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Chapter 18

Free Energy and Thermodynamics

Educators

LP
LF

Problem 1

What is the first law of thermodynamics, and how does it relate to energy use?

Dang S.
Numerade Educator

Problem 2

What is nature's heat tax, and how does it relate to energy use?

LP
Lucas P.
Numerade Educator

Problem 3

What is a perpetual motion machine? Can such a machine exist given the laws of thermodynamics?

Dang S.
Numerade Educator

Problem 4

Is it more efficient to heat your home with a natural gas furnace or an electric furnace? Explain.

LP
Lucas P.
Numerade Educator

Problem 5

What is a spontaneous process? Provide an example.

Dang S.
Numerade Educator

Problem 6

Explain the difference between the spontaneity of a reaction (which depends on thermodynamics) and the speed at which the reaction occurs (which depends on kinetics). Can a catalyst make a nonspontaneous reaction spontaneous?

LP
Lucas P.
Numerade Educator

Problem 7

What is the precise definition of entropy? What is the significance of entropy being a state function?

Dang S.
Numerade Educator

Problem 8

Why does the entropy of a gas increase when it expands into a vacuum?

LP
Lucas P.
Numerade Educator

Problem 9

Explain the difference between macrostates (external arrangements of particles) and microstates (internal arrangements of particles.

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Problem 10

Based on its fundamental definition, explain why entropy is a measure of energy dispersion.

LP
Lucas P.
Numerade Educator

Problem 11

State the second law of thermodynamics. How does the second law explain why heat travels from a substance at higher temperature to one at lower temperature?

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Problem 12

What happens to the entropy of a sample of matter when it changes state from a solid to a liquid? From a liquid to a gas?

LP
Lucas P.
Numerade Educator

Problem 13

Explain why water spontaneously freezes to form ice below $0^{\circ} \mathrm{C}$ even though the entropy of the water decreases during the state transition. Why is the freezing of water not spontaneous above $0^{\circ} \mathrm{C} ?$

Dang S.
Numerade Educator

Problem 14

Why do exothermic processes tend to be spontaneous at low temperatures? Why does their tendency toward spontaneity decrease with increasing temperature?

LP
Lucas P.
Numerade Educator

Problem 15

What is the significance of the change in Gibbs free energy $(\Delta G)$ for a reaction?

Dang S.
Numerade Educator

Problem 16

Predict the spontaneity of a reaction (and the temperature dependence of the spontaneity) for each possible combination of signs for $\Delta H$ and $\Delta S$ (for the system).
\begin{equation}\begin{array}{ll}{\text { a. } \Delta H \text { negative, } \Delta S \text { positive }} & {\text { b. } \Delta H \text { positive, } \Delta S \text { negative }} \\ {\text { c. }} {\Delta H \text { negative, } \Delta S \text { negative }} & {\text { d. } \Delta H \text { positive, } \Delta S \text { positive }}\end{array}\end{equation}

LF
Leila F.
Numerade Educator

Problem 17

State the third law of thermodynamics and explain its significance.

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Problem 18

Why is the standard entropy of a substance in the gas state greater than its standard entropy in the liquid state?

LP
Lucas P.
Numerade Educator

Problem 19

How does the standard entropy of a substance depend on its molar mass? On its molecular complexity?

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Problem 20

How can you calculate the standard entropy change for a reaction from tables of standard entropies?

LP
Lucas P.
Numerade Educator

Problem 21

What are three different methods to calculate $\Delta G^{\circ}$ for a reaction? Which method would you choose to calculate $\Delta G^{\circ}$ for a reaction at a temperature other than $25^{\circ} \mathrm{C}$ ?

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Problem 22

Why is free energy "free"?

LP
Lucas P.
Numerade Educator

Problem 23

Explain the difference between $\Delta G^{\circ}$ and $\Delta G .$

Dang S.
Numerade Educator

Problem 24

Why does water spilled on the floor evaporate even though $\Delta G^{\circ}$ for the evaporation process is positive at room temperature?

LP
Lucas P.
Numerade Educator

Problem 25

How do you calculate the change in free energy for a reaction under nonstandard conditions?

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Problem 26

How does the value of $\Delta G^{\circ}$ for a reaction reaction relate to the equilibrium constant for the reaction? What does a negative $\Delta G^{\circ}$ for a reaction imply about $K$ for the reaction? A positive $\Delta G^{\circ} ?$

LP
Lucas P.
Numerade Educator

Problem 27

Which of these processes is spontaneous?
\begin{equation}\begin{array}{l}{\text { a. the combustion of natural gas }} \\ {\text { b. the extraction of iron metal from iron ore }} \\ {\text { c. a hot drink cooling to room temperature }} \\ {\text { d. drawing heat energy from the ocean's surface to power a ship }}\end{array}\end{equation}

Dang S.
Numerade Educator

Problem 28

Which of these processes are nonspontaneous? Are thenonspontaneous processes impossible?
\begin{equation}\begin{array}{l}{\text { a. a bike going up a hill }} \\ {\text { b. a meteor falling to Earth }} \\ {\text { c. obtaining hydrogen gas from liquid water }} \\ {\text { d. a ball rolling down a hill }}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 29

Two systems, each composed of two particles represented by circles, have 20 $\mathrm{J}$ of total energy. Which system, A or $\mathrm{B},$ has the greater entropy? Why?

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Problem 30

Two systems, each composed of three particles represented by circles, have 30 $\mathrm{J}$ of total energy. How many energetically equivalent ways can you distribute the particles in each system?
Which system has greater entropy?

LP
Lucas P.
Numerade Educator

Problem 31

Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol $\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\right)$ melts at its melting point $\left(-89.5^{\circ} \mathrm{C}\right) .$ See Table 11.9 for heats of fusion.

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Problem 32

Calculate the change in entropy that occurs in the system when 1.00 mole of diethyl ether $\left(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\right)$ condenses from a gas to a liquid at its normal boiling point $\left(34.6^{\circ} \mathrm{C}\right) .$ See Table 11.7 for heats of vaporization.

LP
Lucas P.
Numerade Educator

Problem 33

Calculate the change in entropy that occurs in the system when 45.0 g of acetone $\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)$ freezes at its melting point $\left(-94.8^{\circ} \mathrm{C}\right) .$
See Table 11.9 for heats of fusion.

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Problem 34

Calculate the change in entropy that occurs in the system when 55.0 g of water vaporizes from a liquid to a gas at its boiling point $\left(100.0^{\circ} \mathrm{C}\right) .$ See Table 11.7 for heats of vaporization.

