Determine whether or not is possible for sodium to reduce aluminium oxide to aluminium at `298K`. Also, calculate equilibrium constant for this reaction at `298K`.
`Delta_(f)G^(Theta)Al_(2)O_(3)(s) =- 1582 kJ mol^(-1)`
`Delta_(f)G^(Theta)Na_(2)O(s) =- 377.7 kJ mol^(-1)`

Explanation

To determine whether sodium can reduce aluminum oxide (Al₂O₃) to aluminum at 298 K, we need to calculate the standard Gibbs free energy change (ΔG°) for the reaction and check its sign. If ΔG° is negative, the reaction is feasible; if it is positive, the reaction is not feasible.

### Step 1: Write the balanced chemical equation
The balanced reaction for the reduction of aluminum oxide by sodium can be written as:
\[ \text{Al}_2\text{O}_3(s) + 6\text{Na}(s) \rightarrow 2\text{Al}(s) + 3\text{Na}_2\text{O}(s) \]

### Step 2: Identify the standard Gibbs free energy of formation values
From the problem, we have the following values:
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