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Give the chemical reactions involved in the leaching of alumina from bauxite

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`Al_(2)O_(3)(s)+2NaOH(aq)+3H_(2)O(l)to2Na[Al(OH)_(4)]`
`2Na[Al(OH)_(4)]+CO_(2)toAl_(2)O_(3).xH_(2)O+2NaHCO_(3)`
`Al_(2)O_(3).xH_(2)O(s)overset(1470K)(to)Al_(2)O_(3)(s)+xH_(2)O(g)`
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