Coke does not cause reduction of `Al_(2)O_(3)`. Explain `Delta G^(@)` (in kJ `mol^(-1)`) for `Al_(2)O_(3)` : -1582, CO = - 137.2.

Explanation

To explain why coke (carbon) does not cause the reduction of \( \text{Al}_2\text{O}_3 \), we will analyze the Gibbs free energy change (\( \Delta G^0 \)) for the reaction. The given values are \( \Delta G^0 \) for \( \text{Al}_2\text{O}_3 \) as -1582 kJ/mol and for CO as -137.2 kJ/mol.

### Step-by-Step Solution:

1. **Write the Reaction**:
The reduction of aluminum oxide by carbon can be represented as:
\[
\text{Al}_2\text{O}_3 + 3\text{C} \rightarrow 2\text{Al} + 3\text{CO}
...