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Chapter 17: Problem 13

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\) (b) \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(g)\) (c) \(\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)\)

Short Answer

Expert verified
Question: Predict the sign of the entropy change (∆S°) for each of the following reactions: (a) O3(g) ⟶ O2(g)+O(g) (b) PCl3(g)+Cl2(g) ⟶ PCl5(g) (c) CuSO4(s)+5 H2O(l) ⟶ CuSO4 · 5 H2O(s) Answer: (a) The sign of ∆S° for this reaction is positive. (b) The sign of ∆S° for this reaction is negative. (c) The sign of ∆S° for this reaction is negative.

Step by step solution

01

Reaction (a)

For the reaction \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\), we can see that there is 1 gaseous reactant and 2 gaseous products. The number of particles increases from the reactant to the products, and therefore, the entropy increases. This means the sign of \(\Delta S^\circ\) will be positive.
02

Reaction (b)

For the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g)\), there are 2 gaseous reactants and 1 gaseous product. The number of particles decreases from the reactants to the products, making the system more ordered. Thus, the sign of \(\Delta S^\circ\) will be negative.
03

Reaction (c)

For the reaction \(\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)\), there is a solid reactant and liquid reactants coming together to form a more ordered solid product. Since there is a change from less ordered states (solid and liquid) to a more ordered state (solid), the system becomes more ordered. Consequently, the sign of \(\Delta S^\circ\) will be negative.

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Most popular questions from this chapter

For the reaction $$ \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g) $$ \(K=50.0\) at \(721 \mathrm{~K}\) (a) What is \(\Delta G^{\circ}\) at \(721 \mathrm{~K} ?\) (b) What is \(K\) at \(25^{\circ} \mathrm{C}\) ? \(\left(\Delta G_{f}^{\circ} \mathrm{I}_{2}(g)=+19.4 \mathrm{~kJ} / \mathrm{mol}\right.\) )

Oxygen can be made in the laboratory by reacting sodium peroxide and water. $$ \begin{gathered} 2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{NaOH}(s)+\mathrm{O}_{2}(g) \\ \Delta H^{\circ}=-109.0 \mathrm{~kJ} ; \Delta G^{\circ}=-148.4 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\). Is the sign reasonable? (b) Calculate \(S^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\). (c) Calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\).

Which of the following processes are spontaneous? (a) a snowman melting in the sun (b) building a house of cards (c) sorting clothes in a laundry basket

How many moles of ATP must be converted to ADP by the reaction \(\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{ADP}(a q)+\mathrm{HPO}_{4}^{2-}(a q)+2 \mathrm{H}^{+}(a q)\) $$ \Delta G^{\circ}=-31 \mathrm{~kJ} $$ to bring about a nonspontaneous biochemical reaction in which \(\Delta G^{\circ}=+372 \mathrm{~kJ}\) ?

Phosgene, \(\mathrm{COCl}_{2}\), can be formed by the reaction of chloroform, \(\mathrm{CHCl}_{3}(l)\), with oxygen: $$ \begin{gathered} 2 \mathrm{CHCl}_{3}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{COCl}_{2}(g)+2 \mathrm{HCl}(g) \\ \Delta H^{\circ}=-353,2 \mathrm{~kJ} ; \Delta G^{\circ}=-452.4 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\) for the reaction. Is the sign reasonable? (b) Calculate \(S^{\circ}\) for phosgene. (c) Calculate \(\Delta H_{f}^{\circ}\) for phosgene.
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