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Chemistry The Central Science

Theodore E. Brown, Theodore L. Brown, H. Eugene LeMaytion Compounds

Chapter 19

Chemical Thermodynamics - all with Video Answers

Educators

Chapter Questions

01:44

Problem 1

Two different gases occupy the two bulbs shown here. Consider the process that occurs when the stopcock is opened, assuming the gases behave ideally. (a) Draw the final (equilibrium) state. (b) Predict the signs of $\Delta H$ and $\Delta S$ for the process. (c) Is the process that occurs when the stopcock is opened a reversible one? (d) How does the process affect the entropy of the surroundings? [Sections 19.1 and 19.2 ]

Aadit Sharma
Aadit Sharma
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04:37

Problem 2

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane $\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~F}_{2}\right),$ which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects.
(a) Based on your experience, is the vaporization a spontaneous process at room temperature?
(b) Defining the 1,1 -difluoroethane as the system, do you expect $q_{\mathrm{sys}}$ for the process to be positive or negative? Explain. (c) Predict whether $\Delta S$ is positive or negative for this process.
(d) Given your answers to (a), (b), and
(c), do you think the operation of this product depends more on heat flow or more on entropy change?

Christopher Nilsen
Christopher Nilsen
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04:03

Problem 3

(a) What are the signs of $\Delta S$ and $\Delta H$ for the process depicted here? (b) How might temperature affect the sign of $\Delta G ?$ (c) If energy can flow in and out of the system to maintain a constant temperature during the process, what can you say about the entropy change of the surroundings as a result of this process? [Sections 19.2 and 19.5$]$

Christopher Nilsen
Christopher Nilsen
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03:42

Problem 4

Predict the sign of $\Delta S$ accompanying this reaction. Explain your choice. [Section 19.3$]$

Christopher Nilsen
Christopher Nilsen
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03:25

Problem 5

The accompanying diagram shows how entropy varies with temperature for a substance that is a gas at the highest temperature shown. (a) What processes correspond to the entropy increases along the vertical lines labeled 1 and 2 ? (b) Why is the entropy change for 2 larger than that for $1 ?$ [Section 19.3 ]

Christopher Nilsen
Christopher Nilsen
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03:03

Problem 6

Isomers are molecules that have the same chemical formula but different arrangements of atoms, as shown here for two isomers of pentane, $\mathrm{C}_{5} \mathrm{H}_{12} .$ (a) Do you expect a significant difference in the enthalpy of combustion of the two isomers? Explain. (b) Which isomer do you expect to have the higher standard molar entropy? Explain. [Section 19.4$]$

Christopher Nilsen
Christopher Nilsen
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01:17

Problem 7

The accompanying diagram shows how $\Delta H$ (red line) and $T \Delta S$ (blue line) change with temperature for a hypothetical reaction. (a) What is the significance of the point at $300 \mathrm{~K}$, where $\Delta H$ and $T \Delta S$ are equal? (b) In what temperature range is this reaction spontaneous? [Section 19.6$]$

Aadit Sharma
Aadit Sharma
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02:33

Problem 8

The accompanying diagram shows how $\Delta G$ for a hypothetical reaction changes as temperature changes. (a) At what temperature is the system at equilibrium? (b) In what temperature range is the reaction spontaneous? (c) Is $\Delta H$ positive or negative? (d) Is $\Delta S$ positive or negative? [Sections 19.5 and 19.6$]$

Qiao Ruan
Qiao Ruan
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05:21

Problem 9

Consider a reaction $\mathrm{A}_{2}(g)+\mathrm{B}_{2}(g) \rightleftharpoons 2 \mathrm{AB}(g),$ with atoms of A shown in red in the diagram and atoms of B shown in blue. (a) If $K_{c}=1,$ which box represents the system at equilibrium? (b) What is the sign of $\Delta G$ for any process in which the contents of a reaction vessel move to equilibrium? (c) Rank the boxes in order of increasing magnitude of $\Delta G$ for the reaction. [Sections 19.5 and 19.7$]$

Christopher Nilsen
Christopher Nilsen
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01:53

Problem 11

The accompanying diagram shows how the free energy, $G$, changes during a hypothetical reaction $\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow$ $\mathrm{C}(g) .$ On the left are pure reactants, each at $1 \mathrm{~atm},$ and on the right is the pure product, also at 1 atm.
(a) What is the significance of the minimum in the plot? (b) What does the quantity $x$, shown on the right side of the diagram, represent? $[$ Section 19.7$]$

Christopher Nilsen
Christopher Nilsen
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02:30

Problem 11

Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of hot coffee, $(\mathrm{c})$ the reaction of nitrogen atoms to form $\mathrm{N}_{2}$ molecules at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm},$ (d) lightning, (e) formation of $\mathrm{CH}_{4}$ and $\mathrm{O}_{2}$ molecules from $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ at room temperature and 1 atm of pressure?

Aadit Sharma
Aadit Sharma
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02:43

Problem 12

Which of the following processes are spontaneous: (a) the melting of ice cubes at $-10^{\circ} \mathrm{C}$ and 1 atm pressure;
(b) separating a mixture of $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ into two separate samples, one that is pure $\mathrm{N}_{2}$ and one that is pure $\mathrm{O}_{2} ;$ (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor; (e) the dissolution of $\mathrm{HCl}(g)$ in water to form concentrated hydrochloric acid?

Christopher Nilsen
Christopher Nilsen
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04:13

Problem 13

(a) Give two examples of endothermic processes that are spontaneous. (b) Give an example of a process that is spontaneous at one temperature but nonspontaneous at a different temperature.

Christopher Nilsen
Christopher Nilsen
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02:40

Problem 14

The crystalline hydrate $\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s)$ loses water when placed in a large, closed, dry vessel:
$$
\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g)
$$
This process is spontaneous and $\Delta H$ is positive. Is this process an exception to Bertholet's generalization that all spontaneous changes are exothermic? Explain.

Christopher Nilsen
Christopher Nilsen
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02:24

Problem 15

Consider the vaporization of liquid water to steam at a pressure of 1 atm. (a) Is this process endothermic or exothermic?
(b) In what temperature range is it a spontaneous process?
(c) In what temperature range is it a nonspontaneous process?
(d) At what temperature are the two phases in equilibrium?

Aadit Sharma
Aadit Sharma
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01:20

Problem 16

The normal freezing point of $n$ -octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ is $-57{ }^{\circ} \mathrm{C}$.
(a) Is the freezing of $n$ -octane an endothermic or exothermic process? (b) In what temperature range is the freezing of $n$ -octane a spontaneous process?
(c) In what temperature range is it a nonspontaneous process? (d) Is there any temperature at which liquid $n$ -octane and solid $n$ -octane are in equilibrium? Explain.

Qiao Ruan
Qiao Ruan
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03:50

Problem 17

(a) What is special about a reversible process? (b) Suppose a reversible process is reversed, restoring the system to its original state. What can be said about the surroundings after the process is reversed? (c) Under what circumstances will the vaporization of water to steam be a reversible process?
(d) Are any of the processes that occur in the world around us reversible in nature? Explain.

