To determine the mass of magnesium (Mg) in grams for [tex]\(7.43 \times 10^{22}\)[/tex] atoms of magnesium, we’ll use the following steps:
### Step 1: Understand the Constants Involved
We need some key constants for our calculations:
- Molar mass of magnesium (Mg) is [tex]\(24.30 \, \text{g/mol}\)[/tex].
- Avogadro's number, which is the number of atoms in one mole, is [tex]\(6.022 \times 10^{23} \, \text{atoms/mol}\)[/tex].
### Step 2: Convert Atoms to Moles
First, we convert the given number of atoms to moles. The formula to convert atoms to moles is:
[tex]\[
\text{moles of Mg} = \frac{\text{number of atoms of Mg}}{\text{Avogadro's number}}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of Mg} = \frac{7.43 \times 10^{22} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}}
\][/tex]
This calculation gives us:
[tex]\[
\text{moles of Mg} \approx 0.12338093656592496 \, \text{mol}
\][/tex]
### Step 3: Convert Moles to Grams
Next, we convert the moles of magnesium to grams using the molar mass of magnesium. The formula is:
[tex]\[
\text{mass of Mg (in grams)} = \text{moles of Mg} \times \text{molar mass of Mg}
\][/tex]
Substituting the values we have:
[tex]\[
\text{mass of Mg} = 0.12338093656592496 \, \text{mol} \times 24.30 \, \text{g/mol}
\][/tex]
This calculation results in:
[tex]\[
\text{mass of Mg} \approx 2.9981567585519766 \, \text{grams}
\][/tex]
### Conclusion
Therefore, there are approximately [tex]\(2.998\)[/tex] grams of magnesium in [tex]\(7.43 \times 10^{22}\)[/tex] atoms of magnesium.
