c
at anode \(\left[2O^{2-}+4 e^{-} \rightarrow O_{2}\right] \times 3\)

at cathode \(\left[\mathrm{Al}^{3+} \rightarrow \mathrm{Al}+3 \mathrm{e}^{-}\right] \times 4\)

Net reaction

\(4 \mathrm{Al}+6O^{2-} \rightarrow 3O_{2}+4 \mathrm{Al}\)

\(\frac 43 A l+2O^{2} \rightarrow O_{2}+\frac 43 A l\)

\(n=\frac {12}3=4\)

\(\Delta G^{\circ}=-n F E^{\circ}\)

\(\Delta \mathrm{G}^{\circ}=+960 \mathrm{kJ} \mathrm{mol}^{-1}\)

\(=960 \times 1000 \mathrm{J} \mathrm{mol}^{-1}\)

\(n=4\)

\(\mathrm{F}=96500\) Coulomb

\(960 \times 1000=-4 \times 96500 \times E^{\circ}\)

\(E^{\circ}=-\frac{960000}{4 \times 96500}\)

\(=-2.48 \mathrm{V}\)

potential difference \(\approx 2.5 \mathrm{V}\)