Chapter 12

How is the entropy change that accompanies a reaction related to the entropy change that happens when the reaction runs in reverse?

Identify the following processes as spontaneous or nonspontaneous, and explain your choice. a. A photo voltaic cell in a portable device charges your cell phone. b. Dry icc (solid \(\mathrm{CO}_{2}\) ) sublimes at room temperature. c. A radio pharmaceutical imaging agent containing technetium emits gamma rays.

You flip three coins, assigning the values +1 for heads and -1 for tails. Each outcome of the three flips constitutes a micro state. How many different micro states are possible from flipping the three coins? Which value or values for the sums in the micro states are most likely? Hint: The sequence HHT \((+1+1-1)\) is one possible outcome, or micro state. Note, however, that this outcome differs from THH \((-1+1+1)\), even though the two sequences sum to the same value.

Imagine you have four identical chairs to arrange on four steps leading up to a stage, one chair on each step. The chairs have numbers on their backs: \(1,2,3,\) and \(4 .\) How many different micro states for the chairs are possible? (When viewed from the front, all the micro states look the same. When viewed from the back, you can identify the different micro states because you can distinguish the chairs by their numbers.)

Which of the following ionic solutes experiences the greatest increase in entropy when 0.0100 mol of it dissolves in 1.00 liter of water? (a) \(\mathrm{CaCl}_{2},\) (b) \(\mathrm{NaBr},(\mathrm{c}) \mathrm{KCl}\) (d) \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3},\) (e) \(\mathrm{LiOH}\).

Which component in each of the following pairs has the greater entropy? a. 1 mole of \(\mathrm{S}_{2}(g)\) or 1 mole of \(\mathrm{S}_{8}(g)\) b. 1 mole of \(S_{2}(g)\) or 1 mole of \(S_{8}(s)\) c. 1 mole of \(\mathrm{O}_{2}(g)\) or 1 mole of \(\mathrm{O}_{3}(g)\)

Diamond and the fullerenes are allotropes of carbon. On the basis of their different structures and properties, predict which has the higher standard molar entropy.

The 1996 Nobel Prize in Physics was awarded to Douglas Osheroff, Robert Richardson, and David Lee for discovering superfluidity (apparently frictionless flow) in \(^{3} \mathrm{He} .\) When \(^{3} \mathrm{He}\) is cooled to \(2.7 \mathrm{mK},\) the liquid settles into an ordered super fluid state. Predict the sign of the entropy change for the conversion of liquid \(^{3} \mathrm{He}\) into its super fluid state.

Rank the compounds in each of the following groups in order of increasing standard molar entropy \(\left(S^{\circ}\right):\). a. \(\mathrm{CH}_{4}(g), \mathrm{CF}_{4}(g),\) and \(\mathrm{CCl}_{4}(g)\) b. \(\mathrm{CH}_{2} \mathrm{O}(g), \mathrm{CH}_{3} \mathrm{CHO}(g),\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}(g)\) c. \(\mathrm{HF}(g), \mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{NH}_{3}(g)\)

Rank the compounds in each of the following groups in order of increasing standard molar entropy \(\left(S^{\circ}\right):\) a. \(\mathrm{CH}_{4}(g), \mathrm{CH}_{3} \mathrm{CH}_{3}(g),\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g)\) b. \(\mathrm{CCl}_{4}(\ell), \mathrm{CHCl}_{3}(\ell),\) and \(\mathrm{CH}_{2} \mathrm{Cl}_{2}(\ell)\) c. \(\mathrm{CO}_{2}(\ell), \mathrm{CO}_{2}(g),\) and \(\mathrm{CS}_{2}(g)\)

Ice cubes melt in a glass of lemonade, cooling the lemonade from \(10.0^{\circ} \mathrm{C}\) to \(0.0^{\circ} \mathrm{C} .\) If the ice cubes are the system, what are the signs of \(\Delta S_{\mathrm{sys}}\) and \(\Delta S_{\text {surr }} ?\).

Adding sidewalk deicer (calcium chloride) to water causes the temperature of the water to increase. If solid \(\mathrm{CaCl}_{2}\) is the system, what are the signs of \(\Delta S_{\mathrm{sys}}\) and \(\Delta S_{\mathrm{surr}} ?\)

Which of the following combinations of entropy changes for a process are mathematically possible? a. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}>0\) b. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}<0, \Delta S_{\text {univ }}>0\) c. \(\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0\)

Which of the following combinations of entropy changes for a process are mathematically possible? a. \(\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}>0\) b. \(\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}<0, \Delta S_{\text {univ }}>0\) c. \(\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0\)

Predict whether the entropy of the system increases or decreases for the following reaction, which describes the process used to remove hydrogen sulfide from natural gas: $$8 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow 3 \mathrm{S}_{8}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$$

If the value of \(\Delta S_{\text {rxn }}\) of the non spontaneous reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) is \(-66.0 \mathrm{J} / \mathrm{K},\) what is the maximum entropy change in the reaction's surroundings?

