To balance the chemical equation [tex]\( C_3H_8 + O_2 \rightarrow 3 CO_2 + 4 H_2O \)[/tex], we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms on the product side. Here’s how we can balance the equation step-by-step:
1. Count the number of each type of atom on both sides:
- On the reactant side ([tex]\( C_3H_8 + O_2 \)[/tex]):
- Carbon (C): 3 atoms from [tex]\( C_3H_8 \)[/tex]
- Hydrogen (H): 8 atoms from [tex]\( C_3H_8 \)[/tex]
- Oxygen (O): 2 atoms from [tex]\( O_2 \)[/tex]
- On the product side ([tex]\( 3 CO_2 + 4 H_2O \)[/tex]):
- Carbon (C): [tex]\( 3 \times 1 = 3 \)[/tex] atoms from [tex]\( 3 CO_2 \)[/tex]
- Hydrogen (H): [tex]\( 4 \times 2 = 8 \)[/tex] atoms from [tex]\( 4 H_2O \)[/tex]
- Oxygen (O): [tex]\( 3 \times 2 = 6 \)[/tex] atoms from [tex]\( 3 CO_2 \)[/tex] and [tex]\( 4 \times 1 = 4 \)[/tex] atoms from [tex]\( 4 H_2O \)[/tex], which totals to [tex]\( 6 + 4 = 10 \)[/tex] oxygen atoms.
2. Balance the oxygen atoms:
- We have 10 oxygen atoms on the product side.
- Since each [tex]\( O_2 \)[/tex] molecule contains 2 oxygen atoms, we need [tex]\( \frac{10}{2} = 5 \)[/tex] molecules of [tex]\( O_2 \)[/tex].
Therefore, the coefficient of [tex]\( O_2 \)[/tex] that is needed to balance the equation is 5.
So, the correct answer is:
C. 5
