Chemistry A Molecular Approach

Nivaldo J. Tro

Chapter 17

Free Energy and Thermodynamics - all with Video Answers

Educators

Chapter Questions

Problem 1

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

Linhan Yang

Linhan Yang

Numerade Educator

Problem 2

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

Kevin Chimex

Numerade Educator

Problem 3

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

Dang Sia

Numerade Educator

Problem 4

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

Kevin Chimex

Numerade Educator

Problem 5

What is a spontaneous process? Provide an example.

Linhan Yang

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?

Lucas Pressley

Numerade Educator

Problem 7

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

Linhan Yang

Numerade Educator

Problem 8

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

Lucas Pressley

Numerade Educator

Problem 9

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

Aadit Sharma

Numerade Educator

Problem 10

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

Kevin Chimex

Numerade Educator

Problem 11

Provide the definition of 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?

Elif Kucukefe

Numerade Educator

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?

Lucas Pressley

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 Sia

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?

Lucas Pressley

Numerade Educator

Problem 15

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

Dang Sia

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).
a. $\Delta H$ negative, $\Delta S$ positive
b. $\Delta H$ positive, $\Delta S$ negative
c. $\Delta H$ negative, $\Delta S$ negative
d. $\Delta H$ positive, $\Delta S$ positive

LF

Leila Filien

Numerade Educator

Problem 17

State the third law of thermodynamics and explain its significance.

Linhan Yang

Numerade Educator

Problem 18

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

Lucas Pressley

Numerade Educator

Problem 19

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

Linhan Yang

Numerade Educator

Problem 20

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

Kevin Chimex

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 $25^{\circ} \mathrm{C}$ ?

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 22

Why is free energy "free"?

Kevin Chimex

Numerade Educator

Problem 23

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

Dang Sia

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?

Lucas Pressley

Numerade Educator

Problem 25

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

Linhan Yang

Numerade Educator

Problem 26

How does the value of $\Delta G^{\circ}$ for a 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 $\Delta G^{\circ}$ ?

Lucas Pressley

Numerade Educator

Problem 27

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

Dang Sia

Numerade Educator

Problem 28

Which of these processes are nonspontaneous? Are the nonspontaneous processes impossible?
a. a bike going up a hill
b. a meteor falling to Earth
c. obtaining hydrogen gas from liquid water
d. a ball rolling down a hill

Kevin Chimex

Numerade Educator

Problem 29

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 30

Suppose 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?

Kevin Chimex

Numerade Educator

Problem 31

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

Dang Sia

Numerade Educator

Problem 32

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

Lucas Pressley

Numerade Educator

Problem 33

Without doing any calculations, determine the sign 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.
a. $\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$
b. $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+182.6 \mathrm{~kJ}^{\circ}=-2044 \mathrm{~kJ}$
c. $2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{~N}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+163.2 \mathrm{~kJ}$
d. $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
$\Delta H_{\text {rxn }}^{\circ}=-906 \mathrm{~kJ}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 34

Without doing any calculations, determine the sign 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.
a. $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-566.0 \mathrm{~kJ}$
b. $2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \Delta H_{\mathrm{rxn}}^{\circ}=+113.1 \mathrm{~kJ}$
c. $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-483.6 \mathrm{~kJ}$
d. $\mathrm{CO}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{O}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+393.5 \mathrm{~kJ}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 35

Calculate $\Delta S_{\text {surr }}$ at the indicated temperature for each reaction.
a. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 298 \mathrm{~K}$
b. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 77 \mathrm{~K}$
c. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 298 \mathrm{~K}$
d. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 77 \mathrm{~K}$

JK

Jay Kothari

Numerade Educator

Problem 36

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?

