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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 20

Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions

Educators


Problem 1

Distinguish between the terms spontaneous and instantaneous. Give an example of a process that is spontaneous but very slow, and one that is very fast but not spontaneous.

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Problem 2

Distinguish between the terms spontaneous and nonspontaneous. Can a nonspontaneous process occur? Explain.

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Problem 3

State the first law of thermodynamics in terms of (a) the energy of the universe; (b) the creation or destruction of energy; (c) the energy change of system and surroundings. Does the first law reveal the direction of spontaneous change? Explain.

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Problem 4

State qualitatively the relationship between entropy and freedom of particle motion. Use this idea to explain why you will probably never (a) be suffocated because all the air near you has moved to the other side of the room; (b) see half the water in your cup of tea freeze while the other half boils.

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Problem 5

Why is $\Delta S_{\text { vap }}$ of a substance always larger than $\Delta S_{\text { fus }} ?$

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Problem 6

How does the entropy of the surroundings change during an exothermic reaction? An endothermic reaction? Other than the examples in text, describe a spontaneous endothermic process.

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Problem 7

(a) What is the entropy of a perfect crystal at 0 $\mathrm{K}$ ?
(b) Does entropy increase or decrease as the temperature rises?
(c) Why is $\Delta H_{\mathrm{f}}^{\circ}=0$ but $S^{\circ}>0$ for an element?
(d) Why does Appendix $\mathrm{B}$ list $\Delta H_{\mathrm{f}}^{\circ}$ values but not $\Delta S_{\mathrm{f}}^{\circ}$ values?

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Problem 8

Which of these processes are spontaneous? (a) Water evaporates from a puddle. (b) A lion chases an antelope. (c) An isotope undergoes radioactive disintegration.

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Problem 9

Which of these processes are spontaneous? (a) Earth moves around the Sun. (b) A boulder rolls up a hill. (c) Sodium metal and chlorine gas form solid sodium chloride.

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Problem 10

Which of these processes are spontaneous? (a) Methane burns in air. (b) A teaspoonful of sugar dissolves in a cup of hot coffee. (c) A soft-boiled egg becomes raw.

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Problem 11

Which of these processes are spontaneous? (a) A satellite falls to Earth. (b) Water decomposes to $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ at 298 $\mathrm{K}$ and 1 $\mathrm{atm} .(\mathrm{c})$ Average car prices increase.

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Problem 12

Predict the sign of $\Delta S_{\mathrm{sys} \text { for each process: (a) A piece of }}$ wax melts. (b) Silver chloride precipitates from solution. (c) Dew forms on a lawn in the morning.

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Problem 13

Predict the sign of $\Delta S_{\mathrm{sys}}$ for each process: (a) Gasoline vapors mix with air in a car engine. (b) Hot air expands. (c) Humidity condenses in cold air.

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Problem 14

Predict the sign of $\Delta S_{\mathrm{sys}}$ for each process: (a) Alcohol evap- orates. $(b)$ A solid explosive converts to a gas. $(c)$ Perfume vapors diffuse through a room.

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Problem 15

Predict the sign of $\Delta S_{\mathrm{sys}}$ for each process: (a) A pond freezes in winter. (b) Atmospheric $\mathrm{CO}_{2}$ dissolves in the ocean. (c) An apple tree bears fruit.

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Problem 16

Without using Appendix $\mathrm{B}$ , predict the sign of $\Delta S^{\circ}$ for
(a) $2 \mathrm{K}(s)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{KF}(s)$
(b) $\mathrm{NH}_{3}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Br}(s)$
(c) $\mathrm{NaClO}_{3}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{ClO}_{3}^{-}(a q)$

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Problem 17

Without using Appendix $\mathrm{B}$ , predict the sign of $\Delta S^{\circ}$ for
(a) $\mathrm{H}_{2} \mathrm{S}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \stackrel{1}{8} \mathrm{S}_{8}(s)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \longrightarrow \mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$
(c) 2 $\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$

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Problem 18

Without using Appendix $\mathrm{B}$ , predict the sign of $\Delta S^{\circ}$ for
(a) $\mathrm{CaCO}_{3}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{CaCl}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)$
(b) $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
(c) $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

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Problem 19

Without using Appendix $\mathrm{B}$ , predict the sign of $\Delta S^{\circ}$ for
(a) $\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s)$
(b) $\mathrm{KBr}(s) \longrightarrow \mathrm{KBr}(a q)$

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Problem 20

Predict the sign of $\Delta S$ for each process
$$\begin{array}{l}{\text { (a) } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)(350 \mathrm{K} \text { and } 500 \text { torr) } \longrightarrow} \\ {\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)(350 \mathrm{K} \text { and } 250 \text { torr) }}\end{array}$$
$$\begin{array}{l}{\text { (b) } \mathrm{N}_{2}(g)(298 \mathrm{K} \text { and } 1 \mathrm{atm}) \longrightarrow \mathrm{N}_{2}(a q)(298 \mathrm{K} \text { and } 1 \mathrm{atm})} \\ {\text { (c) } \mathrm{O}_{2}(a q)(303 \mathrm{K} \text { and } 1 \mathrm{atm}) \longrightarrow \mathrm{O}_{2}(g)(303 \mathrm{K} \text { and } 1 \mathrm{atm})}\end{array}$$

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Problem 21

Predict the sign of $\Delta S$ for each process:
(a) $\mathrm{O}_{2}(g)(1.0 \mathrm{L} \text { at } 1 \mathrm{atm}) \rightarrow \mathrm{O}_{2}(g)(0.10 \mathrm{L} \text { at } 10 \mathrm{atm})$
(b) $\mathrm{Cu}(s)\left(350^{\circ} \mathrm{C} \text { and } 2.5 \mathrm{atm}\right) \longrightarrow \mathrm{Cu}(s)\left(450^{\circ} \mathrm{C} \text { and } 2.5 \mathrm{atm}\right)$
(c) $\mathrm{Cl}_{2}(g)\left(100^{\circ} \mathrm{C} \text { and } 1 \mathrm{atm}\right) \longrightarrow \mathrm{Cl}_{2}(g)\left(10^{\circ} \mathrm{C} \text { and } 1 \mathrm{atm}\right)$

