Estimate the minimum potential difference needed to reduce `Al_(2)O_(3)` at `500^(@)C` The gibbs energy change for the decomposition reaction `2/3Al_(2)O_(3)rarr4/3Al+O_(2)`is 960 kJ (F=96500 C `mol^(-1))`

Explanation

`Al_(2)O_(3)(2Al^(3+)+3O^(2-))to2Al+(3)/(2)O_(2),n=6e^(-)" "therefore(2)/(3)Al_(2)O_(3)to(4)/(3)Al+O_(2).n=4e^(-)`
substituting `DeltaG=+960kJ=+960,000J and n=4` in the equation, `DeltaG=-nFE`, we get
`960,000=-4xx96500xxE" or "E=-2.487V`
`therefore`Minimum potential difference needed to reduce `Al_(2)O_(3)` is 2.487 V.