To balance the chemical equation [tex]\( C_3H_8 + O_2 \rightarrow 3CO_2 + 4H_2O \)[/tex], we need to ensure that the number of atoms of each element is the same on both sides of the equation.
First, let's count the atoms on the right side of the equation:
- For [tex]\(3CO_2\)[/tex]:
- Carbon (C) atoms: [tex]\(3 \times 1 = 3\)[/tex]
- Oxygen (O) atoms: [tex]\(3 \times 2 = 6\)[/tex]
- For [tex]\(4H_2O\)[/tex]:
- Hydrogen (H) atoms: [tex]\(4 \times 2 = 8\)[/tex]
- Oxygen (O) atoms: [tex]\(4 \times 1 = 4\)[/tex]
Total atoms on the right side:
- Carbon (C): 3
- Hydrogen (H): 8
- Oxygen (O): [tex]\(6 + 4 = 10\)[/tex]
Next, let's count the atoms on the left side of the equation:
- For [tex]\(C_3H_8\)[/tex]:
- Carbon (C) atoms: 3
- Hydrogen (H) atoms: 8
- For [tex]\(O_2\)[/tex]:
- Oxygen (O) atoms: [tex]\(x \times 2 = 2x\)[/tex]
Total atoms on the left side:
- Carbon (C): 3
- Hydrogen (H): 8
- Oxygen (O): [tex]\(2x\)[/tex]
To balance the oxygen atoms, we set the number of oxygen atoms on both sides equal to each other:
[tex]\[ 2x = 10 \][/tex]
Solving for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{10}{2} = 5 \][/tex]
Thus, the coefficient of [tex]\(O_2\)[/tex] needed to balance the equation is [tex]\( \boxed{5} \)[/tex]. Therefore, the correct answer is:
C. 5.