Lucas Pressley

Numerade Educator

Problem 37

Given the values of $\Delta H_{\mathrm{rxn}}^{\circ}, \Delta S_{\mathrm{rxn}}^{\circ}$, and $T$, determine $\Delta S_{\mathrm{univ}}$ and predict whether or not each reaction is spontaneous.
a. $\Delta H_{\mathrm{rxn}}^{\circ}=+115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
b. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
c. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
d. $\Delta H_{\mathrm{rxn}}^{\circ}=-115 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-263 \mathrm{~J} / \mathrm{K} ; T=615 \mathrm{~K}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 38

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.
a. $\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
b. $\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=855 \mathrm{~K}$
c. $\Delta H_{\mathrm{rxn}}^{\circ}=+95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-157 \mathrm{~J} / \mathrm{K} ; T=298 \mathrm{~K}$
d. $\Delta H_{\mathrm{rxn}}^{\circ}=-95 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=+157 \mathrm{~J} / \mathrm{K} ; T=398 \mathrm{~K}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 39

Calculate the change in Gibbs free energy for each of the sets of $\Delta H_{\mathrm{rxn}}, \Delta S_{\mathrm{rxn}}$, and $T$ given in Problem 37. Predict whether or not each reaction is spontaneous at the temperature indicated.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 40

Calculate the change in Gibbs free energy for each of the sets of $\Delta H_{\mathrm{rxn}}, \Delta S_{\mathrm{rxn}}$, and $T$ given in Problem $38 .$ Predict whether or not each reaction is spontaneous at the temperature indicated.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 41

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$. Is the reaction spontaneous?
$$
\begin{gathered}
\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\
\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{~J} / \mathrm{K}
\end{gathered}
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 42

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$. Is the reaction spontaneous?
$$
\begin{gathered}
2 \mathrm{Ca}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CaO}(s) \\
\Delta H_{\mathrm{rxn}}^{\circ}=-1269.8 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=-364.6 \mathrm{~J} / \mathrm{K}
\end{gathered}
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 43

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

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 44

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

Lucas Pressley

Numerade Educator

Problem 45

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

Dang Sia

Numerade Educator

Problem 46

What is the molar entropy of a pure crystal at $0 \mathrm{~K}$ ? What is the significance of the answer to this question?

Lucas Pressley

Numerade Educator

Problem 47

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 the reasons for your choices.
a. $\mathrm{CO}(g) ; \mathrm{CO}_{2}(g)$
b. $\mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)$
c. $\operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)$
d. $\mathrm{CH}_{4}(g) ; \mathrm{SiH}_{4}(g)$
e. $\mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g)$
f. $\operatorname{NaBr}(s) ; \operatorname{NaBr}(a q)$

Elif Kucukefe

Numerade Educator

Problem 48

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 the reasons for your choices.
a. $\mathrm{NaNO}_{3}(s) ; \mathrm{NaNO}_{3}(a q)$
b. $\mathrm{CH}_{4}(\mathrm{~g}) ; \mathrm{CH}_{3} \mathrm{CH}_{3}(g)$
c. $\mathrm{Br}_{2}(l) ; \mathrm{Br}_{2}(g)$
d. $\mathrm{Br}_{2}(g) ; \mathrm{F}_{2}(g)$
e. $\mathrm{PCl}_{3}(g) ; \mathrm{PCl}_{5}(g)$
f. $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) ; \mathrm{SO}_{2}(g)$

Elif Kucukefe

Numerade Educator

Problem 49

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

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 50

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

Lucas Pressley

Numerade Educator

Problem 51

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 52

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 $\Delta S_{\mathrm{rxn}}^{\circ} .$
a. $3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)$
b. $\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Cr}(s)+3 \mathrm{CO}_{2}(g)$
c. $\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)$
d. $\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$

Lucas Pressley

Numerade Educator

Problem 53

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 $\Delta S^{\circ}$.

