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Chemistry: The Molecular Science

John W. Moore, Conrad L. Stanitski, Peter C. Jurs

Chapter 18

Thermodynamics: Directionality of Chemical Reactions - all with Video Answers

Educators

Chapter Questions

01:10

Problem 1

Define the terms "product-favored system" and "reactant favored system." Give one example of each.

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01:06

Problem 2

What are the two ways that a final chemical state of a system can be more probable than its initial state?

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01:47

Problem 3

Define the term "entropy," and give an example of a sample of matter that has zero entropy. What are the units of entropy? How do they differ from the units of enthalpy?

Lottie Adams
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01:44

Problem 4

State five useful qualitative rules for predicting entropy changes when chemical or physical changes occur.

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01:06

Problem 5

State the second law of thermodynamics.

Amanda Hyde
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00:30

Problem 6

In terms of values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$, under what conditions can you be sure that a reaction is product-favored? When can you be sure that it is not product-favored?

Nicole Mabante
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01:18

Problem 7

Define the Gibbs free energy change of a chemical reaction in terms of its enthalpy and entropy changes. Why is the Gibbs free energy change especially useful in predicting

David Collins
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01:13

Problem 8

Why are materials whose reactions release large quantities of Gibbs free energy useful to society? Give two examples of such materials.

Lottie Adams
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00:39

Problem 9

How are materials whose reactions release large quantities of Gibbs free energy important to you? Give two examples of such materials.

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01:23

Problem 10

Define the terms "endergonic" and "exergonic.".

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00:45

Problem 11

What is the citric acid cycle, and why is it important to organisms?

Nicole Mabante
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03:13

Problem 12

Define these important biochemistry terms: metabolism, nutrients, ATP, ADP, oxidative phosphorylation, coupled reactions, phototrophs, chemotrophs, photosynthesis.

Nicole Mabante
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01:30

Problem 13

Describe two ways to cause reactant-favored reactions to form products.

Lottie Adams
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01:25

Problem 14

Describe the process by which sunlight is employed to convert high-entropy, low-Gibbs-free-energy substances into low-entropy, high-Gibbs-free-energy substances.

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01:22

Problem 15

For each process, write a chemical equation and classify the process as reactant-favored or product-favored.
(a) Water decomposes to its elements, hydrogen and oxygen.
(b) Gasoline spilled on the ground evaporates (use octane, $\mathrm{C}_{8} \mathrm{H}_{18}$, to represent gasoline).
(c) Sugar dissolves in water at room temperature.

Lottie Adams
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01:22

Problem 16

For each process, write a chemical equation and classify the process as reactant-favored or product-favored.
(a) Carbon dioxide gas decomposes to its elements, carbon and oxygen.
(b) The steel (mostly iron) body of an automobile rusts.
(c) Gasoline reacts with oxygen to form carbon dioxide and water (use octane, $\mathrm{C}_{8} \mathrm{H}_{18}$, to represent gasoline).

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01:10

Problem 17

Suppose you flip a coin.
(a) What is the probability that the coin will come up heads?
(b) What is the probability that it will come up tails?
(c) If you flip the coin 100 times, what is the most likely number of heads and tails you will see?

Lottie Adams
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01:09

Problem 18

Suppose you make a tetrahedron and put numbers $1,2,3$, and 4 on each of the four sides. You toss the tetrahedron in the air and observe it after it comes to rest.
(a) What is the probability that the tetrahedron will come to rest with the numbers 2,3, and 4 visible?
(b) What is the probability that the tetrahedron will come to rest with the numbers 1,2, and 3 visible?
(c) If you toss the tetrahedron 100 times, what is the most likely number of times you will see a 1 after it comes to rest?

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01:04

Problem 19

Consider two equal-sized flasks connected as in shown in the figure.
(a) Suppose you put one molecule inside. What is the probability that the molecule will be in flask A? What is the probability that it will be in flask $\mathrm{B}$ ?
(b) If you put 100 molecules into the two-flask system, what is the most likely arrangement of molecules? Which arrangement has the highest entropy?

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03:19

Problem 20

Suppose you have four identical molecules labeled $1,2,3$, and $4 .$ Draw 16 simple two-flask diagrams as in the figure for Question 19, and draw all possible arrangements of the four molecules in the two flasks. How many of these arrangements have two molecules in each flask? How many have no molecules in one flask? From these results, what is the most probable arrangement of molecules? Which arrangement has the highest entropy?

David Collins
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02:01

Problem 21

For each process, tell whether the entropy change of the system is positive or negative.
(a) Water vapor (the system) deposits as ice crystals on a cold windowpane.
(b) A can of carbonated beverage loses its fizz. (Consider the beverage but not the can as the system. What happens to the entropy of the dissolved gas?)
(c) A glassblower heats glass (the system) to its softening temperature.

Lottie Adams
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01:28

Problem 22

For each process, tell whether the entropy change of the system is positive or negative.
(a) Water boils.
(b) A teaspoon of sugar dissolves in a cup of coffee. (The system consists of both sugar and coffee.)
(c) Calcium carbonate precipitates out of water in a cave to form stalactites and stalagmites. (Consider only the calcium carbonate to be the system.)

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00:32

Problem 23

For each situation described in Question 15, tell whether the entropy of the system increases or decreases.

Nicole Mabante
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00:54

Problem 24

For each situation described in Question 16, tell whether the entropy of the system increases or decreases.

Nicole Mabante
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00:48

Problem 25

For each pair of items, tell which has the higher entropy, and explain why.
(a) Item 1, a sample of solid $\mathrm{CO}_{2}$ at $-78^{\circ} \mathrm{C}$, or item $2, \mathrm{CO}_{2}$ vapor at $0^{\circ} \mathrm{C}$
(b) Item 1, solid sugar, or item 2, the same sugar dissolved in a cup of tea
(c) Item 1, a 100-mL sample of pure water and a 100 -mL sample of pure alcohol, or item 2, the same samples of water and alcohol after they had been poured together and stirred

Nicole Mabante
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00:41

Problem 26

For each pair of items, tell which has the higher entropy, and explain why.
(a) Item 1, a sample of pure silicon (to be used in a computer chip), or item 2, a piece of silicon having the same mass but containing a trace of some other element, such as $\mathrm{B}$ or $\mathrm{P}$
(b) Item 1, an ice cube at $0{ }^{\circ} \mathrm{C}$, or item 2 , the same mass of liquid water at $0{ }^{\circ} \mathrm{C}$
(c) Item 1, a sample of pure $\mathrm{I}_{2}$ solid at room temperature, or item 2, the same mass of iodine vapor at room temperature

Nicole Mabante
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02:04

Problem 27

Comparing the formulas or states for each pair of substances, tell which you would expect to have the higher entropy per mole at the same temperature, and explain why.
(a) $\mathrm{NaCl}(\mathrm{s})$ or $\mathrm{CaO}(\mathrm{s})$
(b) $\mathrm{Cl}_{2}(\mathrm{~g})$ or $\mathrm{P}_{4}(\mathrm{~g})$
(c) $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s})$ or $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{aq})$

