Question

Based upon the following thermochemical data, show that ozone, \(\mathrm{O}_{3}\), is considerably more stable than a cyclic structure would suggest. The enthalpy for the \(\mathrm{O}-\mathrm{O}\) bond is approximately \(33 \mathrm{Kcal} / \mathrm{mole}\) \(1(1 / 2) \mathrm{O}_{2} \rightarrow \mathrm{O}_{3}, \quad \Delta \mathrm{H}_{\text {formation }}=+34.5 \mathrm{kcal}\) \(\mathrm{O}_{2} \quad \rightarrow 2 \mathrm{O} \quad \Delta \mathrm{H}_{\text {dissociation }}=+119 \mathrm{kcal}\)

Short answer

The enthalpy change for ozone (\(\mathrm{O}_3\)) formation from two oxygen atoms is \(\Delta H_{\text{O}_3} = -25 \mathrm{kcal/mol}\), while the enthalpy change for cyclic structure formation is \(\Delta H_{\text{cyclic}} = 66 \mathrm{kcal/mol}\). Since \(\Delta H_{\text{O}_3}\) is more negative, this indicates that ozone is considerably more stable than a cyclic structure would suggest.

Step-by-step solution

Calculate enthalpy change for the cyclic structure formation

The cyclic structure formation involves formation of two O-O bonds, for which we are given the bond enthalpy as 33 kcal/mol. To find the enthalpy change for the cyclic structure formation, we can assume that the structure is created by connecting two oxygen atoms (\(\mathrm{O}\)) with O-O bonds: \[\mathrm{2O} \rightarrow \mathrm{Cyclic \ structure}, \quad \Delta H_{\text{cyclic}}\] As we have two O-O bonds formed, we will multiply the bond enthalpy with 2: \[\Delta H_{\text{cyclic}} = 2 \times 33 \mathrm{kcal/mol} = 66 \mathrm{kcal/mol}\]

Calculate the enthalpy change for ozone formation by dissociation and formation of bonds

The enthalpy change for ozone formation (\(\Delta H_{\text{formation}}\)) is given as +34.5 kcal/mol. In addition, we have the enthalpy change (\(\Delta H_{\text{dissociation}}\)) for the dissociation of one oxygen molecule into two oxygen atoms, which is +119 kcal/mol. So, to find the enthalpy change to form ozone from two oxygen atoms, we need to subtract the enthalpy change of dissociation from the enthalpy change of formation: \[\Delta H_{\text{O}_3} = \Delta H_{\text{formation}} - (1/2)\Delta H_{\text{dissociation}}\]

Calculate the enthalpy change involved in the formation of O3 from two oxygen atoms

Substituting the given values of enthalpy change in the above equation, we get: \[\Delta H_{\text{O}_3} = 34.5 \mathrm{kcal/mol} - (1/2) \times 119 \mathrm{kcal/mol} = -25 \mathrm{kcal/mol}\]

Compare the enthalpy changes

Now we will compare the enthalpy change for ozone formation (\(\Delta H_{\text{O}_3}\)) with the enthalpy change for the cyclic structure formation (\(\Delta H_{\text{cyclic}}\)): Since \(\Delta H_{\text{O}_3} = -25 \mathrm{kcal/mol}\) and \(\Delta H_{\text{cyclic}} = 66 \mathrm{kcal/mol}\), we see that the enthalpy change for ozone formation is more negative than the enthalpy change for the cyclic structure formation. A more negative enthalpy change indicates a more stable compound, as it releases more energy upon formation. Therefore, ozone (\(\mathrm{O}_3\)) is considerably more stable than a cyclic structure would suggest.

Key concepts

Ozone stability

Ozone (\(\mathrm{O}_3\)) is an important molecule in the atmosphere due to its role in absorbing harmful ultraviolet radiation from the sun. Understanding its stability helps in explaining its persistence in the atmosphere compared to its alternatives, such as hypothetical cyclic structures involving oxygen. The stability of ozone is primarily linked to its energy state and how it compares with other possible forms. This molecule is found to be more stable than a potential cyclic structure because of its thermochemical properties. Stability is largely influenced by enthalpy changes during formation. In simpler terms, the more negative the enthalpy change upon formation, the more stable the compound tends to be. Given that ozone's enthalpy change is significantly more negative than that of a cyclic formation, it indicates that ozone holds energy more favorably, making it a more stable form in nature.

Enthalpy change

Enthalpy change (\(\Delta H\)) represents the heat absorbed or released during a reaction at constant pressure. In the context of ozone, the enthalpy change concerns the energy dynamics during its formation from oxygen molecules.The value of enthalpy change provides insights into whether a reaction is endothermic or exothermic. For ozone, the formation process exhibits a negative enthalpy change, signifying that energy is released, thus forming a more stable compound. A comparison between the enthalpy changes for the formation of ozone and the hypothetical cyclic structure further highlights ozone's greater stability and energy efficiency. By being energetically more favorable, ozone's formation reflects a natural preference for stability and lower energy configurations.

Cyclic structure

A cyclic structure implies a ring-like arrangement of atoms in a molecule. If we consider a potential cyclic structure involving three oxygen atoms, it would theoretically capitalize on O-O bond formation. However, such a formation requires specific enthalpic conditions and bond angles to maintain structural integrity, which can prove energetically less favorable compared to linear forms like ozone. In terms of enthalpy, forming a cyclic compound involves energy costs that reflect an O-O bond enthalpy in each linkage. This energy requirement, combined with the inherent stress of forming a ring, often leads to less stable outcomes when contrasted with more naturally favored linear arrangements such as ozone.

O-O bond enthalpy

Bond enthalpy is a measure of bond strength in a chemical bond, specifically the energy needed to break one mole of bonds in a gaseous molecule.For O-O bonds, the enthalpy is around \(33\,\text{kcal/mol}\), which plays a crucial role in assessing the stability and formation of compounds involving oxygen.In the case of ozone, the incorporation of O-O bonds is balanced by other energetic factors that lead to its overall stability.Conversely, a cyclic structure would require multiple O-O links, increasing the total enthalpy and thus making the formation less favorable.Understanding O-O bond enthalpy helps to elucidate why certain structures prevail over others and why energy-efficient configurations like ozone exist in equilibrium with the atmospheric conditions, while cyclic structures remain theoretical.