The value of ${\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\circ }$for formation of ${\mathrm{Cr}}_2{\mathrm{O}}_3\text{ is }-540{\mathrm{kJmol}}^{-1}$ and that ${\mathrm{Al}}_2{\mathrm{O}}_3\text{ is }-827\mathrm{kJ}{\mathrm{mol}}^{-1}$What is the value of ${\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\circ }$ for the reaction? 
$\frac{4}{3}\mathrm{Al}\left(\mathrm{s}\right)+\frac{2}{3}{\mathrm{Cr}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)\to \frac{2}{3}{\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+\frac{4}{3}\mathrm{Cr}\left(\mathrm{s}\right)$

The two equation are: 
$$\begin{gathered} \frac{4}{3}\mathrm{Al}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to \frac{2}{3}{\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathrm{s}\right),{\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\circ }=-827{\mathrm{kJmol}}^{-1} ...\left(1\right) \\ \frac{4}{3}\mathrm{Cr}\left(\mathrm{s}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to \frac{2}{3}{\mathrm{Cr}}_2{\mathrm{O}}_3\left(\mathrm{s}\right),{\mathrm{\Delta }}_{\mathrm{f}}{\mathrm{G}}^{\circ }=-540\mathrm{kJmol}-1 ...\left(2\right) \end{gathered}$$
Subtracting equation (ii) from equation (i) we have,  
$$\begin{gathered} \frac{4}{3}\mathrm{Al}\left(\mathrm{s}\right)+\frac{2}{3}{\mathrm{Cr}}_2{\mathrm{O}}_3\left(\mathrm{s}\right) \\ \to \frac{2}{3}{\mathrm{Al}}_2{\mathrm{O}}_3\left(\mathrm{s}\right)+\frac{4}{3}\mathrm{Cr}\left(\mathrm{s}\right),{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{G}}^{\circ }=-287\mathrm{kJ}{\mathrm{mol}}^{-1} \end{gathered}$$