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Problem 22

Predict which substance has greater molar entropy. Explain
(a) Butane $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g)$ or 2 -butene $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CHCH}_{3}(g)$
(b) $\operatorname{Ne}(g)$ or $\mathrm{Xe}(g) \quad$ (c) $\mathrm{CH}_{4}(g)$ or $\mathrm{CCl}_{4}(l)$

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Problem 23

Predict which substance has greater molar entropy. Explain.
(a) $\mathrm{NO}_{2}(g)$ or $\mathrm{N}_{2} \mathrm{O}_{4}(g) \qquad$ (b) $\mathrm{CH}_{3} \mathrm{OCH}_{3}(l)$ or $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)$
(c) $\mathrm{HCl}(g)$ or $\mathrm{HBr}(g)$

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Problem 24

Predict which substance has greater molar entropy. Explain.
(a) $\mathrm{CH}_{3} \mathrm{OH}(l)$ or $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \quad$ (b) $\mathrm{KClO}_{3}(s)$ or $\mathrm{KClO}_{3}(a q)$
(c) $\mathrm{Na}(s)$ or $\mathrm{K}(s)$

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Problem 25

Predict which substance has greater molar entropy. Explain.
(a) $\mathrm{P}_{4}(g)$ or $\mathrm{P}_{2}(g) \quad$ (b) $\mathrm{HNO}_{3}(a q)$ or $\mathrm{HNO}_{3}(l)$
(c) $\mathrm{CuSO}_{4}(s)$ or $\mathrm{CuSO}_{4} \cdot \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)$

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Problem 26

Without consulting Appendix $\mathrm{B}$ , arrange each group in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain.
(a) Graphite, diamond, charcoal
(b) Ice, water vapor, liquid water
(c) $\mathrm{O}_{2}, \mathrm{O}_{3},$ O atoms

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Problem 27

Without consulting Appendix $\mathrm{B}$ , arrange each group in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain.
(a) Glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right),$ sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right),$ ribose $\left(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}\right)$
(b) $\mathrm{CaCO}_{3}, \mathrm{Ca}+\mathrm{C}+\frac{3}{2} \mathrm{O}_{2}, \mathrm{CaO}+\mathrm{CO}_{2}$
(c) $\mathrm{SF}_{6}(g), \mathrm{SF}_{4}(g), \mathrm{S}_{2} \mathrm{F}_{10}(g)$

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Problem 28

Without consulting Appendix $\mathrm{B}$ , arrange each group in
order of decreasing standard molar entropy $\left(S^{\circ}\right) .$ Explain.
(a) $\mathrm{ClO}_{4}^{-}(a q), \mathrm{ClO}_{2}^{-}(a q), \mathrm{ClO}_{3}^{-}(a q)$
(b) $\mathrm{NO}_{2}(g), \mathrm{NO}(g), \mathrm{N}_{2}(g)$
(c) $\mathrm{Fe}_{2} \mathrm{O}_{3}(s), \mathrm{Al}_{2} \mathrm{O}_{3}(s), \mathrm{Fe}_{3} \mathrm{O}_{4}(s)$

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Problem 29

Without consulting Appendix $\mathrm{B}$ , arrange each group in order of decreasing standard molar entropy $\left(S^{\circ}\right) .$ Explain.
(a) Mg metal, Ca metal, Ba metal
(b) Hexane $\left(\mathrm{C}_{6} \mathrm{H}_{14}\right),$ benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),$ cyclohexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)$
(c) $\mathrm{PF}_{2} \mathrm{Cl}_{3}(g), \mathrm{PF}_{5}(g), \mathrm{PF}_{3}(g)$

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Problem 30

For the reaction depicted in the molecular scenes, X is red and Y is green.
(a) Write a balanced equation.
(b) Determine the sign of $\Delta S_{\mathrm{rxn}}$
(c) Which species has the highest molar entropy?

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Problem 31

Describe the equilibrium condition in terms of the entropy changes of a system and its surroundings. What does this description mean about the entropy change of the universe?

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Problem 32

For the reaction $\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{HClO}(g),$ you $\mathrm{know} \Delta S_{\mathrm{rxn}}^{\circ}$ and $S^{\circ}$ of $\mathrm{HClO}(g)$ and of $\mathrm{H}_{2} \mathrm{O}(g) .$ Write an expression that can be used to determine $S^{\circ}$ of $\mathrm{Cl}_{2} \mathrm{O}(g) .$

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Problem 33

For each reaction, predict the sign and find the value of $\Delta S_{\mathrm{rxn}}^{\circ}$$$
\begin{array}{l}{\text { (a) } 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g)} \\ {\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\text { (c) } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}
$$

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Problem 34

For each reaction, predict the sign and find the value of $\Delta S_{\mathrm{rxn}}^{\circ}$
(a) $3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g)$
(b) $\mathrm{N}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)$
(c) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$

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Problem 35

Find $\Delta S_{\mathrm{rxn}}^{\circ}$ for the combustion of ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ to carbon dioxide and gaseous water. Is the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$ as expected?

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Problem 36

Find $\Delta S_{\text { rxn }}^{\circ}$ for the combustion of methane to carbon dioxide and liquid water. Is the sign of $\Delta S_{\text { rxn }}^{\circ}$ as expected?

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Problem 37

Find $\Delta S_{\text { rxn }}^{\circ}$ for the reaction of nitrogen monoxide with hydrogen to form ammonia and water vapor. Is the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$ as expected?

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Problem 38

Find $\Delta S_{\mathrm{rxn}}^{\delta}$ for the combustion of ammonia to nitrogen dioxide and water vapor. Is the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$ as expected?

