To find the mass of [tex]\(2.5 \times 10^{24}\)[/tex] atoms of Ne (neon), follow these steps:
1. Determine the number of moles of Ne:
[tex]\[
\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}
\][/tex]
The number of atoms given is [tex]\(2.5 \times 10^{24}\)[/tex].
Avogadro's number is [tex]\(6.02 \times 10^{23}\)[/tex] atoms per mole.
Plugging in the values:
[tex]\[
\text{Number of moles} = \frac{2.5 \times 10^{24}}{6.02 \times 10^{23}} \approx 4.152823920265781 \text{ moles}
\][/tex]
2. Calculate the mass of Ne:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass of Ne}
\][/tex]
The molar mass of Ne is [tex]\(20.18 \text{ grams per mole}\)[/tex].
Using the calculated number of moles:
[tex]\[
\text{Mass} = 4.152823920265781 \text{ moles} \times 20.18 \text{ g/mol} \approx 83.80398671096346 \text{ grams}
\][/tex]
Given the options:
- [tex]\(4.2 \text{ g Ne}\)[/tex]
- [tex]\(0.21 \text{ g Ne}\)[/tex]
- [tex]\(84 \text{ g Ne}\)[/tex]
- [tex]\(1.5 \times 10^{48} \text{ g Ne}\)[/tex]
The closest mass to our calculated value [tex]\(83.80398671096346\)[/tex] grams is [tex]\(84 \text{ g Ne}\)[/tex].
Therefore, the mass of [tex]\(2.5 \times 10^{24}\)[/tex] atoms of Ne is approximately [tex]\(84\)[/tex] grams.
