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

To determine the temperature at which carbon can be used as a reducing agent for magnesium oxide (MgO), we will analyze the given free energies of formation at two different temperatures (1273 K and 2273 K) and apply thermodynamic principles.

### Step-by-Step Solution:

1. **Identify the Reactions and Their Free Energies**:
- At 1273 K:
- Formation of MgO:
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