Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.
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.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.
