To balance the equation \( _ \text{Au}_2\text{O}_3 + _ \text{O}_2 \rightarrow _ \text{Au} \), we need to find the correct set of coefficients that maintains the law of conservation of mass.
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We start by balancing the gold (Au) atoms. In \( \text{Au}_2\text{O}_3 \), there are 2 Au atoms. So we place a coefficient of 2 in front of Au on the product side: \[ \text{Au}_2\text{O}_3 + _ \text{O}_2 \rightarrow 2 \text{Au} \]
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Next, we balance the oxygen atoms. In \( \text{Au}_2\text{O}_3 \), there are 3 oxygen atoms. We need 3 oxygen atoms on the reactant side. Each \( \text{O}_2 \) provides 2 oxygen atoms, so we need 1.5 \( \text{O}_2 \) molecules to obtain 3 oxygen atoms. To eliminate the fraction, we can multiply the entire equation by 2: \[ 2 \text{Au}_2\text{O}_3 + 3 \text{O}_2 \rightarrow 4 \text{Au} \]
Now, our balanced equation looks like this: \[ 2 \text{Au}_2\text{O}_3 + 3 \text{O}_2 \rightarrow 4 \text{Au} \]
Thus, the coefficients arranged from left to right are: 2, 3, 4.
Since this option is not on the list you provided, it seems there may be a misunderstanding about the original equation format or purpose. If the original question was to match a set of coefficients from given options, none of the provided options is correct based on standard balancing rules.
Could you confirm whether the original equation was accurately transcribed (i.e., did it include any additional molecules or elements), or possibly clarify the options? If \( O_2 \) is indeed the only reactant other than \( Au_2O_3 \) and \( Au \) is the only product, balancing leads us to 2, 3, and 4, respectively.