Embibe Experts Solutions for Chapter: General Principles and Processes of Isolation of Metals (metallurgy), Exercise 1: WBJEE 2019

The reaction for obtaining the metal $\left(\mathrm{M}\right)$ from its oxide $\left({\mathrm{M}}_2{\mathrm{O}}_3\right)$ ore is given by

${\mathrm{M}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+2\mathrm{Al}\left(l\right)\stackrel{ \mathrm{Heat} }{⟶}{\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathit{l}\right)+2\mathrm{M}\left(\mathrm{s}\right)$

( $\mathrm{s}=$solid,$l=$liquid)  in that case, $\mathrm{M}$ is

In the extraction of $\mathrm{Ca}$ by electro reduction of molten ${\mathrm{CaCl}}_2$ some ${\mathrm{CaF}}_2$ is added to the electrolyte for the following reason:

In the Bayer's process, the leaching of alumina is done by using