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Chemistry

Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson

Chapter 13

Fundamental Equilibrium Concepts

Educators

MH

Problem 1

What does it mean to describe a reaction as “reversible”?

MH
Matthew H.
Numerade Educator

Problem 2

When writing an equation, how is a reversible reaction distinguished from a nonreversible reaction?

Rikhil M.
Numerade Educator

Problem 3

If a reaction is reversible, when can it be said to have reached equilibrium?

MH
Matthew H.
Numerade Educator

Problem 4

Is a system at equilibrium if the rate constants of the forward and reverse reactions are equal?

Rikhil M.
Numerade Educator

Problem 5

If the concentrations of products and reactants are equal, is the system at equilibrium?

MH
Matthew H.
Numerade Educator

Problem 6

Explain why there may be an infinite number of values for the reaction quotient of a reaction at a given
temperature but there can be only one value for the equilibrium constant at that temperature.

Rikhil M.
Numerade Educator

Problem 7

Explain why an equilibrium between $\mathrm{Br}_{2}(\mathrm{l})$ and $\mathrm{Br}_{2}(g)$ would not be established if the container were not a closed vessel shown in Figure $13.5 .$

MH
Matthew H.
Numerade Educator

Problem 8

If you observe the following reaction at equilibrium, is it possible to tell whether the reaction started with pure $\mathrm{NO}_{2}$ or with pure $\mathrm{N}_{2} \mathrm{O}_{4} ?$
2 $\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g)$

Rikhil M.
Numerade Educator

Problem 9

Among the solubility rules previously discussed is the statement: All chluble except $\mathrm{Hg}_{2} \mathrm{Cl}_{2}, \mathrm{AgCl}$
$\mathrm{PbCl}_{2},$ and CuCl.
(a) Write the expression for the equilibrium constant for the reaction represented by the equation
$\mathrm{AgCl}(s) \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) .$ Is $K_{c}>1,<1,$ or $\approx 1 ?$ Explain your answer.
(b) Write the expression for the equilibrium constant for the reaction represented by the equation
$\mathrm{Pb}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{PbCl}_{2}(s) .$ Is $K_{c}>1,<1,$ or $\approx 1 ?$ Explain your answer.

MH
Matthew H.
Numerade Educator

Problem 10

Among the solubility rules previously discussed is the statement: Carbonates, phosphates, borates, and arsenates—except those of the ammonium ion and the alkali metals—are insoluble.
(a) Write the expression for the equilibrium constant for the reaction represented by the equation
$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(\mathrm{aq}) .$ Is $K_{c}>1,<1,$ or $\approx 1 ?$ Explain your answer.
(b) Write the expression for the equilibrium constant for the reaction represented by the equation
$3 \mathrm{Ba}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons \mathrm{Ba}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s) .$ Is $K_{c}>1,<1,$ or $\approx 1 ?$ Explain your answer.

Rikhil M.
Numerade Educator

Problem 11

Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: 3 $\mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g) .$ Which value of $K_{c}$ would make this reaction most useful commercially? $K_{c} \approx 0.01, K_{c} \approx 1,$ or $K_{c} \approx 10 .$ Explain your answer.

MH
Matthew H.
Numerade Educator

Problem 12

Show that the complete chemical equation, the total ionic equation, and the net ionic equation for the reaction represented by the equation $\mathrm{KI}(a q)+\mathrm{I}_{2}(a q) \rightleftharpoons \mathrm{KI}_{3}(a q)$ give the same expression for the reaction quotient. $\mathrm{KI}_{3}$ is composed of the ions $\mathrm{K}^{+}$ and $\mathrm{I}_{3}^{-}$.

Rikhil M.
Numerade Educator

Problem 13

For a titration to be effective, the reactive, the reaction must be rapid and the reaction must essentially be 100$\% .$ Is $K_{c}>1,<1,$ or $\approx 1$ for a titration reaction?

MH
Matthew H.
Numerade Educator

Problem 14

For a precipitation reaction to be useful in a gravimetric analysis, the product of the reaction must be insoluble. Is $K_{c}>1,<1,$ or $\approx 1$ for a useful precipitation reaction?

Rikhil M.
Numerade Educator

Problem 15

Write the mathematical expression for the reaction quotient, $Q_{\mathrm{c}}$ for each of the following reactions:
(a) $\mathrm{CH}_{4}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{Cl}(g)+\mathrm{HCl}(g)$
(b) $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$
(c) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$
(d) $\mathrm{BaSO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{SO}_{2}(g)$
(e) $\mathrm{P}_{4}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)$
(f) $\mathrm{Br}_{2}(g)=2 \mathrm{Br}(g)$
(g) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g)=\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$
(h) $\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)$

MH
Matthew H.
Numerade Educator

Problem 16

Write the mathematical expression for the reaction quotient, $Q_{c}$ for each of the following reactions:
(a) $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$
(b) $4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
(c) $\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$
(d) $\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(e) $\mathrm{NH}_{4} \mathrm{Cl}(s)=\mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$
(f) $2 \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s)=2 \mathrm{PbO}(s)+4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)$
(g) $2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)$
(h) $\mathrm{S}_{8}(g) \rightleftharpoons 8 \mathrm{S}(g)$

Rikhil M.
Numerade Educator

Problem 17

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction in which each system will proceed to reach equilibrium.
(a) $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \quad K_{c}=17 ;\left[\mathrm{NH}_{3}\right]=0.20 M,\left[\mathrm{N}_{2}\right]=1.00 M,\left[\mathrm{H}_{2}\right]=1.00 \mathrm{M}$
(b) $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$ $K_{P}=6.8 \times 10^{4} ;$ initial pressures: $\mathrm{NH}_{3}=3.0 \mathrm{atm}, \mathrm{N}_{2}=2.0 \mathrm{atm}, \mathrm{H}_{2}=$1.0 $\mathrm{atm}$
(c) $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad K_{c}=0.230 ;\left[\mathrm{SO}_{3}\right]=0.00 M,\left[\mathrm{SO}_{2}\right]=1.00 M,\left[\mathrm{O}_{2}\right]=1.00 \mathrm{M}$
(d) $2 \operatorname{SO}_{3}(g) \rightleftharpoons 2 \operatorname{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad K_{P}=16.5 ;$ initial pressures: $\mathrm{SO}_{3}=1.00 \mathrm{atm}, \mathrm{SO}_{2}=1.00 \mathrm{atm}, \mathrm{O}_{2}=$
1.00 $\mathrm{atm}$
(e) $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) \quad K_{c}=4.6 \times 10^{4} ;[\mathrm{NO}]=1.00 M,\left[\mathrm{Cl}_{2}\right]=1.00 M,[\mathrm{NOCl}]=0 M$
(f) $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{P}=0.050 ;$ initial pressures: $\mathrm{NO}=10.0 \mathrm{atm}, \mathrm{N}_{2}=\mathrm{O}_{2}=5 \mathrm{atm}$

