Given that $\Delta G_{\mathrm{r}}^{\mathrm{r}}\left(\mathrm{Fe}_2 \mathrm{O}_3\right)=-741.0 \mathrm{~kJ} / \mathrm{mol}$ and that $\Delta G_{\mathrm{i}}^{\mathrm{z}}\left(\mathrm{Al}_2 \mathrm{O}_3\right)=-1576.4 \mathrm{~kJ} / \mathrm{mol}$, calculate $\Delta G^{\circ}$ for the following reactions at $25^{\circ} \mathrm{C}$ :
(a) $2 \mathrm{Fe}_2 \mathrm{O}_3(s) \longrightarrow 4 \mathrm{Fe}(s)+3 \mathrm{O}_2(g)$
(b) $2 \mathrm{Al}_2 \mathrm{O}_3(s) \longrightarrow 4 \mathrm{Al}(s)+3 \mathrm{O}_2(g)$