Predict whether it is possible or not to reduce magnesium oxide using carbon at `298K` according to the reaction.
`MgO(s) +C(s) rarr Mg(s) +CO(g)`
`Delta_(r)H^(Theta) = +491.18 kJ mol^(-1)` and `Delta_(r)S^(Theta) = 197.67 J K^(-1) mol^(-1)`
If not at what temperature, the reaction becomes spontaneous.

Explanation

We know
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)`
`DeltaH^(Theta) = +491.18 kJ mol^(-1)`
`DeltaS^(Theta) = 197.67 xx 10^(-3) kJ mol^(-1)K^(-1), T = 298K`
`:. DeltaG^(Theta) = 491.18 kJ mol^(-1) - 298K`
`xx (197.67 xx 10^(-3)kJ mol^(-1) K^(-1))`
`=491.18 kJ mol^(-1) -58.9 kJ mol^(-1)`
`= 432.28 kJ mol^(-1)`
Since Gibbs enegry change is positive, therefore, at `298K`, the reaction is not possible.
Let us calculate `T` at which `Delta_(r)G^(Theta)` becomes zero
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta) = 0`
`:. T = (DeltaH)/(DeltaS) = (491.18 kJ mol^(-1))/(197.67 xx 10^(-3)kJ mol^(-1)K) = 2484.8 K`
Therefore, the reaction will be spontaneous above `2484.8K or 2211.8^(@)C`.