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To determine which chemical equation illustrates the law of conservation of matter, we need to ensure that the number of atoms for each element is balanced on both sides of the equation. Let's analyze each option:
### Option A: [tex]\(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 4 atoms
- Oxygen (O): [tex]\(3 \text{O}_2 = 3 \times 2 = 6\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
This equation balances correctly as there are equal numbers of Aluminum and Oxygen atoms on both sides.
### Option B: [tex]\(2 \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 2 atoms
- Oxygen (O): [tex]\(1 \text{O}_2 = 1 \times 2 = 2\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 1 = 2\)[/tex] atoms
- Oxygen (O): [tex]\(3 \times 1 = 3\)[/tex] atoms
This equation does not balance, because there are 2 oxygen atoms on the left but 3 oxygen atoms on the right.
### Option C: [tex]\(2 \text{Al} + 3 \text{O}_2 \rightarrow \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 2 atoms
- Oxygen (O): [tex]\(3 \text{O}_2 = 3 \times 2 = 6\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 1 = 2\)[/tex] atoms
- Oxygen (O): [tex]\(3 \times 1 = 3\)[/tex] atoms
This equation does not balance, because there are 6 oxygen atoms on the left but only 3 oxygen atoms on the right.
### Option D: [tex]\(4 \text{Al} + \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 4 atoms
- Oxygen (O): [tex]\(1 \text{O}_2 = 1 \times 2 = 2\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
This equation does not balance, because there are 2 oxygen atoms on the left but 6 oxygen atoms on the right.
After checking all the options, we can see that only Option A satisfies the law of conservation of matter, where the number of atoms of each element is the same on both sides of the equation.
Therefore, the correct answer is Option A: [tex]\(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex].
### Option A: [tex]\(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 4 atoms
- Oxygen (O): [tex]\(3 \text{O}_2 = 3 \times 2 = 6\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
This equation balances correctly as there are equal numbers of Aluminum and Oxygen atoms on both sides.
### Option B: [tex]\(2 \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 2 atoms
- Oxygen (O): [tex]\(1 \text{O}_2 = 1 \times 2 = 2\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 1 = 2\)[/tex] atoms
- Oxygen (O): [tex]\(3 \times 1 = 3\)[/tex] atoms
This equation does not balance, because there are 2 oxygen atoms on the left but 3 oxygen atoms on the right.
### Option C: [tex]\(2 \text{Al} + 3 \text{O}_2 \rightarrow \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 2 atoms
- Oxygen (O): [tex]\(3 \text{O}_2 = 3 \times 2 = 6\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 1 = 2\)[/tex] atoms
- Oxygen (O): [tex]\(3 \times 1 = 3\)[/tex] atoms
This equation does not balance, because there are 6 oxygen atoms on the left but only 3 oxygen atoms on the right.
### Option D: [tex]\(4 \text{Al} + \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex]
- Left side:
- Aluminum (Al): 4 atoms
- Oxygen (O): [tex]\(1 \text{O}_2 = 1 \times 2 = 2\)[/tex] atoms
- Right side:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
This equation does not balance, because there are 2 oxygen atoms on the left but 6 oxygen atoms on the right.
After checking all the options, we can see that only Option A satisfies the law of conservation of matter, where the number of atoms of each element is the same on both sides of the equation.
Therefore, the correct answer is Option A: [tex]\(4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3\)[/tex].
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