Nicole Mabante
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00:48

Problem 28

Comparing the formulas or states for each pair of substances, tell which you would expect to have the higher entropy per mole at the same temperature, and explain why.
(a) $\mathrm{CH}_{3} \mathrm{NH}_{2}(\mathrm{~g})$ or $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}(\mathrm{g})$
(b) $\mathrm{Au}(\mathrm{s})$ or $\mathrm{Hg}(\ell)$
(c) $\mathrm{Kr}(\mathrm{g})$ or $\mathrm{C}_{6} \mathrm{H}_{14}(\mathrm{~g})$

Nicole Mabante
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01:03

Problem 29

From each pair of substances listed below, select the one having the larger standard molar entropy at $25^{\circ} \mathrm{C}$. Give reasons for your choice.
(a) $\mathrm{Ga}(\mathrm{s})$ or $\mathrm{Ga}(\ell)$
(b) $\mathrm{AsH}_{3}(\mathrm{~g})$ or $\mathrm{Kr}(\mathrm{g})$
(c) $\mathrm{NaF}(\mathrm{s})$ or $\mathrm{MgO}(\mathrm{s})$

Nicole Mabante
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00:45

Problem 30

From each pair of substances listed below, select the one having the larger standard molar entropy at $25^{\circ} \mathrm{C}$. Give reasons for your choice.
(a) $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ or $\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})$
(b) $\mathrm{CH}_{3} \mathrm{OH}(\ell)$ or $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$
(c) Butane or cyclobutane

Nicole Mabante
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01:35

Problem 31

Without doing a calculation, predict whether the entropy change will be positive or negative when each reaction occurs in the direction it is written.
(a) $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})$
(b) $\mathrm{CH}_{3} \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$
(c) $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})$
(d) $\mathrm{CaCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})$

Lottie Adams
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01:24

Problem 32

Without doing a calculation, predict whether the entropy change will be positive or negative when each reaction occurs in the direction it is written.
(a) $\mathrm{CH}_{3} \mathrm{OH}(\ell) \longrightarrow \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g})$
(b) $\mathrm{Br}_{2}(\ell)+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HBr}(\mathrm{g})$
(c) $\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{CH}_{4}(\mathrm{~g})$
(d) $\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgI}(\mathrm{s})$

Lottie Adams
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00:29

Problem 33

Without consulting a table of standard molar entropies, predict whether $\Delta S_{\text {system }}^{\circ}$ will be positive or negative for each of these reactions.
(a) $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})$
(b) $2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)$
(c) $2 \mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{~g})$

Nicole Mabante
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00:28

Problem 34

Without consulting a table of standard molar entropies, predict whether $\Delta S_{\text {system }}^{\circ}$ will be positive or negative for each of these reactions.
(a) $2 \mathrm{NH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})$
(b) $2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NaCl}(\mathrm{s})$
(c) $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~s}) \longrightarrow 2 \mathrm{HI}(\mathrm{g})$

Nicole Mabante
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00:38

Problem 35

Calculate the entropy change, $\Delta S^{\circ}$, for the vaporization of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$, at the boiling point of $78.3^{\circ} \mathrm{C}$. The heat of vaporization of the alcohol is $39.3 \mathrm{~kJ} / \mathrm{mol}$.
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{g}) \quad \Delta S^{\circ}=?
$$

Nicole Mabante
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01:07

Problem 36

Diethyl ether, $\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}$, was once used as an anesthetic. What is the entropy change, $\Delta S^{\circ}$, for the vaporization of ether if its heat of vaporization is $26.0 \mathrm{~kJ} / \mathrm{mol}$ at the boiling point of $35.0^{\circ} \mathrm{C}$ ?

David Collins
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00:59

Problem 37

Calculate $\Delta S^{\circ}$ for each substance when the quantity of thermal energy indicated is transferred reversibly to the system at the temperature specified. Assume that you have enough of each substance so that its temperature remains constant as the thermal energy is transferred.
(a) $\mathrm{H}_{2}(\mathrm{~g}), 0.775 \mathrm{~kJ}, 295 \mathrm{~K}$
(b) $\mathrm{KCl}(\mathrm{s}), 500 \cdot \mathrm{kJ}, 500 . \mathrm{K}$
(c) $\mathrm{N}_{2}(\mathrm{~g}), 2.45 \mathrm{~kJ}, 1000 . \mathrm{K}$

Nicole Mabante
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00:33

Problem 38

Calculate $\Delta S^{\circ}$ for each of these substances when the quantity of thermal energy indicated is transferred reversibly to the system at the temperature specified. Assume that you have enough of each substance so that its temperature remains constant as the thermal energy is transferred.
(a) $\mathrm{NaCl}(\mathrm{s}), 5.00 \mathrm{~kJ}, 500 . \mathrm{K}$
(b) $\mathrm{N}_{2} \mathrm{O}(\mathrm{g}), 0.30 \mathrm{~kJ}, 300 . \mathrm{K}$

Nicole Mabante
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01:16

Problem 39

The standard molar entropy of methanol vapor, $\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$, is $239.8 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.
(a) Calculate the entropy change for the vaporization of 1 mol methanol (use data from Table $18.1$ or Appendix $J$.
(b) Calculate the enthalpy of vaporization of methanol, assuming that $\Delta S^{\circ}$ doesn't depend on temperature and taking the boiling point of methanol to be $64.6^{\circ} \mathrm{C}$.

Nicole Mabante
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01:34

Problem 40

The standard molar entropy of iodine vapor, $\mathrm{I}_{2}(\mathrm{~g})$, is $260.7 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and the standard molar enthalpy of formation is $62.4 \mathrm{~kJ} / \mathrm{mol}$.
(a) Calculate the entropy change for vaporization of $1 \mathrm{~mol}$ of solid iodine (use data from Table $18.1$ or Appendix $J$.
(b) Calculate the enthalpy change for sublimation of iodine.
(c) Assuming that $\Delta S^{\circ}$ does not change with temperature, estimate the temperature at which iodine would sublime (change directly from solid to gas).

David Collins
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02:10

Problem 41

Check your predictions in Question 31 by calculating the entropy change for each reaction. Standard molar entropies not in Table $18.1$ can be found in Appendix J.

Nicole Mabante
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01:49

Problem 42

Check your predictions in Question 32 by calculating the entropy change for each reaction. Standard molar entropies not in Table $18.1$ can be found in Appendix $\mathrm{J}$

Nicole Mabante
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01:55

Problem 43

Check your predictions in Question 33 by calculating the entropy change for each reaction. Standard molar entropies not in Table $18.1$ can be found in Appendix $\mathrm{J}$.

Nicole Mabante
Nicole Mabante
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01:20

Problem 44

Check your predictions in Question 34 by calculating the entropy change for each reaction. Standard molar entropies not in Table $18.1$ can be found in Appendix $\mathrm{J}$

Nicole Mabante
Nicole Mabante
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01:56

Problem 45

Calculate $\Delta S_{\text {system }}^{\circ}$ at $25^{\circ} \mathrm{C}$ for the reaction
$$
\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)
$$
Can you tell from the result of this calculation whether this reaction is product-favored? If you cannot tell, what additional information do you need? Obtain that information and determine whether the reaction is product-favored.

