To determine how many atoms of gold are in a 4.25-gram gold nugget, we need to follow these steps:
1. Determine the number of moles of gold in the sample:
- The molar mass of gold is given as 196.97 g/mol.
- The mass of the gold nugget is 4.25 g.
- The formula to find the number of moles (n) is:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
- Plugging in the values:
[tex]\[
n = \frac{4.25 \, \text{g}}{196.97 \, \text{g/mol}} \approx 0.0215769 \, \text{mol}
\][/tex]
2. Calculate the number of atoms in the nugget:
- Avogadro's number gives us the number of atoms per mole, which is [tex]\(6.022 \times 10^{23} \)[/tex] atoms/mol.
- To find the number of atoms, we multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = n \times \text{Avogadro's number}
\][/tex]
- Substituting the values:
[tex]\[
\text{Number of atoms} = 0.0215769 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 1.2994 \times 10^{22} \, \text{atoms}
\][/tex]
In conclusion, the number of gold atoms in a 4.25-gram gold nugget is [tex]\(\approx 1.299 \times 10^{22}\)[/tex].
