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Q.
Carbon cannot be used in the reduction of $Al_{2}O_{3}$ because:
General Principles and Processes of Isolation of Elements
Solution:
In Ellingham diagram, the $\Delta_f G^{o}$ of $Al_{2}O_{3}$ lies below that of $CO_{2}$. If reduction is carried out at very high temperature, the $Al$ produced will react with carbon forming $Al_{4}C_{3}$.