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 atoms of each element is the same on both sides of the equation.
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Identify the number of atoms of each element:
- On the left:
- Aluminum (Al): 1
- Oxygen (O): 2
- On the right:
- Aluminum (Al): 2
- Oxygen (O): 3
- On the left:
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Balance aluminum atoms: Since there are 2 aluminum atoms in \( \text{Al}_2\text{O}_3 \), we need to put a coefficient of 2 in front of Al on the left side:
\[ 2\text{Al} + \text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \]
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Balance oxygen atoms: Now, we have 2 oxygen atoms from \( \text{O}_2 \) on the left, but we need 3 from \( \text{Al}_2\text{O}_3 \) on the right. To balance the oxygen atoms, we can change the coefficients for both \( \text{O}_2 \) and \( \text{Al}_2\text{O}_3 \).
Since \( \text{O}_2 \) provides oxygen in pairs, we will use 3/2 (which is 1.5) in front of \( \text{O}_2 \) to get 3 oxygen atoms in total:
\( 2\text{Al} + \frac{3}{2}\text{O}_2 \rightarrow \text{Al}_2\text{O}_3 \)
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Clear the fraction: To eliminate the fraction, multiply the entire equation by 2:
\[ 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3 \]
Now, we have:
- Left:
- Aluminum (Al): 4
- Oxygen (O): 6 (from 3 \( \text{O}_2 \))
- Right:
- Aluminum (Al): 4 (from \( 2\text{Al}_2\text{O}_3 \))
- Oxygen (O): 6 (from 2 \( \text{Al}_2\text{O}_3 \))
The balanced equation is:
\[ 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3 \]