To balance the given chemical equation [tex]\( \text{C}_6\text{H}_{14}( l ) + \text{O}_2(g) \longrightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g) \)[/tex], we follow these steps:
1. Balancing Carbon:
- There are 6 carbons in [tex]\( \text{C}_6\text{H}_{14} \)[/tex]. Therefore, we need 6 [tex]\( \text{CO}_2 \)[/tex] molecules to balance the carbons.
- Updated equation: [tex]\( \text{C}_6\text{H}_{14} + \text{O}_2 \longrightarrow 6 \text{CO}_2 + \text{H}_2\text{O} \)[/tex]
2. Balancing Hydrogen:
- There are 14 hydrogens in [tex]\( \text{C}_6\text{H}_{14} \)[/tex]. To balance the hydrogen, we need 7 [tex]\( \text{H}_2\text{O} \)[/tex] molecules because each water molecule contains 2 hydrogen atoms.
- Updated equation: [tex]\( \text{C}_6\text{H}_{14} + \text{O}_2 \longrightarrow 6 \text{CO}_2 + 7 \text{H}_2\text{O} \)[/tex]
3. Balancing Oxygen:
- Now we need to balance the oxygen atoms. On the right side of the equation, there are oxygen atoms contributed by both [tex]\( \text{CO}_2 \)[/tex] and [tex]\( \text{H}_2\text{O} \)[/tex]:
- From 6 [tex]\( \text{CO}_2 \)[/tex]: [tex]\( 6 \times 2 = 12 \)[/tex] oxygen atoms.
- From 7 [tex]\( \text{H}_2\text{O} \)[/tex]: [tex]\( 7 \times 1 = 7 \)[/tex] oxygen atoms.
- Total oxygen atoms needed on the right side is [tex]\( 12 + 7 = 19 \)[/tex].
4. Balancing the Reactants:
- Since oxygen molecules ([tex]\( \text{O}_2 \)[/tex]) contain 2 oxygen atoms each, to get 19 oxygen atoms on the left side, we need [tex]\( \frac{19}{2} = 9.5 \)[/tex] [tex]\( \text{O}_2 \)[/tex] molecules.
- To ensure all coefficients are integers, we multiply the entire equation by 2:
[tex]\[
2(\text{C}_6\text{H}_{14}) + 2(9.5 \, \text{O}_2) \longrightarrow 2(6 \, \text{CO}_2) + 2(7 \, \text{H}_2\text{O})
\][/tex]
[tex]\[
2 \text{C}_6\text{H}_{14} + 19 \text{O}_2 \longrightarrow 12 \text{CO}_2 + 14 \text{H}_2\text{O}
\][/tex]
Thus, the balanced chemical equation is:
[tex]\[ 2 \text{C}_6\text{H}_{14} + 19 \text{O}_2 \longrightarrow 12 \text{CO}_2 + 14 \text{H}_2\text{O} \][/tex]
The coefficient of oxygen ([tex]\( \text{O}_2 \)[/tex]) in the balanced equation is [tex]\( 19 \)[/tex].