Christopher Nilsen
Christopher Nilsen
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04:32

Problem 18

(a) What is meant by calling a process irreversible? (b) After a particular irreversible process, the system is restored to its original state. What can be said about the condition of the surroundings after the system is restored to its original state? (c) Under what conditions will the condensation of a liquid be an irreversible process?

Christopher Nilsen
Christopher Nilsen
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07:32

Problem 19

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from $300 \mathrm{~K}$ to $200 \mathrm{~K}$. (a) Describe how this change might be carried out while keeping the volume of the gas constant. (b) Describe how it might be carried out while keeping the pressure of the gas constant. (c) Does the change in $\Delta E$ depend on the particular pathway taken to carry out this change of state? Explain.

Glyniss A
Glyniss A
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05:23

Problem 20

A system goes from state 1 to state 2 and back to state 1 . (a) What is the relationship between the value of $\Delta E$ for going from state 1 to state 2 to that for going from state 2 back to state $1 ?$ (b) Without further information, can you conclude anything about the amount of heat transferred to the system as it goes from state 1 to state 2 as compared to that upon going from state 2 back to state $1 ?(\mathrm{c})$ Suppose the changes in state are reversible processes. Can you conclude anything about the work done by the system upon going from state 1 to state 2 as compared to that upon going from state 2 back to state $1 ?$

Christopher Nilsen
Christopher Nilsen
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02:28

Problem 21

Consider a system consisting of an ice cube.
(a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is $\Delta E$ zero for the process? Explain.

Christopher Nilsen
Christopher Nilsen
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03:05

Problem 22

Consider what happens when a sample of the explosive TNT (Section 8.8: "Chemistry Put to Work: Explosives and Alfred Nobel") is detonated under atmospheric pressure.
(a) Is the detonation a spontaneous process? (b) What is the sign of $q$ for this process? (c) Can you determine whether $w$ is positive, negative, or zero for the process? Explain. (d) Can you determine the sign of $\Delta E$ for the process? Explain.

Christopher Nilsen
Christopher Nilsen
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02:21

Problem 23

(a) How can we calculate $\Delta S$ for an isothermal process? (b) Does $\Delta S$ for a process depend on the path taken from the initial state to the final state of the system? Explain.

Christopher Nilsen
Christopher Nilsen
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03:19

Problem 24

Suppose we vaporize a mole of liquid water at $25^{\circ} \mathrm{C}$ and another mole of water at $100{ }^{\circ} \mathrm{C}$. (a) Assuming that the enthalpy of vaporization of water does not change much between $25^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C},$ which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:19

Problem 25

The normal boiling point of $\mathrm{Br}_{2}(l)$ is $58.8{ }^{\circ} \mathrm{C},$ and its molar enthalpy of vaporization is $\Delta H_{\text {vap }}=29.6 \mathrm{~kJ} /$ mol. (a) When $\mathrm{Br}_{2}(l)$ boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of $\Delta S$ when $1.00 \mathrm{~mol}$ of $\mathrm{Br}_{2}(l)$ is vaporized at $58.8{ }^{\circ} \mathrm{C}$.

Aadit Sharma
Aadit Sharma
Numerade Educator
05:55

Problem 26

The element gallium (Ga) freezes at $29.8^{\circ} \mathrm{C},$ and its molar enthalpy of fusion is $\Delta H_{\text {fus }}=5.59 \mathrm{~kJ} / \mathrm{mol}$. (a) When molten gallium solidifies to $\mathrm{Ga}(s)$ at its normal melting point, is $\Delta S$ positive or negative? (b) Calculate the value of $\Delta S$ when $60.0 \mathrm{~g}$ of $\mathrm{Ga}(l)$ solidifies at $29.8^{\circ} \mathrm{C}$

Christopher Nilsen
Christopher Nilsen
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04:14

Problem 27

(a) Express the second law of thermodynamics in words. (b) If the entropy of the system increases during a reversible process, what can you say about the entropy change of the surroundings? (c) In a certain spontaneous process the system undergoes an entropy change, $\Delta S=42 \mathrm{~J} / \mathrm{K} .$ What can you conclude about ?

Christopher Nilsen
Christopher Nilsen
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04:10

Problem 28

(a) Express the second law of thermodynamics as a mathematical equation. (b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of $\Delta S_{\text {surr }} ?$ (c) During a certain reversible process, the surroundings undergo an entropy change, $\Delta S_{\text {surr }}=-78 \mathrm{~J} / \mathrm{K}$. What is the entropy change of the system for this process?

Christopher Nilsen
Christopher Nilsen
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03:42

Problem 29

(a) What sign for $\Delta S$ do you expect when the volume of 0.200 mol of an ideal gas at $27^{\circ} \mathrm{C}$ is increased isothermally from an initial volume of $10.0 \mathrm{~L} ?(\mathbf{b})$ If the final volume is 18.5 L, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

Christopher Nilsen
Christopher Nilsen
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04:24

Problem 30

(a) What sign for $\Delta S$ do you expect when the pressure on 0.600 mol of an ideal gas at $350 \mathrm{~K}$ is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

Qiao Ruan
Qiao Ruan
Numerade Educator
03:46

Problem 31

For the isothermal expansion of a gas into a vacuum, $\Delta E=0, q=0$, and $w=0$. (a) Is this a spontaneous process?
(b) Explain why no work is done by the system during this process. (c) In thermodynamics, what is the "driving force" for the expansion of the gas?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
01:55

Problem 32

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of $\Delta S_{\text {surr }}$ ?

Qiao Ruan
Qiao Ruan
Numerade Educator
04:23

Problem 33

How would each of the following changes affect the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:15

Problem 34

(a) Using the heat of vaporization in Appendix B, calculate the entropy change for the vaporization of water at $25^{\circ} \mathrm{C}$ and at $100^{\circ} \mathrm{C}$. (b) From your knowledge of microstates and the structure of liquid water, explain the difference in these two values.

Qiao Ruan
Qiao Ruan
Numerade Educator
04:43

Problem 35

(a) What do you expect for the sign of $\Delta S$ in a chemical reaction in which two moles of gaseous reactants are converted to three moles of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:21

Problem 36

(a) In a chemical reaction two gases combine to form a solid. What do you expect for the sign of $\Delta S ?$ (b) How does the entropy of the system change in the processes described in Exercise $19.12 ?$

Qiao Ruan
Qiao Ruan
Numerade Educator
03:21

Problem 37

(a) In a chemical reaction two gases combine to form a solid. What do you expect for the sign of $\Delta S ?$ (b) How does the entropy of the system change in the processes described in Exercise $19.12 ?$

Qiao Ruan
Qiao Ruan
Numerade Educator
04:02

Problem 38

How does the entropy of the system change when (a) the temperature of the system increases, (b) the volume of a gas increases, $(c)$ equal volumes of ethanol and water are mixed to form a solution?

