For the oxidation of hydrogen sulfide, the balanced chemical equation is given as: 2 H ₂ S(g) + 3 O ₂ (g) 2 H ₂ O(l) + 2 SO ₂ (g) The standard enthalpy of the reaction is -1122 kJ mol ⁻¹ . If the standard enthalpies of formation of H ₂ O(l) and SO ₂ (g) are -285 kJ mol ⁻¹ and -296 kJ mol ⁻¹ respectively, the magnitude of the standard enthalpy of formation of H ₂ S(g) is ________ kJ mol ⁻¹ .

Step-by-step solution

Using Hess's law of constant heat summation: H^ _ rxn = H^ _ f ( products ) - H^ _ f ( reactants ) For the given reaction: H^ _ rxn = [2 H^ _ f ( H ₂ O, l ) + 2 H^ _ f ( SO ₂ , g )] - [2 H^ _ f ( H ₂ S, g ) + 3 H^ _ f ( O ₂ , g )] The standard enthalpy of formation of O ₂ (g) is zero. Substituting the given values: -1122 = [2(-285) + 2(-296)] - [2 H^ _ f ( H ₂ S, g ) + 0] -1122 = [-570 - 592] - 2 H^ _ f ( H ₂ S, g ) -1122 = -1162 - 2 H^ _ f ( H ₂ S, g ) 2 H^ _ f ( H ₂ S, g ) = -1162 + 1122 = -40 kJ mol ⁻¹ H^ _ f (