To balance the chemical equation:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(l) \][/tex]
we need to follow these steps:
1. Balance the Carbon (C) Atoms:
- The reactant C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex] has 6 carbon atoms.
- We need 6 CO[tex]\(_2\)[/tex] on the right side to balance the carbons:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + \text{O}_2(g) \rightarrow 6 \text{CO}_2(g) + \text{H}_2\text{O}(l) \][/tex]
2. Balance the Hydrogen (H) Atoms:
- The reactant C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex] has 12 hydrogen atoms.
- We need 6 H[tex]\(_2\)[/tex]O on the right side to provide 12 hydrogen atoms:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + \text{O}_2(g) \rightarrow 6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \][/tex]
3. Balance the Oxygen (O) Atoms:
- The reactant C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex] has 6 oxygen atoms.
- There are already 12 + 6 = 18 oxygen atoms on the product side (6 from CO[tex]\(_2\)[/tex] and 6 from H[tex]\(_2\)[/tex]O), and we have 6 from C[tex]\(_6\)[/tex]H[tex]\(_{12}\)[/tex]O[tex]\(_6\)[/tex].
- Therefore, we need an additional 12 oxygen atoms from O[tex]\(_2\)[/tex], which requires 6 O[tex]\(_2\)[/tex] molecules:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g) \rightarrow 6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \][/tex]
So the balanced equation is:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g) \rightarrow 6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(l) \][/tex]
The sequence of coefficients that should be placed in the blanks to balance the equation is:
[tex]\[ 1, 6, 6, 6 \][/tex]
Thus, the correct answer is: [tex]\( 1, 6, 6, 6 \)[/tex].
