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At 1273 K, the Delta(f)G^(@) of MgO(s) a...

At 1273 K, the `Delta_(f)G^(@)` of `MgO(s) and CO(g)` and `-941 and -"439 kJ.mol"^(-1).` But at 2273 K, the `Delta_(f)G^(@)` of `MgO(s) and CO(g)` are `-314 and -"628kJ.mol"^(-1)`. On the basis of the given values of `Delta_(f)G^(@)`, predict the temperature at which carbon is used as a reducing agent for `MgO(s).`

Text Solution

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At 1273K, the two redox reactions are :
`2Mg(s)+O_(2)(g)rarr 2Mg(S),`
`Delta_(f)G^(@)=-"941kJ. Mol"^(-1)" …[1]"`
`2C(s)+O_(2)(g)rarr2CO(g),`
`Delta_(f)G^(@)=-"439kJ.mol"^(-1)" …[2]"`
The redox rection for the reduction of `MgO` to `Mg` by coke can be obtained by subtracting equation [1] from eqaution [2].
Thus, `MgO(s)+C(s) rarr Mg(s)+CO(g),`
`Delta_(r)G^(@)=[-439-(-941)]"kJ.mol"^(-1)=+"502kJ.mol"^(-1)`
Since, `Delta_(r)G^(@)` of the reduction of MgO by C is positive, the reaction is not feasible at 1273K. At 2273K, the two redox reaction are :
`2Mg(s)+O_(2)(g)rarr 2MgO(s),`
`Delta_(f)G^(@)=-"314kJ.mol"^(-1)" ...[3]"`
`2C(s)+O_(2)(g)rarr 2CO(g),`
`Delta_(f)G^(@)=-"628kJ.mol"^(-1)" ...[4]"`
The redox equation obtained by substracting equation [3] from equation [4] is ,
`MgO(s)+C(s)rarr Mg(s)+CO(g),`
`Delta_(r)G^(@)=[-628-(-314)]"kJ.mol"^(-1)=-"314kJ.mol"^(-1)`
Since, `Delta_(r)G^(@)` of the above reaction is negative, the (reduction of MgO by coke) at 2273 K is feasible.
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