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Chapter 5: Problem 41

Ozone, \(\mathrm{O}_{3}(g)\), is a form of elemental oxygen that is important in the absorption of ultraviolet radiation in the stratosphere. It decomposes to \(\mathrm{O}_{2}(g)\) at room temperature and pressure according to the following reaction: $$ 2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g) \quad \Delta H=-284.6 \mathrm{~kJ} $$ (a) What is the enthalpy change for this reaction per mole of \(\mathrm{O}_{3}(g) ?(\mathbf{b})\) Which has the higher enthalpy under these condi- $$ \text { tions, } 2 \mathrm{O}_{3}(g) \text { or } 3 \mathrm{O}_{2}(g) ? $$

Short Answer

Expert verified
(a) The enthalpy change per mole of O₃(g) for this reaction is -142.3 kJ/mol. (b) 2 O₃(g) has a higher enthalpy than 3 O₂(g) under these conditions.

Step by step solution

01

Calculation of Enthalpy Change per Mole of O₃(g)

We are given the enthalpy change for the reaction (∆H) as -284.6 kJ. This value corresponds to the enthalpy change for 2 moles of O₃(g), as shown in the balanced chemical equation. To find the enthalpy change per mole of O₃(g), we need to divide this value by the number of moles, which is 2 moles of O₃(g). $$ \frac{-284.6 \mathrm{kj}}{2 \,\mathrm{moles \, of \, O_3(g)}} = -142.3 \mathrm{kJ/mol \, of \, O_3(g)} $$ The enthalpy change per mole of O₃(g) for this reaction is -142.3 kJ/mol.
02

Comparison of Enthalpies of 2 O₃(g) and 3 O₂(g)

Since the given enthalpy change (∆H) for the reaction is negative (-284.6 kJ), this means that the reaction is exothermic. A negative enthalpy change indicates that energy is released as the reaction proceeds, which implies that the reactants have higher enthalpy compared to the products. In this case, that means 2 O₃(g) has a higher enthalpy than 3 O₂(g) under these conditions. In conclusion, (a) The enthalpy change per mole of O₃(g) for this reaction is -142.3 kJ/mol. (b) 2 O₃(g) has a higher enthalpy than 3 O₂(g) under these conditions.

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Most popular questions from this chapter

Using values from Appendix \(\mathrm{C},\) calculate the standard enthalpy change for each of the following reactions: (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)\)

In a thermodynamic study a scientist focuses on the properties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the apparatus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? Explain your choice. (b) If it is not a closed system, what could be done to make it a closed system?

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of the system a state function? Why or why not?

Consider the following unbalanced oxidation-reduction reactions in aqueous solution: $$ \begin{aligned} \mathrm{Ag}^{+}(a q)+\mathrm{Li}(s) & \longrightarrow \mathrm{Ag}(s)+\mathrm{Li}^{+}(a q) \\ \mathrm{Fe}(s)+\mathrm{Na}^{+}(a q) \longrightarrow \mathrm{Fe}^{2+}(a q)+\mathrm{Na}(s) \\ \mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g) \end{aligned} $$ (a) Balance each of the reactions. (b) By using data in Appen\(\operatorname{dix} C,\) calculate \(\Delta H^{\circ}\) for each of the reactions. (c) Based on the values you obtain for \(\Delta H^{\circ}\), which of the reactions would you expect to be thermodynamically favored? (d) Use the activity series to predict which of these reactions should occur. (Section 4.4) Are these results in accord with your conclusion in part (c) of this problem?

From the enthalpies of reaction $$ \begin{aligned} 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{CO}(g) & \Delta H=&-221.0 \mathrm{~kJ} \\ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2}(g) & \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH}(g) & \Delta H=&-402.4 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the reaction $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g) $$
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