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 "`

The Gibbs energy for the decomposition of `Al_(2)O_(3)` at `500^(@)C`

1.	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 "`
Answer» Correct Answer - 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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