Neco 2017 Chemistry Question 16

Metal M forms a trivalent oxide M2O3. The standard Gibbs free energy of formation (in kJ·mol^{-1}) of the oxide and of carbon monoxide are temperature‑dependent as follows: \(\Delta G_f^\circ(\text{M}_2\text{O}_3) = -\bigl(400 + 0.2\,T\bigr)\) and \(\Delta G_f^\circ(\text{CO}) = -\bigl(110 + 0.1\,T\bigr)\), where \(T\) is in kelvin. Carbon and the metal are in their standard states (\(\Delta G_f^\circ = 0\)). The reduction reaction is \(\text{M}_2\text{O}_3 + 3\,\text{C} \rightarrow 2\,\text{M} + 3\,\text{CO}\). (a) Determine the lowest temperature at which the reduction becomes spontaneous (\(\Delta G^\circ < 0\)). (b) Using that temperature, calculate the equilibrium constant \(K\) for the reaction at \(900\ \text{K}\).