LP
Lucas P.
Numerade Educator

Problem 35

Without doing any calculations, determine the sign of $\Delta S_{\text { sys for }}$ each chemical reaction.
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm\ {O}_{2}(g)} \\ {\text { b. } \mathrm{CH}_{2}=\mathrm{CH}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{3}(g)} \\ {\mathrm{c.} \cdot \mathrm{Na}(\mathrm{s})+1 / 2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NaCl}(s)} \\ {\text { d. } \mathrm{N}_{2}(g)+3 \mathrm\ {H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)}\end{array}\end{equation}

Dang S.
Numerade Educator

Problem 36

Without doing any calculations, determine the sign of $\Delta S_{\text { sys }}$ for each chemical reaction.
\begin{equation}\begin{array}{l}{\text { a. } \operatorname{Mg}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{MgCl}_{2}(s)} \\ {\text { b. } 2 \mathrm\ {H}_{2} \mathrm{S}(g)+3 \mathrm\ {O}_{2}(g) \longrightarrow 2 \mathrm\ {H}_{2} \mathrm{O}(g)+2 \mathrm\ {SO}_{2}(g)} \\ {\text { c. } 2 \mathrm\ {O}_{3}(g) \longrightarrow 3 \mathrm\ {O}_{2}(g)} \\ {\text { d. } \mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 37

Without doing any calculations, determine the signs of $\Delta S_{\text { sys }}$ and $\Delta S_{\text { surr }}$ for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous.
\begin{equation}\begin{aligned} \text { a. } \mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow & \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\ & \quad\quad\quad\quad\quad\quad \Delta H_{\mathrm{rxn}}^{\circ}=-2044 \mathrm{kJ}\end{aligned}\end{equation}
\begin{equation}\begin{array}{l}{\text { b. } \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+182.6 \mathrm{kJ}} \\ {\text { c. } 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{N}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+163.2 \mathrm{kJ}} \\ {\text { d. } 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)} \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{\Delta H_{\mathrm{rxn}}^{\mathrm{o}}=-906 \mathrm{kJ}}\end{array}\end{equation}

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Problem 38

Without doing any calculations, determine the signs of $\Delta S_{\text { sys }}$ and $\Delta S_{\text { surf }}$ for each chemical reaction. In addition, predict under what temperatures (all temperatures, low temperatures, or high temperatures), if any, the reaction is spontaneous.
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm\ {CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {CO}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-566.0 \mathrm{kJ}} \\ {\text { b. } 2 \mathrm\ {NO}_{2}(g) \longrightarrow 2 \mathrm\ {NO}(g)+\mathrm{O}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+113.1 \mathrm{kJ}} \\ {\text { c. } 2 \mathrm\ {H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {H}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-483.6 \mathrm{kJ}} \\ {\text { d. } \mathrm{CO}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{O}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+393.5 \mathrm{kJ}}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 39

Calculate $\Delta S_{\text { urr }}$ at the indicated temperature for each reaction.
\begin{equation}\begin{array}{ll}{\text { a. } \Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{kJ} ; 298 \mathrm{K}} & {\text { b. } \Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{kJ} ; 77 \mathrm{K}} \\ {\text { c. } \Delta H_{\mathrm{rxn}}^{\mathrm{o}}=+114 \mathrm{kJ} ; 298 \mathrm{K}} & {\text { d. } \Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{kJ} ; 77 \mathrm{K}}\end{array}\end{equation}

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Problem 40

A reaction has $\Delta H_{\mathrm{rxn}}^{\circ}=-112 \mathrm{kJ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}=354 \mathrm{J} / \mathrm{K}$ . At what temperature is the change in entropy for the reaction equal to the change in entropy for the surroundings?

LP
Lucas P.
Numerade Educator

Problem 41

Given the values of $\Delta H_{\mathrm{rrm}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ},$ and $T,$ determine $\Delta S_{\text { univ }}$ and predict whether or not each reaction is spontaneous. (Assumethat all reactants and products are in their standard states.)
\begin{equation}\begin{array}{l}{\text { a. } \Delta H_{\mathrm{rxn}}^{\circ}=+115 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { b. } \Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+263 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { c. } \Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { d. } \Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{J} / \mathrm{K} ; T=615 \mathrm{K}}\end{array}\end{equation}

Dang S.
Numerade Educator

Problem 42

Given the values of $\Delta H_{\mathrm{rxn}}, \Delta S_{\mathrm{rxn}}$ and $T,$ determine $\Delta S_{\text { univ }}$ and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.)
\begin{equation}\begin{array}{l}{\text { a. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { b. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=855 \mathrm{K}} \\ {\text { c. } \Delta H_{\mathrm{rxn}}^{\circ}=+95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{J} / \mathrm{K} ; T=298 \mathrm{K}} \\ {\text { d. } \Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+157 \mathrm{J} / \mathrm{K} ; T=398 \mathrm{K}}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 43

Calculate the change in Gibbs free energy for each of the sets of $\Delta H_{\text { rxn }}, \Delta S_{\text { rxn }},$ and $T$ given in Problem $41 .$ Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)

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Problem 44

Calculate the change in Gibbs free energy for each of the sets of $\Delta H_{\text { ren }}, \Delta S_{\text { rxn }}$ and $T$ given in Problem $42 .$ Predict whether or not each reaction is spontaneous at the temperature indicated. (Assume that all reactants and products are in their standard states.)

LP
Lucas P.
Numerade Educator

Problem 45

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$ . Is the
reaction spontaneous? (Assume that all reactants and products
are in their standard states.)
$$\begin{array}{c}{\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{J} / \mathrm{K}}\end{array}$$

Dang S.
Numerade Educator

Problem 46

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$ . Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.)
$$\begin{array}{c}{2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s)} \\ {\Delta H_{\mathrm{ren}}^{\mathrm{o}}=-1269.8 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\mathrm{o}}=-364.6 \mathrm{J} / \mathrm{K}}\end{array}$$

LP
Lucas P.
Numerade Educator

Problem 47

Fill in the blanks in the table. Both $\Delta H$ and $\Delta S$ refer to the system.

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Problem 48

Predict the conditions (high temperature, low temperature, all temperatures, or no temperatures) under which each reaction is spontaneous.
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { b. } \mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)} \\ {\text { c. } \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{H}(g)} \\ {\text { d. } 2 \mathrm\ {NO}_{2}(g) \longrightarrow 2 \mathrm\ {NO}(g)+\mathrm{O}_{2}(g) \text { (endothermic) }}\end{array}
\end{equation}

LP
Lucas P.
Numerade Educator

Problem 49

How does the molar entropy of a substance change with increasing temperature?