Christopher Nilsen
Christopher Nilsen
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03:51

Problem 39

(a) State the third law of thermodynamics. (b) Distinguish between translational motion, vibrational motion, and rotational motion of a molecule. (c) Illustrate these three kinds of motion with sketches for the HCl molecule.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
05:19

Problem 40

(a) If you are told that the entropy of a certain system is zero, what do you know about the system and the temperature? (b) The energy of a gas is increased by heating it. Using $\mathrm{CO}_{2}$ as an example, illustrate the different ways in which additional energy can be distributed among the molecules of the gas. (c) $\mathrm{CO}_{2}(g)$ and $\mathrm{Ar}(g)$ have nearly the same molar mass. At a given temperature, will they have the same number of microstates? Explain.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:12

Problem 41

For each of the following pairs, choose the substance with the higher entropy per mole at a given temperature: (a) $\operatorname{Ar}(l)$ or $\mathrm{Ar}(g),$ (b) $\mathrm{He}(g)$ at 3 atm pressure or $\mathrm{He}(g)$ at 1.5 atm pressure, (c) $1 \mathrm{~mol}$ of $\mathrm{Ne}(g)$ in $15.0 \mathrm{~L}$ or $1 \mathrm{~mol}$ of $\mathrm{Ne}(g)$ in $1.50 \mathrm{~L}$,
(d) $\mathrm{CO}_{2}(g)$ or $\mathrm{CO}_{2}(s)$.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:49

Problem 42

For each of the following pairs, indicate which substance possesses the larger standard entropy: (a) $1 \mathrm{~mol}$ of $\mathrm{P}_{4}(g)$ at $300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm},$ or $1 \mathrm{~mol}$ of $\mathrm{As}_{4}(g)$ at $300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm} ;$
(b) $1 \mathrm{~mol}$ of $\mathrm{H}_{2} \mathrm{O}(g)$ at $100^{\circ} \mathrm{C}, 1 \mathrm{~atm},$ or $1 \mathrm{~mol}$ of $\mathrm{H}_{2} \mathrm{O}(l)$ at
$100^{\circ} \mathrm{C}, 1 \mathrm{~atm} ;$ (c) $0.5 \mathrm{~mol}$ of $\mathrm{N}_{2}(g)$ at $298 \mathrm{~K}, 20-\mathrm{L}$ volume, or
$0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)$ at $298 \mathrm{~K}, 20-\mathrm{L}$ volume; (d) $100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)$ at
$30^{\circ} \mathrm{C}$ or $100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)$ at $30^{\circ} \mathrm{C}$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:30

Problem 43

Predict the sign of the entropy change of the system for each of the following reactions:
(a) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$
(b) $\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$
(c) $3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g)$
(d) $\mathrm{Al}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)$

Aadit Sharma
Aadit Sharma
Numerade Educator
04:59

Problem 44

Predict the sign of $\Delta S_{\text {sys }}$ for each of the following processes:
(a) Molten gold solidifies. (b) Gaseous $\mathrm{Cl}_{2}$ dissociates in the stratosphere to form gaseous $\mathrm{Cl}$ atoms. (c) Gaseous CO reacts with gaseous $\mathrm{H}_{2}$ to form liquid methanol, $\mathrm{CH}_{3} \mathrm{OH}$.
(d) Calcium phosphate precipitates upon mixing $\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)$ and $\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}(a q)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
01:56

Problem 45

(a) Using Figure 19.13 as a model, sketch how the entropy of water changes as it is heated from $-50^{\circ} \mathrm{C}$ to $110^{\circ} \mathrm{C}$ at sea level. Show the temperatures at which there are vertical increases in entropy.
(b) Which process has the larger entropy change: melting ice or boiling water? Explain.

Aadit Sharma
Aadit Sharma
Numerade Educator
03:34

Problem 46

Propanol $\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)$ melts at $-126.5^{\circ} \mathrm{C}$ and boils at $97.4{ }^{\circ} \mathrm{C}$.
Draw a qualitative sketch of how the entropy changes as propanol vapor at $150^{\circ} \mathrm{C}$ and 1 atm is cooled to solid propanol at $-150^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
00:56

Problem 47

In each of the following pairs, which compound would you expect to have the higher standard molar entropy:
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(g)$
or $\mathrm{C}_{2} \mathrm{H}_{6}(g)$
(b) $\mathrm{CO}_{2}(g)$ or $\mathrm{CO}(g) ?$ Explain.

Aadit Sharma
Aadit Sharma
Numerade Educator
00:56

Problem 48

In each of the following pairs, which compound would you expect to have the higher standard molar entropy:
(a) $\mathrm{C}_{2} \mathrm{H}_{2}(g)$
or $\mathrm{C}_{2} \mathrm{H}_{6}(g),(\mathbf{b}) \mathrm{CO}_{2}(g)$ or $\mathrm{CO}(g) ?$ Explain.

Aadit Sharma
Aadit Sharma
Numerade Educator
04:54

Problem 49

Use Appendix $\mathrm{C}$ to compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances:
(a) $\mathrm{Sc}(s)$ and $\mathrm{Sc}(g)$,
$\mathrm{NH}_{3}(g)$ and $\mathrm{NH}_{3}(a q)$
(c) $1 \mathrm{~mol} \mathrm{P}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{P}_{2}(g)$,
(d) C(graphite) and C(diamond). In each case explain the difference in the entropy values.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:18

Problem 50

Using Appendix C, compare the standard entropies at $25^{\circ} \mathrm{C}$ for the following pairs of substances:
(a) $\mathrm{CuO}(s)$ and $\mathrm{Cu}_{2} \mathrm{O}(s)$
(b) $1 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{4}(g)$ and $2 \mathrm{~mol} \mathrm{NO}_{2}(g)$,
(c) $\mathrm{SiO}_{2}(s)$ and $\mathrm{CO}_{2}(g)$
(d) $\mathrm{CO}(g)$ and $\mathrm{CO}_{2}(g)$. For each pair, explain the difference in the entropy values.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
02:04

Problem 51

The standard entropies at $298 \mathrm{~K}$ for certain of the group $4 \mathrm{~A}$ elements are as follows: $\mathrm{C}(s,$ diamond $)=2.43 \mathrm{~J} / \mathrm{mol}-\mathrm{K},$ $\mathrm{Si}(s)=18.81 \mathrm{~J} / \mathrm{mol}-\mathrm{K}, \mathrm{Ge}(s)=31.09 \mathrm{~J} / \mathrm{mol}-\mathrm{K},$ and $\operatorname{Sn}(s)=$
$51.818 \mathrm{~J} / \mathrm{mol}-\mathrm{K} .$ All but $\mathrm{Sn}$ have the diamond structure. How do you account for the trend in the $S^{\circ}$ values?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:00

Problem 52

Three of the forms of elemental carbon are graphite, diamond, and buckminsterfullerene. The entropies at $298 \mathrm{~K}$ for graphite and diamond are listed in Appendix C. (a) Account for the difference in the $S^{\circ}$ values of graphite and diamond in light of their structures (Figure 12.30$)$. (b) What would you expect for the $S^{\circ}$ value of buckminsterfullerene (Figure $\left.12.47\right)$ relative to the values for graphite and diamond? Explain.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:15

