The electrochemical extraction of aluminum from bauxite ore involves

The correct option(s) are:
1. the neutralization of aluminate solution by passing CO₂ gas to precipitate hydrated alumina (Al₂O₃·3H₂O).
2. the dissolution of Al₂O₃ in hot aqueous NaOH.
3. the electrolysis of Al₂O₃ mixed with Na₃AlF₆ to give Al and CO₂.

The extraction of aluminum from bauxite ore is primarily carried out in two major industrial stages: the Bayer process (purification of bauxite to obtain pure alumina, Al₂O₃) and the Hall-Héroult process (electrochemical reduction of alumina to aluminum metal).

Let us examine each involved step in detail:

1. Concentration of Bauxite (Bayer Process):
Bauxite contains impurities like Fe₂O₃, SiO₂, and TiO₂. The alumina present in bauxite is amphoteric and dissolves in hot concentrated NaOH solution, leaving impurities behind as red mud.

The chemical reaction for dissolution is:
Al₂O₃(s) + 2NaOH(aq) + 3H₂O(l) → 2Na[Al(OH)₄](aq)

Thus, the dissolution of Al₂O₃ in hot aqueous NaOH is a key step in the extraction process.

2. Precipitation of Hydrated Alumina:
The sodium aluminate solution obtained is neutralized by passing carbon dioxide (CO₂) gas through it. This precipitates hydrated aluminum oxide (Al₂O₃·3H₂O or Al₂O₃·xH₂O).

The chemical reaction for neutralization is:
2Na[Al(OH)₄](aq) + CO₂(g) → Al₂O₃·3H₂O(s) + Na₂CO₃(aq)

Thus, the neutralization of aluminate solution by passing CO₂ gas to precipitate hydrated alumina (Al₂O₃·3H₂O) is also a correct statement regarding the extraction process.

3. Electrochemical Reduction (Hall-Héroult Process):
Pure alumina (Al₂O₃) has a very high melting point (~2072 °C) and is a poor conductor of electricity. Therefore, it is dissolved in a molten mixture of cryolite (Na₃AlF₆) and fluorspar (CaF₂), which lowers the melting temperature to around 950 °C and increases electrical conductivity.

During electrolysis using carbon (graphite) electrodes:
At Cathode: Al³⁺(melt) + 3e^- → Al(l)
At Anode: Carbon anodes react with oxygen released to form CO and CO₂ gas:
C(s) + O^2-(melt) → CO(g) + 2e^-
C(s) + 2O^2-(melt) → CO₂(g) + 4e^-

Overall reaction:
2Al₂O₃ + 3C → 4Al + 3CO₂

Thus, the electrolysis of Al₂O₃ mixed with Na₃AlF₆ to give Al and CO₂ represents the electrochemical extraction step correctly.

Why the remaining option is incorrect:
Direct reduction of Al₂O₃ with coke (C) requires extremely high temperatures (> 2000 ºC) where aluminum forms aluminum carbide (Al₄C₃) instead of pure aluminum metal, making carbothermic reduction unviable commercially.