To balance the chemical equation \( \text{Au}_2\text{O}_3 \rightarrow \text{Au} + \text{O}_2 \) according to the law of conservation of mass, we need to ensure that the number of atoms of each element on the reactants' side matches that on the products' side.
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Identify the number of atoms of each element:
- In \( \text{Au}_2\text{O}_3 \):
- Gold (Au): 2
- Oxygen (O): 3
- In \( \text{Au} + \text{O}_2 \):
- Gold (Au): 1 (from Au)
- Oxygen (O): 2 (from O2)
- In \( \text{Au}_2\text{O}_3 \):
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Balancing gold (Au):
- We have 2 Au on the left, so we need 2 Au on the right. We put a coefficient of 2 in front of Au: \[ \text{Au}_2\text{O}_3 \rightarrow 2\text{Au} + \text{O}_2 \]
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Balancing oxygen (O):
- Now we have 3 O on the left and 2 O on the right. We must find a common way to balance them. The least common multiple of 3 and 2 is 6.
- Therefore, we put a coefficient of 2 in front of \( \text{Au}_2\text{O}_3 \) and a coefficient of 3 in front of \( \text{O}_2 \): \[ 4\text{Au} + 3\text{O}_2 \]
Here’s the balanced equation: \[ 2\text{Au}_2\text{O}_3 \rightarrow 4\text{Au} + 3\text{O}_2 \]
Thus, the coefficients from left to right are: 2, 4, 3.
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