Chapter 10, Problem 34A

Interpretation Introduction

Interpretation:For the given reaction $\Delta \text{H}$ is to becalculated. 

  $\text{NO}\left(g\right)+\text{O}\left(g\right)\to {\text{NO}}_{\text{2}}\left(g\right)$

Concept introduction:According to Hess' law for any process, the change in enthalpy will not depend on the initial and final states and it is same whether a reaction takes place in one or more than one step.

Answer to Problem 34A

  $\Delta \text{H}$ for the reaction is 233 kJ.

Explanation of Solution

The given equations are as follows:

  ${\text{2O}}_{\text{3}}\left(g\right)\to {\text{3O}}_{\text{2}}\left(g\right)\Delta \text{H=}-427\text{kJ}$ …… (1)

  ${\text{O}}_2\left(g\right)\to 2\text{O}\left(g\right)\Delta \text{H=}495\text{kJ}$ …… (2)

  $\text{NO}\left(g\right)+{\text{O}}_{\text{3}}\to {\text{NO}}_{\text{2}}\left(g\right)+{\text{O}}_{\text{2}}\left(g\right)\Delta \text{H=}-199\text{kJ}$ …… (3)

Divide equation (1) and (2) with 2 is as follows:

  ${\text{O}}_{\text{3}}\left(g\right)\to \frac{\text{3}}{2}{\text{O}}_{\text{2}}\left(g\right)\Delta \text{H=}-\frac{427}{2}\text{kJ}$ …… (4)

  $\frac{1}{2}{\text{O}}_2\left(g\right)\to \text{O}\left(g\right)\Delta \text{H=}\frac{495}{2}\text{kJ}$ …… (5)

Now subtract equation (1) and (2) from equation (3) is as follows:

  $\begin{array}{l}\text{NO}+{\text{O}}_{\text{3}}-{\text{O}}_{\text{3}}-\frac{1}{2}{\text{O}}_{\text{2}}{\text{=NO}}_{\text{2}}+{\text{O}}_{\text{2}}-\frac{3}{2}{\text{O}}_{\text{2}}-\text{O}\Delta \text{H=}-199\text{kJ}-\left(-\frac{427}{2}+\frac{495}{2}\right)\text{kJ}\\ \text{NO}-\frac{1}{2}{\text{O}}_{\text{2}}={\text{NO}}_{\text{2}}-{\text{O+O}}_{\text{2}}-\frac{3}{2}{\text{O}}_{\text{2}}\Delta \text{H=}-199\text{kJ+}\frac{427}{2}\text{kJ}-\frac{495}{2}\text{kJ}\\ {\text{NO+O=NO}}_{\text{2}}\Delta \text{H=}233\text{kJ}\end{array}$

Thus, $\Delta \text{H}$ for the reaction is 233 kJ.

Conclusion

Given overall equation is as follows:

  $\text{NO}\left(g\right)+\text{O}\left(g\right)\to {\text{NO}}_{\text{2}}\left(g\right)$

For this reaction $\Delta \text{H}$ is 233kJ.