The Gibbs' energy for the decomposition of $ {Al2O3 }$ at $500^{\circ} C$ is as follows:
$ { \frac{2}{3} Al_2 O_3 -> \frac{4}{3} Al + O_2 ;
\Delta_r G = + 960 \, kJ \, mol^{-1} }$
The potential difference needed for the electrolytic reduction of aluminium oxide $ {(Al2O3)}$ at $500^{\circ} C$ is at least