Nicole Mabante
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01:47

Problem 46

Calculate $\Delta S_{\text {system }}^{\circ}$ at $25^{\circ} \mathrm{C}$ for the reaction
$$
\mathrm{C}_{6} \mathrm{H}_{6}(\ell)+4 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{14}(\ell)
$$
Can you tell from the result of this calculation whether this reaction is product-favored? If you cannot tell, what additional information do you need? Obtain that information and determine whether the reaction is product-favored.

David Collins
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00:43

Problem 47

Is this reaction predicted to favor the products at low temperatures, at high temperatures, or both? Explain your answer briefly.
$$
\mathrm{Mg}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{MgO}(\mathrm{s}) \quad \Delta H^{\circ}=-601.70 \mathrm{~kJ}
$$

Nicole Mabante
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00:43

Problem 48

Is this reaction predicted to favor the products at low temperatures, at high temperatures, or both? Explain your answer briefly.
$$
\mathrm{MgCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \quad \Delta H^{\circ}=116.48 \mathrm{~kJ}
$$

Nicole Mabante
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01:33

Problem 49

Explain briefly why the exothermic combustion of propane is product-favored.
$$
\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})
$$

Lottie Adams
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01:19

Problem 50

Explain briefly why the exothermic reaction of a metal carbonate with an acid is product-favored.
$$
\mathrm{CuCO}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow \mathrm{CuSO}_{4}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell)
$$

Lottie Adams
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01:21

Problem 51

Sodium reacts violently with water according to the equation
$$
\mathrm{Na}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{NaOH}(\mathrm{aq})+\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g})
$$
(a) Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction.
(b) Verify your predictions with calculations.

Nicole Mabante
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01:17

Problem 52

Once ignited, magnesium reacts vigorously with oxygen in air according to the equation
$$
2 \mathrm{Mg}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{MgO}(\mathrm{s})
$$
(a) Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction.
(b) Verify your predictions with calculations.

Nicole Mabante
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02:00

Problem 53

Hydrogen burns in air with considerable heat transfer to the surroundings. Consider the decomposition of water to gaseous hydrogen and oxygen. Without doing any calculations, and basing your prediction on the enthalpy change and the entropy change, is this reaction product-favored at $25{ }^{\circ} \mathrm{C}$ ? Explain your answer briefly.

Lottie Adams
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01:51

Problem 54

Hydrogen gas combines with chlorine gas in an exothermic reaction to form HCl(g). Consider the decomposition of gaseous hydrogen chloride to hydrogen and chlorine. Without doing any calculations, and basing your prediction on the enthalpy change and the entropy change, is this reaction product-favored at $25^{\circ} \mathrm{C}$ ? Explain your answer briefly.

Lottie Adams
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02:13

Problem 55

For each reaction, calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ and predict whether the reaction is always product-favored, productfavored only at low temperatures, product-favored only at high temperatures, or never product-favored.
(a) $\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s})+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})$
(b) $\mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g})$

Nicole Mabante
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02:22

Problem 56

For each reaction, calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ and predict whether the reaction is always product-favored, productfavored only at low temperatures, product-favored only at high temperatures, or never product-favored.
(a) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell)$
(b) $\mathrm{MgO}(\mathrm{s})+\mathrm{C}$ (graphite) $\longrightarrow \mathrm{Mg}(\mathrm{s})+\mathrm{CO}(\mathrm{g})$

Nicole Mabante
Nicole Mabante
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02:43

Problem 57

Determine whether the combustion of ethane, $\mathrm{C}_{2} \mathrm{H}_{6}$, is product-favored at $25^{\circ} \mathrm{C}$.
$$
\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+\frac{7}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)
$$
(a) Calculate $\Delta S_{\text {universe }}$. Required values of $\Delta H_{f}^{\circ}$ and $\mathrm{S}^{\circ}$ are in Appendix J.
(b) Verify your result by calculating the value of $\Delta G^{\circ}$ for the reaction.
(c) Do your calculated answers in parts (a) and (b) agree with your preconceived idea of this reaction?

Nicole Mabante
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02:47

Problem 58

The reaction of magnesium with water can be used as a means for heating food.
$$
\mathrm{Mg}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{~s})+\mathrm{H}_{2}(\mathrm{~g})
$$
Determine whether this reaction is product-favored at $25^{\circ} \mathrm{C} .$
(a) Calculate $\Delta S_{\text {universe }}$. See Appendix $J$ for the needed data.
(b) Verify your result by calculating $\Delta G^{\circ}$ for the reaction.

Nicole Mabante
Nicole Mabante
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01:14

Problem 59

Add a column for the sign of the Gibbs free energy to Table $18.2$ (p. 882). For the first and last lines in the table, tell whether $\Delta G$ is positive or negative.

David Collins
David Collins
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01:14

Problem 60

Based on your table from Question 59, when $\Delta H_{\text {system }}$ and $\Delta S_{\text {svstem }}$ are both negative, is $\Delta G$ is positive or negative or does the sign depend on temperature? If the sign depends on temperature, does the reaction become product-favored at high or low temperatures?

David Collins
David Collins
Numerade Educator
00:42

Problem 61

Use a mathematical equation to show how the statement leads to the conclusion cited: If a reaction is exothermic (negative $\Delta H$ ) and if the entropy of the system increases (positive $\Delta S$ ), then $\Delta G$ must be negative, and the reaction will be product-favored.

Nicole Mabante
Nicole Mabante
Numerade Educator
00:42

Problem 61

Use a mathematical equation to show how the statement leads to the conclusion cited: If a reaction is exothermic (negative $\Delta H$ ) and if the entropy of the system increases (positive $\Delta S$ ), then $\Delta G$ must be negative, and the reaction will be product-favored.

Nicole Mabante
Nicole Mabante
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01:53

Problem 62

Use a mathematical equation to show how the statement leads to the conclusion cited: If $\Delta H$ and $\Delta S$ have the same sign, then the magnitude of $T$ determines whether $\Delta G$ will be negative and whether the reaction will be productfavored.

David Collins
David Collins
Numerade Educator
00:46

Problem 63

Predict whether the reaction below is product-favored or reactant-favored by calculating $\Delta G^{\circ}$ from the entropy and enthalpy changes for the reaction at $25^{\circ} \mathrm{C}$.
$\begin{aligned} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow & \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \\ \Delta H^{\circ}=41.17 \mathrm{~kJ} & \Delta S^{\circ}=42.08 \mathrm{~J} / \mathrm{K} \end{aligned}$

Nicole Mabante
Nicole Mabante
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01:11

Problem 64

Predict whether this reaction is product-favored at $25^{\circ} \mathrm{C}$ by calculating the change in standard Gibbs free energy from the entropy and enthalpy changes.
$\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$
$\Delta H^{\circ}=52.96 \mathrm{~kJ} \quad \Delta S^{\circ}=166.4 \mathrm{~J} / \mathrm{K}$

Nicole Mabante
Nicole Mabante
Numerade Educator
00:53

Problem 65

If this reaction were product-favored, it would be a good way to make pure silicon, crucial in the semiconductor industry, from sand $\left(\mathrm{SiO}_{2}\right)$.
$$
\mathrm{SiO}_{2}(\mathrm{~s})+\mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{Si}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})
$$
Calculate $\Delta G^{\circ}$ from data in Appendix $J$ and decide whether the reaction can be used to produce silicon at $25^{\circ} \mathrm{C}$.

