Chemistry: An Atoms-Focused Approach

Thomas R. Gilbert, Rein V. Kirss, Natalie Foster

Chapter 12

Thermodynamics: Why Chemical Reactions Happen - all with Video Answers

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Chapter Questions

Problem 1

The marbles in Figure $P 12.1$ occupy two of the three depressions in each of the blocks. After the black divider is removed, the marbles in each block can occupy any of the sites in that block. How many arrangements of the marbles are possible before and after removal of the divider in the (a) block and in the (b) block?
(FIGURE A,AND B, CANT COPY)

TB

Timothy Behan

Numerade Educator

Problem 2

The marbles in Figure P12.2 occupy two of the four depressions in each of the blocks. After the black divider is removed, the marbles in each block can occupy any of the sites in that block. How many arrangements of the marbles are possible before and after removal of the divider in the (a) block and in the (b) block?
(FIGURE A AND B, CANT COPY)

TB

Timothy Behan

Numerade Educator

Problem 3

Two tires shown in cross section in Figure $\mathrm{P} 12.3$ are inflated at the same temperature to the same volume, though more air is used to inflate the tire on the right. In which tire is the gas under greater internal pressure and in which does the gas have greater entropy?
(FIGURES CANT COPY)

Lottie Adams

Numerade Educator

Problem 4

Two cubic containers (Figure $\mathrm{P} 12.4$ ) contain the same quantity of gas at the same temperature.
a. Which cube contains the gas with more entropy?b. If the sample in cube (b) is left unchanged but the sample in cube (a) is cooled so that it condenses, which sample has the higher entropy?
(FIGURE A, AND B ,CANT COPY)

Lottie Adams

Numerade Educator

Problem 5

Figure $P 12.5$ shows two connected bulbs that have just been filled with a mixture of two ideal gases: A (red spheres) and $\mathrm{B}$ (blue spheres). If the molar mass of $\mathrm{A}$ is twice that of $\mathrm{B}$ will the atoms of A eventually fill the bottom bulb and the atoms of B fill the top bulb? Why or why not?
(FIGURE CANT COPY)

Lottie Adams

Numerade Educator

Problem 6

The box on the left in Figure P12.6 represents a mixture of two diatomic gases: $A_{2}$ (red sphercs) and $B_{2}$ (bluc sphercs). How do the cntropics of $\mathrm{A}_{2}$ and $\mathrm{B}_{2}$ change as a result of the process depicted by the arrow?
(FIGURE CANT COPY)

Lottie Adams

Numerade Educator

Problem 7

Is the process in Figure $\mathrm{P} 12.6$ more likely to be spontaneous at high temperature or low temperature, or is it unaffected by changing temperature?

Lottie Adams

Numerade Educator

Problem 8

Figure $P 12.8$ shows the plots of $\Delta H$ and $T \Delta S$ for a phase change as a function of temperature.(FIGURE CANT COPY)a. What is the status of the process at the point where the two lines intersect?
b. Over what temperature range is the process spontaneous?

Lottie Adams

Numerade Educator

Problem 9

Of the six phase changes-melting, vaporization, condensation, freezing, sublimation, and deposition- which ones have thermodynamic profiles that fit the pattern in Figure $\mathrm{P} 12.8 ?$

Lottie Adams

Numerade Educator

Problem 10

Use representations [A] through [I] in Figure $\mathrm{P} 12.10$ to answer questions a-f.
a. What is the sign of $\Delta S_{\text {sys }}$ for the formation of frost on a window pane in image [B]? Under what conditions would this process not be spontaneous?
b. Image [H] shows a neutralization reaction between antacid tablets (sodium bicarbonate) and stomach acid, HCl(aq). What is the sign of $\Delta S_{\text {ren }} ?$
c. Image [D] depicts the mixing of two colorless solutions that results in image $[\mathrm{F}] .$ Is $\Delta S_{r x n}$ greater than, less than, or equal to zero?
d. If you mix the particulate substances in $[\mathrm{A}]$ and $[\mathrm{C}]$ to create the mixture in $[\mathrm{E}]$, does the entropy increase, decrease, or remain unchanged?
c. When you mix the particulate substances in $[\mathrm{G}]$ ad $[\mathrm{I}]$ to form mixture [E], how does the change in volume affect the entropy?
E. Docs all mixing lead to an increase in entropy?
(FIGURES CANT COPY)

Shubham Kumar

Numerade Educator

Problem 11

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

Katie Miller

Numerade Educator

Problem 12

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.

