To balance the equation Al₂O₃ + Au + O₂, we first identify the reactants and products.
The equation can be represented as:
\[\text{Al}_2\text{O}_3 + \text{Au} + \text{O}_2 \rightarrow \text{products}\]
Since you asked for coefficients while maintaining the law of conservation of mass, we should balance the number of atoms for each element on both sides.
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From the left:
- Aluminum (Al): 2 from Al₂O₃
- Oxygen (O): 3 from Al₂O₃ + 2 from O₂ (which we'll need to determine)
- Gold (Au): 1 (based on the coefficients we set)
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From the right:
- We should have an equal number of each type of atom.
To balance this properly:
- There are 2 aluminums, so we need 2 Au,
- There are a total of 5 oxygens (3 from Al₂O₃ and 2 from O₂), which suggests we need to adjust the coefficients accordingly.
Let's denote the coefficients:
- For Al₂O₃, let it be \(a\),
- For Au, let it be \(b\),
- For O₂, let it be \(c\).
The balanced equation could come to be:
2 Al₂O₃ + 4 Au + 3 O₂ → 2 Al + 4 Au + 6 O
With that:
- Al: 2 on left and 2 on right,
- O: 6 on the left and 6 on the right,
- Au: 4 on the left and 4 on the right.
Thus, the coefficients from left to right necessary for balancing would be:
2, 4, 3.