To determine the number of moles in [tex]\(3.75 \times 10^{23}\)[/tex] atoms of cobalt (Co), we need to use Avogadro's number, which is [tex]\(6.02 \times 10^{23}\)[/tex] atoms per mole. We'll use this constant to convert the given number of atoms to moles. Here is the step-by-step solution:
1. Identify the Known Values:
- Number of atoms of Co: [tex]\(3.75 \times 10^{23}\)[/tex] atoms
- Avogadro's number: [tex]\(6.02 \times 10^{23}\)[/tex] atoms per mole
2. Set Up the Conversion Factor:
We need to convert atoms of Co to moles of Co. The appropriate conversion factor is:
[tex]\[
\frac{1 \text{ mole Co}}{6.02 \times 10^{23} \text{ atoms Co}}
\][/tex]
This conversion factor allows us to cancel out atoms and leave moles in the calculation.
3. Perform the Conversion:
Apply the conversion factor to the given number of atoms:
[tex]\[
3.75 \times 10^{23} \text{ atoms Co} \times \frac{1 \text{ mole Co}}{6.02 \times 10^{23} \text{ atoms Co}}
\][/tex]
4. Cancel Units and Calculate:
The atoms unit cancels out, leaving:
[tex]\[
\frac{3.75 \times 10^{23}}{6.02 \times 10^{23}} \text{ mole Co}
\][/tex]
5. Obtain the Result:
The numerical calculation gives:
[tex]\[
3.75 \div 6.02 \approx 0.6229235880398671 \text{ mole Co}
\][/tex]
Therefore, there are approximately [tex]\(0.6229\)[/tex] moles of cobalt in [tex]\(3.75 \times 10^{23}\)[/tex] atoms of cobalt. The correct conversion setup is:
[tex]\[
\frac{1 \text{ mole Co}}{6.02 \times 10^{23} \text{ atom Co}}
\][/tex]
