Estimate the minimum potential difference needed to reduce `Al_(2)O_(3)` at `500^(@)C` The gibbs energy change for the decomposition reaction `2/3Al_(2)O_(3)rarr4/3Al+O_(2)` is 960 kJ (F=96500 C `mol^(-1))`

Explanation

To estimate the minimum potential difference needed to reduce \( \text{Al}_2\text{O}_3 \) at \( 500^\circ C \), we will follow these steps:

### Step 1: Write the decomposition reaction
The decomposition reaction for aluminum oxide can be represented as:
\[ \frac{2}{3} \text{Al}_2\text{O}_3 \rightarrow \frac{4}{3} \text{Al} + \text{O}_2 \]

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