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The Gibbs energy for the decomposition o...

The Gibbs energy for the decomposition of `Al_(2)O_(3)` at `500^(@)C` is as follows:
`(2)/(3)Al_(2)O_(3) rarr (4)/(3)Al + O_(2), Delta_(r)G = +966kJ mol^(-1)`
The potential difference needed for electrolytic reduction of `Al_(2)O_(3)` at `500^(@)C` is at least:

A

-5.0 V

B

-4.5 V

C

-3.0 V

D

-2.5 V

Text Solution

Verified by Experts

The correct Answer is:
D
The ionic reactions are : 2/3 x `(2Al^(3+)) + 4e^(-) to ` 4/3 Al
2/3 x `(3O^(2-)) to O_2 + 4e^(-)`
Thus, no of electrons transferred, n=4, `DeltaG`= -nFE = - 4 x 96500 x E
or 966 x `10^3`= -4 x 96500 x E
`rArr E= - (966xx10^3)/(4xx96500)`=-2.5 V
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