Answer:
A. To find the number of moles in a 95.0 g sample of gold (Au), we'll use the molar mass of gold, which is 196.97 g/mol.
Given:
- Mass of gold (Au) sample: 95.0 g
- Molar mass of gold (Au): 196.97 g/mol
We can use the formula:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]
Substitute the given values:
\[ \text{Number of moles} = \frac{95.0 \, \text{g}}{196.97 \, \text{g/mol}} \]
\[ \text{Number of moles} \approx 0.482 \, \text{mol} \]
Therefore, there are approximately 0.482 moles of gold in a 95.0 g sample.
B. To find the number of atoms in a 95.0 g sample of gold (Au), we need to use Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol.
Given:
- Number of moles of gold (Au): 0.482 mol
We can use the relationship:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
Substitute the values:
\[ \text{Number of atoms} = 0.482 \, \text{mol} \times (6.022 \times 10^{23} \, \text{atoms/mol}) \]
\[ \text{Number of atoms} \approx 2.9 \times 10^{23} \, \text{atoms} \]
Therefore, there are approximately \(2.9 \times 10^{23}\) atoms in a 95.0 g sample of gold.