MH
Matthew H.
Numerade Educator

Problem 18

The initial concentrations or pressures of reactants and products are given for each of the following systems. Calculate the reaction quotient and determine the direction in which each system will proceed to reach equilibrium.
(a) $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \quad K_{c}=17 ;\left[\mathrm{NH}_{3}\right]=0.50 M,\left[\mathrm{N}_{2}\right]=0.15 M,\left[\mathrm{H}_{2}\right]=0.12 \mathrm{M}$
(b) $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \quad K_{P}=6.8 \times 10^{4} ;$ initial pressures: $\mathrm{NH}_{3}=2.00 \mathrm{atm}, \mathrm{N}_{2}=10.00 \mathrm{atm}, \mathrm{H}_{2}$
$=10.00 \mathrm{atm}$
(c) $2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad K_{c}=0.230 ;\left[\mathrm{SO}_{3}\right]=2.00 M,\left[\mathrm{SO}_{2}\right]=2.00 M,\left[\mathrm{O}_{2}\right]=2.00 M$
(d) $2 \operatorname{SO}_{3}(g)=2 \operatorname{SO}_{2}(g)+\mathrm{O}_{2}(g) \quad K_{P}=6.5 \mathrm{atm} ;$ initial pressures: $\mathrm{SO}_{2}=1.00 \mathrm{atm}, \mathrm{O}_{2}=1.130 \mathrm{atm}, \mathrm{SO}_{3}$
$=0 \mathrm{atm}$
(e) $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)$$K_{P}=2.5 \times 10^{3} ;$ initial pressures: $\mathrm{NO}=1.00 \mathrm{atm}, \mathrm{Cl}_{2}=1.00 \mathrm{atm}$$\mathrm{NOCl}=0 \mathrm{atm}$
(f) $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{c}=0.050 ;\left[\mathrm{N}_{2}\right]=0.100 \mathrm{M},\left[\mathrm{O}_{2}\right]=0.200 \mathrm{M},[\mathrm{NO}]=1.00 \mathrm{M}$

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Problem 19

The following reaction has $K_{P}=4.50 \times 10^{-5}$ at 720 $\mathrm{K}$$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$
If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? $P\left(\mathrm{NH}_{3}\right)=93 \mathrm{atm}, P\left(\mathrm{N}_{2}\right)=48 \mathrm{atm},$ and $P\left(\mathrm{H}_{2}\right)=52$

MH
Matthew H.
Numerade Educator

Problem 20

Determine if the following system is at equilibrium. If not, in which direction will the system need to shift to reach equilibrium?
$\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)=\mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)$
$\left[\mathrm{SO}_{2} \mathrm{Cl}_{2}\right]=0.12 \mathrm{M},\left[\mathrm{Cl}_{2}\right]=0.16 \mathrm{M}$ and $\left[\mathrm{SO}_{2}\right]=0.050 \mathrm{M} . \mathrm{K}_{c}$ for the reaction is 0.078 .

Rikhil M.
Numerade Educator

Problem 21

Which of the systems described in Exercise 13.15 give homogeneous equilibria? Which give heterogeneous equilibria?

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Matthew H.
Numerade Educator

Problem 22

Which of the systems described in Exercise 13.16 give homogeneous equilibria? Which give heterogeneous equilibria?

Rikhil M.
Numerade Educator

Problem 23

For which of the reactions in Exercise 13.15 does $K_{c}$ (calculated using concentrations) equal $K_{P}$ (calculated using pressures)?

MH
Matthew H.
Numerade Educator

Problem 24

For which of the reactions in Exercise 13.16 does $K_{c}$ (calculated using concentrations) equal $K_{P}$ ( calculated using pressures)?

Rikhil M.
Numerade Educator

Problem 25

Convert the values of $K_{c}$ to values of $K_{P}$ or the values of $K_{P}$ to values of $K_{c}$
$\begin{array}{ll}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)} & {K_{c}=0.50 \mathrm{at} 400^{\circ} \mathrm{C}} \\ {\text { (b) } \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HII}(g)} & {K_{c}=50.2 \text { at } 448^{\circ} \mathrm{C}}\end{array}$
(c) $\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{SO}_{4}(s)+10 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{P}=4.08 \times 10^{-25} \mathrm{at} 25^{\circ} \mathrm{C}$
(d) $\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g) \quad K_{P}=0.122$ at $50^{\circ} \mathrm{C}$

MH
Matthew H.
Numerade Educator

Problem 26

Convert the values of $K_{c}$ to values of $K_{P}$ or the values of $K_{P}$ to values of $K_{c}$
$\begin{array}{ll}{\text { (a) } \mathrm{Cl}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{BrCl}(g)} & {K_{c}=4.7 \times 10^{-2} \mathrm{at} 25^{\circ} \mathrm{C}} \\ {\text { (b) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)} & {K_{P}=48.2 \mathrm{at} 500^{\circ} \mathrm{C}}\end{array}$
$\begin{array}{l}{\text { (c) } \mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s)=\mathrm{CaCl}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)} & {K_{P}=0.196 \mathrm{at} 60^{\circ} \mathrm{C}}\end{array} \quad K_{P}=5.09 \times 10^{-44} \mathrm{at} 25^{\circ} \mathrm{C}$

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Problem 27

What is the value of the equilibrium constant expression for the change $\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ at $30^{\circ} \mathrm{C} ?(\mathrm{See}$
Appendix E.)

MH
Matthew H.
Numerade Educator

Problem 28

Write the expression of the reaction quotient for the ionization of HOCN in water.