Nicole Mabante
Nicole Mabante
Numerade Educator
01:31

Problem 66

From data in Appendix J, calculate $\Delta G^{\circ}$ for the reactions of sand with hydrogen fluoride and hydrogen chloride. Explain why hydrogen fluoride attacks glass, whereas hydrogen chloride does not.
$$
\begin{gathered}
\mathrm{SiO}_{2}(\mathrm{~s})+4 \mathrm{HF}(\mathrm{g}) \longrightarrow \mathrm{SiF}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\
\mathrm{SiO}_{2}(\mathrm{~s})+4 \mathrm{HCl}(\mathrm{g}) \longrightarrow \mathrm{SiCl}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})
\end{gathered}
$$

Nicole Mabante
Nicole Mabante
Numerade Educator
01:37

Problem 67

Use data from Appendix J to calculate $\Delta G^{\circ}$ for each reaction at $25^{\circ} \mathrm{C}$. Which are product-favored?
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})$
(b) $2 \mathrm{SO}_{3}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})$
(c) $4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$

Nicole Mabante
Nicole Mabante
Numerade Educator
02:33

Problem 68

Evaluate $\Delta H^{\circ}$ for each reaction in Question $67 .$ Use your results to calculate standard molar entropies at $25.00^{\circ} \mathrm{C}$ for
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})$
(b) $\mathrm{SO}_{3}(\mathrm{~g})$
(c) $\mathrm{NO}(\mathrm{g})$

Nicole Mabante
Nicole Mabante
Numerade Educator
04:26

Problem 69

If a system falls within the second or third category in Table $18.2$ (p. 882), then there must be a temperature at which it shifts from being reactant-favored to being productfavored. For each reaction, obtain data from Appendix $J$ and calculate what that temperature is.
(a) $\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\ell)$
(b) $2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{C}$ (graphite) $\rightleftharpoons 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{~g})$

David Collins
David Collins
Numerade Educator
04:05

Problem 70

If a system falls within the second or third category in Table $18.2$ (p. 882 ) then there must be a temperature at which it shifts from being reactant-favored to being product-favored. For each reaction, obtain data from Appendix $\mathrm{J}$ and calculate what that temperature is.
(a) $2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})$
(b) $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})$

David Collins
David Collins
Numerade Educator
01:44

Problem 71

Estimate $\Delta G^{\circ}$ at $2000 . \mathrm{K}$ for each reaction in Question $69 .$

David Collins
David Collins
Numerade Educator
01:19

Problem 72

Estimate $\Delta G^{\circ}$ at $2000 . \mathrm{K}$ for each reaction in Question 70

David Collins
David Collins
Numerade Educator
01:52

Problem 73

Many metal carbonates can be decomposed to the metal oxide and carbon dioxide by heating.
$$
\mathrm{CaCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})
$$
(a) What are the enthalpy, entropy, and Gibbs free energy changes for this reaction at $25.00^{\circ} \mathrm{C}$ ?
(b) Is it product-favored or reactant-favored?
(c) Based on the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$, predict whether the reaction is product-favored at all temperatures.
(d) Predict the lowest temperature at which appreciable quantities of products can be obtained.

David Collins
David Collins
Numerade Educator
02:08

Problem 74

Some metal oxides, such as lead(II) oxide, can be decomposed to the metal and oxygen simply by heating.
$$
\mathrm{PbO}(\mathrm{s}) \longrightarrow \mathrm{Pb}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})
$$
(a) Is the decomposition of lead(II) oxide product-favored at $25^{\circ} \mathrm{C}$ ? Explain.
(b) If not, can it become so if the temperature is raised?
(c) As the temperature increases, at what temperature does the reaction first become product-favored?

Lottie Adams
Lottie Adams
Numerade Educator
01:26

Problem 75

Use the thermochemical expression
$$
\begin{aligned}
\mathrm{CaC}_{2}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) \\
\Delta G^{\circ}=-119.282 \mathrm{~kJ}
\end{aligned}
$$
and data from Appendix $J$ to calculate $\Delta G_{f}^{\circ}$ for $\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})$ at $25^{\circ} \mathrm{C}$.

David Collins
David Collins
Numerade Educator
01:07

Problem 76

Use the thermochemical expression
$$
\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{~g}) \quad \Delta G^{\circ}=-37.2 \mathrm{~kJ}
$$
and data from Appendix $\mathrm{J}$ to calculate $\Delta G_{f}^{\circ}$ for $\mathrm{PCl}_{5}(\mathrm{~g})$.

David Collins
David Collins
Numerade Educator
01:37

Problem 77

Use data from Appendix $J$ to obtain the equilibrium constant $K_{P}$ for each reaction at $298.15 \mathrm{~K}$.
(a) $2 \mathrm{HCl}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})$
(b) $\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})$

Lottie Adams
Lottie Adams
Numerade Educator
01:43

Problem 78

Use data from Appendix $J$ to obtain the equilibrium constant $K_{p}$ for each of these reactions at $298 \mathrm{~K}$.
(a) $\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$
(b) $2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})$

Lottie Adams
Lottie Adams
Numerade Educator
01:20

Problem 79

Ethylene reacts with hydrogen to produce ethane.
$$
\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{3}(\mathrm{~g})
$$
(a) Using the data in Appendix J, calculate $\Delta G^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$. Is the reaction predicted to be productfavored under standard conditions?
(b) Calculate $K_{P}$ from $\Delta G^{\circ} .$ Comment on the connection between the sign of $\Delta G^{\circ}$ and the magnitude of $K_{p}$

David Collins
David Collins
Numerade Educator
01:32

Problem 80

Use the data in Appendix $J$ to calculate $\Delta G^{\circ}$ and $K_{P}$ at $25^{\circ} \mathrm{C}$ for the reaction
$$
2 \mathrm{HBr}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HCl}(\mathrm{g})+\mathrm{Br}_{2}(\ell)
$$
Comment on the connection between the sign of $\Delta G^{\circ}$ and the magnitude of $K_{p}$.

David Collins
David Collins
Numerade Educator
02:09

Problem 81

For each chemical reaction, calculate the standard equilibrium constant at $298 \mathrm{~K}$ and at $1000 . \mathrm{K}$ from the thermodynamic data in Appendix J. Indicate whether each reaction is product-favored or reactant-favored at each temperature.
(a) The conversion of nitric oxide to nitrogen dioxide in the atmosphere
$$
2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})
$$
(b) The reaction of an alkali metal with a halogen to produce an alkali metal halide salt
$$
2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NaCl}(\mathrm{s})
$$

David Collins
David Collins
Numerade Educator
02:10

Problem 82

For each chemical reaction, calculate the standard equilibrium constant at $298 \mathrm{~K}$ and at 1000 . $\mathrm{K}$ from the thermodynamic data in Appendix J. Indicate whether each reaction is product-favored or reactant-favored at each temperature.
(a) The oxidation of carbon monoxide to carbon dioxide
$$
2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}_{2}(\mathrm{~g})
$$
(b) The first step in the production of electronic-grade silicon from sand
$$
\mathrm{SiO}_{2}(\mathrm{~s})+2 \mathrm{C}(\mathrm{s}) \rightleftharpoons \mathrm{Si}(\mathrm{s})+2 \mathrm{CO}(\mathrm{g})
$$

