The value of `Delta_f G^@` for the formation of `Cr_2 O_3` is -540 KJ `mol^(-1)` and that of `Al_2 O_3` is -827 KJ `mol^(-1)`. Is reduction of `Cr_2 O_3` possible with Al ?

Explanation

The two equations are :
` ( 4 )/(3) Al (s) + O _ 2 (g) to (2)/(3) Al_ 2 O _ 3 (s), Delta_f G_(Al, Al_2O_3) ^(@) = - 827 kJ mol^( - 1) " " `… (i)
` (4)/(3) Cr (s) + O _2 (g) to (2)/(3) Cr_ 2 O _ 3 (s) , Delta _ f G ^(@) = - 540 kJ mol^(-1) " " `...(ii)
Subtracting Eq. (ii) from Eq. (i), we have,
` (4)/(3) Al(s) + (2)/(3) Cr _2 O _ 3( s ) to ( 2) /(3) Al _ 2 O _ 3 (s) + (4)/(3) Cr (s) , Delta _ r G^(@) = - 287 kJ mol^(- 1 ) `
Since ` Delta _r G^(@) ` of the combined redox reaction is ` - ve `, therefore, reduction of ` Cr_ 2 O _ 3 ` by Al is possible.