To balance the chemical equation for the reaction between sulfur ([tex]$\text{S}_8$[/tex]) and oxygen ([tex]$\text{O}_2$[/tex]) to form sulfur dioxide ([tex]$\text{SO}_2$[/tex]), we need to ensure that the number of atoms for each element on the reactant side matches the number of atoms on the product side.
Let's analyze each choice:
1. [tex]$S_8 + O_{16} \rightarrow 8SO_2$[/tex]
- Reactant side: [tex]$S_8$[/tex] has 8 sulfur atoms, and [tex]$O_{16}$[/tex] has 16 oxygen atoms.
- Product side: [tex]$8SO_2$[/tex] means there are [tex]$8 \times 1 = 8$[/tex] sulfur atoms and [tex]$8 \times 2 = 16$[/tex] oxygen atoms.
- The number of each type of atom is balanced on both sides:
- Sulfur: 8 atoms on both sides
- Oxygen: 16 atoms on both sides
2. [tex]$S_8 + O_2 \rightarrow S_8 + O_2$[/tex]
- Reactant side: [tex]$S_8$[/tex] has 8 sulfur atoms, and [tex]$O_2$[/tex] has 2 oxygen atoms.
- Product side: [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 reaction; the substances are unchanged.
3. [tex]$S_8 + O_2 \rightarrow S_8O_2$[/tex]
- Reactant side: [tex]$S_8$[/tex] has 8 sulfur atoms, and [tex]$O_2$[/tex] has 2 oxygen atoms.
- Product side: [tex]$S_8O_2$[/tex] would have 8 sulfur atoms and 2 oxygen atoms.
- This equation balances but does not represent the formation of sulfur dioxide ([tex]$SO_2$[/tex]).
4. [tex]$S_8 + 8O_2 \rightarrow 8SO_2$[/tex]
- Reactant side: [tex]$S_8$[/tex] has 8 sulfur atoms, and [tex]$8O_2$[/tex] means [tex]$8 \times 2 = 16$[/tex] oxygen atoms.
- Product side: [tex]$8SO_2$[/tex] means [tex]$8 \times 1 = 8$[/tex] sulfur atoms and [tex]$8 \times 2 = 16$[/tex] oxygen atoms.
- The number of each type of atom is balanced on both sides:
- Sulfur: 8 atoms on both sides
- Oxygen: 16 atoms on both sides
By comparing the options, the balanced equation that correctly shows the formation of sulfur dioxide ([tex]$SO_2$[/tex]) from sulfur ([tex]$\text{S}_8$[/tex]) and oxygen ([tex]$\text{O}_2$[/tex]) is:
[tex]\[ S_8 + 8O_2 \rightarrow 8SO_2 \][/tex]
Thus, the correct choice is:
[tex]\[ S_8 + 8O_2 \rightarrow 8SO_2 \][/tex]