Problem 53

Using $S^{\circ}$ values from Appendix C, calculate $\Delta S^{\circ}$ values for the following reactions. In each case account for the sign of $\Delta S^{\circ} .$
(a) $\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)$
(b) $\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
(c) $\mathrm{Be}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BeO}(s)+\mathrm{H}_{2} \mathrm{O}(g)$
(d) $2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$

Aadit Sharma
Aadit Sharma
Numerade Educator
05:27

Problem 54

Calculate $\Delta S^{\circ}$ values for the following reactions by using tabulated $S^{\circ}$ values from Appendix C. In each case explain the sign of $\Delta S^{\circ}$
(a) $\mathrm{HNO}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{NO}_{3}(s)$
(b) $2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g)$
(c) $\mathrm{CaCO}_{3}(s,$ calcite $)+2 \mathrm{HCl}(g) \longrightarrow$
$\mathrm{CaCl}_{2}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
(d) $3 \mathrm{C}_{2} \mathrm{H}_{6}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)+6 \mathrm{H}_{2}(\mathrm{~g})$

Qiao Ruan
Qiao Ruan
Numerade Educator
03:07

Problem 55

(a) For a process that occurs at constant temperature, express the change in Gibbs free energy in terms of changes in the enthalpy and entropy of the system. (b) For a certain process that occurs at constant $T$ and $P,$ the value of $\Delta G$ is positive. What can you conclude? (c) What is the relationship between $\Delta G$ for a process and the rate at which it occurs?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:18

Problem 56

(a) What is the meaning of the standard free-energy change, $\Delta G^{\circ},$ as compared with $\Delta G$ ? (b) For any process that occurs at constant temperature and pressure, what is the significance of $\Delta G=0 ?(c)$ For a certain process, $\Delta G$ is large and negative. Does this mean that the process necessarily occurs rapidly?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
02:04

Problem 57

For a certain chemical reaction, $\Delta H^{\circ}=-35.4 \mathrm{~kJ}$ and $\Delta S^{\circ}=-85.5 \mathrm{~J} / \mathrm{K} .$ (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system?
(c) Calculate $\Delta G^{\circ}$ for the reaction at $298 \mathrm{~K} .(\mathbf{d})$ Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Aadit Sharma
Aadit Sharma
Numerade Educator
02:10

Problem 58

A certain reaction has $\Delta H^{\circ}=+23.7 \mathrm{~kJ}$ and $\Delta S^{\circ}=$ $+52.4 \mathrm{~J} / \mathrm{K} .$ (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate $\Delta G^{\circ}$ for the reaction at $298 \mathrm{~K} .(\mathbf{d})$ Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Qiao Ruan
Qiao Ruan
Numerade Educator
11:42

Problem 59

Using data in Appendix C, calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ at $298 \mathrm{~K}$ for each of the following reactions. In each case show that $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ} .$
(a) $\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)$
(b) $\mathrm{C}(s,$ graphite $)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CCl}_{4}(g)$
(c) $2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{POCl}_{3}(g)$
(d) $2 \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
12:21

Problem 60

Use data in Appendix $\mathrm{C}$ to calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each of the following reactions. In each case show that $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$
(a) $2 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CrO}_{3}(s)$
(b) $\mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)$
(c) $2 \mathrm{P}(s)+10 \mathrm{HF}(g) \longrightarrow 2 \mathrm{PF}_{5}(g)+5 \mathrm{H}_{2}(g)$
(d) $\mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{KO}_{2}(s)$

Lori Mccoy
Lori Mccoy
Numerade Educator
05:51

Problem 61

Use data in Appendix C to calculate $\Delta H^{\circ}, \Delta S^{\circ}$, and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each of the following reactions. In each case show that $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$
(a) $2 \mathrm{Cr}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CrO}_{3}(s)$
(b) $\mathrm{BaCO}_{3}(s) \longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)$
(c) $2 \mathrm{P}(s)+10 \mathrm{HF}(g) \longrightarrow 2 \mathrm{PF}_{5}(g)+5 \mathrm{H}_{2}(g)$
(d) $\mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{KO}_{2}(s)$

Lori Mccoy
Lori Mccoy
Numerade Educator
10:38

Problem 62

Using data from Appendix $\mathrm{C},$ calculate the change in Gibbs free energy for each of the following reactions. In each case indicate whether the reaction is spontaneous at $298 \mathrm{~K}$ under standard conditions.
(a) $2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)$
(b) $\mathrm{P}_{4} \mathrm{O}_{6}(s)+12 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$
(d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:29

Problem 63

Octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline.
(a) Write a balanced equation for the combustion of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ to form $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ (b) Without using thermochemical data, predict whether $\Delta G^{\circ}$ for this reaction is more negative or less negative than $\Delta H^{\circ}$.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
08:19

Problem 64

Octane $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ is a liquid hydrocarbon at room temperature that is the primary constituent of gasoline.
(a) Write a balanced equation for the combustion of $\mathrm{C}_{8} \mathrm{H}_{18}(l)$ to form $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l) .$ (b) Without using thermochemical data, predict whether $\Delta G^{\circ}$ for this reaction is more negative or less negative than $\Delta H^{\circ}$.

Glyniss A
Glyniss A
Numerade Educator
05:59

Problem 65

Classify each of the following reactions as one of the four possible types summarized in Table 19.3 :
(a) $\mathrm{N}_{2}(g)+3 \mathrm{~F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)$
$$
\Delta H^{\circ}=-249 \mathrm{~kJ} ; \Delta S^{\circ}=-278 \mathrm{~J} / \mathrm{K}
$$
(b) $\mathrm{N}_{2}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NCl}_{3}(g)$
$$
\Delta H^{\circ}=460 \mathrm{~kJ} ; \Delta S^{\circ}=-275 \mathrm{~J} / \mathrm{K}
$$
(c) $\mathrm{N}_{2} \mathrm{~F}_{4}(g) \longrightarrow 2 \mathrm{NF}_{2}(g)$
$$
\Delta H^{\circ}=85 \mathrm{~kJ} ; \Delta S^{\circ}=198 \mathrm{~J} / \mathrm{K}
$$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
08:17

Problem 66

From the values given for $\Delta H^{\circ}$ and $\Delta S^{\circ},$ calculate $\Delta G^{\circ}$ for each of the following reactions at $298 \mathrm{~K}$. If the reaction is not spontaneous under standard conditions at $298 \mathrm{~K},$ at what temperature (if any) would the reaction become spontaneous?
$$
\begin{array}{l}
\text { (a) } 2 \mathrm{PbS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{PbO}(s)+2 \mathrm{SO}_{2}(g) \\
\qquad \begin{array}{c}
\Delta H^{\circ}=-844 \mathrm{~kJ} ; \Delta S^{\circ}=-165 \mathrm{~J} / \mathrm{K} \\
\text { (b) } 2 \mathrm{POCl}_{3}(g) \longrightarrow 2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g) \\
\Delta H^{\circ}=572 \mathrm{~kJ} ; \Delta S^{\circ}=179 \mathrm{~J} / \mathrm{K}
\end{array}
\end{array}
$$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
01:38

