Question

The Gibbs energy for the decomposition of ${AI}_2{O}_3$ at ${500}^{0}C$ is as fellow:

$\frac{2}{3}{AI}_2{O}_3⟶\frac{4}{3}AI+O_2;{△}_{r}G=+966kJ{mol}^{-1}$.

The potential difference needed for the electrolytic reduction of ${AI}_2{O}_3$ at ${500}^{0}C$ is at least:

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

Answer 1

Answer: (B)

5.0 V

$\frac{2}{3}A{l}_2{O}_3⟶\frac{4}{3}Al+O_2$

$6e^{-}+2A{l}^{+3}⟶2Al$

$6O^{2-}⟶3O_2+6e^{-}$

no. of electrons transferred according to given reaction.

$n=\frac{6}{3}=2e^{-}$ $s$

$\Delta G=nF{E}_{cell}$

$⟹966\times 1000=2\times 96500\times E_{cell}$

$⟹E_{cell}=5$ $Volts$