Write the formula of Cryolite. Give its function in the extraction of Aluminium.

Hint: We need to know what Cryolite is along with its formula and understand its function in the extraction of Aluminium. Sodium aluminium hexafluoride is an inorganic chemical found in the mineral cryolite and is widely employed in the industrial manufacturing of aluminium metal. It was once used as an aluminium ore and later in the electrolytic processing of bauxite, an aluminum-rich oxide mineral. The use of cryolite as a flux to dissolve the oxide mineral solved the problem of separating aluminium from oxygen in oxide ore(s).

Complete answer:
The inorganic compound sodium aluminium hexafluoride has the formula \[N{a_3}Al{F_6}\]. This white solid, discovered by Peder Christian Abildgaard $\left( {1740 - 1801} \right)$ in $1799$ as the mineral cryolite, occurs naturally and is widely employed in the industrial manufacturing of aluminium metal. The sodium salt of the hexafluoroaluminate ion is the compound.
The use of cryolite as a flux to dissolve the oxide mineral solved the problem of separating aluminium from oxygen in oxide ore(s). Pure cryolite melts at $1012^\circ C\left( {1285K} \right)$, and it dissolves the aluminium oxides well enough to allow for facile electrolytic extraction of the metal. Both heating the materials and electrolysis need a significant amount of energy, but it is far more energy-efficient than melting the oxides themselves. Synthetic sodium aluminium fluoride is made from the common mineral fluorite since real cryolite is currently too scarce to be utilised for this purpose.

Note:
We must note that in the Hall–Héroult method, molten cryolite is utilised as a solvent for aluminium oxide. It lowers the melting point of molten aluminium oxide from $2000$ to $2500$ degrees Celsius to $900 - 1000^\circ C$ and boosts its conductivity, making aluminium extraction more cost-effective. The Hall–Héroult process is the most used industrial smelting method for aluminium. It entails dissolving aluminium oxide (alumina) in molten cryolite and electrolyzing the molten salt bath, often in a purpose-built cell, which is derived most frequently from bauxite, aluminium's principal resource, using the Bayer process. At $940 - 980^\circ C$, the Hall–Héroult method generates $99.5 - 99.8$ percent pure aluminium on an industrial scale.