of hydrogen atoms by 6 to find the number of acetone molecules.
3. Calculate the number of carbon atoms in the sample. Each acetone molecule contains 3 carbon atoms, so multiply the number of acetone molecules by 3 to find the total number of carbon atoms.
4. Use Avogadro's number \( (6.02 \times 10^{23} \text{ atoms/mol}) \) to convert the number of carbon atoms to moles of carbon. Divide the total number of carbon atoms by Avogadro's number.
5. Finally, calculate the mass of carbon in grams. Multiply the moles of carbon by the molar mass of carbon \( (12.01 \text{ g/mol}) \) to find the mass of carbon in the sample.