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

To determine whether the reduction of magnesium oxide (MgO) using carbon (C) is spontaneous at 298 K, we need to calculate the Gibbs free energy change (ΔG) for the reaction. The reaction is as follows:

\[ \text{MgO(s)} + \text{C(s)} \rightarrow \text{Mg(s)} + \text{CO(g)} \]

We are given:
- ΔH° (enthalpy change) = +491.18 kJ/mol
- ΔS° (entropy change) = 197.67 J/K·mol

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