Rikhil M.
Numerade Educator

Problem 29

Write the reaction quotient expression for the ionization of $\mathrm{NH}_{3}$ in water.

MH
Matthew H.
Numerade Educator

Problem 30

What is the approximate value of the equilibrium constant $K_{P}$ for the change
$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}(l) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}(g)$ at $25^{\circ} \mathrm{C}$ . (Vapor pressure was described in the previous chapter on liquids
and solids; refer back to this chapter to find the relevant information needed this problem.)

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Problem 31

The following equation represents a reversible decomposition:
$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$

MH
Matthew H.
Numerade Educator

Problem 32

Explain how to recognize the conditions under which changes in pressure would affect systems at equilibrium.

Rikhil M.
Numerade Educator

Problem 33

What property of a reaction can we use to predict the effect of a change in temperature on the value of an equilibrium constant?

MH
Matthew H.
Numerade Educator

Problem 34

What would happen to the color of the solution in part (b) of Figure 13.8 if a small amount of NaOH were added and Fe(OH) $_{3}$ precipitated? Explain your answer.

Rikhil M.
Numerade Educator

Problem 35

The following reaction occurs when a burner on a gas stove is lit:
$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
Is an equilibrium among $\mathrm{CH}_{4}, \mathrm{O}_{2}, \mathrm{CO}_{2},$ and $\mathrm{H}_{2} \mathrm{O}$ established under these conditions? Explain your answer.

MH
Matthew H.
Numerade Educator

Problem 36

A necessary step in the manufacture of sulfuric acid is the formation of sulfur trioxide, $\mathrm{SO}_{3}$ , from sulfur dioxide, $\mathrm{SO}_{2},$ and oxygen, $\mathrm{O}_{2},$ shown here. At high temperatures, the rate of formation of $\mathrm{SO}_{3}$ is higher, but the
equilibrium amount (concentration or partial pressure) of $\mathrm{SO}_{3}$ is lower than it would be at lower temperatures. $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \operatorname{SO}_{3}(g)$
(a) Does the equilibrium constant for the reaction increase, decrease, or remain about the same as the temperature increases?
(b) Is the reaction endothermic or exothermic?

Rikhil M.
Numerade Educator

Problem 37

Suggest four ways in which the concentration of hydrazine, $\mathrm{N}_{2} \mathrm{H}_{4}$ , could be increased in an equilibrium described by the following equation:
$\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{H}_{4}(g) \quad \Delta H=95 \mathrm{kJ}$

MH
Matthew H.
Numerade Educator

Problem 38

Suggest four ways in which the concentration of $\mathrm{PH}_{3}$ could be increased in an equilibrium described by the
following equation:
$P_{4}(g)+6 \mathrm{H}_{2}(g) \rightleftharpoons 4 \mathrm{PH}_{3}(g) \quad \Delta H=110.5 \mathrm{kJ}$

Rikhil M.
Numerade Educator

Problem 39

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?
(a) $2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \qquad \Delta H=92 \mathrm{kJ}$
(b) $\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad \Delta H=181 \mathrm{kJ}$ (c) $2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) \quad \Delta H=-285 \mathrm{kJ}$
(c) $2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) \quad \Delta H=-285 \mathrm{kJ}$
(d) $\mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{CaCO}_{3}(s) \quad \Delta H=-176 \mathrm{kJ}$

MH
Matthew H.
Numerade Educator

Problem 40

How will an increase in temperature affect each of the following equilibria? How will a decrease in the volume of the reaction vessel affect each?
$\begin{array}{ll}{\text { (a) } 2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)} & {\Delta H=484 \mathrm{kJ}} \\ {\text { (b) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)} & {\Delta H=-92.2 \mathrm{kJ}}\end{array}$ $\begin{array}{ll}{\text { (c) } 2 \mathrm{Br}(g)=\mathrm{Br}_{2}(g)} & {\Delta H=-224 \mathrm{kJ}} \\ {\text { (d) } \mathrm{H}_{2}(g)+\mathrm{I}_{2}(s) \rightleftharpoons 2 \mathrm{HIC}(g)} & {\Delta H=53 \mathrm{kJ}}\end{array}$

Rikhil M.
Numerade Educator

Problem 41

Water gas is a $1 : 1$ mixture of carbon monoxide and hydrogen gas and is called water gas because it is formed from steam and hot carbon in the following reaction: $\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}(g) .$ Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and hydrogen at high temperature and pressure in the presence of a suitable catalyst.
(a) Write the expression for the equilibrium constant $\left(K_{c}\right)$ for the reversible reaction
$2 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) \quad \Delta H=-90.2 \mathrm{kJ}$
(b) What will happen to the concentrations of $\mathrm{H}_{2}, \mathrm{CO},$ and $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium if more $\mathrm{H}_{2}$ is added?
(c) What will happen to the concentrations of $\mathrm{H}_{2}, \mathrm{CO},$ and $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium if $\mathrm{CO}$ is removed?
(d) What will happen to the concentrations of $\mathrm{H}_{2}, \mathrm{CO},$ and $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium if $\mathrm{CH}_{3} \mathrm{OH}$ is added?
(e) What will happen to the concentrations of $\mathrm{H}_{2}, \mathrm{CO}$ , and $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium if the temperature of the system is
increased?
(f) What will happen to the concentrations of $\mathrm{H}_{2}, \mathrm{CO},$ and $\mathrm{CH}_{3} \mathrm{OH}$ at equilibrium if more catalyst is added?

MH
Matthew H.
Numerade Educator

Problem 42

Nitrogen and oxygen react at high temperatures.
(a) Write the expression for the equilibrium constant $\left(K_{c}\right)$ for the reversible reaction
$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad \Delta H=181 \mathrm{kJ}$
(b) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{NO}$ at equilibrium if more $\mathrm{O}_{2}$ is added?
(c) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{NO}$ at equilibrium if $\mathrm{N}_{2}$ is removed?
(d) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and NO at equilibrium if NO is added?
(e) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and $\mathrm{NO}$ at equilibrium if the pressure on the system is increased by reducing the volume of the reaction vessel?
(f) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and NO at equilibrium if the temperature of the system is
increased?
(g) What will happen to the concentrations of $\mathrm{N}_{2}, \mathrm{O}_{2},$ and NO at equilibrium if a catalyst is added?