David Collins
David Collins
Numerade Educator
03:18

Problem 83

For each reaction, estimate $K^{\circ}$ at the temperature indicated.
(a) $2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $800 . \mathrm{K}$
(b) $2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})$ at $500 . \mathrm{K}$
(c) $2 \mathrm{HF}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g})$ at $2000 . \mathrm{K}$

Lottie Adams
Lottie Adams
Numerade Educator
02:04

Problem 84

For each reaction, estimate $K^{\circ}$ at the temperature indicated.
(a) $\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})$ at $500 . \mathrm{K}$
(b) $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})$ at $400 . \mathrm{K}$
(c) $\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $800 . \mathrm{K}$

Lottie Adams
Lottie Adams
Numerade Educator
01:18

Problem 85

For each reaction, an equilibrium constant at $298 \mathrm{~K}$ is given. Calculate $\Delta G^{\circ}$ for each reaction.
$$
\begin{array}{lr}
\text { (a) } \mathrm{Br}_{2}(\ell)+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g}) & K_{P}=4.4 \times 10^{18} \\
\text { (b) } \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & K_{P}=3.17 \times 10^{-2} \\
\text { (c) } \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) & K_{c}=3.5 \times 10^{8}
\end{array}
$$

David Collins
David Collins
Numerade Educator
01:09

Problem 86

For each reaction, an equilibrium constant at $298 \mathrm{~K}$ is given. Calculate $\Delta G^{\circ}$ for each reaction.
$$
\begin{array}{ll}
\text { (a) } \frac{1}{8} \mathrm{~S}_{8}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{~g}) & K_{P}=4.2 \times 10^{52} \\
\text { (b) } 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & K_{c}=3.3 \times 10^{81} \\
\text { (c) } \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) & K_{c}=9.4 \times 10^{-1}
\end{array}
$$

David Collins
David Collins
Numerade Educator
01:30

Problem 87

Which of these reactions are capable of being harnessed to do useful work at $298 \mathrm{~K}$ and 1 bar? Which require that work be done to make them occur?
(a) $2 \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+15 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 12 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$
(b) $2 \mathrm{NF}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g})$
(c) $\mathrm{TiO}_{2}(\mathrm{~s}) \longrightarrow \mathrm{Ti}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g})$

Lottie Adams
Lottie Adams
Numerade Educator
01:17

Problem 88

Which of these reactions are capable of being harnessed to do useful work at $298 \mathrm{~K}$ and 1 bar? Which require that work be done to make them occur?
(a) $\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s}) \longrightarrow 2 \mathrm{Al}(\mathrm{s})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g})$
(b) $2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})$
(c) $\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})$

Lottie Adams
Lottie Adams
Numerade Educator
01:50

Problem 89

For each of the reactions in Question 87 that requires work to be done, calculate the minimum mass of graphite that would have to be oxidized to $\mathrm{CO}_{2}(\mathrm{~g})$ to provide the necessary work.

Crystal Wang
Crystal Wang
Numerade Educator
02:06

Problem 90

For each of the reactions in Question 88 that requires work to be done, calculate the minimum mass of hydrogen gas that would have to be burned to form water vapor to pro-
vide the necessary work.

Crystal Wang
Crystal Wang
Numerade Educator
01:35

Problem 91

Titanium is obtained from its ore, $\mathrm{TiO}_{2}(\mathrm{~s})$, by heating the ore in the presence of chlorine gas and coke (carbon) to produce gaseous titanium(IV) chloride and carbon monoxide.
(a) Write a balanced equation for this process.
(b) Calculate $\Delta H^{\circ}, \Delta S^{\circ}$, and $\Delta G^{\circ}$ for the reaction.
(c) Is this reaction product-favored or reactant-favored at $25^{\circ} \mathrm{C} ?$
(d) Does the reaction become more product-favored or more reactant-favored as the temperature increases?

Crystal Wang
Crystal Wang
Numerade Educator
02:56

Problem 92

To obtain a metal from its ore, the decomposition of the metal oxide to form the metal and oxygen is often coupled with oxidation of coke (carbon) to carbon monoxide. For each metal oxide listed, write a balanced equation for the decomposition of the oxide and for the overall reaction when the decomposition is coupled to oxidation of coke to carbon monoxide. Calculate the overall value of $\Delta G^{\circ}$ for each coupled reaction at $25^{\circ} \mathrm{C}$. Which of the metals could be obtained from these ores at $25^{\circ} \mathrm{C}$ by this method?
(a) $\mathrm{CuO}(\mathrm{s})$
(b) $\mathrm{Ag}_{2} \mathrm{O}(\mathrm{s})$
(c) $\mathrm{HgO}(\mathrm{s})$
(d) $\mathrm{MgO}(\mathrm{s})$
(e) $\mathrm{PbO}(\mathrm{s})$

Crystal Wang
Crystal Wang
Numerade Educator
03:00

Problem 93

From which of the metal oxides in Question 92 could the metal be obtained by coupling reduction of the oxide with oxidation of coke to carbon monoxide at $800^{\circ} \mathrm{C}$ ?

Crystal Wang
Crystal Wang
Numerade Educator
01:56

Problem 94

From which of the metal oxides in Question 92 could the metal be obtained by coupling reduction of the oxide with oxidation of coke to carbon monoxide at $1500^{\circ} \mathrm{C}$ ?

Crystal Wang
Crystal Wang
Numerade Educator
03:21

Problem 95

The molecular structure of one form of glucose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$, looks like this:
Glucose can be oxidized to carbon dioxide and water according to the equation
(a)Using the method described in Section $8.6$ ( $\longleftarrow$ p. 347) for estimating enthalpy changes from bond energies, estimate $\Delta H^{\circ}$ for the oxidation of this form of glucose. Make a list of all bonds broken and all bonds formed in this process.
(b) Compare your result with the experimental value of $-2816 \mathrm{~kJ}$ for combustion of a mole of glucose. Why might there be a difference between this value and the one you calculated in part (a)?

Crystal Wang
Crystal Wang
Numerade Educator
01:47

Problem 96

Another step in the metabolism of glucose, which occurs after the formation of glucose 6 -phosphate, is the conversion of fructose 6 -phosphate to fructose 1,6 -bisphosphate ("bis"means two): fructose 6-phosphate(aq) $+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(\mathrm{aq}) \longrightarrow$ fructose 1,6 -bisphosphate $(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})$
(a) This reaction has a Gibbs free energy change of $+16.7 \mathrm{~kJ}$ per mole of fructose 6 -phosphate. Is it endergonic or exergonic?
(b) Write the equation for the formation of $1 \mathrm{~mol}$ ADP from ATP, for which $\Delta G^{\circ}=-30.5 \mathrm{~kJ}$
(c) Couple these two reactions to get an exergonic process; write its overall chemical equation, and calculate the Gibbs free energy change.

