Question

The Gibbs energy for the decomposition of $A{l}_2{O}_3$ at $500$ ${}^{o}C$ is as follows:
$2/3A{l}_2{O}_3\to 4/3Al+O_2;{\Delta }_{r}G=+966$ kJ/mol.
The potential difference needed for electrolytic reduction of $A{l}_2{O}_3$ at ${500}^o$C is at least:

• A. $5.0$V
• B. $4.5$V
• C. $3.0$V
• D. $2.5$V

Answer 1

The correct option is D $2.5$V

The ionic reactions are,

$\frac{2}{3}\times \left(2A{l}^{3+}\right)+4e^{-}\to \frac{4}{3}Al$

$\frac{2}{3}\times \left(3O^{2-}\right)\to O_2+4e^{-}$

Thus the number of electrons transferred, $n=4$

$\Delta F=-nFe=-4\times 96500\times E$

$966\times {10}^3=-4\times 96500\times E$

$⟹E=-\frac{966\times {10}^3}{4\times 96500}=-2.5V$