To determine which among the given options is the correct balanced chemical equation for the reaction between iron ([tex]\( Fe \)[/tex]) and oxygen ([tex]\( O_2 \)[/tex]) to form iron(III) oxide ([tex]\( Fe_2O_3 \)[/tex]), we need to ensure that the number of atoms of each element on the reactants side is equal to the number on the products side.
Let's begin with the unbalanced equation:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
1. Identify the number of each type of atom in the unbalanced equation:
- Reactants: [tex]\( Fe \)[/tex] (1 atom of Fe), [tex]\( O_2 \)[/tex] (2 atoms of O)
- Products: [tex]\( Fe_2O_3 \)[/tex] (2 atoms of Fe, 3 atoms of O)
2. Balance the iron atoms:
In [tex]\( Fe_2O_3 \)[/tex], there are 2 atoms of iron. Therefore, to balance the iron atoms, we need 4 iron atoms on the reactants side because:
[tex]\[ 4 Fe + O_2 \rightarrow 2 Fe_2O_3 \][/tex]
3. Balance the oxygen atoms:
Now, we need to balance the oxygen atoms. On the products side, we have 2 molecules of [tex]\( Fe_2O_3 \)[/tex], which gives us:
[tex]\[ 2 \times 3 = 6 \text{ oxygen atoms (from } 2 Fe_2O_3 \text{)} \][/tex]
To get 6 oxygen atoms from [tex]\( O_2 \)[/tex] molecules, we need 3 molecules of [tex]\( O_2 \)[/tex]:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
4. Verify balance:
- Reactants: [tex]\( Fe \)[/tex] (4 atoms), [tex]\( O \)[/tex] (6 atoms)
- Products: [tex]\( Fe \)[/tex] (4 atoms), [tex]\( O \)[/tex] (6 atoms)
Since the number of atoms for each element is equal on both sides of the equation, it is now balanced.
The correct balanced equation 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]
