To determine which equation correctly balances the chemical reaction [tex]\( Fe + O_2 \rightarrow Fe_2O_3 \)[/tex], we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's walk through the steps involved in balancing the equation:
1. Identify the initial equation:
[tex]\[
Fe + O_2 \rightarrow Fe_2O_3
\][/tex]
2. Count the atoms of each element in the unbalanced equation:
- Iron (Fe): 1 atom on the reactant side.
- Oxygen (O): 2 atoms on the reactant side.
- Iron (Fe): 2 atoms on the product side.
- Oxygen (O): 3 atoms on the product side.
3. Balance the number of iron (Fe) atoms:
- The product side has 2 iron atoms, so we need 2 iron atoms on the reactant side. We multiply the reactant [tex]\( Fe \)[/tex] by 2:
[tex]\[
2Fe + O_2 \rightarrow Fe_2O_3
\][/tex]
4. Balance the number of oxygen (O) atoms:
- The product side has 3 oxygen atoms from [tex]\( Fe_2O_3 \)[/tex]. To balance, we need the same number of oxygen atoms on the reactant side. Since each [tex]\( O_2 \)[/tex] molecule has 2 oxygen atoms, we need [tex]\( \frac{3}{2} \)[/tex] molecules of [tex]\( O_2 \)[/tex] to get 3 oxygens. To remove the fractional coefficient, it is common practice to multiply all coefficients by 2:
[tex]\[
2 \times (2Fe + \frac{3}{2}O_2 \rightarrow Fe_2O_3) \implies 4Fe + 3O_2 \rightarrow 2Fe_2O_3
\][/tex]
5. Verify the balanced equation:
- Reactants: 4 iron atoms and 6 oxygen atoms (3 [tex]\( O_2 \)[/tex] molecules each contributing 2 oxygen atoms).
- Products: 4 iron atoms (2 [tex]\( Fe_2O_3 \)[/tex] molecules each contributing 2 iron atoms) and 6 oxygen atoms (2 [tex]\( Fe_2O_3 \)[/tex] molecules each contributing 3 oxygen atoms).
Each element has the same number of atoms on both sides of the equation.
Therefore, the correct balanced equation for the reaction is:
[tex]\[
4Fe + 3O_2 \rightarrow 2Fe_2O_3
\][/tex]
So, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \)[/tex]
