To balance the combustion reaction of octane, [tex]\( C_8H_{18} \)[/tex], with oxygen, [tex]\( O_2 \)[/tex], into carbon dioxide, [tex]\( CO_2 \)[/tex], and water, [tex]\( H_2O \)[/tex], we need to ensure that we have the same number of each type of atom on both sides of the equation. Here is the step-by-step process to balance the equation:
1. Write the unbalanced equation:
[tex]\[
C_8H_{18} + O_2 \rightarrow \_ CO_2 + \_ H_2O
\][/tex]
2. Balance the number of carbon (C) atoms:
- There are 8 carbon atoms in [tex]\( C_8H_{18} \)[/tex].
- We need 8 carbon atoms in the products, which will be in the form of [tex]\( CO_2 \)[/tex].
- Therefore, the coefficient for [tex]\( CO_2 \)[/tex] will be 8:
[tex]\[
C_8H_{18} + O_2 \rightarrow 8 CO_2 + \_ H_2O
\][/tex]
3. Balance the number of hydrogen (H) atoms:
- There are 18 hydrogen atoms in [tex]\( C_8H_{18} \)[/tex].
- Water ([tex]\( H_2O \)[/tex]) contains 2 hydrogen atoms per molecule.
- To balance 18 hydrogen atoms, we need [tex]\( \frac{18}{2} = 9 \)[/tex] water molecules:
[tex]\[
C_8H_{18} + O_2 \rightarrow 8 CO_2 + 9 H_2O
\][/tex]
4. Balance the number of oxygen (O) atoms:
- On the right-hand side, we have:
- [tex]\( 8 CO_2 \)[/tex] molecules, each providing 2 oxygen atoms, totaling [tex]\( 8 \times 2 = 16 \)[/tex] oxygen atoms.
- [tex]\( 9 H_2O \)[/tex] molecules, each providing 1 oxygen atom, totaling 9 oxygen atoms.
- Therefore, the total number of oxygen atoms on the right-hand side is [tex]\( 16 + 9 = 25 \)[/tex].
- Oxygen ([tex]\( O_2 \)[/tex]) contains 2 oxygen atoms per molecule.
- To balance 25 oxygen atoms, we need [tex]\( \frac{25}{2} = 12.5 \)[/tex] oxygen molecules:
[tex]\[
C_8H_{18} + 12.5 O_2 \rightarrow 8 CO_2 + 9 H_2O
\][/tex]
5. Avoid fractions by multiplying the entire equation by 2:
- This will give us whole numbers for all coefficients:
[tex]\[
2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O
\][/tex]
Thus, the balanced combustion reaction for octane, [tex]\( C_8H_{18} \)[/tex], is:
[tex]\[
2 C_8H_{18} + 25 O_2 \rightarrow 16 CO_2 + 18 H_2O
\][/tex]
In this balanced equation, the coefficients are:
- [tex]\( C_8H_{18} \)[/tex]: 2
- [tex]\( O_2 \)[/tex]: 25
- [tex]\( CO_2 \)[/tex]: 16
- [tex]\( H_2O \)[/tex]: 18
So, the coefficients for the balanced equation are:
[tex]\[ [2, 25, 16, 18] \][/tex]