Amanda Hyde

Numerade Educator

Problem 13

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.

Lottie Adams

Numerade Educator

Problem 14

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.)

Lottie Adams

Numerade Educator

Problem 15

Use the appropriate standard molar entropy value in Appendix 4 to calculate how many micro states are available to a single molecule of liquid $\mathrm{H}_{2} \mathrm{O}$ at $298 \mathrm{K}$.

Lottie Adams

Numerade Educator

Problem 16

Use the appropriate standard molar entropy value in Appendix 4 to calculate how many microstates are available to a single molecule of $\mathrm{N}_{2}$ at $298 \mathrm{K}$.

Lottie Adams

Numerade Educator

Problem 17

The three identical glass spheres in Figure $\mathrm{P} 12.17$ contain the same number of particles at the same temperature. Rank the containers in order of increasing number of microstates accessible to the particles inside them.
(FIGURES CANT COPY)

Lottie Adams

Numerade Educator

Problem 18

Figure $P 12.18(a)$ shows a cylinder within a cylinder that contains a population of gaseous molecules. The volume occupied by the molecules can be increased by pulling the inside cylinder out (Figure $\mathrm{P} 12.18 \mathrm{b}$ ), much like a telescope. The number of molecules within the cylinder remains the same during this operation. Compare the number of microstates available to the molecules in Figure $\mathrm{P} 12.18(\mathrm{a})$ and (b).
(FIGURES CANT COPY)

Lottie Adams

Numerade Educator

Problem 19

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) $\mathrm{LiOH}$.

Ronald Prasad

Numerade Educator

Problem 20

Which of the following molecular solutes experience an increase in entropy when dissolved in water? (a) $\mathrm{CO}_{2}(g)$.
(b) $\mathrm{HF}(g),$ (c) $\mathrm{CH}_{3} \mathrm{OH}(\ell),$ (d) $\mathrm{CH}_{3} \mathrm{COOH}(\ell)$
(e) $\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)$.

Lottie Adams

Numerade Educator

Problem 21

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 $\mathrm{O}_{3}(g)$

Albert T.

Numerade Educator

Problem 22

Metabolism of Pharmaceuticals When some pharmaceutical agents like the pain killer morphine are metabolized (Fig. P12.22), our bodies add a molecule of sugar to the active compound to make it more polar and hence more readily excreted. Will the morphine molecule experience an increase or decrease in entropy as a result of this process?
(FIGURE CANT COPY)

CC

Cevannah Coleman

Numerade Educator

Problem 23

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.

Lottie Adams

Numerade Educator

Problem 24

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.

Lottie Adams

Numerade Educator

Problem 25

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 $\mathrm{NH}_{3}(g)$

Katie Miller

Numerade Educator

Problem 26

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 $\mathrm{CS}_{2}(g)$

Lottie Adams

Numerade Educator

Problem 27

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 $\Delta S_{\text {surr }} ?$.

Katie Miller

Numerade Educator

Problem 28

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 $\Delta S_{\mathrm{surr}} ?$

Carina Carlos

Numerade Educator

Problem 29

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. $\Delta S_{\text {sys }}>0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0$

Lottie Adams

Numerade Educator

Problem 30

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. $\Delta S_{\text {sys }}<0, \Delta S_{\text {surr }}>0, \Delta S_{\text {univ }}<0$

Lottie Adams

Numerade Educator

Problem 31

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:
$$8 \mathrm{H}_{2} \mathrm{S}(g)+\mathrm{O}_{2}(g) \rightarrow 3 \mathrm{S}_{8}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$$

Albert T.

Numerade Educator

Problem 32

Predict whether the entropy of the system increases or decreases for the following reaction, which describes the process used industrially to produce sodium hydroxide and chlorine by passing electric current through brine:
$2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)$.

Albert T.

Numerade Educator

Problem 33

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?

Katie Miller

Numerade Educator

Problem 34

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?

Carina Carlos

Numerade Educator

Problem 35

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

Albert T.

Numerade Educator

Problem 36

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

Albert T.

Numerade Educator

Problem 37

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

Albert T.

Numerade Educator

Problem 38

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. $\mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)$

Albert T.

Numerade Educator

Problem 39

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. $2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$

Albert T.

Numerade Educator

Problem 40

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. $S(g)+O_{2}(g) \rightarrow S O_{2}(g)$.

