How many atoms of gold (Au) are present in a 90.2-g sample? The molar mass of gold is 197.0 g/mol.

• A. 1.09 × 10^{25} atoms
• B. 2.76 × 10^{23} atoms
• C. 2.75 × 10^{22} atoms
• D. 4.60 × 10^{24} atoms

Answer: (B)

Verified step by step guidance

1. Identify the given information: the mass of the gold sample is 90.2 g, and the molar mass of gold (Au) is 197.0 g/mol.
2. Calculate the number of moles of gold in the sample using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{90.2\,\text{g}}{197.0\,\text{g/mol}}\).
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 total number of gold atoms by multiplying the number of moles by Avogadro's number: \(\text{atoms} = \text{moles} \times 6.022 \times 10^{23}\).
5. Express the final answer in scientific notation to match the format of the given options.