Aadit Sharma

Numerade Educator

Problem 54

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

Lucas Pressley

Numerade Educator

Problem 55

Methanol 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 56

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 $\Delta G_{\mathrm{rxn}}^{\circ}$ at $25^{\circ} \mathrm{C}$. Is photosynthesis spontaneous?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 57

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 $25^{\circ} \mathrm{C} ?$
a. $\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$
b. $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)$
c. $3 \mathrm{H}_{2}(g)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)$
d. $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 58

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 $25^{\circ} \mathrm{C}$ ?
a. $2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)$
b. $2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g)$
c. $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)$
d. $2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 59

Use standard free energies of formation to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each reaction in Problem $57 .$ 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 60

Use standard free energies of formation to calculate $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for each reaction in Problem 58 . 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?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 61

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.)
a. $298 \mathrm{~K}$
b. $715 \mathrm{~K}$
c. $855 \mathrm{~K}$

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 62

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.)
a. $298 \mathrm{~K}$
b. $1055 \mathrm{~K}$
c. $1455 \mathrm{~K}$

Lucas Pressley

Numerade Educator

Problem 63

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 64

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 65

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 66

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 67

Consider the reaction:
$$\mathrm{CH}_{3} \mathrm{OH}(g) \rightleftharpoons \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$$
Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions:
$P_{\mathrm{CH}_{3} \mathrm{OH}}=0.855 \mathrm{~atm}$
$P_{\mathrm{CO}}=0.125 \mathrm{~atm}$
$P_{\mathrm{H}_{2}}=0.183 \mathrm{~atm}$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 68

Consider the reaction:
$$\mathrm{CO}_{2}(g)+\mathrm{CCl}_{4}(g) \rightleftharpoons 2 \mathrm{COCl}_{2}(g)$$
Calculate $\Delta G$ for this reaction at $25^{\circ} \mathrm{C}$ under the following conditions:
$$
\begin{aligned}
&P_{\mathrm{CO}_{2}}=0.112 \mathrm{~atm} \\
&P_{\mathrm{CCl}_{4}}=0.174 \mathrm{~atm} \\
&P_{\mathrm{COCl}_{2}}=0.744 \mathrm{~atm}
\end{aligned}
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 69

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

Aadit Sharma

Numerade Educator

Problem 70

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

Lucas Pressley

Numerade Educator

Problem 71

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

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 72

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 73

Estimate the value of the equilibrium constant at $525 \mathrm{~K}$ for each reaction in Problem 69 .

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 74

Estimate the value of the equilibrium constant at $655 \mathrm{~K}$ for each reaction in Problem 70. ( $\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{BrCl}$ is $14.6 \mathrm{~kJ} / \mathrm{mol}$.)

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 75

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 $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ for the reaction.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 76

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.
$$\begin{array}{lc}
\text { Temperature } & \boldsymbol{K}_{\mathbf{p}} \\
170 \mathrm{~K} & 3.8 \times 10^{-3} \\
\hline 180 \mathrm{~K} & 0.34 \\
\hline 190 \mathrm{~K} & 18.4 \\
\hline 200 \mathrm{~K} & 681
\end{array}$$

Aadit Sharma

Numerade Educator

Problem 77

The change in enthalpy ( $\Delta H_{\mathrm{rxn}}^{\circ}$ ) 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 $655 \mathrm{~K}$ ?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 78

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 $\Delta H_{\mathrm{rxn}}^{\circ}$ for the reaction.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 79

Determine the sign of $\Delta S_{\text {sys }}$ for each process:
a. water boiling
b. water freezing
c.

Ronald Prasad

Numerade Educator

Problem 80

Determine the sign of $\Delta S_{\text {sys }}$ for each process:
a. dry ice subliming
b. dew forming
c.

Aadit Sharma

Numerade Educator

Problem 81

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:
$$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$
a. Calculate $\Delta G^{\circ}$ and $K_{\mathrm{p}}$ for this reaction at $298 \mathrm{~K}$. Is the reaction spontaneous?
b. Estimate $\Delta G^{\circ}$ at $2000 \mathrm{~K}$. Does the reaction become more spontaneous as temperature increases?

