Join the growing community of curious minds on IDNLearn.com and get the answers you need. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.
Sagot :
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.
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.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.
