To determine the correct balanced equation for the reaction of iron (Fe) with atmospheric oxygen (O₂) to form iron oxide (Fe₂O₃), we will follow a systematic approach to ensure that the number of atoms of each element is the same on both sides of the equation:
Given the general, unbalanced chemical equation:
[tex]\[ \text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \][/tex]
We need to balance this equation.
### Step 1: Write down the number of each type of atom in the unbalanced equation.
- On the left side (reactants):
- Fe: 1 atom
- O: 2 atoms (from [tex]\( \text{O}_2 \)[/tex])
- On the right side (products):
- Fe: 2 atoms (from [tex]\( \text{Fe}_2\text{O}_3 \)[/tex])
- O: 3 atoms (from [tex]\( \text{Fe}_2\text{O}_3 \)[/tex])
### Step 2: Balance the iron (Fe) atoms.
Since there are 2 Fe atoms on the right side and only 1 on the left side, we put a coefficient of 2 in front of Fe on the left side:
[tex]\[ 2\text{Fe} + \text{O}_2 \rightarrow \text{Fe}_2\text{O}_3 \][/tex]
Now, the left side has:
- Fe: 2 atoms
- O: 2 atoms
The right side has:
- Fe: 2 atoms
- O: 3 atoms
### Step 3: Balance the oxygen (O) atoms.
There are 3 oxygen atoms on the right side and only 2 oxygen atoms on the left side. To balance the oxygen atoms, we need to find a common multiple for the number of oxygen atoms on both sides:
- The least common multiple of 2 and 3 is 6.
To get 6 oxygen atoms on both sides, we will use coefficients that allow us to multiply as needed. Hence, we need to have 3 [tex]\( \text{O}_2 \)[/tex] molecules (providing 6 oxygen atoms) on the left side and 2 [tex]\( \text{Fe}_2\text{O}_3 \)[/tex] molecules (which contain 6 oxygen atoms) on the right side.
So, we balance the equation as follows:
[tex]\[ 4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3 \][/tex]
### Step 4: Verify the balance of the final equation.
- Left side (reactants):
- Fe: 4 atoms
- O: 6 atoms (from 3 [tex]\( \text{O}_2 \)[/tex])
- Right side (products):
- Fe: 4 atoms (from 2 [tex]\( \text{Fe}_2\text{O}_3 \)[/tex])
- O: 6 atoms (from 2 [tex]\( \text{Fe}_2\text{O}_3 \)[/tex])
Hence, the balanced equation is:
[tex]\[ 4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3 \][/tex]
### Conclusion
The correct balanced equation is:
[tex]\[ \boxed{4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3} \][/tex]
Therefore, the correct choice is:
A. [tex]\( 4 \text{Fe} + 3 \text{O}_2 \rightarrow 2 \text{Fe}_2 \text{O}_3 \)[/tex]
