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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

2.5 V

B

5.0 V

C

4.5V

D

3.0V

Text Solution

Verified by Experts

The correct Answer is:
A
`(2)/(3)Al_(2)O_(3)to(4)/(3)Al+O_(2),Delta_(r)G=+966" kJ "mol^(-1)`
Thus, `(2)/(3)xx(3O^(2-)), i.e., 2O^(2-)toO_(2),n=4`
`DeltaG=-nFE`
`therefore966xx10^(3)=-4xx96500xxE` or `E=-2.50V` ltBrgt Thus, minimum potential difference required =2.50V.
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