To balance the chemical equation for the reaction of iron ([tex]\(Fe\)[/tex]) with oxygen ([tex]\(O_2\)[/tex]) to form ferric oxide ([tex]\(Fe_2O_3\)[/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.
The unbalanced equation provided is:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
Step-by-step process to balance the equation:
1. Count the number of atoms for each element on both sides of the equation
- Reactants:
- [tex]\( Fe \)[/tex]: 1
- [tex]\( O \)[/tex]: 2
- Products:
- [tex]\( Fe \)[/tex]: 2
- [tex]\( O \)[/tex]: 3
2. Balance the iron (Fe) atoms
We have 1 [tex]\(Fe\)[/tex] atom on the reactant side and 2 [tex]\(Fe\)[/tex] atoms on the product side. To balance the [tex]\(Fe\)[/tex] atoms, put a coefficient of 4 in front of [tex]\(Fe\)[/tex] on the reactant side since we need 4 [tex]\(Fe\)[/tex] atoms in total to balance with the 2 [tex]\(Fe_2\)[/tex] on the product side:
[tex]\[ 4 Fe + O_2 \rightarrow 2 Fe_2O_3 \][/tex]
3. Balance the oxygen (O) atoms
We have now:
- Reactants: 4 [tex]\(Fe\)[/tex] atoms and 2 [tex]\(O_2\)[/tex] molecules (total 4 [tex]\(O\)[/tex] atoms)
- Products: 4 [tex]\(Fe\)[/tex] atoms and 2 molecules of [tex]\( Fe_2O_3 \)[/tex] (total 6 [tex]\(O\)[/tex] atoms)
To balance the oxygen atoms, we need 6 [tex]\(O\)[/tex] atoms on the reactant side. Since each [tex]\(O_2\)[/tex] molecule contains 2 oxygen atoms, we would need 3 [tex]\(O_2\)[/tex] molecules:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
Now, we have:
- Reactants: 4 [tex]\(Fe\)[/tex] atoms and 6 [tex]\(O\)[/tex] atoms
- Products: 4 [tex]\(Fe\)[/tex] atoms and 6 [tex]\(O\)[/tex] atoms
As both sides of the equation have the same number of each type of atom, this equation is balanced.
The balanced equation for the reaction is:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
Thus, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \)[/tex]
