Free energies of formation `(Delta_(f) G^(Ө))` of `MgO(s)` and `CO_((g))` at `1273 K` and `2273 K` are given below :
`Delta_(f) G^(Ө) (MgO_((s) )) = -941 kJ//mol at 1273 K`
`Delta_(f) G^(Ө) (MeO_((s))) = -314 kJ//mol at 2273 K`
`Delta_(f) G^(Ө) (CO_((g))) = - 439 kJ//mol at at 1273 K`
`Delta_(f) G^(Ө) (CO_((g))) = -628 kJ//mol at 2273 K`
On the basis of above data, predict the temperature at which carbon can be used as a reducing for agent `MgO_((s))`.

Explanation

The equation for reduction of MgO by carbon may be written as
` MgO (s) + C (s) to M g O (s) + CO (g) `
The free energy ` (Delta _ r G ) ` of the above reaction at two different temperature may be calculated as follows :
` " "Delta _ r G = Delta_f G [CO (g) ] - Delta _f G [MgO (s)] `
At 1273 K, `" " Delta _ r G = - 439 - (-941) = + 502 kJ mol ^(-1) `
At 2273 K, ` " " Delta_r G = - 623 - (-314) = - 314 kJ mol^(-1) `
Since ` Delta_r G ` is - ve at 2273 K, therefore , carbon can be used as a reducing agent for MgO at 2273K.