Dang S.
Numerade Educator

Problem 50

What is the molar entropy of a pure crystal at 0 K? What is the significance of the answer to this question?

LP
Lucas P.
Numerade Educator

Problem 51

For each pair of substances, choose the one that you expect to have the higher standard molar entropy $\left(S^{\circ}\right)$ at $25^{\circ} \mathrm{C} .$ Explain your choices.
\begin{equation}\begin{array}{ll}{\text { a. } \mathrm{CO}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { b. } \mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)} \\ {\text { c. } \operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { d. } \mathrm{CH}_{4}(g) ; \operatorname{siH}_{4}(g)} \\ {\text { e. } \mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) \quad \text { f. } \operatorname{NaBr}(s) ; \mathrm{NaBr}(a q)}\end{array}\end{equation}

Dang S.
Numerade Educator

Problem 52

For each pair of substances, choose the one that you expect to have the higher standard molar entropy $\left(S^{\circ}\right)$ at $25^{\circ} \mathrm{C} .$ Explain your choices.
\begin{equation}
\begin{array}{ll}{\text { a. } \operatorname{NaNO}_{3}(s) ; \mathrm{NaNO}_{3}(a q)} \quad {\text { b. } \mathrm{CH}_{4}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{3}(g)} \\ {\text { c. } \mathrm{Br}_{2}(l) ; \mathrm{Br}_{2}(g)} \quad\quad\quad\quad\quad {\text { d. } \operatorname{Br}_{2}(g) ; \mathrm{F}_{2}(g)} \\ {\text { e. } \mathrm{PCl}_{3}(g) ; \mathrm{PCl}_{5}(g) \quad\quad\quad\quad \text { f. } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) ; \mathrm{SO}_{2}(g)}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 53

Rank each set of substances in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain your reasoning.
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{NH}_{3}(g) ; \mathrm{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \mathrm{He}(g)} \\ {\text { b. } \mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(l) ; \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { c. } \mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)}\end{array}\end{equation}

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Problem 54

Rank each set of substances in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain your reasoning.
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{I}_{2}(g) ; \mathrm{F}_{2}(g) ; \mathrm{Br}_{2}(g) ; \mathrm{Cl}_{2}(g)} \\ {\text { b. } \mathrm{H}_{2} \mathrm{O}(g) ; \mathrm{H}_{2} \mathrm{O}_{2}(g) ; \mathrm{H}_{2} \mathrm{S}(g)} \\ {\text { c. } \mathrm{C}(s, \text { graphite }) ; \mathrm{C}(s, \text { diamond }) ; \mathrm{C}(s, \text { amorphous) }}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 55

Use data from Appendix IIB to calculate $\Delta S_{\mathrm{rxn}}^{\circ}$ for each of the reactions. In each case, try to rationalize the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)} \\ {\text { b. } \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)} \\ {\text { c. } \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)} \\ {\text { d. } 2 \mathrm\ {H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {H}_{2} \mathrm{O}(l)+2 \mathrm\ {SO}_{2}(g)}\end{array}\end{equation}

Dang S.
Numerade Educator

Problem 56

Use data from Appendix IIB to calculate $\Delta S_{\mathrm{rxn}}^{\circ}$ for each of the reactions. In each case, try to rationalize the sign of $\Delta S_{\mathrm{rxn}}^{\circ}$
\begin{equation}\begin{array}{l}{\text { a. } 3 \mathrm\ {NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm\ {HNO}_{3}(a q)+\mathrm{NO}(g)} \\ {\text { b. } \mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm\ {CO}_{2}(g)} \\ {\text { c. } \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)} \\ {\text { d. } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm\ {H}_{2} \mathrm{O}(g)}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 57

Find $\Delta S^{\circ}$ for the formation of $\mathrm{CH}_{2} \mathrm{Cl}_{2}(g)$ from its gaseous elements in their standard states. Rationalize the sign of $\Delta S^{\circ} .$

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Problem 58

Find $\Delta S^{\circ}$ for the reaction between nitrogen gas and fluorine gas to form nitrogen trifluoride gas. Rationalize the sign of $\Delta S^{\circ} .$

LP
Lucas P.
Numerade Educator

Problem 59

Methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ burns in oxygen to form carbon dioxide and water. Write a balanced equation for the combustion of liquid methanol and calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$ and $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$ . Is the combustion of methanol spontaneous?

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Problem 60

In photosynthesis, plants form glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ and oxygen from carbon dioxide and water. Write a balanced equation for photosynthesis and calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ},$ and $\Delta G_{\mathrm{ren}}^{\circ}$ at $25^{\circ} \mathrm{C}$ . Is photosynthesis spontaneous?

LP
Lucas P.
Numerade Educator

Problem 61

For each reaction, calculate $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$ and $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$ and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from $25^{\circ} \mathrm{C} ?$
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)} \\ {\text { b. } \mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)} \\ {\text { c. } 3 \mathrm{H}_{2}(g)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { d. } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm\ {NH}_{3}(g)}\end{array}\end{equation}

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Problem 62

For each reaction, calculate $\Delta H_{\mathrm{rxn}}^{\mathrm{o}}, \Delta S_{\mathrm{rm}}^{\circ}$ and $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$ and state whether or not the reaction is spontaneous. If the reaction is not spontaneous, would a change in temperature make it spontaneous? If so, should the temperature be raised or lowered from $25^{\circ} \mathrm{C} ?$
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm\ {CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)} \\ {\text { b. } 2 \mathrm\ {NH}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)} \\ {\text { c. } \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {NO}(g)} \\ {\text { d. } 2 \mathrm\ {KClO}_{3}(s) \longrightarrow 2 \mathrm\ {KCl}(s)+3 \mathrm{O}_{2}(g)}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 63

Use standard free energies of formation to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$
for each reaction in Problem 61. How do the values of $\Delta G^{\circ}$ calculated this way compare to those calculated from $\Delta H^{\circ}$ and $\Delta S^{\circ} ?$ Which of the two methods could be used to determine how $\Delta G^{\circ}$ changes with temperature?

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Problem 64

Use standard free energies of formation to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$
for each reaction in Problem $62 .$ How well do the values of $\Delta G^{\circ}$ calculated this way compare to those calculated from $\Delta H^{\circ}$ and $\Delta S^{\circ} ?$ Which of the two methods could be used to determine how $\Delta G^{\circ}$ changes with temperature?

