To determine how many moles are in [tex]\( 3.75 \times 10^{23} \)[/tex] atoms of cobalt (Co), we'll use Avogadro's number. Avogadro's number, which is approximately [tex]\( 6.02 \times 10^{23} \)[/tex], is the number of atoms or molecules in one mole of a substance.
Here's the step-by-step solution:
1. Identify the given data:
- Number of atoms of Co: [tex]\( 3.75 \times 10^{23} \)[/tex] atoms
- Avogadro's number: [tex]\( 6.02 \times 10^{23} \)[/tex] atoms/mole
2. Set up the calculation:
The relationship between the number of atoms and moles is given by the formula:
[tex]\[
\text{{Number of moles}} = \frac{\text{{Number of atoms}}}{\text{{Avogadro's number}}}
\][/tex]
Plugging in the given values:
[tex]\[
\text{{Number of moles}} = \frac{3.75 \times 10^{23} \text{ atoms}}{6.02 \times 10^{23} \text{ atoms/mole}}
\][/tex]
3. Divide the numbers:
[tex]\[
\text{{Number of moles}} = \frac{3.75}{6.02}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{3.75}{6.02} \approx 0.62
\][/tex]
Therefore, the calculation tells us that there are approximately [tex]\( 0.62 \)[/tex] moles of cobalt (Co) in [tex]\( 3.75 \times 10^{23} \)[/tex] atoms of Co.
