At 298 K , the standard enthalpies of formation for NH ₃( g ) and H ₂ O ( l ) are -46 kJ mol ⁻¹ and -286 kJ mol ⁻¹ , respectively. The enthalpies of the following reactions at 298 K are given: N ₂( g ) + 2 O ₂( g ) 2 NO ₂( g ) , H ^ = +66 kJ N ₂( g ) + O ₂( g ) 2 NO ( g ) , H ^ = +180 kJ The magnitude of the standard enthalpy change for the oxidation of ammonia, 4 NH ₃( g ) + 7 O ₂( g ) 4 NO ₂( g ) + 6 H ₂ O ( l ) is

Step-by-step solution

The standard enthalpy of reaction is given by: H ^ _ rxn = H ^ _ f ( products ) - H ^ _ f ( reactants ) From the given data: H ^ _ f ( NH ₃, g ) = -46 kJ mol ⁻¹ H ^ _ f ( H ₂ O , l ) = -286 kJ mol ⁻¹ For NO ₂( g ) , the standard formation reaction is 1 2 N ₂( g ) + O ₂( g ) NO ₂( g ) . Given N ₂( g ) + 2 O ₂( g ) 2 NO ₂( g ) with H ^ = 66 kJ , we have: H ^ _ f ( NO ₂, g ) = 66 2 = 33 kJ mol ⁻¹ . (The reaction for NO is extra information and not needed). Now, substituting these values into the formula for the given