Calcium carbonate decomposes when heated to form calcium oxide and carbon dioxide.

CaCO₃(s) → CaO(s)  + CO₂(g)

a. Calculate the entropy change of the system for this reaction.

(Values for S^θin J K^–1 mol^–1: CaCO₃(s) = +92.9, CaO(s) = +39.7, CO₂(g) = +213.6)

b. Calculate the enthalpy change for this reaction.

(Values for ΔH^θ_f in kJ^–1 mol^–1: CaCO₃(s) = –1206.9, CaO(s) = –635.1, CO₂(g) = –393.5)

c. Use your answers to parts a and b to calculate the Gibbs free energy change of this reaction at 298 K by a method that does not include calculating the entropy change of the surroundings.

d. Explain why the reaction is not spontaneous at 298 K even though the entropy change of the system has a positive value.