To determine the balanced combustion reaction for cyclohexane ([tex]$\text{C}_6\text{H}_{12}$[/tex]), we need to ensure that the number of atoms of each element (carbon, hydrogen, and oxygen) is the same on both the reactant and product sides of the equation.
### Step-by-Step Solution:
1. Write the general formula for combustion:
Combustion of an organic compound typically involves the compound reacting with oxygen ([tex]$\text{O}_2$[/tex]), resulting in the formation of carbon dioxide ([tex]$\text{CO}_2$[/tex]) and water ([tex]$\text{H}_2\text{O}$[/tex]), along with the release of heat.
[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:
Cyclohexane has 6 carbon atoms. Therefore, we need 6 molecules of [tex]$\text{CO}_2$[/tex] to balance the carbon atoms:
[tex]\[
\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow 6 \text{CO}_2 + \text{H}_2\text{O} + \text{heat}
\][/tex]
3. Balance the hydrogen atoms:
Cyclohexane has 12 hydrogen atoms. Therefore, we need 6 molecules of [tex]$\text{H}_2\text{O}$[/tex] to balance the hydrogen atoms (since each [tex]$\text{H}_2\text{O}$[/tex] molecule has 2 hydrogen atoms):
[tex]\[
\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O} + \text{heat}
\][/tex]
4. Balance the oxygen atoms:
- On the product side, there are 6 molecules of [tex]$\text{CO}_2$[/tex] and 6 molecules of [tex]$\text{H}_2\text{O}$[/tex].
- Each [tex]$\text{CO}_2$[/tex] molecule has 2 oxygen atoms, so 6 [tex]$\text{CO}_2$[/tex] molecules have [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms.
- Each [tex]$\text{H}_2\text{O}$[/tex] molecule has 1 oxygen atom, so 6 [tex]$\text{H}_2\text{O}$[/tex] molecules have 6 oxygen atoms.
- In total, we need [tex]\(12 + 6 = 18\)[/tex] oxygen atoms on the product side.
Since each [tex]$\text{O}_2$[/tex] molecule has 2 oxygen atoms, we need [tex]\(18 \div 2 = 9\)[/tex] [tex]$\text{O}_2$[/tex] molecules:
[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]
Thus, the balanced combustion reaction for cyclohexane 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 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]
