To determine the enthalpy change for the reaction, we need to use the concept of Hess's Law and the enthalpies of formation. Hess's Law states that the overall enthalpy change of a reaction is independent of the pathway taken, as long as the initial and final conditions are the same.
The reaction you provided is: NO + 1/2 O2 → NO2
We can break down this reaction into the following steps, using the enthalpies of formation:
Formation of NO2 (target reaction): 2NO + O2 → 2NO2 (∆H₁)
Formation of NO (reverse reaction): NO2 → NO + 1/2O2 (∆H₂)
According to Hess's Law, the enthalpy change (∆H) for the target reaction can be calculated as follows:
∆H = ∆H₁ - ∆H₂
Given that the enthalpies of formation (∆Hf) for NO and NO2 are +90.2 KJ/mol and +32.2 KJ/mol, respectively, we can rewrite the equation as follows:
∆H = [2∆Hf(NO2)] - [2∆Hf(NO) + ∆Hf(O2)]
Substituting the values, we get:
∆H = [2(32.2 KJ/mol)] - [2(90.2 KJ/mol) + 0 KJ/mol] ∆H = 64.4 KJ/mol - 180.4 KJ/mol ∆H = -116 KJ/mol
Therefore, the enthalpy change for the reaction NO + 1/2O2 → NO2 is approximately -116 KJ/mol. The negative sign indicates that the reaction is exothermic, releasing energy.