To balance the chemical equation [tex]\( \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \)[/tex], follow these steps:
1. Balance Carbons (C):
- On the left side, there are 4 carbon atoms in [tex]\( \text{C}_4\text{H}_{10} \)[/tex].
- To balance the carbon atoms, place a coefficient of 4 in front of [tex]\( \text{CO}_2 \)[/tex] on the right side:
[tex]\[
\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + \text{H}_2\text{O}
\][/tex]
2. Balance Hydrogens (H):
- On the left side, there are 10 hydrogen atoms in [tex]\( \text{C}_4\text{H}_{10} \)[/tex].
- To balance the hydrogen atoms, place a coefficient of 5 in front of [tex]\( \text{H}_2\text{O} \)[/tex] on the right side:
[tex]\[
\text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O}
\][/tex]
3. Balance Oxygens (O):
- On the right side, the number of oxygen atoms from [tex]\( 4\text{CO}_2 \)[/tex] is [tex]\( 4 \times 2 = 8 \)[/tex] and from [tex]\( 5\text{H}_2\text{O} \)[/tex] is [tex]\( 5 \times 1 = 5 \)[/tex]. Thus, the total number of oxygen atoms on the right side is [tex]\( 8 + 5 = 13 \)[/tex].
- On the left side, oxygen atoms come from [tex]\( \text{O}_2 \)[/tex] molecules. Therefore, to have 13 oxygen atoms on the left side, we need:
[tex]\[
\frac{13}{2} = 6.5 \text{ molecules of } \text{O}_2
\][/tex]
So, the balanced equation is:
[tex]\[
\text{C}_4\text{H}_{10} + 6.5\text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O}
\][/tex]
Therefore, the coefficient of [tex]\( \text{O}_2 \)[/tex] after balancing the equation is:
[tex]\[ \boxed{6.5} \][/tex]
The answer is:
A. 6.5