Lottie Adams
Lottie Adams
Numerade Educator
01:32

Problem 97

In muscle cells under the condition of vigorous exercise, glucose is converted to lactic acid ("lactate"), $\mathrm{CH}_{3} \mathrm{CHOHCOOH}$, by the chemical reaction $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{CH}_{3} \mathrm{CHOHCOOH}$ $\Delta G^{0 \prime}=-197 \mathrm{~kJ}$
(a) If all of the Gibbs free energy from this reaction were used to convert ADP to ATP, how many moles of ATP could be produced per mole of glucose?
(b) The actual reaction involves the production of 3 mol ATP per mole of glucose. What is the $\Delta G^{\circ}$ for this reaction?
(c) Is the overall reaction in part (b) reactant-favored or product-favored?

Crystal Wang
Crystal Wang
Numerade Educator
01:47

Problem 98

The biological oxidation of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$, is also a source of Gibbs free energy.
(a) Does the oxidation of $1 \mathrm{~g}$ ethanol give more or less energy than the oxidation of $1 \mathrm{~g}$ glucose? (Hint: Write the balanced equation for the production of carbon dioxide and water from ethanol and oxygen, and use Appendix J.)
(b) Comment on potential problems of replacing glucose with ethanol in your diet.

Lottie Adams
Lottie Adams
Numerade Educator
01:21

Problem 99

What are the resources human society uses to supply Gibbs free energy? (Hint: Consider information you learned in Chapter 6.)

Crystal Wang
Crystal Wang
Numerade Educator
01:31

Problem 100

For one day, keep a log of all the activities you undertake that consume Gibbs free energy. Distinguish between Gibbs free energy provided by nutrient metabolism and that provided by other energy resources.

Lottie Adams
Lottie Adams
Numerade Educator
02:15

Problem 101

Billions of pounds of acetic acid are made each year, much of it by the reaction of methanol with carbon monoxide.
$$
\mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(\ell)
$$
(a) By calculating the standard Gibbs free energy change, $\Delta G^{\circ}$, for this reaction, show that it is product-favored.
(b) Determine the standard Gibbs free energy change, $\Delta G^{\circ}$, for the reaction of acetic acid with oxygen to form gaseous carbon dioxide and liquid water.
(c) Based on this result, is acetic acid thermodynamically stable compared with $\mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(\ell) ?$
(d) Is acetic acid kinetically stable compared with $\mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(\ell) ?$

Crystal Wang
Crystal Wang
Numerade Educator
01:30

Problem 102

Determine the standard Gibbs free energy change, $\Delta G^{\circ}$, for the reactions of liquid methanol, of $\mathrm{CO}(\mathrm{g})$, and of ethyne, $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})$, with oxygen gas to form gaseous carbon dioxide and (if hydrogen is present) liquid water. Use your calculations to decide which of these substances are kinetically stable and which are thermodynamically stable: $\mathrm{CH}_{3} \mathrm{OH}(\ell)$, $\mathrm{CO}(\mathrm{g}), \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g}), \mathrm{CO}_{2}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\ell) .$

Lottie Adams
Lottie Adams
Numerade Educator
01:52

Problem 103

There are millions of organic compounds known, and new ones are being discovered or made at a rate of more than 100,000 compounds per year. Organic compounds burn readily in air at high temperatures to form carbon dioxide and water. Several classes of organic compounds are listed, with a simple example of each. Write a balanced chemical equation for the combustion in $\mathrm{O}_{2}$ of each of these compounds, and then use the data in Appendix $J$ to show that each reaction is product-favored at room temperature.
$$
\begin{array}{ll}
\hline \text { Class of Organics } & \text { Simple Example } \\
\hline \text { Aliphatic hydrocarbons } & \text { Methane, } \mathrm{CH}_{4} \\
\text { Aromatic hydrocarbons } & \text { Benzene, } \mathrm{C}_{6} \mathrm{H}_{6} \\
\text { Alcohols } & \text { Methanol, } \mathrm{CH}_{3} \mathrm{OH} \\
\hline
\end{array}
$$
From these results, it is reasonable to hypothesize that all organic compounds are thermodynamically unstable in an oxygen atmosphere (i.e., their room-temperature reaction with $\mathrm{O}_{2}(\mathrm{~g})$ to form $\mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(\ell)$ is product-favored). If this hypothesis is true, how can organic compounds exist on earth?

Lottie Adams
Lottie Adams
Numerade Educator
01:37

Problem 104

Actually, the carbon in $\mathrm{CO}_{2}(\mathrm{~g})$ is thermodynamically unstable with respect to the carbon in calcium carbonate (limestone). Verify this by determining the standard Gibbs free energy change for the reaction of lime, $\mathrm{CaO}(\mathrm{s})$, with $\mathrm{CO}_{2}(\mathrm{~g})$ to make $\mathrm{CaCO}_{3}(\mathrm{~s})$

Lottie Adams
Lottie Adams
Numerade Educator
02:01

Problem 105

This problem will help you understand the dependence of the U.S. economy on energy. Referring to the figure, calculate the energy (in joules) used by the agriculture, mining, and construction industries
(a) in one year.
(b) in one day.
(c) in one second.
(d) Remembering that 1 watt is the expenditure of 1 joule every second, calculate the average power needs of these industries in watts.
(e) Assuming a U.S. population of 300 million people, calculate the power needed by the agriculture, mining, and construction industries per person in the United States.

Crystal Wang
Crystal Wang
Numerade Educator
04:46

Problem 106

Suppose you signed a contract to provide to the agriculture, mining, and construction industries the energy they use each year (see Question 105) by eating glucose and giving them the resulting energy from its oxidation in your body.
(a) How much glucose would you have to eat each day to meet your contract? Assume that it is someone else's job to figure out how to get the energy stored in your ATP to the industries!
(b) An Olympic sprinter uses energy at the rate of 700 to 900 watts in a sprint. Compare this figure with the one you calculated in part (a), and draw conclusions about the feasibility of fulfilling your contract.
$$
\begin{array}{cccc}
\hline \text { Reaction } & \text { Chemical Equation } & \boldsymbol{K}_{\mathbf{c}} & \Delta \boldsymbol{H}^{\circ}(\mathbf{k J}) \\
\hline 1 & \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons & 3.6 \times 10^{20} & -115.4 \\
& \mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & & \\
2 & \mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{~s}) \rightleftharpoons & 1.24 \times 10^{-5} & 81.1 \\
& \mathrm{MgO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) & & \\
3 & 2 \mathrm{CH}_{4}(\mathrm{~g}) \rightleftharpoons & 9.5 \times 10^{-13} & 64.9 \\
& \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) & & \\
4 & 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons & 3.76 & -90.7 \\
& \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g}) & & \\
5 & \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons & 1.9 \times 10^{24} & -103.7 \\
& 2 \mathrm{HBr}(\mathrm{g}) & & \\
\hline
\end{array}
$$

Rabeya Zahid
Rabeya Zahid
Numerade Educator
01:51

Problem 107

The table above provides data at $25^{\circ} \mathrm{C}$ for five reactions. For which (if any) of the reactions 1 through 5 is
(a) $K_{p}$ greater than $K_{c} ?$
(b) the reaction product-favored?
(c) there only a single concentration in the $K_{c}$ expression?
(d) there an increase in the concentrations of products when the temperature increases?
(e) there a change in the sign of $\Delta G^{\circ}$ if water is liquid instead of gas?

