How many atoms are present in a 591 g sample of gold (Au)? (Atomic mass of Au = 197 g/mol)

• A. 9.02 × 10^{25} atoms
• B. 1.81 × 10^{24} atoms
• C. 3.02 × 10^{24} atoms
• D. 5.91 × 10^{23} atoms

Answer: (B)

Verified step by step guidance

1. Identify the given information: the mass of the gold sample is 591 g, and the atomic mass of gold (Au) is 197 g/mol.
2. Calculate the number of moles of gold in the sample using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{591\ \text{g}}{197\ \text{g/mol}}\).
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 total number of 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 provided options.