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Problem 39

(a) Find $\Delta S_{\text { rxn }}^{\circ}$ for the formation of $\mathrm{Cu}_{2} \mathrm{O}(s)$ from its elements.
(b) Calculate $\Delta S_{\text { univ }}$ , and state whether the reaction is spontaneous at 298 $\mathrm{K} .$

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Problem 40

(a) Find $\Delta S_{\mathrm{rxn}}^{\circ}$ for the formation of HI(g) from its elements.
(b) Calculate $\Delta S_{\text { univ }},$ and state whether the reaction is spontaneous
at 298 $\mathrm{K}$ .

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Problem 41

(a) Find $\Delta S_{\mathrm{rxn}}^{\circ}$ for the formation of $\mathrm{CH}_{3} \mathrm{OH}(l)$ from its elements.
(b) Calculate $\Delta S_{\text { univ }},$ and state whether the reaction is spontaneous at 298 $\mathrm{K}$ .

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Problem 42

(a) Find $\Delta S_{\text { rxn }}^{\circ}$ for the formation of $\mathrm{N}_{2} \mathrm{O}(g)$ from its elements.
(b) Calculate $\Delta S_{\text { univ }},$ and state whether the reaction is spontaneous
at 298 $\mathrm{K}$ .

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Problem 43

Sulfur dioxide is released in the combustion of coal. Scrubbers use aqueous slurries of calcium hydroxide to remove the $\mathrm{SO}_{2}$ from flue gases. Write a balanced equation for this reaction and calculate $\Delta S_{\mathrm{rxn}}^{\circ}$ at 298 $\mathrm{K}\left[S^{\circ} \text { of } \mathrm{CaSO}_{3}(s)=101.4 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\right]$

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Problem 44

xyacetylene welding is used to repair metal structures, including bridges, buildings, and even the Statue of Liberty. Calculate $\Delta S_{\mathrm{xn}}^{\circ}$ for the combustion of 1 mol of acetylene $\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$

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Problem 45

What is the advantage of calculating free energy changes rather than entropy changes to determine reaction spontaneity?

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Problem 46

20.46 Given that $\Delta G_{\mathrm{sys}}=-T \Delta S_{\text { univ }},$ explain how the sign of $\Delta G_{\mathrm{sys}}$ correlates with reaction spontaneity.

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Problem 47

(a) Is an endothermic reaction more likely to be spontaneous at higher temperatures or lower temperatures? Explain.
(b) The change depicted below occurs at constant pressure. Explain your answers to each of the following: (1) What is the sign of $\Delta H_{\text { sys }} ?(2)$ What is the sign of $\Delta S_{\text { sys }} ?(3)$ What is the sign of $\Delta S_{\text { surr }} ?(4)$ How does the sign of $\Delta G_{\text { sys }}$ vary with temperature?

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Problem 48

Explain your answers to each of the following for the change depicted below. (a) What is the sign of $\Delta H_{\text { sys }} ?(b)$ What is the sign of $\Delta S_{S y s} ?(c)$ What is the sign of $\Delta S_{\text { surr }} ?(\text { d) How does the }$ sign of $\Delta G_{\text { sys }}$ vary with temperature?

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Problem 49

With its components in their standard states, a certain reaction is spontaneous only at high $T$ . What do you know about the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ} ?$ Describe a process for which this is true.

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Problem 50

How can $\Delta S^{\circ}$ be relatively independent of $T$ if $S^{\circ}$ of each reactant and product increases with $T ?$

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Problem 51

20.51 Calculate $\Delta G^{\circ}$ for each reaction using $\Delta G_{\mathrm{f}}^{\circ}$ values:
(a) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$
(b) $2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{BaO}(s)+\mathrm{CO}_{2}(g) \longrightarrow 2 \mathrm{aCO}_{3}(s)$

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Problem 52

Calculate $\Delta G^{\circ}$ for each reaction using $\Delta G_{\mathrm{f}}^{\circ}$ values:
(a) $\mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \longrightarrow 2 \mathrm{HI}(g)$
(b) $\mathrm{MnO}_{2}(s)+2 \mathrm{CO}(g) \longrightarrow \operatorname{Mn}(s)+2 \mathrm{CO}_{2}(g)$
(c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$

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Problem 53

Find $\Delta G^{\circ}$ for the reactions in Problem 20.51 using $\Delta H_{\mathrm{f}}^{\circ}$ and $S^{\circ}$ values. 20.54 Find $\Delta G^{\circ}$ for the reactions in Problem 20.52 using $\Delta H_{f}^{\circ}$ and $S^{\circ}$ values.

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Problem 54

Find $\Delta G^{\circ}$ for the reactions in Problem 20.52 using $\Delta H_{\mathrm{f}}^{\circ}$ and$S^{\circ}$ values.

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Problem 55

Consider the oxidation of carbon monoxide:
$$\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)$$
(a) Predict the signs of $\Delta S^{\circ}$ and $\Delta H^{\circ} .$ Explain.
(b) Calculate $\Delta G^{\circ}$ by two different methods.

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Problem 56

Consider the combustion of butane gas:
$$\mathrm{C}_{4} \mathrm{H}_{10}(g)+\frac{13}{2} \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{CO}_{2}(g)+5 \mathrm{H}_{2} \mathrm{O}(g)$$
(a) Predict the signs of $\Delta S^{\circ}$ and $\Delta H^{\circ} .$ Explain.
(b) Calculate $\Delta G^{\circ}$ by two different methods.

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Problem 57

For the gaseous reaction of xenon and fluorine to form xenon hexafluoride:
(a) Calculate $\Delta S^{\circ}$ at 298 $\mathrm{K}\left(\Delta H^{\circ}=-402 \mathrm{kJ} / \mathrm{mol} \text { and } \Delta G^{\circ}=\right.$ $-280 . \mathrm{kJ} / \mathrm{mol}$ ).
(b) Assuming that $\Delta S^{\circ}$ and $\Delta H^{\circ}$ change little with temperature, calculate $\Delta G^{\circ}$ at $500 . \mathrm{K}$ .

