To determine the number of moles of oxygen atoms in [tex]\(2.4 \times 10^{24}\)[/tex] molecules of sulfur trioxide ([tex]\(SO_3\)[/tex]), follow these steps:
1. Identify Avogadro's Number:
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] molecules/mole. This constant represents the number of molecules in one mole of a substance.
2. Calculate Moles of [tex]\(SO_3\)[/tex] from Molecules:
Given that there are [tex]\(2.4 \times 10^{24}\)[/tex] molecules of [tex]\(SO_3\)[/tex], you can convert this quantity to moles by dividing by Avogadro's number:
[tex]\[
\text{Moles of } SO_3 = \frac{2.4 \times 10^{24}}{6.022 \times 10^{23}}
\][/tex]
3. Perform the division:
[tex]\[
\text{Moles of } SO_3 \approx 3.985386914646297 \text{ moles}
\][/tex]
4. Determine Moles of Oxygen Atoms:
Each molecule of [tex]\(SO_3\)[/tex] contains 3 oxygen atoms. Therefore, the number of moles of oxygen atoms is three times the number of moles of [tex]\(SO_3\)[/tex].
[tex]\[
\text{Moles of Oxygen Atoms} = 3 \times \text{Moles of } SO_3
\][/tex]
5. Calculate the total moles of oxygen atoms:
[tex]\[
\text{Moles of Oxygen Atoms} = 3 \times 3.985386914646297 \approx 11.956160743938891 \text{ moles}
\][/tex]
Thus, in [tex]\(2.4 \times 10^{24}\)[/tex] molecules of [tex]\(SO_3\)[/tex], there are approximately 11.956160743938891 moles of oxygen atoms.
