If you have 2.00 grams of 13C, how many atoms of 13C are present in this sample?

• A. 1.53 × 10^{22} atoms
• B. 1.20 × 10^{23} atoms
• C. 9.24 × 10^{22} atoms
• D. 6.02 × 10^{23} atoms

Answer: (C)

Verified step by step guidance

1. Identify the given information: mass of the sample is 2.00 grams of carbon-13 (\(^{13}C\)).
2. Recall the molar mass of carbon-13, which is approximately 13.00 grams per mole because the isotope number corresponds to the molar mass in grams per mole.
3. Calculate the number of moles of \(^{13}C\) in the sample using the formula: \[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{2.00}{13.00} \]
4. Use Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol) to convert moles to atoms: \[ \text{number of atoms} = \text{moles} \times 6.022 \times 10^{23} \]
5. Multiply the moles calculated in step 3 by Avogadro's number to find the total number of \(^{13}C\) atoms in the 2.00 gram sample.