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The electrolysis of pure alumina is not feasible because:
A) It is a bad conductor of electricity and its fusion temperature is high
B) It is volatile in nature
C) It is decomposed when fused
D) It is amphoteric

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Hint: Aluminium is a shiny, corrosion-resistant metal. It is obtained from the pure alumina. Alumina is an aluminium hydroxide $\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}$ compound. The electrolysis of alumina is difficult to carry out. It is a fine ceramic material. The alumina has high thermal conductivity and high electrical resistance.

Complete step by step answer:
The electrolysis is a process in which the substance is decomposed into its simpler substances when an electric current is passed through it. The ability to form ions or to get decomposed depends on the ability of the substance to carry the electric current.

The aluminium is shiny, soft, corrosion-resistant metal. It is obtained from the bauxite ore $\text{ (A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\text{.x}{{\text{H}}_{\text{2}}}\text{O) }$. The bauxite is purified by the Baeyer’s process to the pure alumina (aluminium oxide). It is a ceramic solid which is partially ionic and predominantly covalent in nature.

Most of the metals are obtained by the electrolysis of its ore.For example, copper, zinc, etc.
The aluminium cannot be procured by the electrolysis of aqueous aluminium salt. This is because the hydronium ions $\text{ }{{\text{H}}_{\text{3}}}{{\text{O}}^{\text{+}}}\text{ }$ in the aqueous oxidized the aluminium formed during the electrolysis.

The alumina $\text{A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}$ is a predominantly covalent compound, it does not decompose in its ions. It is insoluble in water.it has a high electrical resistance even in presence of strong acid.it has an electrical resistivity of about$\text{ 1}\times \text{ 1}{{\text{0}}^{\text{4}}}\text{ }\Omega \text{.cm}\text{. }$.
Pure alumina (aluminium oxide) has a high melting point of $\text{ 207}{{\text{2}}^{\text{0}}}\text{C }$.this temperature is impractical to achieve and it would be costly.

The alumina does not dissolve in water and thus electrolysis is difficult to carry out.
Because of this resistivity towards the electricity, it has various applications such as electrical insulator, high voltage insulator, electronic substrate.it is also used as the insulation for electrical wire.
Therefore, pure alumina is a bad conductor of electricity and has a high fusion temperature.
So, the correct answer is “Option A”.

Note: the electrolysis of alumina can be done when dissolved in molten cryolite and fluorspar $\text{ Ca}{{\text{F}}_{\text{2}}}\text{ }$ . The cryolite $\text{ (N}{{\text{a}}_{\text{2}}}\text{Al}{{\text{F}}_{\text{6}}}\text{) }$ decreases the melting point to about $\text{ 1173 K }$ and thus increase the electrical conductivity .the overall reaction for the electrolysis of fused alumina is as follows:
$\text{ 2A}{{\text{l}}_{\text{2}}}{{\text{O}}_{\text{3}}}\text{ + 3C }\to \text{ 4Al + 3C}{{\text{O}}_{\text{2}}}\text{ }$
This process is called the Hall Heroult process.