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 82

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 $K_{\mathrm{p}}$ for this reaction at $25{ }^{\circ} \mathrm{C}$ and comment on the spontaneity of the reaction.
$$
3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g)
$$

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 83

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 $\mathrm{K}_{p}$ 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?
$$
\begin{array}{lcc}
\text { Compound } & \Delta H_{\mathrm{f}}^{\circ}(\mathbf{k J} / \mathrm{mol}) & \boldsymbol{S}^{\circ}(\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}) \\
\hline \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(g) & -129.7 & 308.0 \\
\hline \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Br}_{2}(g) & +38.3 & 330.6 \\
\hline \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{l}_{2}(g) & +66.5 & 347.8 \\
\hline
\end{array}
$$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 84

$\mathrm{H}_{2}$ 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?

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 85

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 86

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

Lucas Pressley

Numerade Educator

Problem 87

Living organisms use energy from the metabolism of food to create an energy-rich molecule called adenosine triphosphate (ATP). The ATP then 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 be symbolized as follows:
$\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{ADP}(a q)+\mathrm{P}_{\mathrm{i}}(a q) \quad \Delta G_{\mathrm{rxn}}^{\circ}=-30.5 \mathrm{~kJ}$ where ADP represents adenosine diphosphate and $\mathrm{P}_{\mathrm{i}}$ represents an inorganic phosphate group (such as $\mathrm{HPO}_{4}{ }^{2-}$ ).
a. Calculate the equilibrium constant, $K$, for the given reaction at $298 \mathrm{~K}$.
b. The free energy obtained from the oxidation (reaction with oxygen) of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ to form carbon dioxide and water can be used to re-form ATP by driving the given reaction in reverse. Calculate the standard free energy change for the oxidation of glucose and estimate the maximum number of moles of ATP that can be formed by the oxidation
of one mole of glucose.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 88

The standard free energy change for the hydrolysis of ATP was given in Problem 87 . In a particular cell, the concentrations of ATP, ADP, and $\mathrm{P}_{\mathrm{i}}$ 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 $298 \mathrm{~K}$.)

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 89

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 $\Delta G^{\circ}$.
a. $2 \mathrm{CO}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{CO}_{2}(g)$
b. $5 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
c. $2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
d. $2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)$

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 90

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 91

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 $\Delta S_{f}^{\circ}$. Identify that oxide of nitrogen without reference to thermodynamic data and explain.

Aadit Sharma

Numerade Educator

Problem 92

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

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 93

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 $\mathrm{X}_{2}$ at $755 \mathrm{~K} ;$ the equilibrium partial pressure of $\mathrm{X}$ is 532 torr. Find $\Delta H^{\circ}$ for the reaction.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 94

Dinitrogen tetroxide decomposes to nitrogen dioxide:
$$\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=55.3 \mathrm{~kJ}$$
At $298 \mathrm{~K}$, a reaction vessel initially contains $0.100 \mathrm{~atm}$ 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 $(0.100 \mathrm{~atm})$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 95

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

Aadit Sharma

Numerade Educator

Problem 96

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?

Aadit Sharma

Numerade Educator

Problem 97

A metal salt with the formula $\mathrm{MCl}_{2}$ 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 $18.3 \mathrm{mmHg}$. 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 $760 \mathrm{mmHg}$ ?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 98

The solubility of $\operatorname{AgCl}(s)$ 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 $50.0^{\circ} \mathrm{C}$ ?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 99

Review the box in this chapter entitled Chemistry in Your Day: Making a Nonspontaneous Process Spontaneous. The hydrolysis of ATP, shown in Problem 87 , 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:
$$\begin{aligned}
\mathrm{A}+\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} & \Longrightarrow \mathrm{A}-\mathrm{P}_{\mathrm{i}}+\mathrm{ADP} \\
\mathrm{A}-\mathrm{P}_{\mathrm{i}}+\mathrm{B} & \longrightarrow \mathrm{AB}+\mathrm{P}_{\mathrm{i}} \\
\mathrm{A}+\mathrm{B}+\mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} & \longrightarrow \mathrm{AB}+\mathrm{ADP}+\mathrm{P}_{\mathrm{i}}
\end{aligned}$$
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:
a. Calculate $K$ for the reaction between glutamate and ammonia. (The standard free energy change for the reaction is $+14.2 \mathrm{~kJ} / \mathrm{mol}$. Assume a temperature of $298 \mathrm{~K}$.)
b. Write a set of reactions such as those given showing how the glutamate and ammonia reaction can couple with the hydrolysis of ATP. What is $\Delta G_{\mathrm{rxn}}^{\circ}$ and $K$ for the coupled reaction?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 100

