To determine how many carbon dioxide (CO₂) molecules are produced for every octane (C₈H₁₈) molecule burned, we need to balance the chemical equation for the combustion reaction of octane:
[tex]\[
C_8H_{18} + O_2 \rightarrow CO_2 + H_2O + \text{heat}
\][/tex]
Step-by-Step Solution:
1. Balance Carbon Atoms:
- Octane (C₈H₁₈) contains 8 carbon atoms.
- Therefore, we need 8 CO₂ molecules to balance the carbon atoms on both sides of the equation.
- The equation now looks like:
[tex]\[
C_8H_{18} + O_2 \rightarrow 8 CO_2 + H_2O
\][/tex]
2. Balance Hydrogen Atoms:
- Octane (C₈H₁₈) contains 18 hydrogen atoms.
- Each water (H₂O) molecule contains 2 hydrogen atoms.
- To balance the 18 hydrogen atoms in octane, we need 9 H₂O molecules (since [tex]\(9 \times 2 = 18\)[/tex]).
- The equation now looks like:
[tex]\[
C_8H_{18} + O_2 \rightarrow 8 CO_2 + 9 H_2O
\][/tex]
3. Balance Oxygen Atoms:
- On the right side of the equation, we have:
- 8 CO₂ molecules, contributing [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- 9 H₂O molecules, contributing [tex]\(9 \times 1 = 9\)[/tex] oxygen atoms.
- In total, there are [tex]\(16 + 9 = 25\)[/tex] oxygen atoms on the right side.
- To balance 25 oxygen atoms on the left side using O₂ molecules (each contributing 2 oxygen atoms), we need [tex]\( \frac{25}{2} = 12.5\)[/tex] O₂ molecules.
- The equation is:
[tex]\[
C_8H_{18} + 12.5 O_2 \rightarrow 8 CO_2 + 9 H_2O
\][/tex]
4. Ensure Whole Number Coefficients:
- We cannot have half a molecule in the balanced equation, so we multiply the entire equation by 2 to get whole numbers:
[tex]\[
2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O
\][/tex]
From the balanced equation, we see that for every 2 molecules of octane burned, 16 molecules of carbon dioxide are produced. Therefore, for every 1 molecule of octane burned, 8 molecules of carbon dioxide are produced.
Thus, the correct answer is [tex]\( \boxed{8} \)[/tex].
