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))`

Options

A. `2.14V`
B. `4.28 V`
C. `6.42 V`
D. `8.56 V`

Answer

A

Explanation

(a) `(4)/(3)Al+O_(2) to (2)/(3)Al_(2)O_(3), DeltaG=-827 kJ mol^(-1)`
`12e^(-)+6O^(2-) to 3O_(2)`
`4Al^(3+) to Al+12e^(-)`
`or (4)/(3) Al^(3+) to (4)/(3) Al+4e^(-)`
`4e^(-)+2O^(2-) to O_(2)`
`Delta G=-nEF^(@)" " ` (n=4)
`-827xx10^(3)J =-4xxE^(@)xx96500`
`E=(827xx10^(3))/(4xx96500)`
`E^(@)=2.14 V`