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Problem 58

For the gaseous reaction of carbon monoxide and chlorine to form phosgene $\left(\mathrm{COCl}_{2}\right) :$
(a) Calculate $\Delta S^{\circ}$ at 298 $\mathrm{K}\left(\Delta H^{\circ}=-220 . \mathrm{kJ} / \mathrm{mol} \text { and } \Delta G^{\circ}=\right.$ $-206 \mathrm{kJ} / \mathrm{mol}$ ).
(b) Assuming that $\Delta S^{\circ}$ and $\Delta H^{\circ}$ change little with temperature, calculate $\Delta G^{\circ}$ at $450 . \mathrm{K}$ .

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Problem 59

One reaction used to produce small quantities of pure $\mathrm{H}_{2}$ is
$$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$
(a) Determine $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction at 298 $\mathrm{K}$ .
(b) Assuming that these values are relatively independent of temperature, calculate $\Delta G^{\circ}$ at $28^{\circ} \mathrm{C}, 128^{\circ} \mathrm{C},$ and $228^{\circ} \mathrm{C}$ .
(c) What is the significance of the different values of $\Delta G^{\circ} ?$
(d) At what temperature (in $\mathrm{K} )$ does the reaction become spontaneous?

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Problem 60

A reaction that occurs in the internal combustion engine is
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$
(a) Determine $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the reaction at 298 $\mathrm{K}$ .
(b) Assuming that these values are relatively independent of temperature, calculate $\Delta G^{\circ}$ at $100 .^{\circ} \mathrm{C}, 2560 .^{\circ} \mathrm{C},$ and $3540 .^{\circ} \mathrm{C} .$
(c) What is the significance of the different values of $\Delta G^{\circ} ?$
(d) At what temperature (in $\mathrm{K} )$ does the reaction become spontaneous?

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Problem 61

As a fuel, $\mathrm{H}_{2}(g)$ produces only nonpolluting $\mathrm{H}_{2} \mathrm{O}(g)$ when
it burns. Moreover, it combines with $\mathrm{O}_{2}(g)$ in a fuel cell (Chapter 21 ) to provide electrical energy.
(a) Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ per mole of $\mathrm{H}_{2}$ at 298 $\mathrm{K}$ .
(b) Is the spontaneity of this reaction dependent on $T ?$ Explain.
(c) At what temperature does the reaction become spontaneous?

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Problem 62

The U.S. government requires automobile fuels to contain a renewable component. Fermentation of glucose from corn yields ethanol, which is added to gasoline to fulfill this requirement:
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g)$$
Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$ . Is the spontaneity of this reaction dependent on $T ?$ Explain.

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Problem 63

(a) If $K<<1$ for a reaction, what do you know about the sign and magnitude of $\Delta G^{\circ} ?(\mathrm{b})$ If $\Delta G^{\circ}<<0$ for a reaction, what do you know about the magnitude of $K ?$ Of $Q ?$

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Problem 64

How is the free energy change of a process related to the work that can be obtained from the process? Is this quantity of work obtainable in practice? Explain

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Problem 65

The scenes and the graph relate to the reaction of $\mathrm{X}_{2}(g)(\text {black})$ with $\mathrm{Y}_{2}(g)$ (orange) to form $\mathrm{XY}(g)$ . (a) If reactants and products are in their standard states, what quantity is represented on the graph by $x ?$ (b) Which scene represents point 1$?$ Explain. (c) Which scene represents point 2$?$ Explain.

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Problem 66

What is the difference between $\Delta G^{\circ}$ and $\Delta G ?$ Under what circumstances does $\Delta G=\Delta G^{\circ} ?$

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Problem 67

Calculate $K$ at 298 $\mathrm{K}$ for each reaction:
$$\begin{array}{l}{\text { (a) } \mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q)} \\ {\text { (b) } \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(l)}\end{array}$$

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Problem 68

Calculate $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for each reaction:
$$\begin{array}{l}{\text { (a) } 2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{SO}_{2}(g)} \\ {K=6.57 \times 10^{173}} \\ {\text { (b) } \mathrm{H}_{2} \mathrm{SO}_{4}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{3}(g) ; K=4.46 \times 10^{-15}}\end{array}$$

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Problem 69

Calculate $K$ at 298 $\mathrm{K}$ for each reaction:
$$\begin{array}{l}{\text { (a) } \mathrm{HCN}(a q)+\mathrm{NaOH}(a q) \rightleftharpoons \mathrm{NaCN}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (b) } \mathrm{SrSO}_{4}(s) \rightleftharpoons \mathrm{Sr}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)}\end{array}$$

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Problem 70

Calculate $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for each reaction:
$$\begin{array}{l}{\text { (a) } 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) ; K=1.58 \times 10^{7}} \\ {\text { (b) } \mathrm{Cu}_{2} \mathrm{S}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Cu}(s)+\mathrm{SO}_{2}(g) ; K=3.25 \times 10^{37}}\end{array}$$

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Problem 71

Use $\Delta H^{\circ}$ and $\Delta S^{\circ}$ values for the following process at 1 atm
to find the normal boiling point of $\mathrm{Br}_{2}$ :
$$\mathrm{Br}_{2}(l) \rightleftharpoons \mathrm{Br}_{2}(g)$$

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Problem 72

Use $\Delta H^{\circ}$ and $\Delta S^{\circ}$ values to find the temperature at which these sulfur allotropes reach equilibrium at 1 atm:
S(rhombic) $\rightleftharpoons$ S(monoclinic)

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Problem 73

Use Appendix $\mathrm{B}$ to determine the $K_{\mathrm{sp}}$ of $\mathrm{Ag}_{2} \mathrm{S}$

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Problem 74

Use Appendix $\mathrm{B}$ to determine the $K_{\mathrm{sp}}$ of $\mathrm{CaF}_{2}$

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Problem 75

For the reaction $\mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) \Longrightarrow 2 \mathrm{ICl}(g),$ calculate $K_{\mathrm{p}}$
at $25^{\circ} \mathrm{C}\left[\Delta G_{\mathrm{f}}^{\circ} \text { of } \mathrm{ICl}(g)=-6.075 \mathrm{kJ} / \mathrm{mol}\right]$

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Problem 76

For the reaction $\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g),$ calculate the equilibrium $P_{\mathrm{CO}_{2}}$ at $25^{\circ} \mathrm{C} .$

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Problem 77

The $K_{\mathrm{sp}}$ of $\mathrm{PbCl}_{2}$ is $1.7 \times 10^{-5}$ at $25^{\circ} \mathrm{C} .$ What is $\Delta G^{\circ}$ Is it possible to prepare a solution that contains $\mathrm{Pb}^{2+}(a q)$ and $\mathrm{Cl}^{-}(a q),$ at their standard-state concentrations?

