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The value of Delta(f)G^(@) for formation...

The value of `Delta_(f)G^(@)` for formation `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 aluminium?

Text Solution

Verified by Experts

The two equations are :
`(4)/(3)Al_((s))+O_(2(g))rarr(2)/(3)Al_(2)O_(3(s))`
`Delta_(f)G^(@)=-827kJmol^(-1)" "...(i)`
`(4)/(3)Cr_((s))+O_(2(g))rarr(2)/(3)Cr_(2)O_(3(s))`
`Delta_(f)G^(@)=-540kJmol^(-1)" "...(ii)`
Subtracting equation (ii) from equation (i), we get
`(4)/(3)Al(s)+(2)/(3)Cr_(2)O_(3)(s)rarr(2)/(3)Al_(2)O_(3)(s)+(4)/(3)Cr(s)`,
`Delta_(f)G^(@)=-287kJmol^(-1)`
As `Delta_(f)G^(@)` of the combined redox reaction is negative, therefore, reduction of `Cr_(2)O_(3)` by Al is possible.
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