Answer :

To find the total mass of [tex]\(3.01 \times 10^{23}\)[/tex] atoms of helium gas, we can follow these steps:

1. Understand the concept of Avogadro's number:
Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us how many atoms or molecules are in one mole of a substance.

2. Know the molar mass of helium:
The molar mass of helium is 4.00 grams per mole. This means that one mole of helium atoms weighs 4.00 grams.

3. Calculate the number of moles of helium:
To find out how many moles of helium are in [tex]\(3.01 \times 10^{23}\)[/tex] atoms, we divide the number of atoms by Avogadro's number:
[tex]\[
\text{Number of moles} = \frac{3.01 \times 10^{23} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}}
\][/tex]
This calculation gives approximately 0.5 moles of helium.

4. Calculate the total mass of helium:
Now, using the number of moles and the molar mass of helium, we can find the total mass:
[tex]\[
\text{Total mass} = \text{Number of moles} \times \text{Molar mass of helium}
\][/tex]
[tex]\[
\text{Total mass} = 0.5 \text{ moles} \times 4.00 \text{ g/mol} = 2.00 \text{ grams}
\][/tex]

Thus, the total mass of [tex]\(3.01 \times 10^{23}\)[/tex] atoms of helium is [tex]\(2.00\)[/tex] grams. Therefore, the correct answer is option 2: [tex]\(2.00\, \text{g}\)[/tex].

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