To balance the 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 each type of atom is the same on both sides of the equation.
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In \( \text{Au}_2\text{O}_3 \):
- There are 2 gold (Au) atoms.
- There are 3 oxygen (O) atoms.
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To balance the equation:
- We need 2 Au on the right side, so we put a coefficient of 2 in front of Au.
- We need to balance the oxygen. Since there are 3 oxygen atoms in the reactant and O2 contains 2 oxygen atoms, we can use 3/2 (or 1.5) for O2, but that will give us a fraction, which is not conventional in balancing equations. Instead, we can multiply everything through by 2 to eliminate the fraction:
The balanced equation becomes: \[ 2 \text{Au}_2\text{O}_3 \rightarrow 4 \text{Au} + 3 \text{O}_2 \]
So in terms of the coefficients, we have:
- For \( \text{Au}_2\text{O}_3 \): 2
- For \( \text{Au} \): 4
- For \( \text{O}_2 \): 3
Thus, the answer is \(2, 4, 3\).
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