To solve the problem of determining the number of moles of sulfur (S) in [tex]\(3.6 \times 10^{24}\)[/tex] formula units of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex], the correct pathway is:
[tex]\[ \text{particles } \text{Al}_2\text{S}_3 \rightarrow \text{moles } \text{Al}_2\text{S}_3 \rightarrow \text{moles } \text{S} \][/tex]
Here is the step-by-step solution:
1. Determine the number of moles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex]:
Given the number of particles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex] is [tex]\(3.6 \times 10^{24}\)[/tex], and Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex], we can find the number of moles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex] by dividing the given particles by Avogadro's number.
[tex]\[
\text{moles of Al}_2\text{S}_3 = \frac{3.6 \times 10^{24}}{6.022 \times 10^{23}} \approx 5.978
\][/tex]
2. Determine the number of moles of S:
In one mole of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex], there are 3 moles of sulfur (S) atoms. Therefore, to calculate the moles of S from moles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex], we multiply the moles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex] by 3.
[tex]\[
\text{moles of S} = 3 \times \text{moles of Al}_2\text{S}_3 \approx 3 \times 5.978 \approx 17.934
\][/tex]
Thus, from [tex]\(3.6 \times 10^{24}\)[/tex] formula units of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex], we have approximately [tex]\(5.978\)[/tex] moles of Al[tex]\(_2\)[/tex]S[tex]\(_3\)[/tex] and approximately [tex]\(17.934\)[/tex] moles of sulfur (S).
