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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 reeduction 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
(d) The ionic reactions are : `2//3 Al_(2)^(3+)+4e^(-) to 4//3 Al`
`2//3 O_(3)^(2-) to O_(2)+4e^(-)`
No. of electrons =4
`DeltaG=-nFE_(cell)`
`E_(cell)=-(DeltaG)/(nF)=(966xx10^(3)(CV))/(4xx96500(V))=2.5" V"`.
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