CG
Chirag Gupta
Numerade Educator
05:14

Problem 108

The table above provides data at $25^{\circ} \mathrm{C}$ for five reactions. For which (if any) of the reactions 1 through 5 is
(a) $K_{P}$ less than $K_{c}$ ?
(b) there a decrease in the concentrations of products when the pressure increases?
(c) the value of $\Delta S^{\circ}$ positive?
(d) the sign of $\Delta G^{\circ}$ dependent on temperature?

Shalini Tyagi
Shalini Tyagi
Numerade Educator
02:19

Problem 109

Consider the gas phase decomposition of sulfur trioxide to sulfur dioxide and oxygen.
(a) Calculate $\Delta G^{\circ}$ for the reaction at $25^{\circ} \mathrm{C} .$
(b) Is the reaction product-favored under standard conditions at $25^{\circ} \mathrm{C}$ ?
(c) If the reaction is not product-favored at $25^{\circ} \mathrm{C}$, is there a temperature at which it will become so?
(d) Estimate $K_{P}$ for the reaction at $1500 .{ }^{\circ} \mathrm{C}$.
(e) Estimate $K_{c}$ for the reaction at $1500 .{ }^{\circ} \mathrm{C}$.

Sriparna Bhattacharjee
Sriparna Bhattacharjee
Numerade Educator
02:20

Problem 110

The Haber process for the synthesis of ammonia involves the reaction
$$
\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})
$$
Using data from Appendix J, estimate the amount (in moles) of $\mathrm{NH}_{3}(\mathrm{~g})$ that would be produced from $1 \mathrm{~mol} \mathrm{~N}_{2}(\mathrm{~g})$ and $3 \mathrm{~mol} \mathrm{H}_{2}(\mathrm{~g})$ once equilibrium is reached at $450{ }^{\circ} \mathrm{C}$ and a total pressure of 1000 . atm.

Stephen Ho
Stephen Ho
Numerade Educator
02:55

Problem 111

Mercury is a poison, and its vapor is readily absorbed through the lungs. Therefore it is important that the partial pressure of mercury be kept as low as possible in any area where people could be exposed to it (such as a dentist's office). The relevant equilibrium reaction is
$$
\operatorname{Hg}(\ell) \rightleftharpoons \mathrm{Hg}(\mathrm{g})
$$
For $\mathrm{Hg}(\mathrm{g}), \Delta H_{f}^{\circ}=61.4 \mathrm{~kJ} / \mathrm{mol}, S^{\circ}=175.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$, and
$\Delta G_{f}^{\circ}=31.8 \mathrm{~kJ} / \mathrm{mol}$. Use data from Appendix $\mathrm{J}$ and these values to evaluate the vapor pressure of mercury at different temperatures. (Remember that concentrations of pure liquids and solids do not appear in the equilibrium constant expression, and for gases $K^{\circ}$ involves pressures in bars.)
(a) Calculate $\Delta G^{\circ}$ for vaporization of mercury at $25^{\circ} \mathrm{C}$.
(b) Write the equilibrium constant expression for vaporization of mercury.
(c) Calculate $K^{\circ}$ for this reaction at $25^{\circ} \mathrm{C}$.
(d) What is the vapor pressure of mercury at $25^{\circ} \mathrm{C}$ ?
(e) Estimate the temperature at which the vapor pressure of mercury reaches $10 \mathrm{~mm} \mathrm{Hg}$.

Lottie Adams
Lottie Adams
Numerade Educator
01:06

Problem 112

A friend says that the boiling point of water is twice that of cyclopentane, which boils at $50^{\circ} \mathrm{C}$. Write a brief statement about the validity of this observation.

Lottie Adams
Lottie Adams
Numerade Educator
01:16

Problem 113

Using the second law of thermodynamics, explain why it is very difficult to unscramble an egg. Who was HumptyDumpty? Why did his moment of glory illustrate the second law of thermodynamics?

Lottie Adams
Lottie Adams
Numerade Educator
01:36

Problem 114

Appendix J lists standard molar entropies $S^{\circ}$, not standard entropies of formation $\Delta S_{f}^{\circ} .$ Why is this possible for entropy but not for internal energy, enthalpy, or Gibbs free energy?

Lottie Adams
Lottie Adams
Numerade Educator
02:50

Problem 115

When calculating $\Delta S^{\circ}$ from $S^{\circ}$ values, it is necessary to look up all substances, including elements in their standard state, such as $\mathrm{O}_{2}(\mathrm{~g}), \mathrm{H}_{2}(\mathrm{~g})$, and $\mathrm{N}_{2}(\mathrm{~g})$. When calculating $\Delta H^{\circ}$ from $\Delta H_{f}^{\circ}$ values, however, elements in their standard state can be ignored. Why is the situation different for $S^{\circ}$ values?

David Collins
David Collins
Numerade Educator
02:00

Problem 116

In the Cbemistry You Can Do experiment in Chapter 6 $(\leftarrow p .239)$ you considered the heat generated when iron rusts to form iron oxide. Look at the enthalpies of formation of other metal oxides in Table $6.3$ or Appendix $\mathrm{J}$ and $\mathrm{com}-$ ment on your observations. Are oxidations of metals generally endothermic or exothermic? Are they usually reactantfavored or product-favored?

David Collins
David Collins
Numerade Educator
00:37

Problem 117

Explain why the entropy of the system increases when solid NaCl dissolves in water.

Nicole Mabante
Nicole Mabante
Numerade Educator
01:36

Problem 118

Explain how the entropy of the universe increases when an aluminum metal can is made from aluminum ore. The first step is to extract the ore, which is primarily a form of $\mathrm{Al}_{2} \mathrm{O}_{3}$, from the ground. After it is purified by freeing it from oxides of silicon and iron, aluminum oxide is changed to the metal by an input of electrical energy.
$$
2 \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s}) \stackrel{\text { electrical energy }}{\longrightarrow} 4 \mathrm{Al}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g})
$$

Lottie Adams
Lottie Adams
Numerade Educator
03:09

Problem 119

Suppose that at a certain temperature $T$ a chemical reaction is found to have a standard equilibrium constant $K^{\circ}$ of $1.0$. Indicate whether each statement is truc or false and explain why.
(a) The cnthalpy change for the reaction, $\Delta H^{\circ}$, is zero.
(b) The entropy change for the reaction, $\Delta S^{\circ}$, is zero.
(c) The Gibbs free energy change for the reaction, $\Delta G^{\circ}$, is zero.
(d) $\Delta H^{\circ}$ and $\Delta S^{\circ}$ have the same sign.
(c) $\Delta H^{\circ} / T=\Delta S^{\circ}$ at the temperature $T$.

David Collins
David Collins
Numerade Educator
01:42

Problem 120

When you eat a candy bar, how does your body store the Gibbs free energy that is released during oxidation of the sugars (glucose and other carbohydrates) in the candy bar? What was the original source of the Gibbs free energy needed to synthesize the sugars before they went into the candv bar?

Lottie Adams
Lottie Adams
Numerade Educator
02:09

Problem 121

Explain how biological systems make use of coupled reactions to maintain the high degree of order found in all living organisms.

Lottie Adams
Lottie Adams
Numerade Educator
01:20

Problem 122

How can kinetically stable substances exist at all, if they are not thermodynamically stable?