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Problem 43

Water gas, a mixture of $\mathrm{H}_{2 \mathrm{and}} \mathrm{CO}, \mathrm{is}$ an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon.
(a) Write the expression for the equilibrium constant for the reversible reaction
$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g) \quad \Delta H=131.30 \mathrm{kJ}$
(b) What will happen to the concentration of each reactant and product at equilibrium if more $\mathrm{C}$ is added?
(c) What will happen to the concentration of each reactant and product at equilibrium if $\mathrm{H}_{2} \mathrm{O}$ is removed?
(d) What will happen to the concentration of each reactant and product at equilibrium if $\mathrm{CO}$ is added?
(e) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

MH
Matthew H.
Numerade Educator

Problem 44

Pure iron metal can be produced by the reduction of iron(III) oxide with hydrogen gas.
(a) Write the expression for the equilibrium constant $\left(K_{c}\right)$ for the reversible reaction
$\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H=98.7 \mathrm{kJ}$
(b) What will happen to the concentration of each reactant and product at equilibrium if more Fe is added?
(c) What will happen to the concentration of each reactant and product at equilibrium if $\mathrm{H}_{2} \mathrm{O}$ is removed?
(d) What will happen to the concentration of each reactant and product at equilibrium if $\mathrm{H}_{2}$ is added?
(e) What will happen to the concentration of each reactant and product at equilibrium if the pressure on the system is increased by reducing the volume of the reaction vessel?
(f) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

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Problem 45

Ammonia is a weak base that reacts with water according to this equation:
$\mathrm{NH}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{NH}_{4}^{+}(a q)+\mathrm{OH}^{-}(a q)$
Will any of the following increase the percent of ammonia that is converted to the ammonium ion in water?
(a) Addition of NaOH
(b) Addition of HCl
(c) Addition of $\mathrm{NH}_{4} \mathrm{Cl}$

MH
Matthew H.
Numerade Educator

Problem 46

Acetic acid is a weak acid that reacts with water according to this equation:
$\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(a q)+\mathrm{H}_{2} \mathrm{O}(a q) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(a q)$
Will any of the following increase the percent of acetic acid that reacts and produces $\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}$ ion?
(a) Addition of $\mathrm{HCl}$
(b) Addition of $\mathrm{NaOH}$
(c) Addition of $\mathrm{NaCH}_{3} \mathrm{CO}_{2}$

Rikhil M.
Numerade Educator

Problem 47

Suggest two ways in which the equilibrium concentration of Ag' can be reduced in a soluced in a solution of $\mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{Ag}^{+}$
and $\mathrm{NO}_{3}-,$ in contact with solid AgCl.
$\mathrm{Na}^{+}(a q)+\mathrm{Cl}^{-}(a q)+\mathrm{Ag}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \rightleftharpoons \mathrm{AgCl}(s)+\mathrm{Na}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)$
$\Delta H=-65.9 \mathrm{kJ}$

MH
Matthew H.
Numerade Educator

Problem 48

How can the pressure of water vapor be increased in the following equilibrium?
$\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H=41 \mathrm{kJ}$

Rikhil M.
Numerade Educator

Problem 49

Additional solid silver sulfate, a slightly soluble solid, is added to a solution of silver ion and sulfate ion at
equilibrium with solid silver sulfate.
$2 \mathrm{Ag}^{+}(a q)+\mathrm{SO}_{4}^{2-}(a q) \rightleftharpoons \mathrm{Ag}_{2} \mathrm{SO}_{4}(s)$
Which of the following will occur?
(a) $\mathrm{Ag}^{+}$ or $\mathrm{SO}_{4}^{2-}$ concentrations will not change.
(b) The added silver sulfate will dissolve.
(c) Additional silver sulfate will form and precipitate from solution as Ag' ions and $\mathrm{SO}_{4}^{2-}$ ions combine.
(d) The Ag' ion concentration will increase and the $\mathrm{SO}_{4}^{2-}$ ion concentration will decrease.

MH
Matthew H.
Numerade Educator

Problem 50

The amino acid alanine has two isomers, ?-alanine and ?-alanine. When equal masses of these two compounds are dissolved in equal amounts of a solvent, the solution of ?-alanine freezes at the lowest temperature. Which form, ?-alanine or $\beta$ -alanine, has the larger equilibrium constant for ionization $\left(\mathrm{HX} \rightleftharpoons \mathrm{H}^{+}+\mathrm{X}^{-}\right) ?$

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Problem 51

A reaction is represented by this equation:
$\mathrm{A}(a q)+2 \mathrm{B}(a q) \rightleftharpoons 2 \mathrm{C}(a q) \quad K_{c}=1 \times 10^{3}$
(a) Write the mathematical expression for the equilibrium constant.
(b) Using concentrations ?1 M, make up two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

MH
Matthew H.
Numerade Educator

Problem 52

A reaction is represented by this equation: $2 \mathrm{W}(a q) \rightleftharpoons \mathrm{X}(a q)+2 \mathrm{Y}(a q) \quad K_{c}=5 \times 10^{-4}$
(a) Write the mathematical expression for the equilibrium constant.
(b) Using concentrations of ?1 M, make up two sets of concentrations that describe a mixture of W, X, and Y at equilibrium.