Albert T.

Numerade Educator

Problem 41

Ozone Layer The following reaction plays a key role in the destruction of ozone in the atmosphere:
$$\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)
$$.The standard entropy change $\left(\Delta S_{\mathrm{rxn}}^{\circ}\right)$ is $19.9 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$.Use the standard molar entropies $\left(S^{\circ}\right)$ in Appendix 4 to calculate the $S^{\circ}$ value of $\mathrm{ClO}(g)$.

Albert T.

Numerade Educator

Problem 42

Calculate the $\Delta S^{\circ}$ value for the conversion of ozone to
oxygen,$$2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g)$$
in the absence of $\mathrm{Cl}$ atoms, and compare it with the $\Delta S^{\circ}$ value in Problem 12.41

Albert T.

Numerade Educator

Problem 43

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

Albert T.

Numerade Educator

Problem 44

What does the sign of $\Delta G$ tell you about the rate of a reaction?

Albert T.

Numerade Educator

Problem 45

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

Katie Miller

Numerade Educator

Problem 46

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

Albert T.

Numerade Educator

Problem 47

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

Katie Miller

Numerade Educator

Problem 48

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

Prashant Bana

Numerade Educator

Problem 49

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.

Katie Miller

Numerade Educator

Problem 50

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.

Carina Carlos

Numerade Educator

Problem 51

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.
$$\begin{array}{lcc}\hline & \Delta H_{\text {solution }}^{\circ}(\mathrm{k} J / \mathrm{mol}) & \Delta S_{\text {solution }}^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\\text { NaBr } & -0.60 & 57 \\\hline \text { Nal } & -7.5 & 74 \\\hline\end{array}$$

Albert T.

Numerade Educator

Problem 52

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.

Albert T.

Numerade Educator

Problem 53

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.

Albert T.

Numerade Educator

Problem 54

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

Albert T.

Numerade Educator

Problem 55

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:$$\mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)$$.

Albert T.

Numerade Educator

Problem 56

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?

Albert T.

Numerade Educator

Problem 57

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.

Albert T.

Numerade Educator

Problem 58

One source of sulfuric acid aerosols in the atmosphere is the combustion of high-sulfur fuels, which releases $\mathrm{SO}_{2}$ gas that then is further oxidized to $\mathrm{SO}_{3}$ :$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)$$.Use the appropriate $\Delta G_{f}^{\circ}$ data in Appendix 4 to calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ for this combination reaction at $25^{\circ} \mathrm{C} .$ Is it spontaneous under standard conditions?

Albert T.

Numerade Educator

Problem 59

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

Katie Miller

Numerade Educator

Problem 60

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

Carina Carlos

Numerade Educator

Problem 61

What is the lowest temperature at which the following reaction (see Problem 12.53 ) is spontaneous?
$$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightarrow \mathrm{H}_{2}(g)+\mathrm{CO}(g)$$.

Katie Miller

Numerade Educator

Problem 62

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.

Albert T.

Numerade Educator

Problem 63

Use the data in Appendix 4 to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the vaporization of hydrogen peroxide:$$\mathrm{H}_{2} \mathrm{O}_{2}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{O}_{2}(g)$$
Assuming that the calculated values are independent of temperature, what is the boiling point of hydrogen peroxide at $P=1.00$ atm?

Lottie Adams

Numerade Educator

Problem 64

Volcanoes Deposits of elemental sulfur are often seen near active volcanoes. Their presence there may be due to the following reaction of $\mathrm{SO}_{2}$ with $\mathrm{H}_{2} \mathrm{S}$ :
$$\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow \frac{3}{8} \mathrm{S}_{8}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)$$.Assuming the values of $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ do not change appreciably with temperature, over what temperature range is the reaction spontaneous?

Albert T.

Numerade Educator

Problem 65

Which of the following reactions is spontaneous (i) only at low temperatures; (ii) only at high temperatures; (iii) at all temperatures?
a. $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$
b. $2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)$
c. $\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2} \mathrm{O}(g)$

Katie Miller

Numerade Educator

Problem 66

Which of the following reactions is spontaneous (i) only at low temperatures; (ii) only at high temperatures; (iii) at all temperatures?
a. $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{MgO}(s)$
b. $2 \mathrm{CH}_{3} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(\ell)$
c. $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)$

Albert T.

Numerade Educator

Problem 67

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?

Albert T.