LP
Lucas P.
Numerade Educator

Problem 65

Consider the reaction:
$$2 \mathrm\ {NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {NO}_{2}(g)$$
Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.)
\begin{equation}\begin{array}{lllll}{\text { a. } 298 \mathrm{K}} & {\text { b. } 715 \mathrm{K}} & {\text { c. } 855 \mathrm{K}}\end{array}\end{equation}

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Problem 66

Consider the reaction:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
Estimate $\Delta G^{\circ}$ for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change too much within the given temperature range.)
\begin{equation}\begin{array}{lllll}{\text { a. } 298 \mathrm{K}} & {\text { b. } 1055 \mathrm{K}} & {\text { c. } 1455 \mathrm{K}}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 67

Determine $\Delta G^{\circ}$ for the reaction:
$$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \operatorname{cog}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g)$$
Use the following reactions with known $\Delta G_{\mathrm{rxn}}^{\circ}$ values:
$$\begin{array}{ll}{2 \mathrm\ {Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)} & {\Delta G_{\mathrm{rm}}^{\circ}=-742.2 \mathrm{kJ}} \\ {\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)} & {\Delta G_{\mathrm{mn}}^{\circ}=-257.2 \mathrm{kJ}}\end{array}$$

Dang S.
Numerade Educator

Problem 68

Calculate $\Delta G_{\mathrm{rn}}^{\circ}$ for the reaction:
$$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$$
Use the following reactions and given $\Delta G_{\mathrm{ren}}^{\circ}$ values:
$$\begin{array}{l}{\mathrm{Ca}(s)+\mathrm{CO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CaCO}_{3}(s) \quad \Delta G_{\mathrm{rm}}^{\circ}=-734.4 \mathrm{kJ}} \\ {2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s)} \quad\quad\quad\quad\quad\quad \Delta G_{\mathrm{rxn}}^{\circ}=-1206.6 \mathrm{kJ}\end{array}$$

LP
Lucas P.
Numerade Educator

Problem 69

Consider the sublimation of iodine at $25.0^{\circ} \mathrm{C} :$
$$\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)$$
\begin{equation}\begin{array}{l}{\text { a. Find } \Delta G_{\mathrm{rxn}}^{\circ} \text { at } 25.0^{\circ} \mathrm{C} \text { . }} \\ {\text { b. Find } \Delta G_{\mathrm{rm}} \text { at } 25.0^{\circ} \mathrm{C} \text { under the following nonstandard }} \\ {\text { conditions: }} \\ \quad{\text { i. } P_{1_{2}}=1.00 \mathrm{mm} \mathrm{Hg}} \\ \quad{\text { ii. } P_{1_{2}}=0.100 \mathrm{mm} \mathrm{Hg}} \\ {\text { c. Explain why iodine spontaneously sublimes in open air at }} \\ {25.0^{\circ} \mathrm{C} .}\end{array}\end{equation}

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Problem 70

Consider the evaporation of methanol at $25.0^{\circ} \mathrm{C} :$
$$\mathrm{CH}_{3} \mathrm{OH}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$
\begin{equation}\begin{array}{l}{\text { a. Find } \Delta G_{\mathrm{r}}^{\circ} \text { at } 25.0^{\circ} \mathrm{C} \text { . }} \\ {\text { b. Find } \Delta G_{\mathrm{r}} \text { at } 25.0^{\circ} \mathrm{C} \text { under the following nonstandard }} \\ {\text { conditions: }} \\ \quad {\text { i. } P_{\mathrm{CH}_{3} \mathrm{OH}}=150.0 \mathrm{mm} \mathrm{Hg}} \\ \quad{\text { ii. } P_{\mathrm{CH}_{3} \mathrm{OH}}=100.0 \mathrm{mmHg}} \\ \quad{\text { iii. } P_{\mathrm{CH}_{1} \mathrm{OH}}=10.0 \mathrm{mm} \mathrm{Hg}} \\ {\text { c. Explain why methanol spontaneously evaporates in open air }} \\ {\text { at } 25.0^{\circ} \mathrm{C} .}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 71

Consider the reaction:
$$\mathrm{CH}_{3} \mathrm{OH}(g) \Longrightarrow \mathrm{CO}(g)+2 \mathrm\ {H}_{2}(g)$$
Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions:
\begin{equation}\begin{array}{l}{\text { i. } P_{\mathrm{CH}_{3} \mathrm{OH}}=0.855 \mathrm{atm}} \\ {\text { ii. } P_{\mathrm{CO}}=0.125 \mathrm{atm}} \\ {\text { iii. } P_{\mathrm{H}_{2}}=0.183 \mathrm{atm}}\end{array}\end{equation}

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Problem 72

Consider the reaction:
$$\mathrm{CO}_{2}(g)+\mathrm{CCl}_{4}(g) \Longrightarrow 2 \mathrm{COCl}_{2}(g)$$
Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions:
\begin{equation}\begin{array}{l}{\text { i. } P_{\mathrm{CO}_{2}}=0.112 \mathrm{atm}} \\ {\text { ii. } P_{\mathrm{CCl}_{4}}=0.174 \mathrm{atm}} \\ {\text { iii. } P_{\mathrm{COC}_{2}}=0.744 \mathrm{atm}}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 73

Use data from Appendix IIB to calculate the equilibrium constants at $25^{\circ} \mathrm{C}$ for each reaction.
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm\ {CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm\ {CO}_{2}(g)} \\ {\text { b. } 2 \mathrm\ {H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm\ {H}_{2}(g)+\mathrm{S}_{2}(g)}\end{array}\end{equation}

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Problem 74

Use data from Appendix IIB to calculate the equilibrium constants at $25^{\circ} \mathrm{C}$ for each reaction. $\Delta G_{\mathrm{f}}^{\circ}$ for BrCl $(g)$ is $-1.0 \mathrm{kJ} / \mathrm{mol}$ .
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm\ {NO}_{2}(g) \Longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)} \\ {\text { b. } \mathrm{Br}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm\ {BrCl}(g)}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 75

Consider the reaction:
$$\begin{array}{c}{\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)} \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{K_{\mathrm{p}}=2.26 \times 10^{4} \text { at } 25^{\circ} \mathrm{C}}\end{array}$$
Calculate $\Delta G_{\mathrm{rxn}}$ for the reaction at $25^{\circ} \mathrm{C}$ under each of the following conditions:
\begin{equation}\begin{array}{l}{\text { a. standard conditions }} \\ {\text { b. at equilibrium }} \\ {\text { c. } P_{\mathrm{CH}_{3} \mathrm{OH}}=1.0 \mathrm{atm} ; P_{\mathrm{CO}}=P_{\mathrm{H}_{2}}=0.010 \mathrm{atm}}\end{array}\end{equation}

