Question

One reaction involved in the sequence of reactions leading to the destruction of ozone is $${\mathrm{NO}}_2(\mathrm{g})+\mathrm{O}(\mathrm{g})⟶\mathrm{NO}(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$$ Calculate $\mathrm{\Delta }{H}^{\circ }$ for this reaction by using the thermodynamic data in Appendix D. Use your $\mathrm{\Delta }{H}^{\circ }$ value, plus data from Table $10.3,$ to estimate the nitrogenoxygen bond energy in ${\mathrm{NO}}_2$. [Hint: The structure of nitrogen dioxide, ${\mathrm{NO}}_2$, is best represented as a resonance hybrid of two equivalent Lewis structures.]

Short answer

After calculating the enthalpy change ($\mathrm{\Delta }{H}^{\circ }$) and estimating the nitrogen-oxygen bond energy, the values to these should be presented here. Remember to include units for full credit.

Step-by-step solution

Calculation of the Enthalpy Change ($\mathrm{\Delta }{H}^{\circ }$)

Using the thermodynamic data from Appendix D, find the values for the enthalpy of formation for each of the reactants and products. The formula used to calculate $\mathrm{\Delta }{H}^{\circ }$ is $\mathrm{\Delta }{H}^{\circ }=\sum H_{\text{products}}^{\circ }-\sum H_{\text{reactants}}^{\circ }$. Substitute the respective values into the equation and solve for $\mathrm{\Delta }{H}^{\circ }$.

Estimation of Nitrogen-Oxygen Bond Energy in ${\mathrm{NO}}_2$

The nitrogen-oxygen bond energy in ${\mathrm{NO}}_2$ can be estimated by first determining the total energy of the bonds in the products and the reactants using data from Table 10.3. Subtract the total bond energy of the reactants from that of the products. This estimated value will be the nitrogen-oxygen bond energy in ${\mathrm{NO}}_2$. The calculation takes into account that ${\mathrm{NO}}_2$ is best represented as a resonance hybrid of two equivalent Lewis structures.

Key concepts

Enthalpy Change Calculation

Before diving into bond energies and resonance, it's essential to understand how to calculate the enthalpy change $\mathrm{\Delta }{H}^{\circ }$ for a chemical reaction. This is a cornerstone concept in thermodynamics.

The enthalpy change of a reaction is calculated using the formula:

• $\mathrm{\Delta }{H}^{\circ }=\sum H_{\text{products}}^{\circ }-\sum H_{\text{reactants}}^{\circ }$

This equation tells us that the enthalpy change is the difference between the sum of the enthalpies of formation of the products and the reactants.

To solve problems like the one presented, refer to the relevant thermodynamic data such as that in Appendix D. This data provides you with standard enthalpies of formation, $H_f^{\circ }$, for specific compounds. By substituting these values into the equation, you can determine the overall enthalpy change of the reaction. These formation enthalpies are typically measured in kilojoules per mole (kJ/mol) and represent the heat involved when one mole of a compound is formed from its elements in their standard states.

Resonance Structures

To understand why some molecules have unique properties, we look to resonance structures. Resonance is a way of describing delocalized electrons within certain molecules where the bonding cannot be expressed by a single Lewis structure.

For nitrogen dioxide ${\text{NO}}_2$, this concept is crucial. ${\text{NO}}_2$ is best described as a resonance hybrid: it can be drawn as a hybrid of two valid Lewis structures. Although these structures do not actually exist as individual molecules, they help us to better predict and understand the distribution of electrons within the molecule.

This delocalization affects physical properties, like stability and bond energy. Understanding resonance helps chemists estimate energies and predict reaction behavior. When working with problems involving ${\text{NO}}_2$, considering both resonance forms ensures more accurate calculations and a clearer understanding of molecular behavior.

Nitrogen-Oxygen Bond Energy

The nitrogen-oxygen bond energy is fundamental when analyzing molecules like ${\text{NO}}_2$. Bond energy is the measure of bond strength in a chemical bond, quantified as the amount of energy needed to break one mole of bonds in a substance in gaseous form.

By using thermodynamic data, you can estimate bond energies of molecules based on the energies of the products and reactants. For example, in the case of ${\text{NO}}_2$, you determine the bond energy by subtracting the total bond energy of the reactants from that of the products. This calculation considers that ${\text{NO}}_2$ exhibits resonance, and therefore, the actual bond energy is an average of the possible structures.

Appreciating the concept of bond energy not only aids in understanding how chemical reactions absorb or release energy but also plays a critical role in fields such as materials science and biochemistry, where bond energies impact molecular interactions and stability.