$(i)$ ${\text{C}}{{\text{r}}_2}{{\text{O}}_3} + 2{\text{Al}}({\text{R}}{\text{.A}}.)\xrightarrow{\Delta }{\text{A}}{{\text{l}}_2}{{\text{O}}_3} + 2{\text{Cr}}$ ;       $\Delta H=-\mathrm{ve}$ $(ii)$  $Mg$ is extracted by electrolysis of fused $\mathrm{MgCl}_{2}$ and $NaCl$ $(iii)$ ${\text{PbS}} + \frac{3}{2}{{\text{O}}_2} \to {\text{PbO}} + {\text{S}}{{\text{O}}_2}$ ${\text{PbO}} + {\text{C}} \to {\text{Pb}} + {\text{CO}}$ $(iv)$ Red Bauxite is purified by Baeyer's process