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On the basis of information available from the reaction
$\frac{4}{3} \mathrm{Al}+\mathrm{O}_2 \rightarrow \frac{2}{3} \mathrm{Al}_2 \mathrm{O}_3, \Delta \mathrm{G}=-827 \mathrm{~kJ} \mathrm{mol}^{-1}$
of $\mathrm{O}_2$, the minimum e.m.f required to carry out an electrolysis of $\mathrm{Al}_2 \mathrm{O}_3$ is $(\mathrm{F}=$ $\left.96500 \mathrm{C} \mathrm{mol}^{-1}\right):$
Options:
$\frac{4}{3} \mathrm{Al}+\mathrm{O}_2 \rightarrow \frac{2}{3} \mathrm{Al}_2 \mathrm{O}_3, \Delta \mathrm{G}=-827 \mathrm{~kJ} \mathrm{mol}^{-1}$
of $\mathrm{O}_2$, the minimum e.m.f required to carry out an electrolysis of $\mathrm{Al}_2 \mathrm{O}_3$ is $(\mathrm{F}=$ $\left.96500 \mathrm{C} \mathrm{mol}^{-1}\right):$
Solution:
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Verified Answer
The correct answer is:
$2.14 \mathrm{~V}$
For $\mathrm{O}_2, \Delta \mathrm{G}=-n \mathrm{FE}^{\circ}$
$\mathrm{E}^{\circ}=\frac{\Delta \mathrm{G}}{-n \mathrm{~F}}=\frac{-8,27,000}{-2 \times 96,500}=4.28$
Minimum EMF required to carry out electrolysis of $\mathrm{Al}_2 \mathrm{O}_3$
$=\frac{4.28}{2}=2.14 \mathrm{~V}$
$\mathrm{E}^{\circ}=\frac{\Delta \mathrm{G}}{-n \mathrm{~F}}=\frac{-8,27,000}{-2 \times 96,500}=4.28$
Minimum EMF required to carry out electrolysis of $\mathrm{Al}_2 \mathrm{O}_3$
$=\frac{4.28}{2}=2.14 \mathrm{~V}$
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