To determine which of the given equations is balanced, we must ensure that the number of each type of atom on the reactants side is equal to the number of the same type of atom on the products side. Let's analyze each equation step by step.
1. [tex]\(2 \text{Al} + 3 \text{O}_2 \rightarrow \text{Al}_2 \text{O}_3\)[/tex]
- Reactants:
- Aluminum: [tex]\(2 \text{Al}\)[/tex]
- Oxygen: [tex]\(3 \text{O}_2 = 3 \times 2 = 6 \text{O}\)[/tex]
- Products:
- Aluminum in [tex]\(\text{Al}_2 \text{O}_3\)[/tex]: [tex]\(2 \text{Al}\)[/tex]
- Oxygen in [tex]\(\text{Al}_2 \text{O}_3\)[/tex]: [tex]\(3 \text{O}\)[/tex]
Clearly, the number of oxygens is not balanced:
- Reactants: 6 O
- Products: 3 O
Thus, this equation is not balanced.
2. [tex]\(\text{N}_2 + 2 \text{H}_2 \rightarrow 2 \text{NH}_3\)[/tex]
- Reactants:
- Nitrogen: [tex]\(1 \text{N}_2 = 2 \text{N}\)[/tex]
- Hydrogen: [tex]\(2 \text{H}_2 = 2 \times 2 = 4 \text{H}\)[/tex]
- Products:
- Nitrogen in [tex]\(2 \text{NH}_3\)[/tex]: [tex]\(2 \times 1 = 2 \text{N}\)[/tex]
- Hydrogen in [tex]\(2 \text{NH}_3\)[/tex]: [tex]\(2 \times 3 = 6 \text{H}\)[/tex]
The number of hydrogen atoms is not balanced:
- Reactants: 4 H
- Products: 6 H
Thus, this equation is not balanced.
3. [tex]\(\text{CH}_4 + 3 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2 \text{O}\)[/tex]
- Reactants:
- Carbon: [tex]\(1 \text{C}\)[/tex]
- Hydrogen: [tex]\(4 \text{H}\)[/tex]
- Oxygen: [tex]\(3 \text{O}_2 = 3 \times 2 = 6 \text{O}\)[/tex]
- Products:
- Carbon in [tex]\(\text{CO}_2\)[/tex]: [tex]\(1 \text{C}\)[/tex]
- Hydrogen in [tex]\(2 \text{H}_2 \text{O}\)[/tex]: [tex]\(2 \times 2 = 4 \text{H}\)[/tex]
- Oxygen in [tex]\(\text{CO}_2 + 2 \text{H}_2 \text{O}\)[/tex]:
[tex]\(\text{CO}_2 = 2 \text{O}\)[/tex]
[tex]\(2 \text{H}_2 \text{O} = 2 \times 1 = 2 \text{O}\)[/tex]
Total Oxygen = [tex]\(1 \times 2 + 2 \times 1 = 2 + 4 = 4 \text{O}\)[/tex]
The number of oxygen atoms is not balanced:
- Reactants: 6 O
- Products: 4 O
Thus, this equation is not balanced.
4. [tex]\(2 \text{Fe}_2 \text{O}_3 + 3 \text{C} \rightarrow 4 \text{Fe} + 3 \text{CO}_2\)[/tex]
- Reactants:
- Iron: [tex]\(2 \times 2 = 4 \text{Fe}\)[/tex]
- Oxygen: [tex]\(2 \times 3 = 6 \text{O}\)[/tex]
- Carbon: [tex]\(3 \text{C}\)[/tex]
- Products:
- Iron: [tex]\(4 \text{Fe}\)[/tex]
- Oxygen in [tex]\(3 \text{CO}_2\)[/tex]:
[tex]\(3 \times 2 = 6 \text{O}\)[/tex]
- Carbon in [tex]\(3 \text{CO}_2\)[/tex]:
[tex]\(3 \times 1 = 3 \text{C}\)[/tex]
Here, the counts match perfectly:
- Iron: 4 Fe = 4 Fe
- Oxygen: 6 O = 6 O
- Carbon: 3 C = 3 C
This equation is balanced.
Thus, the only balanced equation among the options is:
[tex]\[
2 \text{Fe}_2 \text{O}_3 + 3 \text{C} \rightarrow 4 \text{Fe} + 3 \text{CO}_2
\][/tex]
Therefore, the correct answer is 4.
