To find the mass of [tex]\( 6.45 \times 10^{25} \)[/tex] atoms of copper (Cu), we need to follow these steps:
1. Determine the number of moles of Cu:
- Given the number of atoms: [tex]\( 6.45 \times 10^{25} \)[/tex]
- Avogadro's number, which is the number of atoms in one mole: [tex]\( 6.02 \times 10^{23} \)[/tex]
To find the number of moles ([tex]\( n \)[/tex]), divide the number of atoms by Avogadro's number:
[tex]\[
n = \frac{6.45 \times 10^{25}}{6.02 \times 10^{23}}
\][/tex]
[tex]\[
n \approx 107.14285714285717 \text{ moles}
\][/tex]
2. Calculate the mass of Cu:
- Number of moles obtained: [tex]\( 107.14285714285717 \text{ moles} \)[/tex]
- Molar mass of Cu: [tex]\( 63.55 \text{ g/mol} \)[/tex]
To find the mass, multiply the number of moles by the molar mass:
[tex]\[
\text{Mass of Cu} = 107.14285714285717 \text{ moles} \times 63.55 \text{ g/mol}
\][/tex]
[tex]\[
\text{Mass of Cu} \approx 6808.9285714285725 \text{ g}
\][/tex]
Therefore, the mass of [tex]\( 6.45 \times 10^{25} \)[/tex] atoms of copper is approximately [tex]\( 6808.93 \)[/tex] grams.
So the correct answer is B. [tex]\( 6,810 \text{ g Cu} \)[/tex].
