When magnesium sulfite decomposes, the solid transforms into magnesium oxide and sulfur dioxide. The reaction is as follows: MgSO3 (s) → MgO (s) + SO2 (g) According to the Gibbs free energy, at what temperature will this reaction be spontaneous?

The reaction is spontaneous for T>1099.3 K

Explanation:

According to the Gibbs free energy (ΔG), a reaction is spontaneous when ΔG < 0. Because ΔG = ΔH - TΔS, the reaction is spontaneous when

ΔH - TΔS < 0

The standards values for enthalpy of formatio (ΔH°f) and entropy (ΔS) can be get by a thermodynamic table, which are:

MgSO₃ (s) : H° = - 1068 kJ/mol; S° = 121 J/K. mol

MgO (s) : H° = - 601.7 kJ/mol; S° = 26.94 J/K. mol

SO₂ (g) : H° = - 296.83 kJ/mol; S° = 248.22 J/K. mol

ΔH = ∑n*Hproducts - ∑n*Hreactant (n is the number of moles)

ΔH = (-601.7 - 296.83) - (-1068) = 169.47 kJ

ΔS = ∑n*Sproducts - ∑n*Sreactant

ΔS = (26.94 + 248.22) - (121) = 154.16 J/K = 0.1542 kJ/K

ΔH - TΔS < 0

169.47 - T*0.1542 < 0

-0.1542*T < - 169.47 (x-1)

0.1542T > 169.47

T > 1099.3 K

So, the reaction is spontaneous for T>1099.3 K