To determine the mass of [tex]\( 8.25 \times 10^{23} \)[/tex] atoms of Magnesium (Mg), we'll go through several steps involving the concepts of Avogadro's number and molar mass. Here is the step-by-step solution:
1. Identify the given data:
- Number of Magnesium atoms ( [tex]\( N_{\text{atoms}} \)[/tex] ) [tex]\( = 8.25 \times 10^{23} \)[/tex] atoms
2. Recall Avogadro's number:
- Avogadro's number ( [tex]\( N_A \)[/tex] ) is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mole. This is the number of atoms in one mole of any substance.
3. Recall the molar mass of Magnesium:
- The molar mass of Magnesium ( [tex]\( M_{\text{Mg}} \)[/tex] ) is [tex]\( 24.305 \)[/tex] grams/mole. This is the mass of one mole of Magnesium.
4. Calculate the number of moles of Magnesium:
- The number of moles ( [tex]\( n \)[/tex] ) can be found using the formula:
[tex]\[
n = \frac{N_{\text{atoms}}}{N_A}
\][/tex]
- Substituting the given values:
[tex]\[
n = \frac{8.25 \times 10^{23}}{6.022 \times 10^{23}}
\][/tex]
- After performing this division, we find that the number of moles of Magnesium is approximately [tex]\( 1.37 \)[/tex] moles.
5. Calculate the mass of Magnesium:
- The mass ( [tex]\( m \)[/tex] ) can be calculated using the formula:
[tex]\[
m = n \times M_{\text{Mg}}
\][/tex]
- Substituting the number of moles and the molar mass:
[tex]\[
m = 1.37 \times 24.305
\][/tex]
- After multiplying these values, we find that the mass of [tex]\( 8.25 \times 10^{23} \)[/tex] atoms of Magnesium is approximately [tex]\( 33.30 \)[/tex] grams.
Therefore, the mass of [tex]\( 8.25 \times 10^{23} \)[/tex] atoms of Magnesium is [tex]\( 33.30 \)[/tex] grams.