Problem 67

A particular constant-pressure reaction is spontaneous at $390 \mathrm{~K}$. The enthalpy change for the reaction is $+23.7 \mathrm{~kJ}$. What can you conclude about the sign and magnitude of $\Delta S$ for the reaction?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
01:43

Problem 68

A certain constant-pressure reaction is nonspontaneous at $45^{\circ} \mathrm{C}$. The entropy change for the reaction is $72 \mathrm{~J} / \mathrm{K}$. What can you conclude about the sign and magnitude of $\Delta H ?$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:22

Problem 69

For a particular reaction, $\Delta H=-32 \mathrm{~kJ}$ and $\Delta S=-98 \mathrm{~J} / \mathrm{K}$. Assume that $\Delta H$ and $\Delta S$ do not vary with temperature. (a) At what temperature will the reaction have $\Delta G=0 ?(\mathbf{b})$ If $T$ is increased from that in part (a), will the reaction be spontaneous or nonspontaneous?

Aadit Sharma
Aadit Sharma
Numerade Educator
05:18

Problem 70

Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds as follows:
$$
\mathrm{CH}_{3} \mathrm{COOH}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CO}(g)
$$
By using data from Appendix $\mathrm{C},$ calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not vary with temberature.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
06:58

Problem 71

Consider the following reaction between oxides of nitrogen:
$$
\mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g)
$$
(a) Use data in Appendix $\mathrm{C}$ to predict how $\Delta \mathrm{G}^{\circ}$ for the reaction varies with increasing temperature. (b) Calculate $\Delta G^{\circ}$ at $800 \mathrm{~K}$, assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?$
(c) Calculate $\Delta G^{\circ}$ at $1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
08:51

Problem 72

Methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ can be made by the controlled oxidation of methane:
$$
\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)
$$
(a) Use data in Appendix C to calculate $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for this reaction. (b) How is $\Delta G^{\circ}$ for the reaction expected to vary with increasing temperature? (c) Calculate $\Delta G^{\circ}$ at $298 \mathrm{~K}$. Under standard conditions, is the reaction spontaneous at this temperature? (d) Is there a temperature at which the reaction would be at equilibrium under standard conditions and that is low enough so that the compounds involved are likely to be stable?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
06:15

Problem 73

(a) Use data in Appendix $\mathrm{C}$ to estimate the boiling point of benzene, $\mathrm{C}_{6} \mathrm{H}_{6}(l) .$ (b) Use a reference source, such as the $\mathrm{CRC}$ Handbook of Chemistry and Physics, to find the experimental boiling point of benzene. How do you explain any deviation between your answer in part (a) and the experimental value?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
08:59

Problem 74

(a) Using data in Appendix $C$, estimate the temperature at which the free-energy change for the transformation from $\mathrm{I}_{2}(s)$ to $\mathrm{I}_{2}(g)$ is zero. What assumptions must you make in arriving at this estimate? (b) Use a reference source, such as Web Elements (www.webelements.com), to find the experimental melting and boiling points of $\mathrm{I}_{2} .$ (c) Which of the values in part (b) is closer to the value you obtained in part (a)? Can you explain why this is so?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
02:42

Problem 75

Acetylene gas, $\mathrm{C}_{2} \mathrm{H}_{2}(g),$ is used in welding.
(a) Write a balanced equation for the combustion of acetylene gas to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(l)$. (b) How much heat is produced in burning $1 \mathrm{~mol}$ of $\mathrm{C}_{2} \mathrm{H}_{2}$ under standard conditions if both reactants and products are brought to $298 \mathrm{~K}$ ? (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

Aadit Sharma
Aadit Sharma
Numerade Educator
03:41

Problem 76

The fuel in high-efficiency natural gas vehicles consists primarily of methane $\left(\mathrm{CH}_{4}\right) .$ (a) How much heat is produced in burning 1 mol of $\mathrm{CH}_{4}(g)$ under standard conditions if reactants and products are brought to $298 \mathrm{~K}$ and $\mathrm{H}_{2} \mathrm{O}(l)$ is formed? (b) What is the maximum amount of useful work that can be accomplished under standard conditions by this system?

Qiao Ruan
Qiao Ruan
Numerade Educator
04:54

Problem 77

Explain qualitatively how $\Delta G$ changes for each of the following reactions as the partial pressure of $\mathrm{O}_{2}$ is increased:
(a) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$
(b) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$
(c) $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
02:58

Problem 78

Indicate whether $\Delta G$ increases, decreases, or does not change when the partial pressure of $\mathrm{H}_{2}$ is increased in each of the following reactions:
(a) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$
(b) $2 \mathrm{HBr}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g)$
(c) $2 \mathrm{H}_{2}(g)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)$

Qiao Ruan
Qiao Ruan
Numerade Educator
03:19

Problem 79

Consider the reaction $2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$. (a) Using
data from Appendix $\mathrm{C},$ calculate $\Delta G^{\circ}$ at $298 \mathrm{~K}$.
(b) Calculate $\Delta G$ at $298 \mathrm{~K}$ if the partial pressures of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ are 0.40 atm and 1.60 atm, respectively.

Qiao Ruan
Qiao Ruan
Numerade Educator
07:17

Problem 80

Consider the reaction $3 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{8}(g)+2 \mathrm{H}_{2}(g)$
(a) Using data from Appendix $\mathrm{C},$ calculate $\Delta G^{\circ}$ at $298 \mathrm{~K}$.
(b) Calculate $\Delta G$ at $298 \mathrm{~K}$ if the reaction mixture consists of 40.0 atm of $\mathrm{CH}_{4}, 0.0100$ atm of $\mathrm{C}_{3} \mathrm{H}_{8}(g),$ and 0.0180 atm of $\mathrm{H}_{2}$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
09:36

Problem 81

Use data from Appendix $\mathrm{C}$ to calculate the equilibrium constant, $K,$ at $298 \mathrm{~K}$ for each of the following reactions:
(a) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{Hl}(g)$
(b) $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(c) $3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
12:21

Problem 82

Using data from Appendix $\mathrm{C}$, write the equilibrium-constant expression and calculate the value of the equilibrium constant for these reactions at $298 \mathrm{~K}$ :
(a) $\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)$
(b) $2 \mathrm{HBr}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\mathrm{Br}_{2}(g)$
(c) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
11:45

Problem 83

Consider the decomposition of barium carbonate:
$$
\mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)
$$
Using data from Appendix C, calculate the equilibrium pressure of $\mathrm{CO}_{2}$ at (a) $298 \mathrm{~K}$ and (b) $1100 \mathrm{~K}$.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
11:07

Problem 84

Consider the reaction
$$
\mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s)+\mathrm{CO}_{2}(g)
$$
Using data in Appendix C, calculate the equilibrium pressure of $\mathrm{CO}_{2}$ in the system at
(a) $400^{\circ} \mathrm{C}$ and
(b) $180^{\circ} \mathrm{C}$.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
04:41

