Certainly! Let's solve this step by step.
### Step 1: Write Down the Unbalanced Chemical Equation
We start with the given chemical equation:
[tex]\[ \text{Fe}_2\text{O}_3 + \text{H}_2 \rightarrow \text{Fe} + \text{H}_2\text{O} \][/tex]
### Step 2: List the Number of Atoms of Each Element on Both Sides
#### Reactants:
- Fe: 2
- O: 3
- H: 2
#### Products:
- Fe: 1
- O: 1
- H: 2
### Step 3: Balance the Equation
To balance the equation, we'll need to ensure the number of atoms of each element is the same on both sides.
#### 1. Balance the Iron (Fe) Atoms:
Initially, there are 2 Fe atoms on the reactants side and 1 Fe atom on the products side. To balance Fe, we place a coefficient of 2 in front of Fe on the products side:
[tex]\[ \text{Fe}_2\text{O}_3 + \text{H}_2 \rightarrow 2\text{Fe} + \text{H}_2\text{O} \][/tex]
#### 2. Balance the Oxygen (O) Atoms:
Now we have 3 O atoms on the reactants side and 1 O atom on the products side. To balance O, we place a coefficient of 3 in front of H₂O on the products side:
[tex]\[ \text{Fe}_2\text{O}_3 + \text{H}_2 \rightarrow 2\text{Fe} + 3\text{H}_2\text{O} \][/tex]
#### 3. Balance the Hydrogen (H) Atoms:
Finally, we have 2 H atoms on the reactants side (from H₂) and 6 H atoms on the products side (from 3 H₂O). To balance H, we need a coefficient of 3 in front of H₂ on the reactants side:
[tex]\[ \text{Fe}_2\text{O}_3 + 3\text{H}_2 \rightarrow 2\text{Fe} + 3\text{H}_2\text{O} \][/tex]
### Step 4: Check the Balance
Let's verify that the number of atoms of each element is now balanced on both sides.
#### Reactants:
- Fe: 2
- O: 3
- H: 6
#### Products:
- Fe: 2
- O: 3
- H: 6
Since the number of each type of atom is equal on both sides, the equation is now balanced.
### Final Balanced Equation:
[tex]\[ \text{Fe}_2\text{O}_3 + 3\text{H}_2 \rightarrow 2\text{Fe} + 3\text{H}_2\text{O} \][/tex]
This is the balanced chemical equation for the reaction of [tex]\( \text{Fe}_2\text{O}_3 \)[/tex] with [tex]\( \text{H}_2 \)[/tex].
