Although thermodynamically feasible, in practice magnesium metal is not used for the reduction of alumina in the metallurgy of aluminium. Why? Answer
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If you compare the magnesium price (about 2$ per pound) to the aluminum price (about $0.80 per pound) you can see it is unprofitable.
Even considering the elements' relative atomic weight, you would still be losing money if you did that and metallurgy is all about business and profit, thus Mg metal is not used for the reduction of Alumina in the metallurgy of Aluminium
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Magnesium is costly and not easily available in free form. So, it is not used for the reduction of alumina in the metallurgy.
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