Lottie Adams
Lottie Adams
Numerade Educator
01:19

Problem 123

Criticize this statement: Provided it occurs at an appreciable rate, any chemical reaction for which $\Delta G<0$ will proceed until all reactants have been converted to products.

Nicole Mabante
Nicole Mabante
Numerade Educator
01:22

Problem 124

Reword the statement in Question 123 so that it is always true.

David Collins
David Collins
Numerade Educator
01:40

Problem 125

Galcuate the entropy change for formation of exactly $1 \mathrm{~mol}$ of cach of these gascous hydrocarbons under standard conditions from carbon (graphite) and hydrogen. What trend do you see in these values? Does $\Delta S^{\circ}$ increase or decrease on adding $\mathrm{H}$ atoms?
(a) acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})$
(b) cthylenc, $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})$
(c) ethane, $\mathbf{C}_{3} \mathrm{H}_{6}(\mathrm{~g})$

Lottie Adams
Lottie Adams
Numerade Educator
01:34

Problem 126

Calcium hydroxide, $\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{~s})$, can be dehydrated to form lime, $\mathrm{CaO}$, by heating. Without doing any calculations, and basing your prediction on the enthalpy change and the cntropy changc, is this reaction product-favored at $25{ }^{\circ} \mathrm{C}$ ? Explain your answer briefly.

Lottie Adams
Lottie Adams
Numerade Educator
04:45

Problem 127

Octane is the product of adding hydrogen to 1 -octene.
$$
\begin{gathered}
\mathrm{C}_{8} \mathrm{H}_{16}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{~g}) \\
\text { 1-octene }
\end{gathered}
$$
The enthalpics of formation are
$$
\begin{aligned}
&\Delta H_{f}^{\circ}\left[C_{8} H_{18}(g)\right]=-82.93 \mathrm{~kJ} / \mathrm{mol} \\
&\Delta H_{f}^{\circ}\left[\mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{~g})\right]=-208.45 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
Predict whether this reaction is product-favored or reactantfavored at $25^{\circ} \mathrm{C}$ and explain your reasoning.

Zubair Abdulla
Zubair Abdulla
Numerade Educator
01:26

Problem 128

This is a group project: Fstimate or look up, to the nearest order of magnitude,
(a) the number of kilograms of $\mathrm{CH}_{3}$ OH made cach ycar
(b) the number of kilograms of $\mathrm{CO}$ in the entire atmosphere
(c) the number of kilograms of $\mathrm{CH}_{5}$ COOH made each year
(d) the number of kilograms of $\mathrm{H}_{2} \mathrm{O}$ on earth
(e) the number of kilograms of $\mathrm{CO}_{2}$ in the atmosphere What do these facts tell you about the difference betwecn kinetic stability and thermodynamic stability?

Lottie Adams
Lottie Adams
Numerade Educator
00:59

Problem 129

From data in Appendix J, estimate
(a) the boiling point of brominc.
(b) the boiling point of tin(IV) chloride.

Lottie Adams
Lottie Adams
Numerade Educator
01:08

Problem 130

From data in Appendix J, estimate
(a) the boiling point of titanium(IV) chloride.
(b) the boiling point of carbon disulfide, $\mathrm{CS}_{2}$, which is a liquid at $25^{\circ} \mathrm{C}$ and $\underline{1}$ bar.

Lottie Adams
Lottie Adams
Numerade Educator
02:06

Problem 131

Nitric oxide and chlorine combine at $25^{\circ} \mathrm{C}$ to produce nitrosyl chloride, NOC1.
$$
2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NOCl}(\mathrm{g})
$$
(a) Calculate the equilibrium constant $K_{P}$ for the reaction.
(b) Is the reaction product-favored or reactant-favored?
(c) Calculate the equilibrium constant $K_{c}$ for the reaction.

Lottie Adams
Lottie Adams
Numerade Educator
02:33

Problem 132

Hydrogen for use in the Haber-Bosch process for ammonia synthesis is generated from natural gas by the reaction
$$
\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})
$$
(a) Calculate $\Delta G^{\circ}$ for this reaction at $25^{\circ} \mathrm{C}$.
(b) Calculate $K_{P}$ for the reaction at $25^{\circ} \mathrm{C}$.
(c) Is the reaction product-favored under standard conditions? If not, at what temperature will it become so?
(d) Estimate $K_{c}$ for the reaction at $1000 . \mathrm{K}$.

Alexander Cheng
Alexander Cheng
Numerade Educator
01:46

Problem 133

It would be very useful if we could use the inexpensive carbon in coal to make more complex organic molccules such as gaseous or liquid fuels. The formation of methane from coal and water is reactant-favored and thus cannot occur unless there is some energy transfer from outside. This problem examines the feasibility of other reactions using coal and watcr.
(a) Write three balanced equations for the reactions of coal (carbon) and steam to make ethane gas, $\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})$, propane gas, $\mathrm{C}_{3} \mathrm{H}_{\mathrm{g}}(\mathrm{g})$, and liquid methanol, $\mathrm{CH}_{3} \mathrm{OH}(\ell)$, with carbon dioxide as a by-product.
(b) Using the data in Appendix $J$, calculate $\Delta H^{\circ}, \Delta S^{\circ}$, and $\Delta G^{\circ}$ for each reaction, and then comment on whether any of them would be a feasible way to make the stated products.

Lottie Adams
Lottie Adams
Numerade Educator
01:27

Problem 134

You are exploring the marketing possibilities of a scheme by which every family in the United States produces enough water for its own needs by the combustion of hydrogen and oxygen. Would the release of Gibbs free energy from the combination of hydrogen and oxygen be sufficient to supply the family's energy needs? Do not try to collect the actual data you would use, but define the problem well enough so that someone else could collect the necessary data and do the calculations that would be needed.

Lottie Adams
Lottie Adams
Numerade Educator
02:24

Problem 135

Quitc often a graph of $\ln K^{\circ}$ versus $1 / T$ is a straight line. Use Equation $18.8$ (p. 889 ) to show how $\Delta H^{\circ}$ and $\Delta S^{\circ}$ can be determined from such a graph. Does the fact that such a graph is straight tell you anything about the dependence of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ on temperature?

Crystal Wang
Crystal Wang
Numerade Educator
01:15

Problem 136

Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not vary with temperaturc, use Equation $18.8$ (p. 889 ) to derive a formula relating $K_{1}^{\circ}$ at temperature $T_{1}$ to $K_{2}^{\circ}$ at temperature $T_{2}$

Nicole Mabante
Nicole Mabante
Numerade Educator
01:12

Problem 137

Without consulting tables of $\Delta H_{f}^{\circ}, S^{\circ}$, or $\Delta G_{f}^{\circ}$ values, predict which of these reactions is
(i) always product-favored.
(ii) product-favored at low temperatures, but not productfavored at high temperatures.
(iii) not product-favored at low temperatures, but productfavored at high temperatures.
(iv) never product-favored.

Lottie Adams
Lottie Adams
Numerade Educator
02:00

Problem 138

Using the reactions
$$
\begin{aligned}
&2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell) \\
&2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})
\end{aligned}
$$
as an example, explain why it may be incorrect to assume for reactions involving solids or liquids that $\Delta S^{\circ}$ and $\Delta H^{\circ}$ do not change appreciably with increasing temperature.

David Collins
David Collins
Numerade Educator