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Problem 76

Consider the reaction:
$$\begin{array}{c}\mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \operatorname{ICl}(g) \\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{K_{\mathrm{p}}=81.9 \text { at } 25^{\circ} \mathrm{C}}\end{array}$$
Calculate $\Delta G_{\mathrm{rxn}}$ for the reaction at $25^{\circ} \mathrm{C}$ under each of the
following conditions:
\begin{equation}\begin{array}{l}{\text { a. standard conditions }} \\ {\text { b. at cquilibrium }} \\ {\text { c. } P_{\mathrm{ICl}}=2.55 \mathrm{atm} ; P_{12}=0.325 \mathrm{atm} ; P_{\mathrm{Cl}_{2}}=0.221 \mathrm{atm}}\end{array}\end{equation}

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Problem 77

Estimate the value of the equilibrium constant at 525 $\mathrm{K}$ for each reaction in Problem $73 .$

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Problem 78

Estimate the value of the equilibrium constant at 655 $\mathrm{K}$ for each reaction in Problem 74. ($\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{BrCl}$ is 14.6 $\mathrm{kJ} / \mathrm{mol.})$

LP
Lucas P.
Numerade Educator

Problem 79

Consider the reaction:
$$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$
The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to find $\Delta H_{\text { rxn }}^{\circ}$ and $\Delta S_{\text { ren }}^{\circ}$ for the reaction.
$$\begin{array}{|c|c|}\hline Temperature & {K_{\mathrm{p}}} \\ \hline 150 \mathrm{K} & {1.4 \times 10^{-4}} \\ \hline 175 \mathrm{K} & {4.6 \times 10^{-4}} \\ \hline 200 \mathrm{K} & {3.6 \times 10^{-2}} \\ \hline 225\mathrm{K} & {11} \\ \hline 250\mathrm{K} & {15.5} \\ \hline\end{array}$$

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Problem 80

Consider the reaction:
$$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$
The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to find $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ for the reaction.
$$\begin{array}{|c|c|}\hline Temperature & {K_{\mathrm{p}}} \\ \hline 170\mathrm{K} & {3.8 \times 10^{-3}} \\ \hline 180\mathrm{K} & {0.34} \\ \hline 190\mathrm{K} & {18.4} \\ \hline 200\mathrm{K} & {681} \\ \hline\end{array}$$

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Problem 81

The change in enthalpy $\left(\Delta H_{\mathrm{rxn}}^{\mathrm{r}}\right)$ for a reaction is $-25.8 \mathrm{kJ} / \mathrm{mol}$ . The equilibrium constant for the reaction is $1.4 \times 10^{3}$ at 298 $\mathrm{K}$ . What is the equilibrium constant for the reaction at 655 $\mathrm{K}$ ?

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Problem 82

A reaction has an equilibrium constant of $8.5 \times 10^{3}$ at 298 $\mathrm{K}$ . At 755 $\mathrm{K}$ , the equilibrium constant is $0.65 .$ Find $\Delta _{\mathrm{rxn}}^{\mathrm{o}}$ for the reaction.

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Problem 83

Determine the sign of $\Delta S_{\mathrm{sys}}$ for each process.
\begin{equation}\begin{array}{l}{\text { a. water boiling }} \\ {\text { b. water freezing }} \\ {\text { c. }}\end{array}\end{equation}

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Problem 84

Determine the sign of $\Delta S_{\mathrm{sys}}$ for each process.
\begin{equation}\begin{array}{l}{\text { a. dry ice subliming }} \\ {\text { b. dew forming }} \\ {\text { c. }}\end{array}\end{equation}

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Problem 85

Our atmosphere is composed primarily of nitrogen and oxygen,
which coexist at $25^{\circ} \mathrm{C}$ without reacting to any significant
extent. However, the two gases can react to form nitrogen
monoxide according to the reaction:
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$
\begin{equation}\begin{array}{l}{\text { a. Calculate } \Delta G^{\circ} \text { and } K_{\mathrm{p}} \text { for this reaction at } 298 \mathrm{K} \text { . Is the }} \\ {\text { reaction spontaneous? }} \\ {\text { b. Estimate } \Delta G^{\circ} \text { at } 2000 \mathrm{K} \text { . Does the reaction become more }} \\ {\text { spontaneous as temperature increases? }}\end{array}\end{equation}

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Problem 86

Nitrogen dioxide, a pollutant in the atmosphere, can combine with water to form nitric acid. One of the possible reactions is shown here. Calculate $\Delta G^{\circ}$ and $K_{p}$ for this reaction at $25^{\circ} \mathrm{C}$ and comment on the spontaneity of the reaction.
$$3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$$

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Problem 87

Ethene $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ can be halogenated by the reaction:
$$\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{X}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{X}_{2}(g)$$
where $\mathrm{X}_{2}$ can be $\mathrm{Cl}_{2}, \mathrm{Br}_{2},$ or $\mathrm{I}_{2} .$ Use the thermodynamic data given to calculate $\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ},$ and $K_{\mathrm{p}}$ for the halogenation reaction by each of the three halogens at $25^{\circ} \mathrm{C}$ . Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions more spontaneous or less spontaneous?

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Problem 88

$\mathrm{H}_{2}$ reacts with the halogens $\left(\mathrm{X}_{2}\right)$ according to the reaction:
$$\mathrm{H}_{2}(g)+\mathrm{X}_{2}(g) \rightleftharpoons 2 \mathrm{HX}(g)$$
where $\mathrm{X}_{2}$ can be $\mathrm{Cl}_{2}, \mathrm{Br}_{2},$ or $\mathrm{I}_{2}$ . Use the thermodynamic data in Appendix IIB to calculate $\Delta H^{\circ}, \Delta S^{\circ}, \Delta G^{\circ},$ and $K_{\mathrm{p}}$ for the reaction between hydrogen and each of the three halogens. Which reaction is most spontaneous? Least spontaneous? What is the main factor responsible for the difference in the spontaneity of the three reactions? Does higher temperature make the reactions
more spontaneous or less spontaneous?