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Problem 53

What is the value of the equilibrium constant at $500^{\circ} \mathrm{C}$ for the formation of $\mathrm{NH}_{3}$ according to the following equation?
$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$
An equilibrium mixture of $\mathrm{NH}_{3}(g), \mathrm{H}_{2}(g),$ and $\mathrm{N}_{2}(g)$ at $500^{\circ} \mathrm{C}$ was found to contain $1.35 \mathrm{M} \mathrm{H}_{2}, 1.15 \mathrm{M}_{2},$ and 4.12 $\times 10^{-1} M \mathrm{NH}_{3}$

MH
Matthew H.
Numerade Educator

Problem 54

Hydrogen is prepared commercially by the reaction of methane and water vapor at elevated temperatures. $\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g)$
What is the equilibrium constant for the reaction if a mixture at equilibrium contains gases with the following concentrations: $\mathrm{CH}_{4}, 0.126 \mathrm{M} ; \mathrm{H}_{2} \mathrm{O}, 0.242 \mathrm{M} ; \mathrm{CO}, 0.126 \mathrm{O}$ ; $0.126 \mathrm{M} ; \mathrm{H}_{2} 1.15 \mathrm{M},$ at a temperature of $760^{\circ} \mathrm{C} ?$

Rikhil M.
Numerade Educator

Problem 55

A 0.72 -mol sample of $\mathrm{PCl}_{5}$ is put into a $1.00-\mathrm{L}$ vessel and heated. At equilibrium, the vessel contains 0.40 $\mathrm{mol}$ of $\mathrm{PCl}_{3}(g)$ and 0.40 $\mathrm{mol}$ of $\mathrm{Cl}_{2}(g) .$ Calculate the value of the equilibrium constant for the decomposition of $\mathrm{PCl}_{5}$ to $\mathrm{PCl}_{3}$ and $\mathrm{Cl}_{2}$ at this temperature.

MH
Matthew H.
Numerade Educator

Problem 56

At 1 atm and $25^{\circ} \mathrm{C}, \mathrm{NO}_{2}$ with an initial concentration of 1.00 $\mathrm{M}$ is $3.3 \times 10^{-30} \%$ decomposed into NO and $\mathrm{O}_{2}$ Calculate the value of the equilibrium constant for the reaction.$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$

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Problem 57

Calculate the value of the equilibrium constant $K_{P}$ for the reaction $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)$ from these equilibrium pressures: NO, 0.050 atm; $\mathrm{Cl}_{2}, 0.30 \mathrm{atm} ; \mathrm{NOCl}, 1.2 \mathrm{atm}$ .

MH
Matthew H.
Numerade Educator

Problem 58

When heated, iodine vapor dissociates according to this equation:
$\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)$
At 1274 $\mathrm{K}$ , a sample exhibits a partial pressure of $\mathrm{I}_{2}$ of 0.1122 atm and a partial pressure due to I atoms of 0.1378 atm. Determine the value of the equilibrium constant, $K_{P},$ for the decomposition at 1274 $\mathrm{K}$ .

Rikhil M.
Numerade Educator

Problem 59

A sample of ammonium chloride was heated in a closed container.
$\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)$
At equilibrium, the pressure of $\mathrm{NH}_{3}(g)$ was found to be 1.75 $\mathrm{atm}$ . What is the value of the equilibrium constant $K_{P}$ for the decomposition at this temperature?

MH
Matthew H.
Numerade Educator

Problem 60

At a temperature of $60^{\circ} \mathrm{C}$ , the vapor pressure of water is 0.196 atm. What is the value of the equilibrium constant $K_{P}$ for the transformation at $60^{\circ} \mathrm{C} ?$
$\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)$

Rikhil M.
Numerade Educator

Problem 61

(a)
$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$
______ $\quad$$\quad$______ $+x$
______ $\quad$$\quad$______ 0.125$M$
(b)
$4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
______ $\quad$$\quad$ 3$x$ ______ $\quad$$\quad$______ $+x$
______ $\quad$$\quad$ 0.24$M$ ______ $\quad$$\quad$______ $+x$
(c) Change in pressure:
$2 \mathrm{CH}_{4}(g)=\mathrm{C}_{2} \mathrm{H}_{2}(g)+3 \mathrm{H}_{2}(g)$
______ $\quad$$\quad$ $x$ $\quad$$\quad$______
______ $\quad$$\quad$ 25 torr$ \quad$$\quad$______
(d) Change in pressure:
$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$
______ $\quad$$\quad$ $x$ ______ $\quad$$\quad$______
______ $\quad$$\quad$ 5 $\mathrm{atm}$ ______ $\quad$$\quad$______
(e)
$\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\qquad \mathrm{HCl}(g)$
$\quad$$\quad$ $x$ $\quad$$\quad$______
$\quad$$\quad$ $1.03 \times 10^{-4} M$ $\quad$$\quad$______
(f) change in pressure:
$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g)$
$\quad$$\quad$ 4$x$ $\quad$$\quad$______
$\quad$$\quad$ 0.40 $\mathrm{atm}$ $\quad$$\quad$______

MH
Matthew H.
Numerade Educator

Problem 62

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.
(a)
$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)$
____ $\quad\quad\quad$ ____ $\quad\quad\quad$ $+2 x$
____ $\quad\quad\quad$ ____ $\quad\quad\quad$ 1.50$M$
(b)
$\mathrm{CS}_{2}(g)+4 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{S}(g)$
$x$ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____
0.020$M$ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____
(c) Change in pressure:
$2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)$
$x$ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____
1.50 $\mathrm{atm}$ $\quad\quad\quad$ ____ $\quad\quad\quad$ ____
(d) Change in pressure:
$2 \mathrm{NH}_{3}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+3 \mathrm{H}_{2} \mathrm{O}(g)$
____ $\quad\quad\quad$____ $\quad\quad\quad$____ $\quad\quad\quad$ $x$
____ $\quad\quad\quad$____ $\quad\quad\quad$____ $\quad\quad\quad$ 60.6 torr
(e)
$\mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\quad \mathrm{H}_{2} \mathrm{S}(g)$
$\quad\quad\quad$$\quad\quad\quad$ $x$ $\quad\quad\quad$ _____
$\quad\quad\quad$$\quad\quad\quad$ $9.8 \times 10^{-6} M$ $\quad\quad\quad$ _____
(f) Change in pressure:
$\mathrm{Fe}(s)+5 \mathrm{CO}(g) \rightleftharpoons \mathrm{Fe}(\mathrm{CO})_{5}(g)$
$\quad\quad\quad$ _____ $\quad\quad\quad$ $x$
$\quad\quad\quad$ _____ $\quad\quad\quad$ 0.012 $\mathrm{atm}$

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Problem 63

Why are there no changes specified for Ni in Exercise 13.61, part (f)? What property of Ni does change?

MH
Matthew H.
Numerade Educator

Problem 64

Why are there no changes specified for $\mathrm{NH}_{4} \mathrm{H}$ S in $\mathrm{NH}_{4} \mathrm{HS}$ in Exercise $13.62, \mathrm{part}(\mathrm{e}) ?$What property of $\mathrm{NH}_{4} \mathrm{HS}$ does change?

