Question

Calculate the enthalpy of the reaction 2NO(g)+O2(g)→2NO2(g)
1/2N2(g)+O2(g)→NO2(g), ΔH∘A=33.2 kJ
1/2N2(g)+12O2(g)→NO(g), ΔH∘B=90.2 kJ

Answer 1

1/2 N2(g) + O2(g) --> NO2(g), deltaH = 33.2 kJ (should be multiplied by 2) 

N2 + 2 O2 -> 2 NO2.........deltaH = +66,4 kJ 

1/2 N2(g) + 1/2O2(g) --> NO(g), delta H = 90.2 kJ (should be multiplied by 2 and inverted) 

2 NO -> N2 + O2..............deltaH = -180,4 kJ 

Now you have: 
N2 + 2 O2 -> 2 NO2.........deltaH = +66,4 kJ 
2 NO -> N2 + O2..............deltaH = -180,4 kJ 
--------------------------------------... 
canceling both N2 and 2 O2 with O2, you will find the given reaction: 
2 NO + O2 -> 2 NO2........deltaH = 66,4 - 180,4 = -114.0 kJ <--- Answer 

Answer 2

The enthalpy of the reaction:

2NO(g)+O₂(g)→2NO₂(g) ΔH = -114 kJ/mol

Further explanation

The change in enthalpy in the formation of 1 mole of the elements is called enthalpy of formation

The enthalpy of formation measured in standard conditions (25 ° C, 1 atm) is called the standard enthalpy of formation (ΔHf °)

Determination of the enthalpy of formation of a reaction can be through a calorimetric experiment, based on the principle of Hess's Law, enthalpy of formation table, or from bond energy data

(ΔH) can be positive (endothermic = requires heat) or negative (exothermic = releasing heat)

The value of ° H ° can be calculated from the change in enthalpy of standard formation:

∆H ° rxn = ∑n ∆Hf ° (product) - ∑n ∆Hf ° (reactants)

The elements in standard conditions are not included in the enthalpy calculations because the enthalpy of those elements under the standard conditions is zero.

From the problem can be known

∆Hf ° A: NO₂ = 33.2 kJ / mol

∆Hf ° B: NO = 90.2 kJ / mol,

In reaction:

2NO (g) + O₂ (g) → 2NO₂ (g)

Since the reaction coefficients of NO₂ and NO are 2, then ΔHf ° is also multiplied by 2

∆H ° rxn = ∑n ∆Hf ° (product) - ∑n ∆Hf ° (reactants)

∆H ° rxn = 2.∆Hf ° NO₂ - 2. ∆Hf ° NO (O₂ not included)

$\rm \Delta H^orxn=2\times 33.2-2\times 90.2\\\\\Delta H^orxn=66.4-180.4\\\\\Delta H^orxn=\boxed{-114\:kJ/mol}}$

Learn more

Delta H solution

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an exothermic reaction

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as endothermic or exothermic

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