Given that the molar mass of gold (Au) is 197 g/mol, how many atoms are present in a 3.00 g sample of gold?

• A. 1.83 × 10^{22} atoms
• B. 1.02 × 10^{20} atoms
• C. 3.06 × 10^{23} atoms
• D. 9.18 × 10^{21} atoms

Answer: (D)

Verified step by step guidance

1. Identify the given information: the mass of the gold sample is 3.00 g, and the molar mass of gold (Au) is 197 g/mol.
2. Calculate the number of moles of gold in the sample using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{3.00\ \text{g}}{197\ \text{g/mol}}\).
3. Recall that one mole of any substance contains Avogadro's number of atoms, which is \$6.022 \times 10^{23}$ atoms/mol.
4. Calculate the number of atoms by multiplying the number of moles by Avogadro's number: \(\text{atoms} = \text{moles} \times 6.022 \times 10^{23}\).
5. Perform the multiplication to find the total number of atoms in the 3.00 g gold sample.