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Problem 65

Analysis of the gases in a sealed reaction vessel containing $\mathrm{NH}_{3}, \mathrm{N}_{2},$ and $\mathrm{H}_{2}$ at equilibrium at $400^{\circ} \mathrm{C}$ established the concentration of $\mathrm{N}_{2}$ to be 1.2 $\mathrm{M}$ and the concentration of $\mathrm{H}_{2}$ to be 0.24 $\mathrm{M}$
$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \qquad K_{c}=0.50$ at $400^{\circ} \mathrm{C}$
Calculate the equilibrium molar concentration of $\mathrm{NH}_{3}$

MH
Matthew H.
Numerade Educator

Problem 66

Calculate the number of moles of HI that are at equilibrium with 1.25 $\mathrm{mol}$ of $\mathrm{H}_{2}$ and 1.25 $\mathrm{mol}$ of $\mathrm{I}_{2}$ in a $5.00-\mathrm{L}$ flask at $448^{\circ} \mathrm{C}$
$\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI} \quad K_{c}=50.2$ at $448^{\circ} \mathrm{C}$

Rikhil M.
Numerade Educator

Problem 67

What is the pressure of BrCl in an equilibrium mixture of $\mathrm{Cl}_{2}, \mathrm{Br}_{2},$ and $\mathrm{BrCl}$ if the pressure of $\mathrm{Cl}_{2}$ in the mixture is 0.115 atm and the pressure of $\mathrm{Br}_{2}$ in the mixture is 0.450 atm?
$\mathrm{Cl}_{2}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{BrCl}(g) \qquad K_{P}=4.7 \times 10^{-2}$

MH
Matthew H.
Numerade Educator

Problem 68

What is the pressure of $\mathrm{CO}_{2}$ in a mixture at equilibrium that contains $0.50 \mathrm{atm} \mathrm{H}_{2}, 2.0 \mathrm{atm}$ of $\mathrm{H}_{2} \mathrm{O}$ , and 1.0 $\mathrm{atm}$ of $\mathrm{CO}$ at $990^{\circ} \mathrm{C} ?$
$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \qquad K_{P}=1.6 \mathrm{at} 990^{\circ} \mathrm{C}$

Rikhil M.
Numerade Educator

Problem 69

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.
$\mathrm{CoO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Co}(s)+\mathrm{CO}_{2}(g) \quad K_{c}=4.90 \times 10^{2}$ at $550^{\circ} \mathrm{C}$

MH
Matthew H.
Numerade Educator

Problem 70

Carbon reacts with water vapor at elevated temperatures
$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g) \quad K_{c}=0.2 \mathrm{at} 1000^{\circ} \mathrm{C}$
What is the concentration of $\mathrm{CO}$ in an equilibrium mixture with $\left[\mathrm{H}_{2} \mathrm{O}\right]=0.500 \mathrm{M}$ at 1000 $\mathrm{c}$ ?

Rikhil M.
Numerade Educator

Problem 71

Sodium sulfate 10 -hydrate, $\mathrm{Na}_{2} \mathrm{SO}_{4}^{-10 \mathrm{H}} \mathrm{O}$ , dehydrates according to the equation
$\mathrm{Na}_{2} \mathrm{SO}_{4}-10 \mathrm{H}_{2} \mathrm{O}(s)=\mathrm{Na}_{2} \mathrm{SO}_{4}(s)+10 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{P}=4.08 \times 10^{-25} \mathrm{at} 25^{\circ} \mathrm{C}$
What is the pressure of water vapor at equilibrium with a mixture of $\mathrm{Na}_{2} \mathrm{SO}_{4}-10 \mathrm{H}_{2} \mathrm{O}$ and $\mathrm{NaSO}_{4}$ ?

MH
Matthew H.
Numerade Educator

Problem 72

Calcium chloride 6 -hydrate, $\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O},$ dehydrates according to the equation
$\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{CaCl}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{P}=5.09 \times 10^{-44}$ at $25^{\circ} \mathrm{C}$
What is the pressure of water vapor at equilibrium with a mixture of $\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}$ and $\mathrm{CaCl}_{2} ?$
What is the pressure of water vapor at equilibrium with a mixture of $\mathrm{CaCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}$ and $\mathrm{CaCl}_{2} ?$

Rikhil M.
Numerade Educator

Problem 73

A student solved the following problem and found the equilibrium concentrations to be $\left[\mathrm{SO}_{2}\right]=0.590 \mathrm{M},\left[\mathrm{O}_{2}\right]$ $=0.0450 M,$ and $\left[\mathrm{SO}_{3}\right]=0.260$ M. How could this student check the work without reworking the problem? The problem was: For the following reaction at $600^{\circ} \mathrm{C} :$
$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) \quad K_{c}=4.32$

MH
Matthew H.
Numerade Educator

Problem 74

A student solved the following problem and found $\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.16 M$ at equilibrium. How could this student recognize that the answer was wrong without reworking the problem? The problem was: What is the equilibrium concentration of $\mathrm{N}_{2} \mathrm{O}_{4}$ in a mixture formed from a sample of $\mathrm{NO}_{2}$ with a concentration of 0.10 $\mathrm{M}$ ?
$2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) \quad K_{c}=160$

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Problem 75

Assume that the change in concentration of $\mathrm{N}_{2} \mathrm{O}_{4}$ is small enough to be neglected in the following problem.
(a) Calculate the equilibrium concentration of both species in 1.00 $\mathrm{L}$ of a solution prepared from 0.129 mol of $\mathrm{N}_{2} \mathrm{O}_{4}$
with chloroform as the solvent.
$\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad K_{c}=1.07 \times 10^{-5}$ in chloroform
(b) Show that the change is small enough to be neglected.

MH
Matthew H.
Numerade Educator

Problem 76

Assume that the change in concentration of $\mathrm{COCl}_{2}$ is small enough to be neglected in the following problem.
(a) Calculate the equilibrium concentration of all species in an equilibrium mixture that results from the
decomposition of $\mathrm{COCl}_{2}$ with an initial concentration of 0.3166 $\mathrm{M} .$
$\operatorname{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \quad K_{c}=2.2 \times 10^{-10}$
(b) Show that the change is small enough to be neglected.