The value of \(\Delta S_{\mathrm{rxn}}\) of the spontaneous reaction \(\mathrm{D}+\mathrm{E} \rightarrow \mathrm{F}\) is \(72.0 \mathrm{J} / \mathrm{K} .\) What is the minimum value of the entropy change in the reaction's surroundings?

Under standard conditions, the products of a reaction have, overall, greater entropy than the reactants. What is the sign of \(\Delta S_{\mathrm{rxn}}^{\circ} ?\)

Do decomposition reactions tend to have \(\Delta S_{\mathrm{rxn}}^{\circ}\) values that are greater than zero or less than zero? Why?

Do precipitation reactions tend to have \(\Delta S_{\mathrm{rxn}}^{\circ}\) values that are greater than zero or less than zero? Why?

For each of the reactions given, indicate whether \(\Delta S\) should have a positive sign or a negative sign. If it is not possible to judge the sign of \(\Delta S\) based on the information provided, indicate why that is the case. a. \(2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{NaCl}(s)\) b. \(4 \mathrm{H}_{3} \mathrm{PO}_{3}(\ell) \rightarrow \mathrm{PH}_{3}(g)+3 \mathrm{H}_{3} \mathrm{PO}_{4}(\ell)\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)\)

Smog Use the standard molar entropies in Appendix 4 to calculate \(\Delta S^{\circ}\) values for each of the following atmospheric reactions that contribute to the formation of photo chemical smog. a. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)\) b. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) c. \(\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)\) d. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\)

Use the standard molar entropies in Appendix 4 to calculate the \(\Delta S^{\circ}\) value for each of the following reactions of sulfur compounds. a. \(\mathrm{H}_{2} \mathrm{S}(g)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{2}(g)\) b. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) c. \(\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) d. \(S(g)+O_{2}(g) \rightarrow S O_{2}(g)\).

What does the sign of \(\Delta G\) tell you about the spontaneity of a process?

Many 19 th-century scientists believed that all exothermic reactions were spontaneous. Why did so many of them share this belief?

In which direction does a reaction proceed when (a) \(\Delta G_{\text {rxn }}<0 ;\) (b) \(\Delta G_{\text {rxn }}=0 ;\) (c) \(\Delta G_{\text {ren }}>0 ?\)

What are the signs of \(\Delta S, \Delta H,\) and \(\Delta G\) for the sublimation of dry ice (solid \(\mathrm{CO}_{2}\) ) at \(25^{\circ} \mathrm{C} ?\)

What are the signs of \(\Delta S, \Delta H,\) and \(\Delta G\) for the formation of dew on a cool night?

Which of the following processes is/are spontaneous? a. A tornado forms. b. A broken cell phone fixes itself. c. You get an \(A\) in this course. d. Hot soup gets cold before it is served.

Which of the following processes is/are spontaneous? a. Wood burns in air. b. Water vapor condenses on the sides of a glass of iced tea. c. Salt dissolves in water. d. Photosynthesis occurs.

Calculate the free-energy change for the dissolution in water of one mole of \(\mathrm{NaBr}\) and one mole of \(\mathrm{NaI}\) at \(298 \mathrm{K}\) from the values in the following table. $$\begin{array}{lcc}\hline & \Delta H_{\text {solution }}^{\circ}(\mathrm{k} J / \mathrm{mol}) & \Delta S_{\text {solution }}^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\\\text { NaBr } & -0.60 & 57 \\\\\hline \text { Nal } & -7.5 & 74 \\\\\hline\end{array}$$

The values of \(\Delta H_{\mathrm{rxn}}^{\circ}\) and \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ are \(-12 \mathrm{kJ}\) and \(-146 \mathrm{J} / \mathrm{K}\) a. Use these values to calculate \(\Delta G_{\text {rxn }}^{\circ}\) at \(298 \mathrm{K}\) b. Explain why the value of \(\Delta S_{\text {rxn }}^{\circ}\) is negative.

A mixture of \(\mathrm{CO}(g)\) and \(\mathrm{H}_{2}(g)\) is produced by passing steam over hot charcoal: $$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightarrow \mathrm{H}_{2}(g)+\mathrm{CO}(g)$$ Calculate the \(\Delta G_{\text {rxn }}^{\circ}\) value for the reaction from the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4.

Use the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4 to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for the complete combustion of methanol: $$2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$$

Photo chemical Smog Use the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4 to calculate \(\Delta G_{\text {rxn }}^{\circ}\) for the oxidation of NO to \(\mathrm{NO}_{2}-\) a key reaction in the formation of photo chemical smog:$$\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)$$.

Use the free energies of formation from Appendix 4 to calculate the standard free-energy change for the decomposition of ammonia in the following reaction: $$2 \mathrm{NH}_{3}(g) \rightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$$ Is the reaction spontaneous under standard conditions?

