To balance the chemical equation for the reaction of iron with oxygen to produce iron oxide, we follow these steps:
1. Write the given chemical equation:
[tex]\[
4 Fe + x O_2 \rightarrow 2 Fe_2O_3
\][/tex]
2. Determine the number of each type of atom on both sides of the equation:
- On the left side of the equation:
- Fe atoms: 4
- O atoms: [tex]\(2 \times x\)[/tex] (since [tex]\(O_2\)[/tex] has 2 oxygen atoms per molecule)
- On the right side of the equation:
- Fe atoms: [tex]\(2 \times 2 = 4\)[/tex] (since [tex]\(Fe_2O_3\)[/tex] has 2 iron atoms per molecule and we have 2 molecules)
- O atoms: [tex]\(3 \times 2 = 6\)[/tex] (since [tex]\(Fe_2O_3\)[/tex] has 3 oxygen atoms per molecule and we have 2 molecules)
3. Set up the equality for the oxygen atoms to ensure the equation is balanced:
- The number of oxygen atoms on the left side should be equal to the number of oxygen atoms on the right side. Thus, we get:
[tex]\[
2x = 6
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Divide both sides of the equation by 2:
[tex]\[
x = \frac{6}{2}
\][/tex]
[tex]\[
x = 3
\][/tex]
5. Conclusion:
The value of [tex]\(x\)[/tex] that balances the equation is:
[tex]\[
x = 3
\][/tex]
Thus, the balanced chemical equation is:
[tex]\[
4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3
\][/tex]
