How many moles are in [tex]$3.75 \times 10^{23}$[/tex] atoms of Co?

Which is the correct conversion setup?

A. [tex]\frac{1 \text{ mole Co }}{6.02 \times 10^{23} \text{ atoms Co }}[/tex]

B. [tex]\frac{6.02 \times 10^{23} \text{ atoms Co }}{1 \text{ mole Co }}[/tex]



Answer :

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]