The Gibbs energy for the decomposition of `Al_2O_3` at `500^@C` is as follows :
`2//3Al_2O_3 to 4/3Al+ O_2 , Delta_r G`=+966 kJ/mol. The potential difference needed for electrolytic reduction of `Al_2O_3` at `500^@` C is at least

Options

A. 4.5 V
B. 3.0 V
C. 2.5 V
D. 5.0 V

Answer

C

Explanation

`(2)/(3)Al_(2)O_(3)to(4)/(3)Al+O_(2)`
`triangle_(r)G=+966kJmol^(-1)=966xx10^(3)Jmol^(-1)`
`triangleG=-nFE_(cell)`
`966xx10^(3)=-4xx96500xxE_(cell)`
`E_(cell)=2.5V`