The Hall-Heroult process is a key step in the extraction of aluminum metal from its ore, bauxite. This process involves the electrolytic reduction of alumina (Al2O3) to aluminum. Let's examine the given options:
- {Cr_2O_3 + 2Al \rightarrow Al_2O_3 + 2Cr} - This reaction describes the thermite reduction of Cr2O3, not the process for aluminum extraction.
- {Cu^{2+} (aq) + H_2(g) \rightarrow Cu(s) + 2H^{+} (aq)} - This is the reduction of copper ions, not related to aluminum extraction.
- {ZnO + C \xrightarrow{Coke, 1673 K} Zn + CO} - This is the reduction of zinc oxide with carbon, typical for zinc extraction.
- {2Al_2O_3 + 3C \rightarrow 4Al + 3CO_2} - This reaction describes the electrolytic reduction of alumina, which is a crucial part of the Hall-Heroult process.
Therefore, the correct option is the fourth one: {2Al_2O_3 + 3C \rightarrow 4Al + 3CO_2}. Here's why this is the Hall-Heroult process:
- In the Hall-Heroult process, alumina is dissolved in molten cryolite and subjected to electrolytic reduction.
- Carbon acts as an electrode, and it gets consumed during the process, forming carbon dioxide as a by-product, which matches the overall reaction.
- This electrolytic reduction is integral to producing aluminum from its ore in an industrial context.
In conclusion, the correct answer is the option: {2Al_2O_3 + 3C \rightarrow 4Al + 3CO_2}, accurately representing the Hall-Heroult process for aluminum extraction.