Problem 85

The value of $K_{a}$ for nitrous acid $\left(\mathrm{HNO}_{2}\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix D.
(a) Write the chemical equation for the equilibrium that corresponds to $K_{a}$. (b) By using the value of $K_{a}$, calculate $\Delta G^{\circ}$ for the dissociation of nitrous acid in aqueous solution. (c) What is the value of $\Delta G$ at equilibrium? (d) What is the value of $\Delta G$ when $\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-2} \mathrm{M}$ $\left[\mathrm{NO}_{2}^{-}\right]=6.0 \times 10^{-4} \mathrm{M},$ and $\left[\mathrm{HNO}_{2}\right]=0.20 \mathrm{M} ?$

Aadit Sharma
Aadit Sharma
Numerade Educator
04:13

Problem 86

The $K_{b}$ for methylamine $\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)$ at $25^{\circ} \mathrm{C}$ is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to $K_{b} .$ (b) By using the value of $K_{b},$ calculate $\Delta G^{\circ}$ for the equilibrium in part (a).
(c) What is the value of $\Delta G$ at equilibrium?
(d) What is the value of $\Delta G$ when $\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\right]=2.4 \times 10^{-3} \mathrm{M}$
and $\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?$

Qiao Ruan
Qiao Ruan
Numerade Educator
04:16

Problem 87

(a) Which of the thermodynamic quantities $T, E, q, w,$ and $S$ are state functions? (b) Which depend on the path taken from one state to another? (c) How many reversible paths are there between two states of a system? (d) For a reversible isothermal process, write an expression for $\Delta E$ in terms of $q$ and $w$ and an expression for $\Delta S$ in terms of $q$ and $T$.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:08

Problem 88

Indicate whether each of the following statements is true or false. If it is false, correct it. (a) The feasibility of manufacturing $\mathrm{NH}_{3}$ from $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$ depends entirely on the value of $\Delta H$ for the process $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The re-
action of $\mathrm{Na}(s)$ with $\mathrm{Cl}_{2}(g)$ to form $\mathrm{NaCl}(s)$ is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:21

Problem 89

For each of the following processes, indicate whether the signs of $\Delta S$ and $\Delta H$ are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of $\mathrm{Co}(s)$ is lowered from $60^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. (c) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$.

Qiao Ruan
Qiao Ruan
Numerade Educator
01:49

Problem 90

The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous and has a negative value for $\Delta S^{\circ} .$ The second law of thermodynamics states that in any spontaneous process there is always an increase in the entropy of the universe. Is there an inconsistency between this reaction and the second law?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
03:07

Problem 91

Suppose four gas molecules are placed in the left flask in Figure $19.6(\mathrm{a}) .$ Initially, the right flask is evacuated and the stopcock is closed. (a) After the stopcock is opened, how many different arrangements of the molecules are possible? (b) How many of the arrangements from part (a) have all the molecules in the left flask? (c) How does the answer to part (b) explain the spontaneous expansion of the gas?

Christopher Nilsen
Christopher Nilsen
Numerade Educator
06:37

Problem 92

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (a) The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Explain. (b) To which state does each microstate correspond? (c) How many possible states are there for the system?(d) Which state or states have the highest entropy? Explain. (e) Which state or states have the lowest entropy? Explain.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
00:46

Problem 93

Ammonium nitrate dissolves spontaneously and endothermally in water at room temperature. What can you deduce about the sign of $\Delta S$ for this solution process?

Aadit Sharma
Aadit Sharma
Numerade Educator
04:15

Problem 94

A standard air conditioner involves a refrigerant that is typically now a fluorinated hydrocarbon, such as $\mathrm{CH}_{2} \mathrm{~F}_{2}$. An air-conditioner refrigerant has the property that it readily vaporizes at atmospheric pressure and is easily compressed to its liquid phase under increased pressure. The operation of an air conditioner can be thought of as a closed system made up of the refrigerant going through the two stages shown here (the air circulation is not shown in this diagram).
During expansion, the liquid refrigerant is released into an expansion chamber at low pressure, where it vaporizes. The vapor then undergoes compression at high pressure back to its liquid phase in a compression chamber. (a) What is the sign of $q$ for the expansion? (b) What is the sign of $q$ for the compression? (c) In a central air-conditioning system, one chamber is inside the home and the other is outside. Which chamber is where, and why? (d) Imagine that a sample of liquid refrigerant undergoes expansion followed by compression, so that it is back to its original state. Would you expect that to be a reversible process?
(e) Suppose that a house and its exterior are both initially at $31^{\circ} \mathrm{C}$. Some time after the air conditioner is turned on, the house is cooled to $24^{\circ} \mathrm{C}$. Is this process spontaneous or nonspontaneous?

Qiao Ruan
Qiao Ruan
Numerade Educator
06:45

Problem 95

Trouton's rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about $88 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$.
(a) Estimate the normal boiling point of bromine, $\mathrm{Br}_{2}$, by determining $\Delta H_{\text {vap }}^{\circ}$ for $\mathrm{Br}_{2}$ using data from Appendix C. Assume that $\Delta H_{\text {vap }}^{\circ}$ remains constant with temperature and that Trouton's rule holds. (b) Look up the normal boiling point of $\mathrm{Br}_{2}$ in a chemistry handbook or at the WebElements Web site (www.webelements.com).

Christopher Nilsen
Christopher Nilsen
Numerade Educator
04:34

Problem 96

For the majority of the compounds listed in Appendix $\mathrm{C},$ the value of $\Delta G_{f}^{\circ}$ is more positive (or less negative) than the value of $\Delta H_{f}^{\circ} .$ (a) Explain this observation, using $\mathrm{NH}_{3}(g), \mathrm{CCl}_{4}(l)$, and $\mathrm{KNO}_{3}(s)$ as examples. (b) An exception to this observation is $\mathrm{CO}(g)$. Explain the trend in the $\Delta H_{f}^{\circ}$ and $\Delta G_{f}^{\circ}$ values for this molecule.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
16:27

Problem 97

Consider the following three reactions:
(i) $\mathrm{Ti}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{TiCl}_{4}(g)$
(ii) $\mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{CCl}_{4}(g)+6 \mathrm{HCl}(g)$
(iii) $\mathrm{BaO}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{BaCO}_{3}(s)$
(a) For each of the reactions, use data in Appendix $\mathrm{C}$ to calculate $\Delta H^{\circ}, \Delta G^{\circ},$ and $\Delta S^{\circ}$ at $25^{\circ} \mathrm{C}$. (b) Which of these reactions are spontaneous under standard conditions at $25^{\circ} \mathrm{C} ?(\mathrm{c})$ For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
19:44

