To balance the chemical equation [tex]\( \text{C}_3\text{H}_8 + \text{O}_2 \rightarrow 3 \text{CO}_2 + 4 \text{H}_2\text{O} \)[/tex], we need to ensure that the number of atoms for each element is equal on both sides of the equation.
1. Balance Carbon (C):
- On the reactant side, there are 3 carbon atoms in [tex]\( \text{C}_3\text{H}_8 \)[/tex].
- On the product side, each [tex]\( \text{CO}_2 \)[/tex] molecule contains 1 carbon atom. Thus, we need 3 [tex]\( \text{CO}_2 \)[/tex] molecules to have 3 carbon atoms:
[tex]\[
3 \times \text{CO}_2 = 3 \text{CO}_2
\][/tex]
So the carbon atoms are balanced.
2. Balance Hydrogen (H):
- On the reactant side, there are 8 hydrogen atoms in [tex]\( \text{C}_3\text{H}_8 \)[/tex].
- On the product side, each [tex]\( \text{H}_2\text{O} \)[/tex] molecule contains 2 hydrogen atoms. Thus, we need 4 [tex]\( \text{H}_2\text{O} \)[/tex] molecules to have 8 hydrogen atoms:
[tex]\[
4 \times \text{H}_2\text{O} = 4 \text{H}_2\text{O}
\][/tex]
So the hydrogen atoms are balanced.
3. Balance Oxygen (O):
- On the product side, there are:
- 3 [tex]\( \text{CO}_2 \)[/tex] molecules, each containing 2 oxygen atoms, resulting in [tex]\( 3 \times 2 = 6 \)[/tex] oxygen atoms.
- 4 [tex]\( \text{H}_2\text{O} \)[/tex] molecules, each containing 1 oxygen atom, resulting in [tex]\( 4 \times 1 = 4 \)[/tex] oxygen atoms.
Thus, the total number of oxygen atoms on the product side is:
[tex]\[
6 + 4 = 10 \text{ atoms of oxygen}
\][/tex]
- On the reactant side, since [tex]\( \text{O}_2 \)[/tex] molecules contain 2 oxygen atoms each, we need:
[tex]\[
\frac{10}{2} = 5 \text{ molecules of } \text{O}_2
\][/tex]
Therefore, the coefficient of [tex]\( \text{O}_2 \)[/tex] needed to balance the equation is 5.
The correct answer is:
C. 5
