1.

On the basis of information available from the reaction `(4)/(3)Al+O_(2) rarr (2)/(3)Al_(2)O_(3),DeltaG = -827kJ mol^(-1)` of `O_(2)`, the minimum emf required to carry out of the electrolysis of `Al_(2)O_(3)` is `(F=96,500 C mol^(-1))`A. `2.14 V`B. `4.28 V`C. `6.42 V`D. `8.56 V`

Answer» Correct Answer - A
We are given
`(4)/(3) Al+O_(2) rarr (2)/(3) Al_(2)O_(3)`
For every `1` mol of `O_(2)`, we need to perform electrolysis of
`(2)/(3)` mol of `Al_(2)O_(3)`:
`(2)/(3) mol Al_(2)O_(3) rarr (4)/(3) Al^(3+)+2O^(2-)`
At cathode
`(4)/(3)Al^(3+)+4e^(-) rarr (4)/(3) Al`
At anode
`2O^(2-) rarr 4e^(-)+O_(2)`
Since
`Delta_(r)G^(@) = -nFE_("cell")^(@)`
we have
`E_("cell")^(@) = (Delta_(r)G^(ɵ))/(-nF)`
`= (-827 xx 10^(3) J mol^(-1))/(-(4 mol) (96,500 C mol^(-1)))`
`= 2.14 V`


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