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

Kevin Chimex

Numerade Educator

Problem 101

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

Natalie Almond

Numerade Educator

Problem 102

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 $-10^{\circ} \mathrm{C}$.

Aadit Sharma

Numerade Educator

Problem 103

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.

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator

Problem 104

The salt ammonium nitrate can follow three modes of decomposition: (a) to $\mathrm{HNO}_{3}(g)$ and $\mathrm{NH}_{3}(g)$, (b) to $\mathrm{N}_{2} \mathrm{O}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g)$,
and (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.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 105

Given the data, calculate $\Delta S_{\mathrm{vap}}$ for each of the first four liquids. $\left(\Delta S_{\text {vap }}=\Delta H_{\text {vap }} / T\right.$, where $T$ is in $\left.\mathrm{K}\right)$
$$
\begin{array}{llcc}
\hline \text { Compound } & \text { Name } & \text { BP }\left({ }^{\circ} \mathbf{C}\right) & \Delta H_{\text {vap }}(\mathbf{k J} / \text { mol }) \text { at BP } \\
\hline \mathrm{C}_{4} \mathrm{H}_{10} 0 & \text { Diethyl ether } & 34.6 & 26.5 \\
\hline \mathrm{C}_{3} \mathrm{H}_{6} 0 & \text { Acetone } & 56.1 & 29.1 \\
\hline \mathrm{C}_{6} \mathrm{H}_{6} 0 & \text { Benzene } & 79.8 & 30.8 \\
\hline \mathrm{CHCl}_{3} & \text { Chloroform } & 60.8 & 29.4 \\
\hline \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} & \text { Ethanol } & 77.8 & 38.6 \\
\hline \mathrm{H}_{2} \mathrm{O} & \text { Water } & 100 & 40.7 \\
\hline
\end{array}
$$
All four values should be close to each other. Predict whether the last two liquids in the table have $\Delta S_{\mathrm{vap}}$ in this same range. If not, predict whether it is larger or smaller and explain. Verify your prediction.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 106

Which is more efficient, a butane lighter or an electric lighter (such as can be found in most automobiles)? Explain.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 107

Which statement is true?
a. A spontaneous reaction is always a fast reaction.
b. A spontaneous reaction is always a slow reaction.
c. The spontaneity of a reaction is not necessarily related to the speed of a reaction.

Kevin Chimex

Numerade Educator

Problem 108

Which process is necessarily driven by an increase in the entropy of the surroundings?
a. the condensation of water
b. the sublimation of dry ice
c. the freezing of water

Aadit Sharma

Numerade Educator

Problem 109

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

Iryna Ivaniuk

Numerade Educator

Problem 110

Which statement is true?
a. A reaction in which the entropy of the system increases can be spontaneous only if it is exothermic.
b. A reaction in which the entropy of the system increases can be spontaneous only if it is endothermic.
c. A reaction in which the entropy of the system decreases can be spontaneous only if it is exothermic.

Aadit Sharma

Numerade Educator

Problem 111

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

Aadit Sharma

Numerade Educator

Problem 112

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?
a. The concentration of the product is greater than the concentration of the reactant.
b. The reaction is at equilibrium.
c. The concentration of the reactant is greater than the concentration of the product.

Aadit Sharma

Numerade Educator

Problem 113

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

Yokshitha Reddy Bathula

Yokshitha Reddy Bathula

Numerade Educator