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Why can't aluminium be reduced by carbon...

Why can't aluminium be reduced by carbon ?

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If `Al_(2)O_(3)` is reduced by carbon, it will involve one of the following reactions.
`2Al_(2)O_(3)+3C to 4Al+3CO_(2)`
`Al_(2)O_(3)+3C to 2Al+3CO`
As `DeltaG^(@)` for both of there reactions is +ve at all temperatures, there reactions are non-spontaneous. This explains as to why `Al_(2)O_(3)` can.t be reduced by carbon.
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