To find the mass of [tex]\( 2.5 \times 10^{24} \)[/tex] atoms of Neon (Ne), we need to follow these steps:
### 1. Determine the number of moles of Neon:
Firstly, the number of moles can be found using Avogadro's number, which is [tex]\( 6.02 \times 10^{23} \)[/tex] atoms per mole.
The formula to find the number of moles is:
[tex]\[
\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}
\][/tex]
Given:
[tex]\[
\text{Number of atoms} = 2.5 \times 10^{24}
\][/tex]
[tex]\[
\text{Avogadro's number} = 6.02 \times 10^{23} \text{ atoms/mol}
\][/tex]
Substitute these values into the formula:
[tex]\[
\text{Number of moles of Ne} = \frac{2.5 \times 10^{24}}{6.02 \times 10^{23}} \approx 4.15 \text{ moles}
\][/tex]
### 2. Calculate the mass of the Neon using the number of moles and molar mass:
To find the mass of Neon, we use the molar mass of Neon, which is [tex]\( 20.18 \)[/tex] grams per mole.
The formula to find the mass is:
[tex]\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}
\][/tex]
We have:
[tex]\[
\text{Number of moles} \approx 4.15 \text{ moles}
\][/tex]
[tex]\[
\text{Molar mass} = 20.18 \text{ g/mol}
\][/tex]
Substitute these values into the formula:
[tex]\[
\text{Mass of Ne} = 4.15 \text{ moles} \times 20.18 \text{ g/mol} \approx 83.8 \text{ grams}
\][/tex]
Thus, the mass of [tex]\( 2.5 \times 10^{24} \)[/tex] atoms of Neon is approximately:
[tex]\[
83.8 \text{ grams}
\][/tex]
### Final Answer
Therefore, the closest option given is:
C. [tex]\( 84 \)[/tex] g Ne
