What is the primary ore for aluminium extraction, its formula, and the subsequent chemical processes involved?

a)

i) The main ore X used in the extraction of aluminium is bauxite. Its formula is:

$$\boxed{\text{Al}_2\text{O}_3}$$

ii)

a) The main residue formed after filtration in step I is iron(III) oxide.

$$\boxed{\text{Fe}_2\text{O}_3}$$

b) Substance Q is hot concentrated sodium hydroxide.

$$\boxed{\text{NaOH}}$$

iii) This part is not visible in the image.

iv) The sodium aluminate in Solution R is separated from the impurity silicon(IV) oxide by cooling and diluting the solution, then seeding it with aluminium hydroxide crystals. This causes aluminium hydroxide to precipitate, which is then filtered off. The sodium silicate (formed from silicon(IV) oxide) remains in solution.

v) The purpose of the addition of substance S in step III is to lower the melting point of aluminium oxide from over $2000^\circ\text{C}$ to about $950^\circ\text{C}$ and to act as a solvent for the aluminium oxide, allowing it to conduct electricity. Substance S is cryolite ($\text{Na}_3\text{AlF}_6$).

b)

i) The anode in the extraction of aluminium is replaced periodically because the carbon anodes react with the oxygen gas produced during electrolysis at high temperatures, forming carbon dioxide gas. This causes the anodes to be consumed and thus they must be replaced regularly.

ii) The equation for the formation of Aluminium at the cathode is:

$$\boxed{\text{Al}^{3+}(l) + 3e^- \rightarrow \text{Al}(l)}$$