Octane [tex]\((C_8H_{18})\)[/tex] is found in gasoline. It is burned for fuel in a combustion reaction. The unbalanced combustion reaction for octane is shown below:

[tex]\[ C_8H_{18} + O_2 \rightarrow CO_2 + H_2O + \text{heat} \][/tex]

When the reaction is balanced, how many carbon dioxide molecules are produced for every octane molecule burned?

A. 2
B. 4
C. 8
D. 1



Answer :

To determine the number of carbon dioxide ([tex]\( \text{CO}_2 \)[/tex]) molecules produced per octane ([tex]\( \text{C}_8\text{H}_{18} \)[/tex]) molecule burned in a combustion reaction, we need to first balance the given reaction:

[tex]\[ \text{C}_8\text{H}_{18} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{heat} \][/tex]

Here are the steps:

1. Balance the Carbon Atoms:
- Octane ([tex]\( \text{C}_8\text{H}_{18} \)[/tex]) has 8 carbon atoms.
- To balance the carbons, each of these carbon atoms will form one molecule of carbon dioxide ([tex]\( \text{CO}_2 \)[/tex]).
- Therefore, we'll need 8 [tex]\(\text{CO}_2 \)[/tex] molecules to balance the carbon atoms on both sides.

The equation becomes:
[tex]\[ \text{C}_8\text{H}_{18} + \text{O}_2 \rightarrow 8\text{CO}_2 + \text{H}_2\text{O} \][/tex]

2. Balance the Hydrogen Atoms:
- Octane has 18 hydrogen atoms ([tex]\( \text{H}_{18} \)[/tex]).
- Water ([tex]\( \text{H}_2\text{O} \)[/tex]) has 2 hydrogen atoms per molecule.
- To balance the 18 hydrogen atoms, we'll need 9 water molecules [tex]\((\text{H}_2\text{O})\)[/tex].

The equation now becomes:
[tex]\[ \text{C}_8\text{H}_{18} + \text{O}_2 \rightarrow 8\text{CO}_2 + 9\text{H}_2\text{O} \][/tex]

3. Balance the Oxygen Atoms:
- On the product side, we have:
- 8 molecules of [tex]\(\text{CO}_2\)[/tex] contribute [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- 9 molecules of [tex]\(\text{H}_2\text{O}\)[/tex] contribute [tex]\(9 \times 1 = 9\)[/tex] oxygen atoms.
- In total, [tex]\(16 + 9 = 25\)[/tex] oxygen atoms are needed.
- Since [tex]\(\text{O}_2\)[/tex] is diatomic (each molecule contains 2 oxygen atoms), we will need [tex]\(\frac{25}{2} = 12.5\)[/tex] molecules of [tex]\(\text{O}_2\)[/tex] to provide the necessary oxygen atoms.

So, the balanced equation is:
[tex]\[ \text{C}_8\text{H}_{18} + 12.5\text{O}_2 \rightarrow 8\text{CO}_2 + 9\text{H}_2\text{O} \][/tex]

Now that the reaction is fully balanced, we can clearly see that for every molecule of octane ([tex]\(\text{C}_8\text{H}_{18}\)[/tex]) burned, 8 molecules of carbon dioxide ([tex]\(\text{CO}_2\)[/tex]) are produced.

Thus, the correct answer is:

C. 8