Estimate the minimum potential difference required to reduce `Al_(2)O_(3)` at `500^(@)` C. The free energy change for the decomposition reaction :
`2/3Al_(2)O_(3) to 4/3 Al + O_(2)` is `DeltaG = 960 kJ`
1 F = 96500 C `mol^(-1)`.

Explanation

The following data is provided
`DeltaG^(@) = +960 kJ = 960 xx 10^(3) J, 1F = 96500 C mol^(-1)`
The reduction equation may be written as:
`4/3 Al^(3+) + 4e^(-) to 4/3 Al`. Thus, n=4.
Use the following relation to calculate potential difference.
`DeltaG^(@) = -nFE^(@)`
`=-960 xx 10^(3) J =-4 xx 96500 C mol^(-1) xx E^(@)` volt
or `E^(@) = (960 xx 10^(3) J)/(4 xx 96500 C mol^(-1)"volt") = +2.48 V`