To determine the number of atoms of Bismuth (Bi) in a 41.8-gram sample, we need to follow these steps:
1. Determine the molar mass of Bismuth (Bi):
- The molar mass of Bismuth (Bi) is given as 208.98 grams per mole (g/mol).
2. Calculate the number of moles of Bi:
- To calculate the number of moles, we use the formula:
[tex]\[
\text{moles of Bi} = \frac{\text{mass of the sample}}{\text{molar mass of Bi}}
\][/tex]
- Given:
[tex]\[
\text{mass of the sample} = 41.8 \text{ grams}
\][/tex]
[tex]\[
\text{molar mass of Bi} = 208.98 \text{ g/mol}
\][/tex]
- Substituting these values into the formula:
[tex]\[
\text{moles of Bi} = \frac{41.8 \text{ grams}}{208.98 \text{ g/mol}} \approx 0.20001914058761602 \text{ moles}
\][/tex]
3. Use Avogadro's Number to calculate the number of atoms of Bi:
- Avogadro's Number is given as [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole.
- To find the number of atoms, we multiply the number of moles by Avogadro's Number:
[tex]\[
\text{number of atoms of Bi} = \text{moles of Bi} \times \text{Avogadro's Number}
\][/tex]
- Substituting the values:
[tex]\[
\text{number of atoms of Bi} = 0.20001914058761602 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \approx 1.2045152646186236 \times 10^{23} \text{ atoms}
\][/tex]
Therefore, in a 41.8 gram sample of Bismuth, there are approximately [tex]\(1.2045152646186236 \times 10^{23}\)[/tex] atoms of Bi.
