Question

The Gibbs energy for the decomposition of `Al_(2)O_(3)` at `500^(@)C` is as follow :
`(2)/(3)Al_(2)O_(3) rarr (4)/(3)Al+O_(2), Delta_(r)G= +960 kJ mol^(-1)`
The potential difference needed for the electrolytic reduction of aluminium oxide `(Al_(2)O_(3))` at `500^(@)C` is
A. `5.0 V`
B. `4.5 V`
C. `3.0 V`
D. `2.5 V`

Answer 1

Correct Answer - D
We are given decomposition reaction:
`(2)/(3)Al_(2)O_(3) rarr (4)/(3)Al+O_(2)`
The electrolyte `Al_(2)O_(3)` splits into ions as follows:
`Al_(2)O_(3) rarr 2Al^(3+)+3O^(2-)`
At cathode
`2Al^(3+)+6e^(-) rarr 2Al`
At anode
`3O^(2-) rarr 6e^(-)+(3)/(2)O_(2)`
We have `Delta_(r)G^(ɵ) = -nfE_("cell")^(ɵ)`
or `E_("cell")^(ɵ) = (Delta_(r)G^(ɵ))/(-nF) = (960 xx 10^(3)J mol^(-1))/(-(6 mol)(96500 C)) = -1.66 V`