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Problem 89

Consider this reaction occurring at $298 \mathrm{K} :$
$$\mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons 3 \mathrm\ {NO}(g)$$
\begin{equation}\begin{array}{l}{\text { a. Show that the reaction is not spontaneous under standard }} \\ {\text { conditions by calculating } \Delta G_{\mathrm{rm}}^{\circ} .} \\ {\text { b. If a reaction mixture contains only } \mathrm{N}_{2} \mathrm{O} \text { and } \mathrm{NO}_{2} \text { at partial }} \\ {\text { pressures of } 1.0 \text { atm each, the reaction will be spontaneous }} \\ {\text { until someNO forms in the mixture. What maximum partial }} \\ {\text { pressure of NO builds up before the reaction ceases to be }} \\ {\text { spontaneous? }} \\ {\text { c. Can the reaction be made more spontaneous by an increase or }} \\ {\text { decrease in temperature? If so, what temperature is required to }} \\ {\text { make the reaction spontaneous under standard conditions? }}\end{array} \end{equation}

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Problem 90

Consider this reaction occurring at $298 \mathrm{K} :$
$$\mathrm{BaCO}_{3}(s) \Longrightarrow \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)$$
\begin{equation}\begin{array}{l}{\text { a. Show that the reaction is not spontaneous under standard }} \\ {\text { conditions by calculating } \Delta G_{\mathrm{rxn} \text { . }}^{\circ} .} \\ {\text { b. If } \mathrm{BaCO}_{3} \text { is placed in an evacuated flask, what is the partial }} \\ {\text { pressure of } \mathrm{CO}_{2} \text { when the reaction reaches equilibrium? }} \\ {\text { c. Can the reaction be made more spontaneous by an increase }} \\ {\text { or decrease in temperature? If so, at what temperature is the }} \\ {\text { partial pressure of carbon dioxide } 1.0 \text { atm? }}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 91

Living organisms use energy from the metabolism of food to
create an energy-rich molecule called adenosine triphosphate (ATP). The ATP acts as an energy source for a variety of reactions that the living organism must carry out to survive. ATP provides energy through its hydrolysis, which can besymbolized as follows:
$$\operatorname{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \operatorname{ADP}(a q)+\mathrm{P}_{1}(a q) \quad \Delta G_{\mathrm{rxn}}^{\circ}=-30.5 \mathrm{kJ}$$
where ADP represents adenosine diphosphate and $P_{1}$ represents an inorganic phosphate group (such as HPO $_{4}\ ^{2-} ) .$
\begin{equation}\begin{array}{l}{\text { a. Calculate the equilibrium constant, } K, \text { for the given reaction }} \\ {\text { at } 298 \mathrm{K} .} \\ {\text { b. The free energy obtained from the oxidation (reaction with }} \\ {\text { oxygen) of glucose }\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) \text { to form carbon dioxide and }} \\ {\text { water can be used to re-form ATP by driving the given reac- }} \\ {\text { tion in reverse. Calculate the standard free energy change for }} \\ {\text { the oxidation of glucose and estimate the maximum number }} \\ {\text { of moles of ATP that can be formed by the oxidation of one }} \\ {\text { mole of glucose. }}\end{array}\end{equation}

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Problem 92

The standard free energy change for the hydrolysis of ATP was given in Problem 91. In a particular cell, the concentrations of ATP, ADP, and $P_{1}$ are $0.0031 \mathrm{M}, 0.0014 \mathrm{M},$ and $0.0048 \mathrm{M},$ respectively. Calculate the free energy change for the hydrolysis of ATP under these conditions. (Assume a temperature of 298 $\mathrm{K.}$ .

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Problem 93

These reactions are important in catalytic converters in automobiles. Calculate $\Delta G^{\circ}$ for each at 298 $\mathrm{K}$ . Predict the effect of increasing temperature on the magnitude of $\Delta G^{\circ} .$
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm{CO}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{CO}_{2}(g)} \\ {\text { b. } 5 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { c. } 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { d. } 2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}\end{equation}

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Problem 94

Calculate $\Delta G^{\circ}$ at 298 $\mathrm{K}$ for these reactions and predict the effect
on $\Delta G^{\circ}$ of lowering the temperature.
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{NH}_{3}(g)+\mathrm{HBr}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Br}(s)} \\ {\text { b. } \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} \\ {\text { c. } \mathrm{CH}_{4}(g)+3 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{CHCl}_{3}(g)+3 \mathrm{HCl}(g)} \\ {\quad\left(\Delta G_{\mathrm{f}}^{\circ} \text { for } \mathrm{CHCl}_{3}(g) \text { is }-70.4 \mathrm{kJ} / \mathrm{mol.}\right)}\end{array}\end{equation}

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Problem 95

All the oxides of nitrogen have positive values of $\Delta G_{\mathrm{f}}^{\circ}$ at 298 $\mathrm{K}$ ,
but only one common oxide of nitrogen has a positive $\Delta S_{\mathrm{f}}^{\text { . }}$
Identify that oxide of nitrogen without reference to thermodynamic data and explain.

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Problem 96

The values of $\Delta G_{\mathrm{f}}^{\circ}$ for the hydrogen halides become less negative with increasing atomic number. The $\Delta G_{\mathrm{f}}^{\circ}$ of HI is slightly positive. However, the trend in $\Delta S_{\mathrm{f}}^{\circ}$ is to become more positive with increasing atomic number. Explain.

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Problem 97

Consider the reaction $\mathrm{X}_{2}(g) \longrightarrow 2 \mathrm{X}(g) .$ When a vessel initially containing 755 torr of $\mathrm{X}_{2}$ comes to equilibrium at $298 \mathrm{K},$ the equilibrium partial pressure of $\mathrm{X}$ is 103 torr. The same reaction is repeated with an initial partial pressure of 748 torr of $X_{2}$ at 755 $\mathrm{K}$ ; the equilibrium partial pressure of $\mathrm{X}$ is 532 torr. Find $\Delta H^{\circ}$ for the reaction.