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Problem 78

The $K_{\mathrm{sp}}$ of $\mathrm{ZnF}_{2}$ is $3.0 \times 10^{-2}$ at $25^{\circ} \mathrm{C} .$ What is $\Delta G^{\circ} ? \mathrm{Is}$ it possible to prepare a solution that contains $\mathrm{Zn}^{2+}(a q)$ and $\mathrm{F}^{-}(a q)$ at their standard-state concentrations?

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Problem 79

The equilibrium constant for the reaction
$$2 \mathrm{Fe}^{3+}(a q)+\mathrm{Hg}_{2}^{2+}(a q) \rightleftharpoons 2 \mathrm{Fe}^{2+}(a q)+2 \mathrm{Hg}^{2+}(a q)$$
is $K_{c}=9.1 \times 10^{-6}$ at 298 $\mathrm{K}$
(a) What is $\Delta G^{\circ}$ at this temperature?
(b) If standard-state concentrations of the reactants and products are mixed, in which direction does the reaction proceed?
(c) Calculate $\Delta G$ when $\left[\mathrm{Fe}^{3+}\right]=0.20 M,\left[\mathrm{Hg}_{2}^{2+}\right]=0.010 M,$ $\left[\mathrm{Fe}^{2+}\right]=0.010 M,$ and $\left[\mathrm{Hg}^{2+}\right]=0.025 M$ . In which direction will the reaction proceed to achieve equilibrium?

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Problem 80

The formation constant for the reaction
$$\mathrm{Ni}^{2+}(a q)+6 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}(a q)$$
$$K_{\mathrm{f}}=5.6 \times 10^{8} \text { at } 25^{\circ} \mathrm{C}$$
(a) What is $\Delta G^{\circ}$ at this temperature?
(b) If standard-state concentrations of the reactants and products are mixed, in which direction does the reaction proceed?
(c) Determine $\Delta G$ when $\left[\mathrm{Ni}\left(\mathrm{NH}_{3}\right)_{6}^{2+}\right]=0.010 M,\left[\mathrm{Ni}^{2+}\right]=$ $0.0010 M,$ and $\left[\mathrm{NH}_{3}\right]=0.0050 M .$ In which direction will the reaction proceed to achieve equilibrium?

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Problem 81

The scenes below depict three gaseous mixtures in which $\mathrm{A}$ is reacting with itself to form $\mathrm{A}_{2}$ . Assume that each particle represents 0.10 $\mathrm{mol}$ and the volume is 0.10 $\mathrm{L}$ .
(a) If $K=0.33$ , which mixture is at equilibrium? (b) Rank the
mixtures from the most positive $\Delta G$ to the most negative $\Delta G .$

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Problem 82

The scenes below depict three gaseous mixtures in which $\mathrm{X}$
(orange) and $\mathrm{Y}_{2}$ (black) are reacting to form $\mathrm{XY}$ and $\mathrm{Y}$ . Assume that each gas has a partial pressure of 0.10 $\mathrm{atm} .$
(a) If $K=4.5$ , which mixture is at equilibrium? (b) Rank the mixtures from the most positive $\Delta G$ to the most negative $\Delta G .$

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Problem 83

High levels of ozone $\left(\mathrm{O}_{3}\right)$ cause rubber to deteriorate, green plants to turn brown, and many people to have difficulty breathing. (a) Is the formation of $\mathrm{O}_{3}$ from $\mathrm{O}_{2}$ favored at all $T,$ no $T,$ high $T$ or low $T ?$ (b) Calculate $\Delta G^{\circ}$ for this reaction at 298 $\mathrm{K}$ .
(c) Calculate $\Delta G$ at 298 $\mathrm{K}$ for this reaction in urban smog where

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Problem 84

$\mathrm{ABaSO}_{4}$ slurry is ingested before the gastrointestinal tract is $\mathrm{x}$ -rayed because it is opaque to $\mathrm{x}$ -rays and defines the contours of the tract. $\mathrm{Ba}^{2+}$ ion is toxic, but the compound is nearly insoluble. if $\Delta G^{\circ}$ at $37^{\circ} \mathrm{C}$ (body temperature) is 59.1 $\mathrm{kJ} / \mathrm{mol}$ for the process
$$\mathrm{BaSO}_{4}(s) \rightleftharpoons \mathrm{Ba}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)$$
what is $\left[\mathrm{Ba}^{2+}\right]$ in the intestinal tract? (Assume that the only source
of $\mathrm{SO}_{4}^{2-}$ is the ingested slurry.)

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Problem 85

According to advertisements, “a diamond is forever.”
(a) Calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for the phase change
(b) Given the conditions under which diamond jewelry is normally kept, argue for and against the statement in the ad.
(c) Given the answers in part (a), what would need to be done to make synthetic diamonds from graphite?
(d) Assuming $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature, can graphite be converted to diamond spontaneously at 1 $\mathrm{atm} ?$

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Problem 86

Replace each question mark with the correct information:

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Problem 87

Among the many complex ions of cobalt are the following:
$$\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}(a q)+3 \mathrm{en}(a q) \rightleftharpoons \mathrm{Co}(\mathrm{en})_{3}^{3+}(a q)+6 \mathrm{NH}_{3}(a q)$$
where "en" stands for ethylenediamine, $\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2} .$ Six$\mathrm{Co}-\mathrm{N}$ bonds are broken and six $\mathrm{Co}-\mathrm{N}$ bonds are formed in this reaction, so $\Delta H_{\mathrm{rn}}^{\circ} \approx 0 ;$ yet $K>1 .$ What are the signs of $\Delta S^{\circ}$ and
$\Delta G^{\circ} ?$ What drives the reaction?