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Problem 77

Assume that the change in pressure of $\mathrm{H}_{2} \mathrm{S}$ is small enough to be neglected in the following problem.
(a) Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of $\mathrm{H}_{2} \mathrm{S}$ with an initial pressure of 0.824 $\mathrm{atm} .$
$2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \qquad K_{P}=2.2 \times 10^{-6}$
(b) Show that the change is small enough to be neglected.

MH
Matthew H.
Numerade Educator

Problem 78

What are all concentrations after a mixture that contains $\left[\mathrm{H}_{2} \mathrm{O}\right]=1.00 \mathrm{M}$ and $\left[\mathrm{Cl}_{2} \mathrm{O}\right]=1.00 \mathrm{M}$ comes to equilibrium at $25^{\circ} \mathrm{C}$ ?
$\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g) \quad K_{c}=0.0900$

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Problem 79

What are the concentrations of $\mathrm{PCl}_{5}, \mathrm{PCl}_{3},$ and $\mathrm{Cl}_{2}$ and $\mathrm{Cl}_{2}$ in an equilibrium mixture produced by the decomposition of a sample of pure $\mathrm{PC}_{5}$ with $\mathrm{PCl}_{5}=2.00 \mathrm{M}$ ?
$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \qquad K_{c}=0.0211$

MH
Matthew H.
Numerade Educator

Problem 80

Calculate the pressures of all species at equilibrium in a mixture of NOCl, NO, and Cl_oduced when a
sample of NOCl with a pressure of 10.0 atm comes to equilibrium according to this reaction:
$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \qquad K_{P}=4.0 \times 10^{-4}$

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Problem 81

Calculate the equilibrium concentrations of NO, $\mathrm{O}_{2},$ and $\mathrm{NO}_{2}$ in a mixture at $250^{\circ} \mathrm{C}$ that results from the reaction of 0.20 $\mathrm{M} \mathrm{NO}$ and 0.10 $\mathrm{M} \mathrm{O}_{2}$ . (Hint: $K$ is large; assume the reaction goes to completion then comes back to equilibrium.)
$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad K_{c}=2.3 \times 10^{5} \mathrm{at} 250^{\circ} \mathrm{C}$

MH
Matthew H.
Numerade Educator

Problem 82

Calculate the equilibrium concentrations that result when 0.25 $\mathrm{M} \mathrm{O}_{2}$ and 1.0 $\mathrm{M}$ HCl react and come to equilibrium.
$4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \quad K_{c}=3.1 \times 10^{13}$

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Problem 83

One of the important reactions in the formation of smog is represented by the equation
$\mathrm{O}_{3}(g)+\mathrm{NO}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \qquad K_{P}=6.0 \times 10^{34}$
What is the pressure of $\mathrm{O}_{3}$ remaining after a mixture of $\mathrm{O}_{3}$ with a pressure of $1.2 \times 10^{-8} \mathrm{atm}$ and NO with a pressure of $1.2 \times 10^{-8} \mathrm{atm}$ comes to equilibrium? (Hint: $K_{P}$ is large; assume the reaction goes to completion then comes back to equilibrium.)

MH
Matthew H.
Numerade Educator

Problem 84

Calculate the pressures of NO, $\mathrm{Cl}_{2},$ and $\mathrm{NOCl}$ in an equilibrium mixtured by the reaction of a starting mixture with 4.0 $\mathrm{atm} \mathrm{NO}$ and 2.0 $\mathrm{atm} \mathrm{Cl}_{2}$ . (Hint: $K_{P}$ is small; assume the reverse reaction goes to completion then
comes back to equilibrium.)$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g) \qquad K_{P}=2.5 \times 10^{3}$

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Problem 85

Calculate the number of grams of HI that are at equilibrium with 1.25 $\mathrm{mol}$ of $\mathrm{H}_{2}$ and 63.5 $\mathrm{g}$ of iodine at 448
$^{\circ} \mathrm{C} .$
$\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI} \quad K_{c}=50.2 \mathrm{at} 448^{\circ} \mathrm{C}$

MH
Matthew H.
Numerade Educator

Problem 86

Butane exists as two isomers, $n$ -butane and isobutane.
$K_{P}=2.5$ at $25^{\circ} \mathrm{C}$
What is the pressure of isobutane in a container of the two isomers at equilibrium with a total pressure of 1.22 atm?

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Problem 87

What is the minimum mass of CaCO_ required to establish equilibrium at a certain temperature in a $6.50-\mathrm{L}$ . container if the equilibrium constant $\left(K_{c}\right)$ is 0.050 for the decomposition reaction of $\mathrm{CaCO}_{3}$ at that temperature?
$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$

MH
Matthew H.
Numerade Educator

Problem 88

The equilibrium constant $\left(K_{c}\right)$ for this reaction is 1.60 at $990^{\circ} \mathrm{C} :$
$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$
Calculate the number of moles of each component in the final equilibrium mixture obtained from adding 1.00 mol of $\mathrm{H}_{2}, 2.00 \mathrm{mol}$ of $\mathrm{CO}_{2}, 0.750 \mathrm{mol}$ of $\mathrm{H}_{2} \mathrm{O},$ and 1.00 $\mathrm{mol}$ of $\mathrm{CO}$ to a $5.00-\mathrm{L}$ container at $990^{\circ} \mathrm{C}$

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Problem 89

At $25^{\circ} \mathrm{C}$ and at 1 atm, the partial pressures in an equilibrium mixture of $\mathrm{N}_{2} \mathrm{O}_{4}$ and $\mathrm{NO}_{2}$ are $\mathrm{P}_{\mathrm{N}_{2} \mathrm{O}_{4}}=0.70 \mathrm{atm}$ and $\mathrm{P}_{\mathrm{NO}_{2}}=0.30 \mathrm{atm} .$
(a) Predict how the pressures of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ will change if the total pressure increases to 9.0 $\mathrm{atm}$ . Will they
increase, decrease, or remain the same?
(b) Calculate the partial pressures of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ when they are at equilibrium at 9.0 $\mathrm{atm}$ and $25^{\circ} \mathrm{C}$

MH
Matthew H.
Numerade Educator

Problem 90

In a 3.0 -L vessel, the following equilibrium partial pressures are measured: $\mathrm{N}_{2}, 190$ tor; $\mathrm{H}_{2}, 317$ torr; $\mathrm{NH}_{3}$ . $1.00 \times 10^{3}$ torr.
$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$
(a) How will the partial pressures of $\mathrm{H}_{2}, \mathrm{N}_{2}$ , and $\mathrm{NH}_{3}$ change if $\mathrm{H}_{2}$ is removed from the system? Will they increase,
decrease, or remain the same?
(b) Hydrogen is removed from the vessel until the partial pressure of nitrogen, at equilibrium, is 250 torr. Calculate the partial pressures of the other substances under the new conditions.

