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

Answer

C

Explanation

`(2)/(3)Al_(2)O_(3) rarr (4)/(3)Al + O_(2), Delta_(r)G = +966 kJ`
`:. (2)/(3) (3O^(2-)), 2O^(2-) rarr O_(2), :. N = 4`
`:' DeltaG = -nFE :. E = (-DeltaG)/(nF)`
`E = -(966 xx 10^(3))/(4 xx 96500) = -2.5 V`
`:.` The minimum potential difference required for the reeduction `= 2.5 V`.