The value of`Delta _(f) f^(Ө)` for formation of `Cr_(2) O_(3)` is – 540 kJmol−1and that of `Al_(2) O_(3)` is `– 827 kJmol^(−1)`. Is the reduction of `Cr_(2) O_(3)` possible with Al ?

Explanation

chemical equaltion for the foramtion of `Cr_(3)O_(3)` and `Al_(2)O_(3)` are as follows
(a) `(4)/(3) Cr(s) +(3)/(2)O_(2)(g) to (2)/(3) Cr_(2) O_(3) (s) :`
`DeltaG_(f)^(@)` =- 540kj mol^(-1)`
`(b) (4)/(3) Al (s) +(3)/(2) O_(2) (g) to (2)/(3) Al_(2)O_(3) (s) :`
` Delta G_(f)^@)=- 827 Kj mol^(-1)` Substring equcation (a) from equaction (b) ,we get
`(4/93)Al(s) +(2)/(3) Cr_(2)O_(3) (s) to`
`(2)/(3) Al_(2)O_(3) (s) +(4)/(3)Cr(s) DeltaG_(f)^(@)=- 287 kjmol^(-1)`
As can be seen `Delta _(r)G^(@)` is nagative , thius , reducation of `Cr_(2)O_(3)` Al is possible.