For the decomposition of $Al_2O_3$ at $500\,^{\circ}C$,the Gibbs energy change is given by $\frac{2}{3} Al_2O_3 \rightarrow \frac{4}{3} Al + O_2$,$\Delta G = 966 \, kJ \, mol^{-1}$. What is the potential difference (in $V$) required for the electrolytic reduction of $Al_2O_3$ at $500\,^{\circ}C$?

• A
  $5$
• B
  $4.5$
• C
  $3$
• D
  $2.5$