Acid Precipitation Aerosols (fine droplets) of sulfuric acid form in the atmosphere as a result of the following combination reaction:$$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)$$.Use the appropriate \(\Delta G_{f}^{\circ}\) data in Appendix 4 to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for this reaction.

Are exothermic reactions spontaneous only at low temperature? Explain your answer.

Are endothermic reactions never spontaneous at low temperature? Explain your answer.

Above what temperature does nitrogen monoxide form from nitrogen and oxygen? $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)$$ Assume that the values of \(\Delta H_{\mathrm{rxn}}^{\circ}\) and \(\Delta S_{\mathrm{rxn}}^{\circ}\) do not change appreciably with temperature.

One method for the industrial production of methanol uses the following reaction: $$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\ell)$$ a. Use the data in Appendix 4 to calculate \(\Delta G^{\circ}\) for this reaction at \(298 \mathrm{K}\) b. The reaction is normally run at a minimum temperature of \(475 \mathrm{K}\). What is the value of \(\Delta G\) at that temperature? Is the reaction spontaneous at that temperature?

Gas streams containing \(\mathrm{CO}_{2}\) are frequently passed through absorption tubes filled with \(\mathrm{CaO}(s),\) where the following reaction takes place to remove the \(\mathrm{CO}_{2}\) from the stream:$$\mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)$$. a. Use the data in Appendix 4 to calculate \(\Delta G^{\circ}\) at \(298 \mathrm{K}\) for this reaction. b. Is the reaction spontaneous at \(298 \mathrm{K} ?\) c. Calculate \(\Delta G\) for this reaction at \(1500 \mathrm{K},\) a typical temperature for a lime kiln. (Assume \(\Delta H\) and \(\Delta S\) do not change with temperature.) d. Is the reaction as written spontaneous at \(1500 \mathrm{K}\) ? e. In a lime kiln, calcium carbonate (in the form of oyster shells) is roasted to produce \(\mathrm{CaO}\) and \(\mathrm{CO}_{2} .\) Is this process spontaneous at the temperature of a kiln?

How do you calculate the value of \(\Delta G^{\circ}\) for a reaction that is the result of coupling a spontaneous reaction \(\left(\Delta G_{\text {spon }}^{\circ}<0\right)\).and a nonspontaneous reaction $$\left(\Delta G_{\text {nonspon }}^{\circ}>0\right) ?$$.

Why is it important that at least some of the spontaneous steps in glycolysis convert ADP to ATP?

Chlorofluorocarbons (CFCs) are no longer used as refrigerants because they catalyze the decomposition of stratospheric ozone. Trichlorofluoromethane (CC1 \(_{3} \mathrm{F}\) ) boils at \(23.8^{\circ} \mathrm{C}\) and its molar heat of vaporization is \(24.8 \mathrm{kJ} / \mathrm{mol}\) What is the molar entropy of vaporization of \(\mathrm{CCl}_{3} \mathrm{F}(\ell) ?\)

Methanogenic bacteria convert liquid acetic acid (CH \(_{3} \mathrm{COOH}\) ) into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{CH}_{4}(g)\). a. Is this process endothermic or exothermic under standard conditions? b. Is the reaction spontaneous under standard conditions?

Consider the precipitation reactions described by the following net ionic equations: $$\begin{aligned}\mathrm{Mg}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) \rightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s) \\\\\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \rightarrow \mathrm{AgCl}(s)\end{aligned}$$.a. Predict the sign of \(\Delta S_{\mathrm{rxn}}^{\circ}\) for the reactions. b. Using the values for \(S^{\circ}\) from Appendix 4, calculate \(\Delta S^{\circ}\) for these reactions. c. Do your calculations support your prediction?

Show that hydrogen cyanide (HCN) is a gas at \(25^{\circ} \mathrm{C}\) by estimating its normal boiling point from the following data:$$\begin{array}{ccc} & \Delta H_{i}^{\circ}(\mathrm{k} J / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\\\mathrm{HCN}(\ell) & 108.9 & 113 \\ \hline \mathrm{HCN}(g) & 135.1 & 202 \\\\\hline\end{array}$$

Write two equations for the complete combustion of one mole of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g),\) in oxygen at \(298 \mathrm{K}:\) in the first equation, the water produced as a product is a liquid; in the second equation, the water is in the gas phase. a. Determine \(\Delta G^{\circ}\) for each reaction. "b. Suggest a way you could determine the difference between the two \(\Delta G^{\circ}\) values without having to solve for \(\Delta G^{\circ}\) for both reactions.

Two allotropes ( \(A\) and \(B\) ) of sulfur interconvert at \(369 \mathrm{K}\) and 1 atm pressure:$$\mathrm{S}_{\mathrm{s}}(s, \mathrm{A}) \rightarrow \mathrm{S}_{\mathrm{g}}(s, \mathrm{B})$$.The enthalpy change in this transition is \(297 \mathrm{J} / \mathrm{mol}\). What is the entropy change?