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Determine whether or not is possible for...

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)`

Text Solution

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The reaction is : `Al_(2)O_(3)(s)+6Na(s)rarr 3Na_(2)O(s)+2Al(s)`
`Delta_(r )G^(Θ)=3xxDelta_(f)G^(Θ)(Na_(2)O)-Delta_(f)G^(Θ)(Al_(2)O_(3))=3xx(-377.07)-(-1582.0)=+451.21 kJ mol^(-1)`
Hence the reaction cannot occur, since `Delta G^(Θ)` is positive.
Also : `Delta_(r )G^(Θ)=-2.303 RT log_(10)K`
`rArr 451.21 =-2.303xx8.314xx10^(-3)xx298 log_(10)K_(eq)`
`rArr log_(10)K_(eq)=-79.0 rArr K_(eq)=1.0xx10^(-79)`
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