Numerade Educator

Problem 68

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?

Amanda Hyde

Numerade Educator

Problem 69

Describe the ways in which two chemical reactions must complement each other so that the decrease in free energy of the spontaneous one can drive the non spontaneous one.

Lottie Adams

Numerade Educator

Problem 70

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 $$\left(\Delta G_{\text {nonspon }}^{\circ}>0\right) ?$$.

Lottie Adams

Numerade Educator

Problem 71

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

Lottie Adams

Numerade Educator

Problem 72

The second step in glycolysis converts glucose 6 -phosphate into fructose 6 -phosphate (Figure P12.72). Suggest a reason why $\Delta G^{\circ}$ for this reaction is close to zero.
(FIGURES CANT COPY)

Katie Miller

Numerade Educator

Problem 73

The methane in natural gas is an important starting material, or feed stock, for producing industrial chemicals, including $\mathrm{H}_{2}$ gas.
a. Use the appropriate $\Delta G_{f}^{\circ}$ value(s) from Appendix 4 to calculate $\Delta G_{\text {rxn }}^{\circ}$ for the reaction known as steam-metban reforming:
$$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$
b. To help drive this nonspontaneous reaction, the CO tham is produced can be oxidized to $\mathrm{CO}_{2}$ using more steam:
$$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$
Use the appropriate $\Delta G_{f}^{\circ}$ value(s) from Appendix 4 to calculate $\Delta G_{\text {rxn }}^{\circ}$ for this reaction, which is known as the water-gas sbift reaction.
c. Combine these two reactions and write the chemical equation of the overall reaction in which methane and steam combine to produce hydrogen gas and carbon dioxide.
d. Calculate the $\Delta G_{\text {rxn }}^{\circ}$ value of the overall reaction. Is it spontaneous under standard conditions?

Albert T.

Numerade Educator

Problem 74

In addition to the reactions described in Problem 12.73 methane can, in theory, be used to produce hydrogen gas by a process in which it decomposes into elemental carbon and hydrogen:
(1) $\quad \mathrm{CH}_{4}(g) \rightarrow \mathrm{C}(s)+2 \mathrm{H}_{2}(g)$
and the carbon produced in the first step is then oxidized to $\mathrm{CO}_{2}:$
$$\text { (2) } \quad \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)$$
a. Calculate the $\Delta G_{\text {rxn }}^{\circ}$ values of reactions (1) and (2)
b. Write a balanced chemical equation describing the overall reaction obtained by coupling reactions ( 1 ) and
(2), and calculate its $\Delta G_{\text {rxn }}^{\circ}$ value. Is the coupled reaction spontaneous under standard conditions?

Albert T.

Numerade Educator

Problem 75

Making Steel Important industrial processes, such as converting iron ore to iron and then to steel, involve coupling a nonspontaneous reaction, such as reducing the iron in $\mathrm{Fe}_{2} \mathrm{O}_{3}$ to metallic iron, with a spontaneous one, such as the oxidation of the carbon in $\mathrm{CO}$ to $\mathrm{CO}_{2}$. Use the appropriate thermodynamic data in Appendix 4 to calculate the $\Delta G_{\mathrm{rxn}}^{\circ}$ value of the following reaction at $1450^{\circ} \mathrm{C}:$
$$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \rightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)$$

Kevin Zaborsky

Numerade Educator

Problem 76

One source of the carbon monoxide reactant in Problem 12.75 is pure hot carbon, called coke, which is derived from coal. What is the overall $\Delta G_{\text {ren }}^{\circ}$ value of the iron reduction reaction at $1450^{\circ} \mathrm{C}$ starting with carbon as the reducing agent instead of carbon monoxide? Assume coke has the thermodynamic properties of graphite.

Ronald Prasad

Numerade Educator

Problem 77

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 $\mathrm{CCl}_{3} \mathrm{F}(\ell) ?$

Albert T.

Numerade Educator

Problem 78

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?

Albert T.

Numerade Educator

Problem 79

At what temperature is the free-energy change for the following reaction equal to zero?
$$\mathrm{NH}_{4} \mathrm{Cl}(s) \rightarrow \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$$

Carina Carlos

Numerade Educator

Problem 80

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?

Carina Carlos

Numerade Educator

Problem 81

Calculate the standard free-energy change of the following reaction. Is it spontaneous?
$$2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$

Carina Carlos

Numerade Educator

Problem 82

Rudolf Clausius $(1822-1888),$ considered one of the founders of thermodynamics, summed up the second law of thermodynamics once by reportedly saying, "The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing." Use concepts and illustrations discussed in this chapter to explain his comment.

