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)AI_(2)O_(3)(s) =- 1582 kJ mol^(-1)`
`Delta_(f)g^(Theta)Na_(2)O(s) =- 377.7 kJ mol^(-1)`

Explanation

The reaction is:
`AI_(2)O_(3)(s) +6Na(s) rarr 3Na_(2)O(s) +2AI(s)`
`Delta_(r)G^(Theta) = Delta_(f)G^(Theta) (Na_(2)O) - Delta_(f)G^(Theta)(AI_(2)O_(3))`
`=3 xx (-377.07) -(-1582.0) =+ 451.21 kJ mol^(-1)`
Hence, the reaction cannot occur, since `DeltaG^(Theta)` is positive.
Also,
`Delta_(r)G^(Theta) = 2.303 RT log K`
`rArr 451.21 =- 2.303 xx 8.314 xx 10^(-3) xx 298 log K_(eq)`
`rArr log K_(eq) =- 79.0 rArr K_(eq) = 1.0 xx 10^(-79)`