In the electrolyic process for the extraction of aluminium the electrolyte is:

A molten mixture of $Al_2O_3$ and $Na_3AlF_6$

The correct answer is Option 3. A molten mixture of $Al_2O_3$ and $Na_3AlF_6$.

In the electrolytic extraction of aluminium, the process used is the Hall-Héroult process, which involves the electrolysis of a molten mixture. Here's how it works:

\(Al_2O_3\) (Alumina): Aluminium oxide is the main ore of aluminium. It is obtained from bauxite through the Bayer process. However, alumina alone has a very high melting point (about 2050°C), making it inefficient for electrolysis at such high temperatures.

\(Na_3AlF_6\) (Cryolite): To lower the melting point of the mixture, cryolite \((Na_3AlF_6)\) is added. This helps bring down the operating temperature to about 950°C–1000°C and improves the electrical conductivity of the mixture.

Electrolysis: During the electrolysis of this molten mixture:

Aluminium is deposited at the cathode (bottom of the electrolytic cell).

Oxygen is liberated at the anode, where it reacts with carbon (graphite electrodes) to form \(CO_2\).

This molten mixture of \(Al_2O_3\) and \(Na_3AlF_6\) is crucial for the efficient and economical extraction of aluminium in large quantities.

Incorrect Options:

\(Al(OH)_3\) in NaOH Solution: This is part of the Bayer process for refining bauxite to obtain pure \(Al_2O_3\), but not for the electrolytic extraction of aluminium.

An aqueous solution of \(Al_2(SO_4)_3\): Aluminium cannot be extracted from an aqueous solution because water would be electrolyzed before the aluminium.

A molten mixture of \(Al_2O_3\) and \(Al(OH)_3\): This mixture is not used because \(Al(OH)_3\) does not help in lowering the melting point or improving the conductivity of the mixture.