Nimi Das

Numerade Educator

Problem 83

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

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 84

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.

Albert T.

Numerade Educator

Problem 85

Tungsten (W) is the favored metal for light bulb filaments, in part because of its high melting point $\left(3422^{\circ} \mathrm{C}\right) .$ The enthalpy of fusion of tungsten is $35.4 \mathrm{kJ} / \mathrm{mol} .$ What is its entropy of fusion?

Carina Carlos

Numerade Educator

Problem 86

The absolute entropy $(S)$ of a perfect, defect-free solid equals zero and has one accessible microstate. It is impossible to make such a material, but, silicon chip manufacturers strive for as few defects as possible in their products. Calculate the absolute molar entropy for a piece of silicon with a number of probable arrangements of (a) $W=16,$ (b) $W=625,$ and $(\mathrm{c}) W=2500$ per atom of $\mathrm{Si}$.

David Collins

Numerade Educator

Problem 87

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?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 88

Over what temperature range is the reduction of tungsten(VI) oxide by hydrogen to give metallic tungsten and water spontaneous? The standard heat of formation of $\mathrm{WO}_{3}(s)$ is $-843 \mathrm{kJ} / \mathrm{mol},$ and its standard molar entropy is $76 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$.

Katie Miller

Numerade Educator

Problem 89

Lime Enormous amounts of lime (CaO) are used in steel industry blast furnaces to remove impurities from iron. Lime is made by heating limestone and other solid forms of $\mathrm{CaCO}_{3}(s) .$ Why is the standard molar entropy of $\mathrm{CaCO}_{3}(s)$ higher than that of $\mathrm{CaO}(s)$ ? At what temperature is the pressure of $\mathrm{CO}_{2}(g)$ over $\mathrm{CaCO}_{3}(s)$ equal to 1.0 atm?$$\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{k} J / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\C a C O_{3}(s) & -1207 & 93 \\\hline \mathrm{CaO}(s) & -636 & 40 \\\hline \mathrm{CO}_{2}(g) & -394 & 214 \\\hline\end{array}$$

Lottie Adams

Numerade Educator

Problem 90

Copper forms two oxides, $\mathrm{Cu}_{2} \mathrm{O}$ and $\mathrm{CuO}$.
a. Name these oxides.
b. Predict over what temperature range this reaction is spontaneous using the following thermodynamic data:$$\mathrm{Cu}_{2} \mathrm{O}(s) \rightarrow \mathrm{CuO}(s)+\mathrm{Cu}(s)$$
$$\begin{aligned}&]\\&\begin{array}{lcc} & \Delta H_{f}^{\circ}(\mathrm{kJ} / \mathrm{mol}) & S^{\circ}[J /(\mathrm{mol} \cdot \mathrm{K})] \\C u_{2} \mathrm{O}(s) & -170.7 & 92.4 \\\hline \mathrm{CuO}(s) & -156.1 & 42.6 \\\hline\end{array}\end{aligned}$$.c. Why is the standard molar entropy of $\mathrm{Cu}_{2} \mathrm{O}(s)$ larger than that of $\mathrm{CuO}(s) ?$

Angela Williamson

Angela Williamson

Numerade Educator

Problem 91

Compounds When dicarboxylic acids (compounds with two - COOH groups in their structures) melt, they frequently decompose to produce one mole of $\mathrm{CO}_{2}$ gas for every mole of dicarboxylic acid melted (see Figure $P 12.91)$.
a. What are the signs of $\Delta H$ and $\Delta S$ for the process as written?
b. Do you think the dicarboxylic acid will re-form when the melted material cools? Why or why not?
(FIGURE CANT COPY)

Lottie Adams

Numerade Educator

Problem 92

Melting DNA strands.
a. What is the sign of $\Delta S$ for the separation process?
b. The DNA double helix re-forms as the system cools. What is the sign of $\Delta S$ for the process by which two single strands re-form the double helix?
c. The melting point of DNA is defined as the temperature at which $\Delta G=0 .$ At that temperature, the melting reaction produces two single strands as fast as two single strands recombine to form the double helix. Write an equation that defines the melting temperature
(T) of DNA in terms of $\Delta H$ and $\Delta S$.

Lottie Adams

Numerade Educator