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Chapter 5: Problem 64

The \(\Delta H_{\mathrm{f}}^{\circ}\) values of the two allotropes of oxygen, \(\mathrm{O}_{2}\) and \(\mathrm{O}_{3}\), are 0 and \(142.2 \mathrm{~kJ} / \mathrm{mol}\), respectively, at \(25^{\circ} \mathrm{C}\). Which is the more stable form at this temperature?

Short Answer

Expert verified
O2 is more stable than O3 at 25掳C.

Step by step solution

01

Understanding the Exercise

The exercise asks us to determine which allotrope of oxygen, O2 or O3, is more stable at a given temperature based on their standard enthalpies of formation, \( \Delta H_{\mathrm{f}}^{\circ} \). O2 has a value of 0, and O3 has a value of 142.2 kJ/mol.
02

Concept of Stability and Enthalpy

In thermodynamics, lower enthalpy values indicate more stable substances. Since \( \Delta H_{\mathrm{f}}^{\circ} \) measures the energy change when one mole of a compound is formed from its elements, a higher positive value suggests less stability, since the compound is in a higher energy state.
03

Comparing Enthalpy Values

We compare the given enthalpy values of O2 and O3: \( \Delta H_{\mathrm{f}}^{\circ}(O_2) = 0 \) and \( \Delta H_{\mathrm{f}}^{\circ}(O_3) = 142.2 \text{ kJ/mol} \).O2 has a \( \Delta H_{\mathrm{f}}^{\circ} \) of 0, indicating it is in its standard state and very stable.In contrast, O3 with \( \Delta H_{\mathrm{f}}^{\circ} = 142.2 \text{ kJ/mol} \), indicates it is at a higher energy level, making it less stable.
04

Conclusion

Based on the \( \Delta H_{\mathrm{f}}^{\circ} \) values, O2 is more stable than O3 at 25掳C. This is because O2 is in its elemental form with no energy required for its formation, unlike O3, which requires energy input, thus being less stable.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Enthalpy
Enthalpy (\(H\)) is a fundamental concept in thermodynamics used to quantify the heat content in a system at constant pressure. Understanding enthalpy helps us predict how substances behave during chemical reactions.
It is expressed in units like kilojoules per mole (kJ/mol), which lets us measure the energy changes during transitions or reactions.
In the context of chemical reactions:
  • If the enthalpy change (\(\Delta H\)) is negative, the reaction releases energy, indicating an exothermic process.
  • Conversely, a positive \(\Delta H\) value means the reaction absorbs energy, pointing to an endothermic process.
So, when studying allotropes like \(O_2\) and \(O_3\), their enthalpy values reveal a lot about their stability and tendency to undergo chemical changes.
Stability
Stability in thermodynamics pertains to how likely a substance is to undergo a chemical change. A stable chemical species tends to remain as it is and does not spontaneously convert or react.
Looking at the standard enthalpy of formation can provide insights into a substance's energy stability.
Substances with lower enthalpy values are generally more stable, as they're already in a lower energy state.
  • For example, oxygen exists as \(O_2\) in our environment, with a standard enthalpy of formation (\(\Delta H_{\mathrm{f}}^{\circ}\)) of 0, indicating it's very stable.
  • In contrast, ozone (\(O_3\)) has a \(\Delta H_{\mathrm{f}}^{\circ}\) value of 142.2 kJ/mol, suggesting it's less stable. This is due to its higher energy state, making it more reactive.
Choosing the more stable form often means selecting the one with lower or no required energy for its formation.
Oxygen Allotropes
Oxygen can exist in different forms called allotropes, with \(O_2\) and \(O_3\) being the most commonly discussed. Each allotropic form has distinct properties and implications in chemical reactions.
Oxygen (\(O_2\)) is the familiar diatomic molecule vital for respiration and combustion processes.
It's characterized by stable bonds and an availability in nature, contributing to our breathable air.
  • The molecule \(O_3\), or ozone, is a triatomic form, known for its protective role in the Earth's stratosphere, where it absorbs harmful ultraviolet radiation from the sun.
  • Unlike \(O_2\), ozone is less stable and more reactive, often used for oxidative and disinfectant purposes.
The contrasting stability of these allotropes can be linked to their molecular structure and formation energetics.
Standard Enthalpy of Formation
The standard enthalpy of formation (\(\Delta H_{\mathrm{f}}^{\circ}\)) measures the energy change when one mole of a compound is formed from its elements at standard conditions (usually 25掳C and 1 atm pressure). This thermodynamic quantity is crucial for understanding chemical processes.
It serves as a benchmark for predicting the stability and reactivity of substances.
  • A \(\Delta H_{\mathrm{f}}^{\circ}\) of zero indicates a substance is in its elemental form, revealing no energy change is needed for its formation.
  • Non-zero values suggest the energy required or released, pinpointing the relative position of the compound concerning its elements.
For instance, \(O_2\) has a \(\Delta H_{\mathrm{f}}^{\circ}\) of 0, symbolizing high stability in its elemental form.
Whereas the \(\Delta H_{\mathrm{f}}^{\circ}\) of \(O_3\) as 142.2 kJ/mol reveals the energy required to form it, explaining its less stable nature compared to \(O_2\).

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Most popular questions from this chapter

For which of the following reactions does \(\Delta H_{\mathrm{rxn}}^{\circ}=\Delta H_{\mathrm{f}}^{\circ}\) ? (a) \(\mathrm{H}_{2}(g)+\mathrm{S}(\) rhombic \() \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)\) (b) \(\mathrm{C}(\) diamond \()+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\) (c) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CuO}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cu}(s)\) (d) \(\mathrm{O}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{3}(g)\)

State Hess's law. Explain, with one example, the usefulness of Hess's law in thermochemistry.

A driver's manual states that the stopping distance quadruples as the speed doubles; that is, if it takes \(30 \mathrm{ft}\) to stop a car moving at \(25 \mathrm{mph}\), then it would take \(120 \mathrm{ft}\) to stop a car moving at \(50 \mathrm{mph}\). Justify this statement by using mechanics and the first law of thermodynamics. (Assume that when a car is stopped, its kinetic energy \(\left(\frac{1}{2} m u^{2}\right)\) is totally converted to heat.)

A truck initially traveling at \(60 \mathrm{~km} / \mathrm{h}\) is brought to a complete stop at a traffic light. Does this change violate the law of conservation of energy? Explain.

At \(25^{\circ} \mathrm{C}\), the standard enthalpy of formation of \(\mathrm{HF}(a q)\) is \(-320.1 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{OH}^{-}(a q),\) it is \(-229.6 \mathrm{~kJ} / \mathrm{mol} ;\) of \(\mathrm{F}^{-}(a q)\) it is \(-329.1 \mathrm{~kJ} / \mathrm{mol} ;\) and of \(\mathrm{H}_{2} \mathrm{O}(l),\) it is \(-285.8 \mathrm{~kJ} / \mathrm{mol}\). (a) Calculate the standard enthalpy of neutralization of \(\mathrm{HF}(a q)\) \(\mathrm{HF}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{F}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) Using the value of \(-56.2 \mathrm{~kJ}\) as the standard enthalpy change for the reaction \(\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) calculate the standard enthalpy change for the reaction \(\mathrm{HF}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{F}^{-}(a q)\)
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