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:

Options

A. `4.5V`
B. `3.0V`
C. `2.5V`
D. `5.0V`

Answer

C

Explanation

`(2)/(3)Al_(2)O_(3)rarr(4)/(3)Al+O_(2),Delta_(r)G=+966"kJ"`
`therefore(2)/(3)(3O^(2-)),2O^(2-)rarrO_(2),thereforen=4`
`becauseDeltaG=-nFE`
`thereforeE=-(-DeltaG)/(nF)=-(9.66xx10^(3))/(4xx96500)=-2.5V`
`therefore` The potential difference needed for the reduction `=2.5V`