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The Hall-Heroult process is the industrial method used for the extraction of aluminium from its ore (alumina, $$Al_2O_3$$).
Let us examine each option:
Option A: $$Cr_2O_3 + 2Al \to Al_2O_3 + 2Cr$$ - This is the thermite reaction (aluminothermic process) used for the reduction of chromium oxide.
Option B: $$2Al_2O_3 + 3C \to 4Al + 3CO_2$$ - This represents the Hall-Heroult process. In this process, purified alumina ($$Al_2O_3$$) is dissolved in molten cryolite ($$Na_3AlF_6$$) and electrolyzed using carbon electrodes. At the cathode, aluminium is deposited, and at the carbon anode, oxygen is released which reacts with the carbon anode to form $$CO_2$$. The overall reaction is as shown.
Option C: $$FeO + CO \to Fe + CO_2$$ - This is the reduction of iron oxide in the blast furnace during iron extraction.
Option D: $$2[Au(CN)_2]^-(aq) + Zn(s) \to 2Au(s) + [Zn(CN)_4]^{2-}$$ - This is the MacArthur-Forrest process (cyanide process) used for gold extraction.
The correct answer is Option B: $$2Al_2O_3 + 3C \to 4Al + 3CO_2$$.
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