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Sagot :
To balance a chemical equation, we need to ensure that the number of atoms for each element is the same on the reactant side as it is on the product side.
Given the unbalanced equation:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
### Step-by-Step Solution:
1. Identify the number of atoms of each element:
On the reactant side:
- Fe: 1 atom
- O: 2 atoms
On the product side:
- Fe: 2 atoms (Per [tex]\( Fe_2O_3 \)[/tex])
- O: 3 atoms (Per [tex]\( Fe_2O_3 \)[/tex])
2. Balance the number of Fe atoms:
The reactant side needs 2 Fe atoms to match the 2 Fe atoms in [tex]\( Fe_2O_3 \)[/tex]. Thus, the equation becomes:
[tex]\[ 2 Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
3. Balance the number of O atoms:
Currently, we have 2 oxygen atoms on the reactant side and 3 on the product side. To balance the oxygen atoms, it's helpful to increase the number of [tex]\( Fe_2O_3 \)[/tex] molecules. However, the smallest number to balance oxygen atoms would be 6 on both sides.
If we have 2 [tex]\( Fe_2O_3 \)[/tex] on the product side:
[tex]\[ Fe + O_2 \rightarrow 2 Fe_2O_3\][/tex]
This gives us:
- 4 Fe atoms on the product side (as each [tex]\( Fe_2O_3 \)[/tex] has 2 Fe atoms and we have 2 of them)
- 6 O atoms on the product side (each [tex]\( Fe_2O_3 \)[/tex] has 3 O atoms, so 2 of them will have 6 O atoms)
4. Update Fe atoms to accommodate 4 on each side:
[tex]\[ 4 Fe + O_2 \rightarrow 2 Fe_2O_3 \][/tex]
5. Update O atoms to balance:
We need 6 oxygen atoms on the reactant side, which means we need 3 [tex]\( O_2 \)[/tex] molecules (since each [tex]\( O_2 \)[/tex] provides 2 oxygen atoms):
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
With these steps, the correct balanced chemical equation is:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Therefore, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \)[/tex]
Given the unbalanced equation:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
### Step-by-Step Solution:
1. Identify the number of atoms of each element:
On the reactant side:
- Fe: 1 atom
- O: 2 atoms
On the product side:
- Fe: 2 atoms (Per [tex]\( Fe_2O_3 \)[/tex])
- O: 3 atoms (Per [tex]\( Fe_2O_3 \)[/tex])
2. Balance the number of Fe atoms:
The reactant side needs 2 Fe atoms to match the 2 Fe atoms in [tex]\( Fe_2O_3 \)[/tex]. Thus, the equation becomes:
[tex]\[ 2 Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
3. Balance the number of O atoms:
Currently, we have 2 oxygen atoms on the reactant side and 3 on the product side. To balance the oxygen atoms, it's helpful to increase the number of [tex]\( Fe_2O_3 \)[/tex] molecules. However, the smallest number to balance oxygen atoms would be 6 on both sides.
If we have 2 [tex]\( Fe_2O_3 \)[/tex] on the product side:
[tex]\[ Fe + O_2 \rightarrow 2 Fe_2O_3\][/tex]
This gives us:
- 4 Fe atoms on the product side (as each [tex]\( Fe_2O_3 \)[/tex] has 2 Fe atoms and we have 2 of them)
- 6 O atoms on the product side (each [tex]\( Fe_2O_3 \)[/tex] has 3 O atoms, so 2 of them will have 6 O atoms)
4. Update Fe atoms to accommodate 4 on each side:
[tex]\[ 4 Fe + O_2 \rightarrow 2 Fe_2O_3 \][/tex]
5. Update O atoms to balance:
We need 6 oxygen atoms on the reactant side, which means we need 3 [tex]\( O_2 \)[/tex] molecules (since each [tex]\( O_2 \)[/tex] provides 2 oxygen atoms):
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
With these steps, the correct balanced chemical equation is:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Therefore, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \)[/tex]
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