Let's balance the chemical equation step-by-step.
The unbalanced equation is:
[tex]\[ Fe_2 O_3 + CO \rightarrow Fe + CO_2 \][/tex]
### Step 1: Balance the Iron (Fe) atoms
We need to have the same number of iron (Fe) atoms on both sides of the equation. On the left side, we have 2 iron atoms (in [tex]\(Fe_2 O_3\)[/tex]) and on the right side, there's only 1 iron atom in [tex]\(Fe\)[/tex]. Therefore, we'll place a coefficient of 2 in front of [tex]\(Fe\)[/tex] on the right side.
So, the equation becomes:
[tex]\[ Fe_2 O_3 + CO \rightarrow 2Fe + CO_2 \][/tex]
### Step 2: Balance the Oxygen (O) atoms
Next, we balance the oxygen atoms. On the left side, we have a total of 3 oxygen atoms from [tex]\(Fe_2 O_3\)[/tex] and 1 oxygen atom from CO, which makes a total of 4 oxygen atoms. On the right side, we have 2 oxygen atoms in each [tex]\(CO_2\)[/tex]. To balance the oxygen atoms, we'll need 3 [tex]\(CO_2\)[/tex] molecules on the right side since we need at least 3 x 2 = 6 oxygen atoms on the right side, but placing 3 [tex]\(CO_2\)[/tex] molecules also balances the oxygen appropriately.
So, the equation now is:
[tex]\[ Fe_2 O_3 + 3CO \rightarrow 2Fe + 3CO_2 \][/tex]
### Step 3: Balance the Carbon (C) atoms
Lastly, we balance the carbon atoms. On the left side, we have 3 carbon atoms from 3 [tex]\(CO\)[/tex] molecules, and on the right side, we also have 3 carbon atoms in the 3 [tex]\(CO_2\)[/tex] molecules.
Now, we see that the number of Fe, O, and C atoms are balanced on both sides:
- Fe: 2 atoms on both sides
- O: 6 atoms on both sides
- C: 3 atoms on both sides
Thus, the balanced equation is:
[tex]\[ Fe_2 O_3 + 3CO \rightarrow 2Fe + 3CO_2 \][/tex]
That completes our balanced chemical equation.
