this reaction in house temperature happend: 2SO3----->2SO2+O2 :delta(H)=+19.8 Is delta(G) negative? Why?

Qualitative explantion :
2SO₃(g) → 2SO₂(g) + O₂(g)
The entropy change of the above reaction is rather positive because of the increase in the number of gaseous molecules as 2 moles of gaseous molecules are converted to 3 moles.
ΔG = ΔH - TΔS
The value of ΔH is slightly positive. As ΔS is rather positive, ΔG would be negative at house temperature (T = 298 K).


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Quantitative explanation :
2SO₃(g) → 2SO₂(g) + O₂(g)
ΔS = 2S[SO₂(g)] + S[O₂(g)] - 2S[SO₃(g)] = [2(205) + 249 - 2(256)] J/(mol K) = +147 J/(mol K) = 0.147 kJ/(mol K)
ΔG = ΔH - TΔS = (19.8 - 298 × 0.147) kJ/mol = -24 kJ/mol