To balance a chemical equation, we must ensure that there are equal numbers of each type of atom on both sides of the equation. Let's examine the given reaction and the options systematically.
The unbalanced equation is:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
Let's consider each option:
### Option A: [tex]\( 4Fe + 3O_2 \rightarrow 2Fe_2O_3 \)[/tex]
1. Iron (Fe) atoms:
- Reactants: [tex]\( 4Fe \)[/tex]
- Products: [tex]\( 2 \times Fe_2O_3 \)[/tex] which gives [tex]\( 2 \times 2 = 4Fe \)[/tex]
2. Oxygen (O) atoms:
- Reactants: [tex]\( 3O_2 \)[/tex] which gives [tex]\( 3 \times 2 = 6O \)[/tex]
- Products: [tex]\( 2 \times Fe_2O_3 \)[/tex] which gives [tex]\( 2 \times 3 = 6O \)[/tex]
Since there are 4 iron atoms and 6 oxygen atoms on both sides, Option A is balanced.
### Option B: [tex]\( 3Fe + 4O_2 \rightarrow 2Fe_2O_3 \)[/tex]
1. Iron (Fe) atoms:
- Reactants: [tex]\( 3Fe \)[/tex]
- Products: [tex]\( 2 \times Fe_2O_3 \)[/tex] which gives [tex]\( 2 \times 2 = 4Fe \)[/tex]
Here, 3Fe does not equal 4Fe.
### Option C: [tex]\( 2Fe + 4O_2 \rightarrow 3Fe_2O_3 \)[/tex]
1. Iron (Fe) atoms:
- Reactants: [tex]\( 2Fe \)[/tex]
- Products: [tex]\( 3 \times Fe_2O_3 \)[/tex] which gives [tex]\( 3 \times 2 = 6Fe \)[/tex]
Here, 2Fe does not equal 6Fe.
### Option D: [tex]\( 3Fe + 3O_2 \rightarrow 4Fe_2O_3 \)[/tex]
1. Iron (Fe) atoms:
- Reactants: [tex]\( 3Fe \)[/tex]
- Products: [tex]\( 4 \times Fe_2O_3 \)[/tex] which gives [tex]\( 4 \times 2 = 8Fe \)[/tex]
Here, 3Fe does not equal 8Fe.
### Option E: [tex]\( 4Fe + 4O_2 \rightarrow 3Fe_2O_3 \)[/tex]
1. Iron (Fe) atoms:
- Reactants: [tex]\( 4Fe \)[/tex]
- Products: [tex]\( 3 \times Fe_2O_3 \)[/tex] which gives [tex]\( 3 \times 2 = 6Fe \)[/tex]
Here, 4Fe does not equal 6Fe.
### Conclusion
From the examination, Option A: [tex]\(4Fe + 3O_2 \rightarrow 2Fe_2O_3\)[/tex] is the only balanced equation where both the number of iron atoms and the number of oxygen atoms are the same on both sides of the equation.
Therefore, the correct answer is Option A.
