How would you describe and diagram the electrolysis of aluminium oxide?

Aluminium is prepared by the electrolysis of aluminium oxide, #"Al"_2"O"_3#.

#"Al"_2"O"_3# has a melting point of 2072 °C, so it would be expensive to melt it.

Instead, it is dissolved in molten cryolite, #"Na"_3"AlF"_6#, which melts at 1012 °C.

The dissolved #"Al"_2"O"_3# lowers the melting point further to about 950 °C.

The anodes of the electrolysis cell are made of graphite (carbon), and the graphite lining of a steel tank also serves as the cathode.

The #"Al"^"3+"# ions move to the cathode, and the #"O"^"2-"# ions move to the anode.

The cell reactions are

#"At the cathode": 4×["Al"^"3+" + "3e"^"-" color(white)(mll)→ "Al"]#
#"At the anode": color(white)(m)3×["2O"^"2-" color(white)(mmmmll)→ "O"_2 + "4e"^"-"]#
#"Cell reaction": color(white)(mmmm)"4Al"^(3+) + "3O"^"2-" → "4Al" + "3O"_2#

Aluminium (m.p. 933 °C) forms at the cathode and sinks to the bottom of the tank, where it is tapped off as the pure molten metal.

Oxygen forms at the anodes. It reacts with the graphite, forming carbon dioxide, and the electroded gradually burn away.

The following video give a more detailed description of the extraction of aluminium.