To find out how many moles of sulfur ([tex]\(S\)[/tex]) are needed to produce 15.0 moles of sulfur dioxide ([tex]\(SO_2\)[/tex]), let's first look at the balanced chemical equation:
[tex]\[ S + O_2 \rightarrow SO_2 \][/tex]
The balanced equation tells us that:
- 1 mole of sulfur ([tex]\(S\)[/tex]) reacts with 1 mole of oxygen ([tex]\(O_2\)[/tex]) to produce 1 mole of sulfur dioxide ([tex]\(SO_2\)[/tex]).
This 1:1 molar ratio between sulfur ([tex]\(S\)[/tex]) and sulfur dioxide ([tex]\(SO_2\)[/tex]) means that to produce a specific amount of [tex]\(SO_2\)[/tex], we need an equivalent amount of [tex]\(S\)[/tex].
Given that we want to produce 15.0 moles of sulfur dioxide ([tex]\(SO_2\)[/tex]):
Since 1 mole of [tex]\(S\)[/tex] produces 1 mole of [tex]\(SO_2\)[/tex], for 15.0 moles of [tex]\(SO_2\)[/tex]:
We need 15.0 moles of [tex]\(S\)[/tex].
Thus, 15.0 moles of sulfur (S) are required to produce 15.0 moles of sulfur dioxide ([tex]\(SO_2\)[/tex]).
So, the answer is:
[tex]\[ \text{15.0 mol} \][/tex]
