To balance the chemical equation \( \text{Ag}_2\text{O} \rightarrow \text{Ag} + \text{O}_2 \), we need to ensure that the number of atoms of each element on the left side equals the number on the right side.
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Write down the unbalanced equation: \[ \text{Ag}_2\text{O} \rightarrow \text{Ag} + \text{O}_2 \]
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Count the number of atoms of each element on both sides:
- Left: 2 Ag, 1 O
- Right: 1 Ag, 2 O
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Start by balancing the silver (Ag) atoms:
- To balance the 2 Ag on the left, we put a coefficient of 2 in front of Ag on the right: \[ \text{Ag}_2\text{O} \rightarrow 2\text{Ag} + \text{O}_2 \]
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Now, let's count the elements again:
- Left: 2 Ag, 1 O
- Right: 2 Ag, 2 O
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The oxygen (O) is not balanced. To balance the oxygen, we put a coefficient of \( \frac{1}{2} \) in front of \(\text{O}_2\) on the left side: \[ \text{Ag}_2\text{O} \rightarrow 2\text{Ag} + \frac{1}{2}\text{O}_2 \]
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To avoid using fractions, we can multiply the entire equation by 2 to get whole numbers: \[ 2\text{Ag}_2\text{O} \rightarrow 4\text{Ag} + \text{O}_2 \]
Now, both sides are balanced:
- Left: 4 Ag, 2 O
- Right: 4 Ag, 2 O
The balanced equation is: \[ \boxed{2\text{Ag}_2\text{O} \rightarrow 4\text{Ag} + \text{O}_2} \]