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Problem 88

What is the change in entropy when 0.200 mol of potassium freezes at $63.7^{\circ} \mathrm{C}\left(\Delta H_{\text { fus }}=2.39 \mathrm{kJ} / \mathrm{mol}\right) ?$

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Problem 89

Is each statement true or false? If false, correct it.
(a) All spontaneous reactions occur quickly.
(b) The reverse of a spontaneous reaction is nonspontaneous.
(c) All spontaneous processes release heat.
(d) The boiling of water at $100^{\circ} \mathrm{C}$ and 1 atm is spontaneous.
(e) If a process increases the freedom of motion of the particles of a system, the entropy of the system decreases.
(f) The energy of the universe is constant; the entropy of the universe decreases toward a minimum.
(g) All systems disperse their energy spontaneously.
(h) Both $\Delta S_{\mathrm{sys}}$ and $\Delta S_{\mathrm{surr}}$ equal zero at equilibrium.

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Problem 90

Hemoglobin carries $\mathrm{O}_{2}$ from the lungs to tissue cells, where the $\mathrm{O}_{2}$ is released. The protein is represented as $\mathrm{Hb}$ in its unoxygenated form and as $\mathrm{Hb} \cdot \mathrm{O}_{2}$ in its oxygenated form. One reason
$\mathrm{CO}$ is toxic is that it competes with $\mathrm{O}_{2}$ in binding to Hb:
$$\mathrm{Hb} \cdot \mathrm{O}_{2}(a q)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Hb} \cdot \mathrm{CO}(a q)+\mathrm{O}_{2}(g)$$
(a) If $\Delta G^{\circ} \approx-14 \mathrm{kJ}$ at $37^{\circ} \mathrm{C}$ (body temperature), what is the ratio of [Hb. CO] to $\left[\mathrm{Hb} \cdot \mathrm{O}_{2}\right]$ at $37^{\circ} \mathrm{C}$ with $\left[\mathrm{O}_{2}\right]=[\mathrm{CO}] ?$ (b) How is Le Châtelier's principle used to treat CO poisoning?

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Problem 91

Magnesia (MgO) is used for fire brick, crucibles, and furnace linings because of its high melting point. It is produced by decomposing magnesite $\left(\mathrm{MgCO}_{3}\right)$ at around $1200^{\circ} \mathrm{C} .$
(a) Write a balanced equation for magnesite decomposition.
(b) Use $\Delta H^{\circ}$ and $S^{\circ}$ values to find $\Delta G^{\circ}$ at 298 $\mathrm{K}$ .
(c) Assuming that $\Delta H^{\circ}$ and $S^{\circ}$ do not change with temperature, find the minimum temperature at which the reaction is spontaneous.
(d) Calculate the equilibrium $P_{\mathrm{CO}_{2}}$ above $\mathrm{MgCO}_{3}$ at 298 $\mathrm{K}$ .
(e) Calculate the equilibrium $P_{\mathrm{CO}}$ above $\mathrm{MgCO}_{3}$ at 1200 $\mathrm{K}$

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Problem 92

To prepare nuclear fuel, $\mathrm{U}_{3} \mathrm{O}_{8}(\text { "yellow cake" ) is converted }$ to $\mathrm{UO}_{2}\left(\mathrm{NO}_{3}\right)_{2}$, which is then converted to $\mathrm{UO}_{3}$ and finally UO2. The fuel is enriched (the proportion of the 235U is increased) by a two-step conversion of $\mathrm{UO}_{2}$ into$\mathrm{UF}_{6}$ , a volatile solid, followed by a gaseous-diffusion separation of the 235U and 238U isotopes:
$$\begin{aligned} \mathrm{UO}_{2}(s)+4 \mathrm{HF}(g) & \longrightarrow \mathrm{UF}_{4}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{UF}_{4}(s)+\mathrm{F}_{2}(g) & \longrightarrow \mathrm{UF}_{6}(s) \end{aligned}$$
Calculate $\Delta G^{\circ}$ for the overall process at $85^{\circ} \mathrm{C} :$

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Problem 93

Methanol, a major industrial feedstock, is made by several catalyzed reactions, such as $\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)$
(a) Show that this reaction is thermodynamically feasible.
(b) Is it favored at low or at high temperatures?
(c) One concern about using $\mathrm{CH}_{3} \mathrm{OH}$ as an auto fuel is oxidation
in air to yield formaldehyde, $\mathrm{CH}_{2} \mathrm{O}(g),$ which poses a health
hazard. Calculate $\Delta G^{\circ}$ at $100 .^{\circ} \mathrm{C}$ for this oxidation.

