Question

Calcium carbonate can decompose into calcium oxide and carbon dioxide gas with the (c) reaction: CaCO3 СаО + СО2 The change in enthalpy for this reaction is AH = +178 kJ/mol and the change in entropy is AS = +0.16 kJ/(K. mol) (i) Describe the concept of the Gibbs energy and how it is related to the enthalpy and entropy (ii Hence calculate the minimum temperature for the decomposition of calcium carbonate to proceed spontaneously An Einstein solid consists of N oscillators that share q units of energy (d) For a very small Einstein solid with N = 3 oscillators that share q units of energy (i) lst al possible microstates of the solid for q = 1, q = 2 and q = 3 and hence determine the multiplicity (q, N = 3) for q value N In the limit of large N, the multiplicity is (q, N) = ("a) and the internal energy (ii) is U qe where e is the unit of energy. Determine the entropy, S, of an Einstein solid and show that the internal energy satisfies the equipartition principle

Answer 1

Part (c)

(i) For a spontaneous reaction, the change in Gibb's free energy (∆G) is negative, whereas ∆G is positive if the reaction is non-spontaneous.

The relationship among ∆G, ∆H, and ∆S can be written as follows.

∆G = ∆H - T∆S

(ii) When both ∆H and ∆S are positive, the reaction when she spontaneous (∆G < 0) if T > ∆H/∆S

i.e. T_spontaneous > (178 kJ/mol)/(0.16 kJ/K.mol)

i.e. T_spontaneous > 1112.5 K

Therefore, the required minimum temperature = 1113 K