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Problem 98

Dinitrogen tetroxide decomposes to nitrogen dioxide:
$$\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm\ {NO}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\mathrm{o}}=55.3 \mathrm{kJ}$$
At $298 \mathrm{K},$ a reaction vessel initially contains 0.100 atm of $\mathrm{N}_{2} \mathrm{O}_{4}$ . When equilibrium is reached, 58$\%$ of the $\mathrm{N}_{2} \mathrm{O}_{4}$ has decomposed to $\mathrm{NO}_{2} .$ What percentage of $\mathrm{N}_{2} \mathrm{O}_{4}$ decomposes at 388 $\mathrm{K}$ ? Assume that the initial pressure of $\mathrm{N}_{2} \mathrm{O}_{4}$ is the same $(0.100$ atm $) .$

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Problem 99

Indicate and explain the sign of $\Delta S_{\text { univ }}$ for each process.
\begin{equation}\begin{array}{l}{\text { a. } 2 \mathrm\ {H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm\ {H}_{2} \mathrm{O}(l) \text { at } 298 \mathrm{K}} \\ {\text { b. the electrolysis of } \mathrm{H}_{2} \mathrm{O}(l) \text { to } \mathrm{H}_{2}(g) \text { and } \mathrm{O}_{2}(g) \text { at } 298 \mathrm{K}} \\ {\text { c. the growth of an oak tree from a little acorn }}\end{array}\end{equation}

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Problem 100

The Haber process is very important for agriculture because it converts $\mathrm{N}_{2}(g)$ from the atmosphere into bound nitrogen, which can be taken up and used by plants. The Haber process reaction is $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) .$ The reaction is exothermic but is carried out at relatively high temperatures. Why?

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Problem 101

A metal salt with the formula MCl_ $_{2}$ crystallizes from water to form a solid with the composition $\mathrm{MCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}$ . The equilibrium vapor pressure of water above this solid at 298 $\mathrm{K}$ is 18.3 $\mathrm{mm} \mathrm{Hg} .$ What is the value of $\Delta G$ for the reaction $\mathrm{MCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{MCl}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(g)$ when the pressure of water vapor is 18.3 $\mathrm{mmHg}$ ? When the pressure of water vapor is 760 $\mathrm{mm} \mathrm{Hg}$ ?

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Problem 102

The solubility of $\mathrm{AgCl}(s)$ in water at $25^{\circ} \mathrm{C}$ is $1.33 \times 10^{-5} \mathrm{mol} / \mathrm{L}$ and its $\Delta H^{\circ}$ of solution is 65.7 $\mathrm{kJ} / \mathrm{mol} .$ What is its solubility at $50.0^{\circ} \mathrm{C} ?$

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Problem 103

Review the box in this chapter entitled Chemistry in Your Day: Making a Nonspontaneous Process Spontaneous. The hydrolysis of ATP, shown in Problem $91,$ is often used to drive nonspontaneous processes - such as muscle contraction and protein synthesis-in living organisms. The nonspontaneous process to be driven must be coupled to the ATP hydrolysis reaction. For example, suppose the nonspontaneous process is $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{AB}$ $\left(\Delta G^{\circ}\right.$ positive). The coupling of a nonspontaneous reaction such as this one to the hydrolysis of ATP is often accomplished by the mechanism:
$$\mathrm{A}+\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{A}-\mathrm{P}_{1}+\mathrm{ADP}$$
$$\frac{\mathrm{A}-\mathrm{P}_{1}+\mathrm{B} \longrightarrow \mathrm{AB}+\mathrm{P}_{1}}{\mathrm{A}+\mathrm{B}+\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{AB}+\mathrm{ADP}+\mathrm{P}_{1}}$$
As long as $\Delta G_{\mathrm{rxn}}$ for the nonspontaneous reaction is less than $30.5 \mathrm{kJ},$ the reaction can be made spontaneous by coupling in this way to the hydrolysis of ATP. Suppose that ATP is to drive the reaction between glutamate and ammonia to form glutamine:
\begin{equation}\begin{array}{l}{\text { a. Calculate } K \text { for the reaction between glutamate and ammo- }} \\ {\text { nia. (The standard free energy change for the reaction is }} \\ {+14.2 \mathrm{kJ} / \mathrm{mol} . \text { Assume a temperature of } 298 \mathrm{K} . \text { . }} \\ {\text { b. Write a set of reactions such as those given showing how the }} \\ {\text { glutamate and ammonia reaction can couple with the hy- }} \\ {\text { drolysis of ATP. What is } \Delta G_{\mathrm{rn}}^{\circ} \text { and } K \text { for the coupled reaction? }}\end{array}\end{equation}

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Problem 104

Calculate the entropy of each state and rank the states in order of increasing entropy.
a.
b.
c.

LP
Lucas P.
Numerade Educator

Problem 105

Suppose we redefine the standard state as $P=2$ atm. Find the new standard $\Delta G_{\mathrm{f}}^{\circ}$ values of each substance.
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{HCl}(g)} \\ {\text { b. } \mathrm{N}_{2} \mathrm{O}(g)} \\ {\text { c. } \mathrm{H}(g)}\end{array}\end{equation}
Explain the results in terms of the relative entropies of reactants
and products of each reaction.

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Problem 106

The $\Delta G$ for the freezing of $\mathrm{H}_{2} \mathrm{O}(l)$ at $-10^{\circ} \mathrm{C}$ is $-210 \mathrm{J} / \mathrm{mol},$ and the heat of fusion of ice at this temperature is 5610 $\mathrm{J} / \mathrm{mol}$ . Find the entropy change of the universe when 1 $\mathrm{mol}$ of water freezes at $-10^{\circ} \mathrm{C} .$

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Problem 107

Consider the reaction that occurs during the Haber process:
$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$
The equilibrium constant is $3.9 \times 10^{5}$ at 300 $\mathrm{K}$ and $1.2 \times 10^{-1}$ at 500 $\mathrm{K} .$ Calculate $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ for this reaction.

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Problem 108

The salt ammonium nitrate can follow three modes of decomposition: (a) to $\mathrm{HNO}_{3}(g)$ and $\mathrm{NH}_{3}(g),(\mathrm{b})$ to $\mathrm{N}_{2} \mathrm{O}(g)$ and
$\mathrm{H}_{2} \mathrm{O}(g),$ and $(\mathrm{c})$ to $\mathrm{N}_{2}(g), \mathrm{O}_{2}(g),$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ Calculate $\Delta G_{\mathrm{rxn}}^{\circ}$ for each mode of decomposition at 298 $\mathrm{K}$ . Explain in light of these results how it is still possible to use ammonium nitrate as a fertilizer and the precautions that should be taken when it is used.

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Problem 109

Given the data, calculate $\Delta S_{\text { vap }}$ for each of the first four liquids.
$\left(\Delta S_{\mathrm{vap}}=\Delta H_{\mathrm{vap}} / T\right.$ where $T$ is in $\mathrm{K} )$
All four values should be close to each other. Predict whether the last two liquids in the table have $\Delta S_{\text { vap }}$ in this same range. If not, predict whether it is larger or smaller and explain. Verify your prediction.

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Problem 110

Which is more efficient, a butane lighter or an electric lighter (such as the ones traditionally found on the dashboard of automobiles)? Explain.

