Answer :
To find the mass of [tex]\(3.30 \times 10^{23}\)[/tex] atoms of silver (Ag), follow these steps:
1. Understand the Relationship: We know that Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mol, is the number of atoms in one mole of any substance.
2. Calculate Moles of Silver:
- First, determine how many moles of silver these [tex]\(3.30 \times 10^{23}\)[/tex] atoms represent.
- Divide the number of atoms by Avogadro's number:
[tex]\[
\text{moles of Ag} = \frac{3.30 \times 10^{23} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 0.548 \text{ moles}
\][/tex]
3. Find the Molar Mass of Silver:
- The molar mass of silver (Ag) is 107.8682 g/mol.
4. Calculate the Mass of Silver:
- Now, calculate the mass by multiplying the number of moles by the molar mass:
[tex]\[
\text{mass of Ag} = 0.548 \text{ moles} \times 107.8682 \text{ g/mol} \approx 59.1 \text{ g}
\][/tex]
Therefore, the mass of [tex]\(3.30 \times 10^{23}\)[/tex] atoms of silver is approximately 59.1 grams. So the correct answer is: 59.1 g.
1. Understand the Relationship: We know that Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mol, is the number of atoms in one mole of any substance.
2. Calculate Moles of Silver:
- First, determine how many moles of silver these [tex]\(3.30 \times 10^{23}\)[/tex] atoms represent.
- Divide the number of atoms by Avogadro's number:
[tex]\[
\text{moles of Ag} = \frac{3.30 \times 10^{23} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \approx 0.548 \text{ moles}
\][/tex]
3. Find the Molar Mass of Silver:
- The molar mass of silver (Ag) is 107.8682 g/mol.
4. Calculate the Mass of Silver:
- Now, calculate the mass by multiplying the number of moles by the molar mass:
[tex]\[
\text{mass of Ag} = 0.548 \text{ moles} \times 107.8682 \text{ g/mol} \approx 59.1 \text{ g}
\][/tex]
Therefore, the mass of [tex]\(3.30 \times 10^{23}\)[/tex] atoms of silver is approximately 59.1 grams. So the correct answer is: 59.1 g.
