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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= +966 "kJ mol"^(-1)`
The potential difference needed for electrolytic reduction of `Al_(2)O_(3)` at `500^(@)C` is at least :

A

2.5 V

B

5.0 V

C

4.5 V

D

3.0 V

Text Solution

Verified by Experts

The correct Answer is:
A

`Delta_(r)G= +966 "kJ mol"^(-1)`
No. of electrons involved
`n= 2/3 (3xx2) = 4`
`Delta G^(@)= n FE^(@)`
`966xx10^(3)= -4xx96500xxE^(@)`
`E^(@)= -(966xx10^(3))/(4xx96500) = -2.5V`
`:.` Minimum potential difference needed to reduce `Al_(2)O_(3)` is 2.5 V.
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