LP
Lucas P.
Numerade Educator

Problem 111

Which statement is true?
\begin{equation}\begin{array}{l}{\text { a. A spontaneous reaction is always a fast reaction. }} \\ {\text { b. A spontaneous reaction is always a slow reaction. }} \\ {\text { c. The spontaneity of a reaction is not necessarily related to the }} \\ {\text { speed of a reaction. }}\end{array}\end{equation}

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Problem 112

Which process is necessarily driven by an increase in the entropy of the surroundings?
\begin{equation}\begin{array}{l}{\text { a. the condensation of water }} \\ {\text { b. the sublimation of dry ice }} \\ {\text { c. the freezing of water }}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 113

Consider the changes in the distribution of nine particles into three interconnected boxes shown here. Which has the most negative $\Delta S$ ?

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Problem 114

Which statement is true?
\begin{equation}\begin{array}{l}{\text { a. A reaction in which the entropy of the system increases can }} \\ {\text { be spontaneous only if it it is exothermic. }} \\ {\text { b. A reaction in which the entropy of the system increases can }} \\ {\text { be spontaneous only if it it is endothermic. }} \\ {\text { c. A reaction in which the entropy of the system decreases can }} \\ {\text { be spontaneous only if it is exothermic. }}\end{array}\end{equation}

LP
Lucas P.
Numerade Educator

Problem 115

Which process is spontaneous at 298 K?
\begin{equation}\begin{array}{l}{\text { a. } \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g, 1 \text { atm })} \\ {\text { b. } \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g, 0.10 \mathrm{atm})} \\ {\text { c. } \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g, 0.010 \mathrm{atm})}\end{array}\end{equation}

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Problem 116

The free energy change of the reaction $\mathrm{A}(g) \longrightarrow \mathrm{B}(g)$ is zero under certain conditions. The standard free energy change of the reaction is $-42.5 \mathrm{kJ} .$ Which statement must be true about the reaction?
\begin{equation}\begin{array}{l}{\text { a. The concentration of the product is greater than the }} \\ {\text { concentration of the reactant. }} \\ {\text { b. The reaction is at equilibrium. }} \\ {\text { c. The concentration of the reactant is greater than the }} \\ {\text { concenration of the product. }}\end{array}\end{equation}

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Problem 117

The reaction $\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)$ has an equilibrium constant of 5.8
and under certain conditions has $Q=336 .$ What can you conclude about the sign of $\Delta G_{\mathrm{rxn}}^{\circ}$ and $\Delta G_{\mathrm{rxn}}$ for this reaction under these conditions?

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Problem 118

Imagine that you roll two dice. Write down all the possible rolls that sum to $2 .$ Write all the possible rolls that sum to $12 .$ Write all the possible rolls that sum to $7 .$ Which configuration has the greatest entropy: $2,12,$ or 7$?$

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Problem 119

If you roll 1 million dice, what will be the average of all the dice? If there is a room with 1 million dice and they all have a 1 on the top face, and there is an earthquake strong enough to roll dice around, what is the likelihood that after the earthquake all the top faces will sum to 1 million? To 6 million? How does this thought experiment illustrate the second law of thermodynamics?

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Problem 120

Not all processes in which the system increases in entropy are spontaneous. How can this observation be consistent with the second law? Provide an example and explain your answer in complete sentences.

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Problem 121

Have each group member look up $\Delta H_{\mathrm{f}}^{\circ}$ and $S^{\circ}$ for one substance in the reaction: $3 \mathrm{O}_{2}(g)+6 \mathrm{H}_{2}(g)+6 \mathrm{C}(s,$ graphite) $\longrightarrow$ $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s,$ glucose). What is $\Delta H^{\circ}$ for this reaction? What is $\Delta S^{\circ} ?.$ When is $\Delta H_{\mathrm{f}}^{\circ}$ for a substance equal to zero? When is $S^{\circ}$ for a substance equal to zero?

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Problem 122

Calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for the reaction in the previous question. Is this reaction spontaneous under standard conditions? How do you know? What is the determining factor: the change in energy or the change in entropy or both? Explain.

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Problem 123

Borax (sodium tetraboratedecahydrate), a mineral found in dry lakebeds in California, is used as a preservative and in the manufacturing of soap and glass. By detervining the $K_{\text { sp }}$ of borax at different temperatures, we can determing the $K_{\text { sp }}$ of $\Delta G^{\circ}$ for the dissolution of borax:
$$\begin{array}{c}{\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{4} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow 2 \mathrm{Na}^{+}(a q)+\mathrm{B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{4}^{2-}(a q)+8 \mathrm{H}_{2} \mathrm{O}(l)} \\ {(\mathrm{Borax}) \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text (Tetraborate)}\end{array}$$
The relationship:
$$\ln \left(K_{\mathrm{sp}}\right)=\frac{-\Delta H^{\circ}}{R T}+\frac{\Delta S^{\circ}}{R}$$
has the form of a linear equation $y=m x+b,$ where $y$ is the $\ln K_{\text { sp }}$ and $x$ is 1$/ T(T$ in Kelvin). The slope is equal to $-\Delta H / R,$ and the $y$ intercept is $\Delta S^{\circ} / R,$ where $R$ is the gas constant, 8.314 $\mathrm{J} /$ $\mathrm{K}$ mol. Determining $K_{\mathrm{sp}}$ at several different temperatures allows us to plot a graph of lnK versus 1$/ T$ as shown in Figure a
Knowing the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ at a specific tempera-
ture allows the calculation of the change in Gibbs free energy
for the reaction $\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$
$$\begin{array}{|l|l|}\hline Temperature \left(^{\circ} \mathrm{C}\right) & {K_{\mathrm{sp}}} \\ \hline 40.0 & {0.041} \\ \hline 45.0 & {0.083} \\ \hline 50.0 & {0.264} \\ \hline 55.0 & {0.486} \\ \hline 60.0 & {0.552} \\ \hline\end{array}$$
Use the information provided in the figure and table to do the following:
\begin{equation}\begin{array}{l}{\text { a. Plot a graph of } \ln K_{\text { sp versus } 1 / T(T \text { in Kelvin })} \text { . }} \\ {\text { b. Determine } \Delta H^{\circ} . \text { Is this process endothermic or exothermic? }} \\ {\text { c. Determine } \Delta S^{\circ} .} \\ {\text { d. Determine } \Delta G^{\circ} \text { at } 298 \mathrm{K} \text { . }} \\ {\text { e. Sketch a graph of lnK versus 1/T for an exothermic process. }}\end{array}\end{equation}

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