To balance the chemical equation for the combustion of sugar ([tex]\(C_6H_{12}O_6\)[/tex]), we need to ensure that the number of atoms for each element is the same on both the reactant and product sides. Here’s the step-by-step process:
1. Identify the initial unbalanced equation:
[tex]\[
C_6H_{12}O_6 + O_2 \rightarrow CO_2 + H_2O
\][/tex]
2. Balance the carbon (C) atoms:
- There are 6 carbon atoms in [tex]\(C_6H_{12}O_6\)[/tex].
- To balance this, we need 6 [tex]\(CO_2\)[/tex] molecules on the product side:
[tex]\[
C_6H_{12}O_6 + O_2 \rightarrow 6 CO_2 + H_2O
\][/tex]
3. Balance the hydrogen (H) atoms:
- There are 12 hydrogen atoms in [tex]\(C_6H_{12}O_6\)[/tex].
- To balance this, we need 6 [tex]\(H_2O\)[/tex] molecules on the product side:
[tex]\[
C_6H_{12}O_6 + O_2 \rightarrow 6 CO_2 + 6 H_2O
\][/tex]
4. Balance the oxygen (O) atoms:
- On the reactant side, we have:
- 6 oxygen atoms from [tex]\(C_6H_{12}O_6\)[/tex]
- On the product side, we now have:
- From [tex]\(6 CO_2\)[/tex]: [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms
- From [tex]\(6 H_2O\)[/tex]: [tex]\(6 \times 1 = 6\)[/tex] oxygen atoms
- Total oxygen atoms on the product side: [tex]\(12 + 6 = 18\)[/tex]
- We already have 6 oxygen atoms from [tex]\(C_6H_{12}O_6\)[/tex], so we need an additional 12 oxygen atoms from [tex]\(O_2\)[/tex]:
- Since each [tex]\(O_2\)[/tex] molecule has 2 oxygen atoms, we need [tex]\( \frac{12}{2} = 6 \)[/tex] molecules of [tex]\(O_2\)[/tex]:
[tex]\[
C_6H_{12}O_6 + 6 O_2 \rightarrow 6 CO_2 + 6 H_2O
\][/tex]
5. Verify the balanced equation:
- Carbon: [tex]\( 6 \)[/tex] atoms on both sides
- Hydrogen: [tex]\( 12 \)[/tex] atoms on both sides
- Oxygen: [tex]\( 18 \)[/tex] atoms on both sides
Thus, the balanced chemical equation is:
[tex]\[
C_6H_{12}O_6 + 6 O_2 \rightarrow 6 CO_2 + 6 H_2O
\][/tex]
The sequence of coefficients needed to balance the equation is:
1, 6, 6, 6
Therefore, the correct answer is:
[tex]\[
\boxed{1, 6, 6, 6}
\][/tex]
