For the formation of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$, values of ${\Delta }_{\mathrm{f}}{\mathrm{G}}^0$ are $540\mathrm{ }\mathrm{k}\mathrm{J}{\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ and $-827\mathrm{ }\mathrm{k}\mathrm{J}{\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$ respectively. What will be the possibility for reaction of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ by Al?

The value of ${\Delta }_r\mathrm{G}°$ for formation of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ is $-540{\mathrm{kJmol}}^{-1}$ is higher than ${\mathrm{Al}}_2{\mathrm{O}}_3$ is $-827\mathrm{ }\mathrm{k}\mathrm{J}{\mathrm{ }\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$. Therefore the reduction of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ with $\mathrm{Al}$ is possible.

${\mathrm{Cr}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+2\mathrm{Al}\left(s\right)\stackrel{\Delta }{⟶}2\mathrm{Cr}\left(l\right)+{\mathrm{Al}}_2{\mathrm{O}}_3$

Hence the correct answer is (A) Reduction of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ by $\mathrm{A}l$ will take place.