Which of the following samples contains the same number of atoms as 24 grams of carbon (C)?

• A. 24 grams of oxygen (O)
• B. 32 grams of sulfur (S)
• C. 24 grams of sodium (Na)
• D. 12 grams of magnesium (Mg)

Answer: (B)

Verified step by step guidance

1. Identify the number of atoms in 24 grams of carbon by first calculating the number of moles. Use the molar mass of carbon (C), which is approximately 12 g/mol, and apply the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).
2. Calculate the number of atoms in 24 grams of carbon by multiplying the moles by Avogadro's number (\$6.022 \times 10^{23}\( atoms/mol): \)\text{atoms} = \text{moles} \times 6.022 \times 10^{23}$.
3. For each given sample (oxygen, sulfur, sodium, magnesium), calculate the number of moles using their respective molar masses: oxygen (O) ~16 g/mol, sulfur (S) ~32 g/mol, sodium (Na) ~23 g/mol, magnesium (Mg) ~24 g/mol, using the same formula as in step 1.
4. Compare the number of moles (and thus atoms) in each sample to the number of moles in 24 grams of carbon. The sample with the same number of moles will have the same number of atoms because the number of atoms is directly proportional to the number of moles.
5. Identify which sample has the same number of atoms as 24 grams of carbon by matching the calculated moles. This will confirm the correct answer without directly calculating the total number of atoms.