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Problem 94

(a) Write a balanced equation for the gaseous reaction between $\mathrm{N}_{2} \mathrm{O}_{5}$ and $\mathrm{F}_{2}$ to form $\mathrm{NF}_{3}$ and $\mathrm{O}_{2} .(\mathrm{b})$ Determine $\Delta G_{\mathrm{rxn}}^{\circ}$ (c) Find $\Delta G_{\mathrm{rxn}}$ at 298 $\mathrm{K}$ if $P_{\mathrm{N}_{2} \mathrm{O}_{5}}=P_{\mathrm{F}_{2}}=0.20 \mathrm{atm}, P_{\mathrm{NF}_{3}}=$
$0.25 \mathrm{atm},$ and $P_{\mathrm{O}_{2}}=0.50 \mathrm{atm} .$

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Problem 95

Consider the following reaction:
$$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{3}(g) \quad K=0.42 \mathrm{at} 373 \mathrm{K}$$
Given that $S^{\circ}$ of $\operatorname{NOBr}(g)=272.6 \mathrm{J} / \mathrm{mol}$ . $\mathrm{K}$ and that $\Delta S_{\mathrm{rxn}}^{\circ}$ and $\Delta H_{\mathrm{rxn}}^{\circ}$ are constant with temperature, find
(a) $\Delta S_{\mathrm{rxn}}^{\circ}$ at 298 $\mathrm{K}$
(b) $\Delta G_{\mathrm{rxn}}^{\circ}$ at 373 $\mathrm{K}$
(c) $\Delta H_{\mathrm{rxn}}^{\circ}$ at 373 $\mathrm{K}$
(d) $\Delta H_{\mathrm{f}}^{\circ}$ of $\mathrm{NOBr}$ at 298 $\mathrm{K}$
(e) $\Delta G_{\text { rxn }}^{\circ}$ at 298 $\mathrm{K}$
(f) $\Delta G_{\mathrm{f}}^{\circ}$ of $\mathrm{NOBr}$ at 298 $\mathrm{K}$

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Problem 96

Hydrogenation is the addition of $\mathrm{H}_{2}$ to double (or triple) carbon-carbon bonds. Peanut butter and most commercial baked goods include hydrogenated oils. Find $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for the hydrogenation of ethene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ to ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ at $25^{\circ} \mathrm{C} .$

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Problem 97

Styrene is produced by catalytic dehydrogenation of ethylbenzene at high temperature in the presence of superheated steam.
(a) Find $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta G_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ},$ given these data at $298 \mathrm{K} :$
(b) At what temperature is the reaction spontaneous?
(c) What are $\Delta G_{\text { rxn }}^{\circ}$ and $K$ at $600 .$ C?
(d) What 5.0 parts steam to 1.0 part ethylbenzene in the reactant mixture and the total pressure kept constant at 1.3 atm, what is $\Delta G$ at $50 . \%$ conversion, that is, when $50 . \%$ of the ethylbenzene has reacted?

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Problem 98

Propylene (propene; $\mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2} )$ is used to produce
polypropylene and many other chemicals. Although most is obtained from the cracking of petroleum, about 2$\%$ is produced by catalytic dehydrogenation of propane $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}\right) :$
$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3} \stackrel{\mathrm{P} / \mathrm{A}_{2} \mathrm{O}_{3}}{\longrightarrow} \mathrm{CH}_{3} \mathrm{CH}=\mathrm{CH}_{2}+\mathrm{H}_{2}$$
Because this reaction is endothermic, heaters are placed between the reactor vessels to maintain the required temperature.
(a) If the molar entropy, $S^{\circ},$ of propylene is 267.1 $\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}$ , find its entropy of formation, $S_{\mathrm{f}}^{\circ}$
(b) Find $\Delta G_{\mathrm{f}}^{\circ}$ of propylene $\left(\Delta H_{\mathrm{f}}^{\circ} \text { for propylene }=20.4 \mathrm{kJ} / \mathrm{mol}\right)$
(c) Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta G_{\mathrm{ran}}^{\circ} \mathrm{for}$ the dehydrogenation.
(d) What is the theoretical yield of propylene at $580^{\circ} \mathrm{C}$ if the initial pressure of propane is 1.00 atm?
(e) Would the yield change if the reactor walls were permeable to H. $?$ Explain.
(f) At what temperature is the dehydrogenation spontaneous, with all substances in the standard state?

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Problem 99

Find K for (a) the hydrolysis of ATP, (b) the dehydrationcondensation to form glucose phosphate, and (c) the coupled reaction between ATP and glucose. (d) How does each K change when $T$ changes from $25^{\circ} \mathrm{C}$ to $37^{\circ} \mathrm{C} ?$

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Problem 100

Energy from ATP hydrolysis drives many nonspontaneous cell reactions:
$$\begin{array}{r}{\mathrm{ATP}^{4-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{ADP}^{3-}(a q)+\mathrm{HPO}_{4}^{2-}(a q)+\mathrm{H}^{+}(a q)} \\ {\Delta G^{\circ \prime}=-30.5 \mathrm{kJ}}\end{array}$$
Energy for the reverse process comes ultimately from glucose metabolism:
$$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$
(a) Find $K$ for the hydrolysis of ATP at $37^{\circ} \mathrm{C}$ .
(b) Find $\Delta G_{\text { rxn }}^{\circ \prime}$ for metabolism of 1 mol of glucose.
(c) How many moles of ATP can be produced by metabolism of 1 mol of glucose?
(d) If 36 $\mathrm{mol}$ of ATP is formed, what is the actual yield?

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Problem 101

From the following reaction and data, find (a) $S^{\circ}$ of $\mathrm{SOCl}_{2}$ and (b) $T$ at which the reaction becomes nonspontaneous:
$$ \mathrm{SO}_{3}(g)+\mathrm{SCl}_{2}(l) \longrightarrow \mathrm{SOCl}_{2}(l)+\mathrm{SO}_{2}(g) \quad \Delta G_{\mathrm{xn}}^{\circ}=-75.2 \mathrm{kJ} $$

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Problem 102

Write equations for the oxidation of Fe and of Al. Use $\Delta G_{\mathrm{f}}^{\circ}$ to determine whether either process is spontaneous at $25^{\circ} \mathrm{C} .$

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Problem 103

The molecular scene depicts a gaseous equilibrium mixture at $460^{\circ} \mathrm{C}$ for the reaction of $\mathrm{H}_{2}(\text {blue})$ and $\mathrm{I}_{2}$ (purple) to form HI. Each molecule represents 0.010 mol and the container volume is 1.0 $\mathrm{L}$ . (a) Is $K_{\mathrm{c}}>,=,$ or $<1 ?$ (b) Is $K_{\mathrm{p}}>=,$ or $<K_{\mathrm{c}} ?(\mathrm{c})$ Calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ . (d) How would the value of $\Delta G_{\mathrm{rxn}}^{\circ}$ change if the purple molecules represented $\mathrm{H}_{2}$ and the blue $\mathrm{I}_{2} ?$ Explain.

