# CHEMISTRY: The Molecular Nature of Matter and Change 2016

## 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}$$\begin{array}{l}{\text { (a) } 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g)} \\ {\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{F}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{NF}_{3}(g)} \\ {\text { (c) } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}$$ Check back soon! 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)$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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$\mathrm{K} .$Check back soon! 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$\mathrm{K}$. Check back soon! 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$\mathrm{K}$. Check back soon! 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$\mathrm{K}$. Check back soon! 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$\mathrm{K}\left[S^{\circ} \text { of } \mathrm{CaSO}_{3}(s)=101.4 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\right]$Check back soon! 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$\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)$Check back soon! Problem 45 What is the advantage of calculating free energy changes rather than entropy changes to determine reaction spontaneity? Check back soon! 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. Check back soon! 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? Check back soon! 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? Check back soon! 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. Check back soon! Problem 50 How can$\Delta S^{\circ}$be relatively independent of$T$if$S^{\circ}$of each reactant and product increases with$T ?$Check back soon! 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)$\mathrm{BaO}(s)+\mathrm{CO}_{2}(g) \longrightarrow 2 \mathrm{aCO}_{3}(s)$Check back soon! 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)$\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$Check back soon! 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. Check back soon! Problem 54 Find$\Delta G^{\circ}$for the reactions in Problem 20.52 using$\Delta H_{\mathrm{f}}^{\circ}$and$S^{\circ}$values. Check back soon! 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. Check back soon! 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. Check back soon! 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$500 . \mathrm{K}$. Check back soon! 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$450 . \mathrm{K}$. Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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. Check back soon! 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$Q ?$Check back soon! 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 Check back soon! 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. Check back soon! Problem 66 What is the difference between$\Delta G^{\circ}$and$\Delta G ?$Under what circumstances does$\Delta G=\Delta G^{\circ} ?$Check back soon! Problem 67 Calculate$K$at 298$\mathrm{K}$for each reaction: $$\begin{array}{l}{\text { (a) } \mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{Mg}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q)} \\ {\text { (b) } \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}_{2}(l)}\end{array}$$ Check back soon! Problem 68 Calculate$\Delta G^{\circ}$at 298$\mathrm{K}$for each reaction: $$\begin{array}{l}{\text { (a) } 2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{SO}_{2}(g)} \\ {K=6.57 \times 10^{173}} \\ {\text { (b) } \mathrm{H}_{2} \mathrm{SO}_{4}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{SO}_{3}(g) ; K=4.46 \times 10^{-15}}\end{array}$$ Check back soon! Problem 69 Calculate$K$at 298$\mathrm{K}$for each reaction: $$\begin{array}{l}{\text { (a) } \mathrm{HCN}(a q)+\mathrm{NaOH}(a q) \rightleftharpoons \mathrm{NaCN}(a q)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (b) } \mathrm{SrSO}_{4}(s) \rightleftharpoons \mathrm{Sr}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)}\end{array}$$ Check back soon! Problem 70 Calculate$\Delta G^{\circ}$at 298$\mathrm{K}$for each reaction: $$\begin{array}{l}{\text { (a) } 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) ; K=1.58 \times 10^{7}} \\ {\text { (b) } \mathrm{Cu}_{2} \mathrm{S}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Cu}(s)+\mathrm{SO}_{2}(g) ; K=3.25 \times 10^{37}}\end{array}$$ Check back soon! 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$\mathrm{Br}_{2}$: $$\mathrm{Br}_{2}(l) \rightleftharpoons \mathrm{Br}_{2}(g)$$ Check back soon! 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) Check back soon! Problem 73 Use Appendix$\mathrm{B}$to determine the$K_{\mathrm{sp}}$of$\mathrm{Ag}_{2} \mathrm{S}$Check back soon! Problem 74 Use Appendix$\mathrm{B}$to determine the$K_{\mathrm{sp}}$of$\mathrm{CaF}_{2}$Check back soon! Problem 75 For the reaction$\mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) \Longrightarrow 2 \mathrm{ICl}(g),$calculate$K_{\mathrm{p}}$at$25^{\circ} \mathrm{C}\left[\Delta G_{\mathrm{f}}^{\circ} \text { of } \mathrm{ICl}(g)=-6.075 \mathrm{kJ} / \mathrm{mol}\right]$Check back soon! 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$25^{\circ} \mathrm{C} .$Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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$\Delta G .$Check back soon! 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$\Delta G .$Check back soon! 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 Check back soon! 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.) Check back soon! 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$\mathrm{atm} ?$Check back soon! Problem 86 Replace each question mark with the correct information: Check back soon! 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? Check back soon! Problem 88 What is the change in entropy when 0.200 mol of potassium freezes at$63.7^{\circ} \mathrm{C}\left(\Delta H_{\text { fus }}=2.39 \mathrm{kJ} / \mathrm{mol}\right) ?$Check back soon! 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. Check back soon! 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? Check back soon! 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$\mathrm{K}$Check back soon! 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$85^{\circ} \mathrm{C} :$Check back soon! 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. Check back soon! 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$P_{\mathrm{O}_{2}}=0.50 \mathrm{atm} .$Check back soon! 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$\mathrm{K}$Check back soon! 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$25^{\circ} \mathrm{C} .$Check back soon! 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? Check back soon! 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? Check back soon! 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$37^{\circ} \mathrm{C} ?$Check back soon! 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? Check back soon! 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: $$\mathrm{SO}_{3}(g)+\mathrm{SCl}_{2}(l) \longrightarrow \mathrm{SOCl}_{2}(l)+\mathrm{SO}_{2}(g) \quad \Delta G_{\mathrm{xn}}^{\circ}=-75.2 \mathrm{kJ}$$ Check back soon! 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$25^{\circ} \mathrm{C} .$Check back soon! 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. Check back soon! 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$\Delta G=-2.50 \mathrm{kJ} / \mathrm{mol}$Check back soon! 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. Check back soon! 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.) Check back soon! 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). Check back soon! 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? Check back soon! 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? Check back soon! 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? Check back soon! 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$\mathrm{H}_{2} \mathrm{O}leaving the reactor are close to the equilibrium amounts for the steam re-forming and water-gas shift reactions: \begin{aligned} \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \text { (steam re-forming) } \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) & \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \text { (water-gas shift) } \end{aligned} (a) At1000 .$', 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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