Problem 98

Using the data in Appendix $C$ and given the pressures listed, calculate $\Delta G^{\circ}$ for each of the following reactions:
$$
\begin{array}{l}
\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \\
\quad P_{\mathrm{N}_{2}}=2.6 \mathrm{~atm}, P_{\mathrm{H}_{2}}=5.9 \mathrm{~atm}, P_{\mathrm{NH}_{3}}=1.2 \mathrm{~atm} \\
\text { (b) } 2 \mathrm{~N}_{2} \mathrm{H}_{4}(g)+2 \mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\
\quad P_{\mathrm{N}_{2} \mathrm{H}_{4}}=P_{\mathrm{NO}_{2}}=5.0 \times 10^{-2} \mathrm{~atm} \\
\quad P_{\mathrm{N}_{2}}=0.5 \mathrm{~atm}, P_{\mathrm{H}_{2} \mathrm{O}}=0.3 \mathrm{~atm} \\
\text { (c) } \mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \\
\quad P_{\mathrm{N}_{2} \mathrm{H}_{4}}=0.5 \mathrm{~atm}, P_{\mathrm{N}_{2}}=1.5 \mathrm{~atm}, P_{\mathrm{H}_{2}}=2.5 \mathrm{~atm}
\end{array}
$$

Susan Hallstrom
Susan Hallstrom
Numerade Educator
04:30

Problem 99

(a) For each of the following reactions, predict the sign of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ and discuss briefly how these factors determine the magnitude of $K$. (b) Based on your general chemical knowledge, predict which of these reactions will have $K>0 .$ (c) In each case indicate whether $K$ should increase or decrease with increasing temperature.
(i) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{MgO}(s)$
(ii) $2 \mathrm{KI}(s) \rightleftharpoons 2 \mathrm{~K}(g)+\mathrm{I}_{2}(g)$
(iii) $\mathrm{Na}_{2}(g) \rightleftharpoons 2 \mathrm{Na}(g)$
(iv) $2 \mathrm{~V}_{2} \mathrm{O}_{5}(s) \rightleftharpoons 4 \mathrm{~V}(s)+5 \mathrm{O}_{2}(g)$

Christopher Nilsen
Christopher Nilsen
Numerade Educator
05:50

Problem 100

Acetic acid can be manufactured by combining methanol with carbon monoxide, an example of a carbonylation reaction:
$$
\mathrm{CH}_{3} \mathrm{OH}(l)+\mathrm{CO}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(l)
$$
(a) Calculate the equilibrium constant for the reaction at $25^{\circ} \mathrm{C}$.
(b) Industrially, this reaction is run at temperatures above $25^{\circ} \mathrm{C}$. Will an increase in temperature produce an increase or decrease in the mole fraction of acetic acid at equilibrium? Why are elevated temperatures used? (c) At what temperature will this reaction have an equilibrium constant equal to 1 ? (You may assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are temperature independent, and you may ignore any phase changes that might occur.)

Qiao Ruan
Qiao Ruan
Numerade Educator
03:38

Problem 101

The oxidation of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ in body tissue produces $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O} .$ In contrast, anaerobic decomposition, which occurs during fermentation, produces ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ and $\mathrm{CO}_{2} .$ (a) Using data given in Appendix $\mathrm{C}$, compare the equilibrium constants for the following reactions:
$$
\begin{aligned}
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) & \rightleftharpoons 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) & \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g)
\end{aligned}
$$
(b) Compare the maximum work that can be obtained from these processes under standard conditions.

Aadit Sharma
Aadit Sharma
Numerade Educator
17:20

Problem 102

The conversion of natural gas, which is mostly methane, into products that contain two or more carbon atoms, such as ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$, is a very important industrial chemical process. In principle, methane can be converted into ethane and hydrogen:
$$
2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)
$$
In practice, this reaction is carried out in the presence of
oxygen:
$$
2 \mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g)
$$
(a) Using the data in Appendix $C,$ calculate $K$ for these reactions at $25^{\circ} \mathrm{C}$ and $500{ }^{\circ} \mathrm{C}$. (b) Is the difference in $\Delta G^{\circ}$ for the two reactions due primarily to the enthalpy term $(\Delta H)$ or the entropy term $(-T \Delta S) ?(\mathbf{c})$ Explain how the preceding reactions are an example of driving a nonspontaneous reaction, as discussed in the "Chemistry and Life" box in Section 19.7 . (d) The reaction of $\mathrm{CH}_{4}$ and $\mathrm{O}_{2}$ to form $\mathrm{C}_{2} \mathrm{H}_{6}$ and $\mathrm{H}_{2} \mathrm{O}$ must be carried out carefully to avoid a competing reaction. What is the most likely competing reaction?

Qiao Ruan
Qiao Ruan
Numerade Educator
01:52

Problem 103

Cells use the hydrolysis of adenosine triphosphate (ATP) as a source of energy (Figure 19.19$)$. The conversion of ATP to ADP has a standard free-energy change of $-30.5 \mathrm{~kJ} / \mathrm{mol}$. If all the free energy from the metabolism of glucose,
$$
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)
$$
goes into the conversion of ADP to ATP, how many moles of ATP can be produced for each mole of glucose?

Aadit Sharma
Aadit Sharma
Numerade Educator
03:07

Problem 104

The potassium-ion concentration in blood plasma is about $5.0 \times 10^{-3} M,$ whereas the concentration in muscle-cell fluid is much greater $(0.15 \mathrm{M})$. The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to $\mathrm{K}^{+}$.
(a) What is $\Delta G$ for the transfer of $1 \mathrm{~mol}$ of $\mathrm{K}^{+}$ from blood plasma to the cellular fluid at body temperature $37^{\circ} \mathrm{C} ?$ (b) What is the minimum amount of work that must be used to transfer this $\mathrm{K}^{+} ?$

Qiao Ruan
Qiao Ruan
Numerade Educator
05:40

Problem 105

The relationship between the temperature of a reaction, its standard enthalpy change, and the equilibrium constant at that temperature can be expressed as the following linear equation:
$$
\ln K=\frac{-\Delta H^{\circ}}{R T}+\text { constant }
$$
(a) Explain how this equation can be used to determine $\Delta H^{\circ}$ experimentally from the equilibrium constants at several different temperatures.
(b) Derive the preceding equation using relationships given in this chapter. To what is the constant equal?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
08:33

Problem 106

One way to derive Equation 19.3 depends on the observation that at constant $T$ the number of ways, $W,$ of arranging $m$ ideal-gas particles in a volume $V$ is proportional to the volume raised to the $m$ power:
$$
W \propto V^{m}
$$
Use this relationship and Boltzmann's relationship between entropy and number of arrangements (Equation 19.5) to derive the equation for the entropy change for the isothermal expansion or compression of $n$ moles of an ideal gas.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
05:45

