To balance the chemical equation [tex]\( \text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \)[/tex], we need to ensure that the number of atoms of each element is the same on both sides of the equation.
1. Write down the unbalanced equation:
[tex]\[ \text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \][/tex]
2. Count the number of each type of atom on both sides of the equation:
- On the left side: 1 Fe atom, 2 O atoms.
- On the right side: 2 Fe atoms, 3 O atoms.
3. Balance the iron (Fe) atoms first. There are 2 Fe atoms in [tex]\(\text{Fe}_2\text{O}_3\)[/tex], so we need 2 Fe atoms on the left side:
[tex]\[ 2\text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \][/tex]
4. Next, we balance the oxygen (O) atoms. There are 3 oxygen atoms in [tex]\(\text{Fe}_2\text{O}_3\)[/tex]. Since each [tex]\(\text{O}_2\)[/tex] molecule provides 2 oxygen atoms, we will need [tex]\( \frac{3}{2} \)[/tex] [tex]\(\text{O}_2\)[/tex] molecules to provide the 3 oxygen atoms:
[tex]\[ 2\text{Fe} + \frac{3}{2}\text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \][/tex]
5. To avoid using fractions, multiply the entire equation by 2 to get whole numbers:
[tex]\[ 4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3 \][/tex]
Hence, the coefficient for [tex]\(\text{O}_2\)[/tex] is 3.
The correct answer is:
C. 3
