To balance the chemical equation \( \text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \), we need to ensure that the number of each type of atom is the same on both sides of the equation.
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Count the atoms:
- On the left side, we have:
- Aluminum (Al): 1
- Oxygen (O): 2
- On the right side, we have:
- Aluminum (Al): 2
- Oxygen (O): 3
- On the left side, we have:
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Balance aluminum (Al):
- Since there are 2 Al atoms in \( \text{Al}_2\text{O}_3 \), we need 2 Al atoms on the left side. So, we put a coefficient of 2 in front of Al: \[ 2\text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \]
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Count the atoms again:
- Left side:
- Al: 2
- O: 2
- Right side:
- Al: 2
- O: 3
- Left side:
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Balance oxygen (O):
- To balance the oxygen, we need to adjust the amount of \( \text{O}_2 \). Since \( \text{Al}_2\text{O}_3 \) has 3 O atoms, we need \( \frac{3}{2} \) \( \text{O}_2 \) on the left. However, to avoid fractional coefficients, we multiply the entire equation by 2: \[ 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3 \]
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Final count:
- Left side:
- Al: 4
- O: 6 (3 \( \text{O}_2 \))
- Right side:
- Al: 4 (2 \( \text{Al}_2\text{O}_3 \))
- O: 6 (2 * 3 from \( \text{Al}_2\text{O}_3 \))
- Left side:
The balanced equation is: \[ 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3 \]
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