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In the electrolysis of alumina using cryolite, the reaction that takes place at cathode is?
A) \[4{H_2}O{\text{ }} + {\text{ }}4e - \to 2{H_2} + {\text{ }}4OH - \]
B) \[4A{l^{3 + }} + {\text{ }}12e - \to 4Al\]
C) \[6{F_2} + {\text{ }}2A{l_2}{O_3} \to 4A{l_3} + {\text{ }}3{O_2}\]
D) \[12F - \to 6{F_2} + {\text{ }}12e - \]

Answer
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Hint:Electrolysis of alumina/cryolite gives aluminium at cathode and oxygen at anode. Aluminium is obtained through reduction of Al(III) cations. Oxygen is obtained through oxidation of oxide ions.

Complete answer:
Cryolite is sodium aluminium-fluoride\[\left( {N{a_3}Al{F_6}} \right)\]​. It is an ore of aluminium. Cryolite and fluorspar acts as a solvent.The electrolytic reduction of alumina is done by hall heroult's process. The reaction at cathode is the reduction of aluminium(III) ions to aluminium metal. In this method, each Al(III) cation gains three electrons to form Al metal.
\[2A{l^{3 + }} + 6e - \to 2Al\;\].
Thus pure aluminium metal is formed at the cathode.

Aluminium oxide ( \[A{l_2}{O_3}\] ) is an ionic compound. When you melt it, you form \[A{l^{3 + }}\]and \[{O^{2 - }}\;\] ions, which are free to move and conduct electricity. In the solid state, the ions are not free and they cannot conduct electricity.

So the reaction taking place at cathode is:
\[\;4A{l^{3 + }} + {\text{ }}12e - \to 4Al\]

Additional information: We can write the reaction taking place at anode as \[6{O^{2 - }} - 12e - \to 3{O_{_2}}\] During this reaction, oxygen is given off at the carbon anode (positive electrode). Hot oxygen reacts with the carbon anode to form carbon dioxide gas. Hence, carbon dioxide is also given off at the carbon anode. You can observe that the oxygen evolved at the anode escapes as a gas or reacts with the carbon anode. The anode is thus oxidized to carbon monoxide which either burns giving \[C{O_2}\] ​ or escapes. Thus, you need to replace anode as it is consumed periodically.

Hence the correct answer is option ‘B’.

Note:Alumina has a very high melting point. During electrolysis of alumina, cryolite is added to decrease the melting point of alumina. Cryolite also increases the conductivity of alumina.