Answer:So, the enthalpy change for the decomposition reaction is −989.2 kJ/mol−989.2kJ/mol.
Explanation:To find the enthalpy change for the decomposition reaction 2SO3(g)→2SO2(g)+O2(g)2SO3(g)→2SO2(g)+O2(g), we apply Hess's Law.Given reactions:S(s)+O2(g)→SO2(g)S(s)+O2(g)→SO2(g) with ΔH=−296.8 kJ/molΔH=−296.8kJ/molS(s)+32O2(g)→SO3(g)S(s)+23O2(g)→SO3(g) with ΔH=−395.6 kJ/molΔH=−395.6kJ/molDouble the second reaction and reverse it: 2SO3(g)→2S(s)+3O2(g)2SO3(g)→2S(s)+3O2(g)Reverse the sign of its enthalpy change: ΔH=395.6 kJ/molΔH=395.6kJ/molMultiply the first reaction by 2: 2S(s)+2O2(g)→2SO2(g)2S(s)+2O2(g)→2SO2(g)Now, sum up the modified reactions:ΔHdecomposition=(2×−296.8)+395.6ΔHdecomposition=(2×−296.8)+395.6ΔHdecomposition=−593.6+395.6=−989.2 kJ/molΔHdecomposition=−593.6+395.6=−989.2kJ/molSo, the enthalpy change for the decomposition reaction is −989.2 kJ/mol−989.2kJ/mol.