To determine which is the balanced equation for the reaction [tex]\(S_8 + O_2 \rightarrow SO_2\)[/tex], we need to ensure that the number of atoms for each element on the reactant side is equal to the number of atoms on the product side.
Let's examine each option:
1. Option 1: [tex]\(S_8 + O_{16} \rightarrow 8 SO_2\)[/tex]:
- Reactants: [tex]\(S_8\)[/tex] has 8 sulfur atoms, and [tex]\(O_{16}\)[/tex] has 16 oxygen atoms.
- Products: [tex]\(8 SO_2\)[/tex] has [tex]\(8 \times 1 = 8\)[/tex] sulfur atoms and [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- This equation is balanced since the number of sulfur and oxygen atoms is the same on both sides.
2. Option 2: [tex]\(S_8 + O_2 \rightarrow S_8 + O_2\)[/tex]:
- Reactants: [tex]\(S_8\)[/tex] has 8 sulfur atoms, and [tex]\(O_2\)[/tex] has 2 oxygen atoms.
- Products: [tex]\(S_8\)[/tex] has 8 sulfur atoms, and [tex]\(O_2\)[/tex] has 2 oxygen atoms.
- This equation is balanced but does not represent a chemical change (no reaction has occurred).
3. Option 3: [tex]\(S_8 + O_2 \rightarrow S_8 O_2\)[/tex]:
- Reactants: [tex]\(S_8\)[/tex] has 8 sulfur atoms, and [tex]\(O_2\)[/tex] has 2 oxygen atoms.
- Products: [tex]\(S_8 O_2\)[/tex] has 8 sulfur atoms and 2 oxygen atoms.
- This equation is balanced but does not represent the formation of [tex]\(SO_2\)[/tex].
4. Option 4: [tex]\(S_8 + 8 O_2 \rightarrow 8 SO_2\)[/tex]:
- Reactants: [tex]\(S_8\)[/tex] has 8 sulfur atoms, and [tex]\(8 O_2\)[/tex] has [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- Products: [tex]\(8 SO_2\)[/tex] has [tex]\(8 \times 1 = 8\)[/tex] sulfur atoms and [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- This equation is balanced and correctly represents the formation of [tex]\(SO_2\)[/tex].
After analyzing all the options, the balanced equation for the reaction [tex]\(S_8 + O_2 \rightarrow SO_2\)[/tex] is:
[tex]\[ \boxed{S_8 + 8 O_2 \rightarrow 8 SO_2} \][/tex]
Therefore, the correct answer is Option 4.
