To determine the balanced chemical equation for the combustion of cyclohexane [tex]\(\text{C}_6\text{H}_{12}\)[/tex], let's carefully look at the balancing process:
1. Write the initial combustion reaction:
[tex]\[
\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{heat}
\][/tex]
2. Balance the carbon atoms:
In cyclohexane ([tex]\(\text{C}_6\text{H}_{12}\)[/tex]), there are 6 carbon atoms. Hence, we need 6 carbon dioxide ([tex]\(\text{CO}_2\)[/tex]) molecules on the right side to balance the carbon atoms:
[tex]\[
\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow 6\text{CO}_2 + \text{H}_2\text{O}
\][/tex]
3. Balance the hydrogen atoms:
Cyclohexane has 12 hydrogen atoms. Hence, we need 6 water ([tex]\(\text{H}_2\text{O}\)[/tex]) molecules on the right side to balance the hydrogen atoms:
[tex]\[
\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O}
\][/tex]
4. Balance the oxygen atoms:
- On the right side, we have:
- [tex]\(6 \times \text{CO}_2\)[/tex] = [tex]\(6 \times 2\)[/tex] = 12 oxygen atoms from the carbon dioxide.
- [tex]\(6 \times \text{H}_2\text{O}\)[/tex] = [tex]\(6 \times 1\)[/tex] = 6 oxygen atoms from the water.
- Total oxygen atoms on the right side = 12 + 6 = 18 oxygen atoms.
- On the left side:
- Oxygen comes from [tex]\(\text{O}_2\)[/tex] molecules.
- To balance 18 oxygen atoms, we need [tex]\(\frac{18}{2} = 9\)[/tex] [tex]\(\text{O}_2\)[/tex] molecules.
So the balanced equation is:
[tex]\[
\text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{heat}
\][/tex]
Therefore, the correct balanced combustion reaction for cyclohexane is:
[tex]\[
\boxed{\text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{heat}}
\][/tex]
Thus, the correct answer is:
C. [tex]\(\text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{heat}\)[/tex]