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Problem 104

A key step in the metabolism of glucose for energy is the isomerization of glucose-- 6 -phosphate $(\mathrm{G} 6 \mathrm{P})$ to fructose 6 -phosphate $(\mathrm{F} 6 \mathrm{P}) : \mathrm{G6P} \quad \rightleftharpoons \mathrm{F6P} ; K=0.510$ at 298 $\mathrm{K}$
(a) Calculate $\Delta G^{\circ}$ at 298 $\mathrm{K}$ .
(b) Calculate $\Delta G$ when $Q$ , the $[\mathrm{F} 6 \mathrm{P}] /[\mathrm{G} 6 \mathrm{P}]$ ratio, equals $10.0 .$
(c) Calculate $\Delta G$ when $Q=0.100$ .
(d) Calculate $Q$ if $\Delta G=-2.50 \mathrm{kJ} / \mathrm{mol}$

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Problem 105

A chemical reaction, such as HI forming from its elements, can reach equilibrium at many temperatures. In contrast, a phase change, such as ice melting, is in equilibrium at a given pressure and temperature. Each of the graphs below depicts $G_{\mathrm{sys}}$ vs. extent of change. (a) Which graph depicts how $G_{\mathrm{sys}}$ changes for the formation of HI? Explain. (b) Which graph depicts how $G_{\mathrm{sys}}$ changes as ice melts at 18C and 1 atm? Explain.

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Problem 106

When heated, the DNA double helix separates into two random coil single strands. When cooled, the random coils reform the double helix: double helix $\Longrightarrow 2$ random coils.
(a) What is the sign of $\Delta S$ for the forward process? Why?
(b) Energy must be added to break $\mathrm{H}$ bonds and overcome dispersion forces between the strands. What is the sign of $\Delta G$ for the forward process when $T \Delta S$ is smaller than $\Delta H ?$
(c) Write an expression for $T$ in terms of $\Delta H$ and $\Delta S$ when the reaction is at equilibrium. (This temperature is called the melting temperature of the nucleic acid.)

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Problem 107

In the process of respiration, glucose is oxidized completely. In fermentation, $\mathrm{O}_{2}$ is absent and glucose is broken down to ethanol and $\mathrm{CO}_{2}$ . Ethanol is oxidized to $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ .
(a) Balance the following equations for these processes:
Respiration: $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
Fermentation: $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{CO}_{2}(g)$
Ethanol oxidation: $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
(b) Calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ for respiration of 1.00 $\mathrm{g}$ of glucose.
(c) Calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ for fermentation of 1.00 $\mathrm{g}$ of glucose.
(d) Calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ for oxidation of the ethanol from part (c).

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Problem 108

Consider the formation of ammonia:
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$
(a) Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are constant with temperature, find the temperature at which $K_{\mathrm{p}}=1.00 .$
(b) Find $K_{\mathrm{p}}$ at $400 .^{\circ} \mathrm{C}$ , a typical temperature for $\mathrm{NH}_{3}$ production.
(c) Given the lower $K_{\mathrm{p}}$ at the higher temperature, why are these conditions used industrially?

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Problem 109

Kyanite, sillimanite, and andalusite all have the formula $\mathrm{Al}_{2} \mathrm{SiO}_{5}$. Each is stable under different conditions (see the graph at right). At the point where the three phases intersect:
(a) Which mineral, if any, has the lowest free energy?
(b) Which mineral, if any, has the lowest enthalpy?
(c) Which mineral, if any, has the highest entropy?
(d) Which mineral, if any, has the lowest density?

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Problem 110

Acetylene is produced commercially by the partial oxidation of methane. At $1500^{\circ} \mathrm{C}$and pressures of 1–10 bar, the yield of acetylene is about 20%. The major side product is carbon monoxide, and some soot and carbon dioxide also form.
(a) At what temperature is the desired reaction spontaneous:
$$2 \mathrm{CH}_{4}+\frac{1}{2} \mathrm{O}_{2} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{2}+2 \mathrm{H}_{2}+\mathrm{H}_{2} \mathrm{O}$$
(b) Acetylene can also be made by the reaction of its elements, carbon (graphite) and hydrogen. At what temperature is this formation reaction spontaneous?
(c) Why must this reaction mixture be immediately cooled?

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Problem 111

Synthesis gas, a mixture that includes the fuels CO and $\mathrm{H}_{2}$, is used to produce liquid hydrocarbons and methanol. It is made at pressures up to 100 atm by oxidation of methane followed by the steam reforming and water-gas shift reactions. Because the process is exothermic, temperatures reach $950-1100^{\circ} \mathrm{C}$, and the conditions are such that the amounts of $\mathrm{H}_{2}, \mathrm{CO}, \mathrm{CO}_{2}, \mathrm{CH}_{4}$, and $\mathrm{H}_{2} \mathrm{O}$ leaving the reactor are close to the equilibrium amounts for the steam re-forming and water-gas shift reactions:
$$\begin{aligned} \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \text { (steam re-forming) } \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \text { (water-gas shift) } \end{aligned}$$
(a) At $1000 .$ ', what are $\Delta G^{\circ}$ and $\Delta H^{\circ}$ for the steam re-forming
reaction and for the water-gas shift reaction?
(b) By doubling the steam re-forming step and adding it to the water-gas shift step, we obtain the following combined reaction:
$$2 \mathrm{CH}_{4}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{CO}(g)+7 \mathrm{H}_{2}(g)$$
Is this reaction spontaneous at $1000 .^{\circ} \mathrm{C}$ in the standard state?
(c) Is it spontaneous at 98 atm and $50 . \%$ conversion (when $50 . \%$ of the starting materials have reacted)?
(d) Is it spontaneous at 98 atm and $90 . \%$ conversion?

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