Problem 107

About $86 \%$ of the world's electrical energy is produced by using steam turbines, a form of heat engine. In his analysis of an ideal heat engine, Sadi Carnot concluded that the maximum possible efficiency is defined by the total work that could be done by the engine, divided by the quantity of heat available to do the work (for example, from hot steam produced by combustion of a fuel such as coal or methane). This efficiency is given by the ratio $\left(T_{\text {high }}-T_{\text {low }}\right) / T_{\text {high }}$, where $T_{\text {high }}$ is the temperature of the heat going into the engine and $T_{\text {low }}$ is that of the heat leaving the engine.
(a) What is the maximum possible efficiency of a heat engine operating between an input temperature of $700 \mathrm{~K}$ and an exit temperature of $288 \mathrm{~K} ?$ (b) Why is it important that electrical power plants be located near bodies of relatively cool water? (c) Under what conditions could a heat engine operate at or near $100 \%$ efficiency?
(d) It is often said that if the energy of combustion of a fuel such as methane were captured in an electrical fuel cell instead of by burning the fuel in a heat engine, a greater fraction of the energy could be put to useful work. Make a qualitative drawing like that in Figure 5.10 that illustrates the fact that in principle the fuel cell route will produce more useful work than the heat engine route from combustion of methane.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
13:34

Problem 108

Most liquids follow Trouton's rule, which states that the molar entropy of vaporization lies in the range of $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows:
(a) Calculate $\Delta S_{\text {vap }}$ for each of the liquids. Do all the liquids obey Trouton's rule?
(b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix $\mathrm{B}$, check the accuracy of your conclusion. (d) Chlorobenzene $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)$ boils at $131.8^{\circ} \mathrm{C}$. Use Trouton's rule to estimate $\Delta H_{\text {van }}$ for this substance.

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:22

Problem 109

In chemical kinetics the entropy of activation is the entropy change for the process in which the reactants reach the activated complex. The entropy of activation for bimolecular processes is usually negative. Explain this observation with reference to Figure 14.17 .

Christopher Nilsen
Christopher Nilsen
Numerade Educator
02:57

Problem 110

The following processes were all discussed in Chapter 18 , "Chemistry of the Environment." Estimate whether the entropy of the system increases or decreases during each process: (a) photodissociation of $\mathrm{O}_{2}(g),(\mathbf{b})$ formation of ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis.

Christopher Nilsen
Christopher Nilsen
Numerade Educator
12:54

Problem 111

Carbon disulfide $\left(\mathrm{CS}_{2}\right)$ is a toxic, highly flammable substance. The following thermodynamic data are available for $\mathrm{CS}_{2}(l)$ and $\mathrm{CS}_{2}(g)$ at $298 \mathrm{~K}$ :
(a) Draw the Lewis structure of the molecule. What do you predict for the bond order of the $\mathrm{C}-\mathrm{S}$ bonds? (b) Use the VSEPR method to predict the structure of the $\mathrm{CS}_{2}$ molecule.
(c) Liquid $\mathrm{CS}_{2}$ burns in $\mathrm{O}_{2}$ with a blue flame, forming $\mathrm{CO}_{2}(g)$ and $\mathrm{SO}_{2}(g)$. Write a balanced equation for this reaction.
(d) Using the data in the preceding table and in Appendix $\mathrm{C},$ calculate $\Delta H^{\circ}$ and $\Delta G^{\circ}$ for the reaction in part $(c)$. Is the reaction exothermic? Is it spontaneous at $298 \mathrm{~K}$ ?
(e) Use the data in the table to calculate $\Delta S^{\circ}$ at $298 \mathrm{~K}$ for the vaporization of $\mathrm{CS}_{2}(l)$ Is the sign of $\Delta S^{\circ}$ as you would expect for a vaporization? (f) Using data in the table and your answer to part (e), estimate the boiling point of $\mathrm{CS}_{2}(l)$. Do you predict that the substance will be a liquid or a gas at $298 \mathrm{~K}$ and $1 \mathrm{~atm} ?$

Qiao Ruan
Qiao Ruan
Numerade Educator
20:52

Problem 112

The following data compare the standard enthalpies and free energies of formation of some crystalline ionic substances and aqueous solutions of the substances:
$$
\begin{array}{lrr}
\text { Substance } & \Delta \boldsymbol{H}_{f}^{\circ}(\mathbf{k} \mathbf{J} / \mathbf{m o l}) & \Delta \mathbf{G}_{f}^{\circ}(\mathbf{k J} / \mathbf{m o l}) \\
\hline \mathrm{AgNO}_{3}(s) & -124.4 & -33.4 \\
\mathrm{AgNO}_{3}(a q) & -101.7 & -34.2 \\
\mathrm{MgSO}_{4}(s) & -1283.7 & -1169.6 \\
\mathrm{MgSO}_{4}(a q) & -1374.8 & -1198.4
\end{array}
$$
(a) Write the formation reaction for $\mathrm{AgNO}_{3}(s) .$ Based on this reaction, do you expect the entropy of the system to increase or decrease upon the formation of $\mathrm{AgNO}_{3}(s) ?$ (b) Use $\Delta H_{f}^{\circ}$ and $\Delta G_{f}^{\circ}$ of $\mathrm{AgNO}_{3}(s)$ to determine the entropy change upon formation of the substance. Is your answer consistent with your reasoning in part (a)? (c) Is dissolving $\mathrm{AgNO}_{3}$ in water an exothermic or endothermic process? What about dissolving $\mathrm{MgSO}_{4}$ in water? (d) For both $\mathrm{AgNO}_{3}$ and $\mathrm{MgSO}_{4},$ use the data to calculate the entropy change when the solid is dissolved in water. (e) Discuss the results from part (d) with reference to material presented in this chapter and in the "A Closer Look" box on page 540 .

Susan Hallstrom
Susan Hallstrom
Numerade Educator
20:43

Problem 113

Consider the following equilibrium:
$$
\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)
$$
Thermodynamic data on these gases are given in Appendix C. You may assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not vary with temperature. (a) At what temperature will an equilibrium mixture contain equal amounts of the two gases? (b) At what temperature will an equilibrium mixture of 1 atm total pressure contain twice as much $\mathrm{NO}_{2}$ as $\mathrm{N}_{2} \mathrm{O}_{4} ?$ (c) At what temperature will an equilibrium mixture of 10 atm total pressure contain twice as
much $\mathrm{NO}_{2}$ as $\mathrm{N}_{2} \mathrm{O}_{4} ?$ (d) Rationalize the results from parts (b) and (c) by using Le Châtelier's principle. [Section 15.7]

Susan Hallstrom
Susan Hallstrom
Numerade Educator
06:14

Problem 114

The reaction
$$
\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)
$$
is the basis of a suggested method for removal of $\mathrm{SO}_{2}$ from power-plant stack gases. The standard free energy of each substance is given in Appendix $\mathrm{C}$.
(a) What is the equilibrium constant for the reaction at $298 \mathrm{~K}$ ? (b) In principle, is this reaction a feasible method of removing $\mathrm{SO}_{2} ?$ (c) If $P_{\mathrm{SO}_{2}}=P_{\mathrm{H}_{2} \mathrm{~S}}$ and the vapor pressure of water is 25 torr, calculate the equilibrium $\mathrm{SO}_{2}$ pressure in the system at $298 \mathrm{~K}$.
(d) Would you expect the process to be more or less effective at higher temperatures?

Aadit Sharma
Aadit Sharma
Numerade Educator
02:20

Problem 115

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here:
Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on). What do you observe? Are your observations consistent with your answer to part (b)?

Qiao Ruan
Qiao Ruan
Numerade Educator