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Chapter 6: Problem 46

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
At \(25^{\circ} \mathrm{C}\), \(\mathrm{O}_{2}\) is the more stable form of oxygen because of its 0 enthalpy of formation compared to \(142.2 \mathrm{~kJ}\)/ \(\mathrm{mol}\) for \(\mathrm{O}_{3}\).

Step by step solution

01

Analyze the provided data

The question provides the \(\Delta H_{\mathrm{f}}^{\circ}\) values for two allotropes of oxygen at \(25^{\circ} \mathrm{C}\): for \(\mathrm{O}_{2}\) it's 0 and for \(\mathrm{O}_{3}\), it's \(142.2 \mathrm{~kJ}\)/ \(\mathrm{mol}\). Remember, the \(\Delta H_{\mathrm{f}}^{\circ}\) value represents the stability of the molecule.
02

Compare the \(\Delta H_{\mathrm{f}}^{\circ}\) values

Comparing the \(\Delta H_{\mathrm{f}}^{\circ}\) values, one can see \(\mathrm{O}_{2}\) has a \(\Delta H_{\mathrm{f}}^{\circ}\) value of 0 which is lower than the \(\Delta H_{\mathrm{f}}^{\circ}\) value of \(\mathrm{O}_{3}\). This indicates that the molecule of \(\mathrm{O}_{2}\) is in a more stable state than \(\mathrm{O}_{3}\).

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Most popular questions from this chapter

A 46-kg person drinks 500 g of milk, which has a "caloric" value of approximately \(3.0 \mathrm{~kJ} / \mathrm{g}\). If only 17 percent of the energy in milk is converted to mechanical work, how high (in meters) can the person climb based on this energy intake? [Hint: The work done in ascending is given by \(m g h,\) where \(m\) is the mass (in kilograms), \(g\) the gravitational acceleration \(\left(9.8 \mathrm{~m} / \mathrm{s}^{2}\right),\) and \(h\) the height (in meters).]

How are the standard enthalpies of an element and a compound determined?

What is heat? How does heat differ from thermal energy? Under what condition is heat transferred from one system to another?

A 44.0-g sample of an unknown metal at \(99.0^{\circ} \mathrm{C}\) was placed in a constant-pressure calorimeter containing \(80.0 \mathrm{~g}\) of water at \(24.0^{\circ} \mathrm{C}\). The final temperature of the system was found to be \(28.4^{\circ} \mathrm{C}\). Calculate the specific heat of the metal. (The heat capacity of the calorimeter is \(\left.12.4 \mathrm{~J} /{ }^{\circ} \mathrm{C} .\right)\)

A 0.1375-g sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of \(3024 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The temperature increases by \(1.126^{\circ} \mathrm{C} .\) Calculate the heat given off by the burning \(\mathrm{Mg},\) in \(\mathrm{kJ} / \mathrm{g}\) and in \(\mathrm{kJ} / \mathrm{mol} .\)
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