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What is the mass of [tex]\(2.5 \times 10^{24}\)[/tex] atoms of [tex]\(Ne\)[/tex]?

- Molar mass of [tex]\(Ne = 20.18 \, \text{g/mol}\)[/tex]
- 1 mole = [tex]\(6.02 \times 10^{23}\)[/tex] atoms

A. [tex]\(4.2 \, \text{g Ne}\)[/tex]
B. [tex]\(0.21 \, \text{g Ne}\)[/tex]
C. [tex]\(84 \, \text{g Ne}\)[/tex]
D. [tex]\(1.5 \times 10^{48} \, \text{g Ne}\)[/tex]

Sagot :

GinnyAnswer
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.
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