To determine the correct balanced equation for the reaction where iron (Fe) reacts with oxygen (O[tex]\(_2\)[/tex]) to form iron oxide (Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex]), we need to ensure that the number of atoms for each element is the same on both sides of the equation.
Let's carefully balance the given equation:
[tex]\[Fe + O_2 \rightarrow Fe_2 O_3\][/tex]
1. Count the number of atoms for each element on both sides of the unbalanced equation:
- Left side: Fe = 1, O = 2
- Right side: Fe = 2, O = 3
The numbers do not match, so the equation is unbalanced.
2. Balance iron atoms:
- To balance Fe atoms, we shall need to have 2 moles of Fe on the left for every Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex] on the right. Since Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex] has 2 Fe atoms, having 4 Fe atoms on the left would mean using 2 Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex].
Hence, the trial equation is:
[tex]\[4 Fe + O_2 \rightarrow 2 Fe_2 O_3\][/tex]
3. Balance oxygen atoms:
- Now on the right side, we have 2 molecules of Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex], each containing 3 oxygen atoms. Thus, we have [tex]\(2 \times 3 = 6\)[/tex] oxygen atoms.
- To have 6 oxygen atoms on the left, we need 3 O[tex]\(_2\)[/tex] molecules because each O[tex]\(_2\)[/tex] molecule contains 2 oxygen atoms [tex]\((3 \times 2 = 6)\)[/tex].
So, the balanced equation becomes:
[tex]\[4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3\][/tex]
Thus, the correct balanced equation is:
[tex]\[4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
