The value of `triangle_(f)G^(0)` for formation of `Cr_(2)O_(3)" is "-540 kJ mol^(-1)" and that of "Al_(2)O_(3)" is "-827 kJ mol^(-1)`. Is the reduction of `Cr_(2)O_(3)` possible with Al?

Explanation

The two thermochemical equations can be written as :
`{:((4)/(3)Al(s)+O_(2)(g)to(2)/(3)Al_(2)O_(3)(s),triangle_(f)G_(Al,Al_(2)O_(3))^(0)= -827 kJ mol^(-1)" ""......."(i)),((4)/(3)Cr(s)+O_(2)(g)to(2)/(3)Cr_(2)O_(3)(s),triangle_(f)G^(0)= -540kJ mol^(-1)" ""........"(ii)):}`
Subtracting equation (ii) from equation (i), we get
`(4)/(3)Al(s)+(2)/(3) Cr_(2)O_(3)(s) to (2)/(3)Al_(2)O_(3)(s)+(4)/(3)Cr(s), triangle_(r )G^(0) = -287 kJ mol^(-1)`
As `triangle(r )G^(0)` of the combined redox reaction is -ve, therefore, reduction of `Cr_(2)O_(3)` by Al is possible.