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Problem 91

The equilibrium constant (K_) for this reaction is 5.0 at a given temperature.
$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$
(a) On analysis, an equilibrium mixture of the substances present at the given temperature was found to contain 0.20 mol of $\mathrm{CO}, 0.30 \mathrm{mol}$ of water vapor, and 0.90 $\mathrm{mol}$ of $\mathrm{H}_{2}$ in a liter. How many moles of $\mathrm{CO}_{2}$ were there in the equilibrium mixture?
(b) Maintaining the same temperature, additional $\mathrm{H}_{2}$ was added to the system, and some water vapor was removed
by drying. A new equilibrium mixture was thereby established containing 0.40 $\mathrm{mol}$ of $\mathrm{CO}, 0.30 \mathrm{mol}$ water vapor, and 1.2 $\mathrm{mol}$ of $\mathrm{H}_{2}$ in a liter. How many moles of $\mathrm{CO}_{2}$ were in the new equilibrium mixture? Compare this with the quantity in part (a), and discuss whether the second value is reasonable. Explain how it is possible for the water vapor concentration to be the same in the two equilibrium solutions even though some vapor was removed before the second equilibrium was established.

MH
Matthew H.
Numerade Educator

Problem 92

Antimony pentachloride decomposes according to this equation:
$\mathrm{SbCl}_{5}(g) \rightleftharpoons \mathrm{SbCl}_{3}(g)+\mathrm{Cl}_{2}(g)$
An equilibrium mixture in a 5.00-L flask at $448^{\circ} \mathrm{C}$ contains 3.85 $\mathrm{g}$ of $\mathrm{SbCl}_{5}, 9.14 \mathrm{g}$ of $\mathrm{SbCl}_{3},$ and 2.84 $\mathrm{g}$ of $\mathrm{Cl}_{2}$. How many grams of each will be found if the mixture is transferred into a $2.00-\mathrm{L}$ flask at the same temperature?

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Problem 93

Consider the reaction between $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ at 1000 $\mathrm{K}$
$$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)$$
$$K_{P}=\frac{\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}{\left(P_{\mathrm{O}_{2}}\right)\left(P_{\mathrm{H}_{2}}\right)^{2}}=1.33 \times 10^{20}$$
If 0.500 atm of $\mathrm{H}_{2}$ and 0.500 atm of $\mathrm{O}_{2}$ are allowed to come to come to equilibrium at this temperature, what are the partial pressures of the components?

MH
Matthew H.
Numerade Educator

Problem 94

An equilibrium is established according to the following equation
$\mathrm{Hg}_{2}^{2+}(a q)+\mathrm{NO}_{3}^{-}(a q)+3 \mathrm{H}^{+}(a q) \rightleftharpoons 2 \mathrm{Hg}^{2+}(a q)+\mathrm{HNO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \quad K_{c}=4.6$
What will happen in a solution that is 0.20$M$ each in $\mathrm{Hg}_{2}^{2+}, \quad \mathrm{NO}_{3}^{-}, \quad \mathrm{H}^{+}, \mathrm{Hg}^{2+},$ and $\mathrm{HNO}_{2} ?$
(a) $\mathrm{Hg}_{2}^{2+}$ will be oxidized and $\mathrm{NO}_{3}^{-}$ reduced.
(b) $\mathrm{Hg}_{2}^{2+}$ will be reduced and $\mathrm{NO}_{3}$ - oxidized.
(c) $\mathrm{Hg}^{2+}$ will be oxidized and $\mathrm{HNO}_{2}$ reduced.
(d) $\mathrm{Hg}^{2+}$ will be reduced and $\mathrm{HNO}_{2}$ oxidized.
(e) There will be no change because all reactants and products have an activity of $1 .$

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Problem 95

Consider the equilibrium
$4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g)$
(a) What is the expression for the equilibrium constant $\left(K_{c}\right)$ of the reaction?
(b) How must the concentration of $\mathrm{NH}_{3}$ change to reach equilibrium if the reaction quotient is less than the equilibrium constant?
(c) If the reaction were at equilibrium, how would a decrease in pressure from an increase in the volume of the reaction vessel) affect the pressure of $\mathrm{NO}_{2} ?$
(d) If the change in the pressure of $\mathrm{NO}_{2}$ is 28 torr as a mixture of the four gases equilibrium, how much will the pressure of $\mathrm{O}_{2}$ change?

MH
Matthew H.
Numerade Educator

Problem 96

The binding of oxygen by hemoglobin (Hb), giving oxyhemoglobin $\left(\mathrm{HbO}_{2}\right),$ is partially regulated by the concentration of $\mathrm{H}_{3} \mathrm{O}^{+}$ and dissolved $\mathrm{CO}_{2}$ in the blood. Although the equilibrium is complicated, it can be summarized as
$\mathrm{HbO}_{2}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}-\mathrm{Hb}-\mathrm{H}^{+}+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$
(a) Write the equilibrium constant expression for this reaction.
(b) Explain why the production of lactic acid and $\mathrm{CO}_{2}$ in a muscle during exertion stimulates release of $\mathrm{O}_{2}$ from the oxyhemoglobin in the blood passing through the muscle.

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Problem 97

The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose.
$\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)$
Rate $=k\left[\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right]$
In neurral solution, $k=2.1 \times 10^{-11} / \mathrm{s}$ at $27^{\circ} \mathrm{C}$ . (As indicated by the rate constant, this is a very slow reaction. In the human body, the rate of this reaction is sped up by a type of catalyst called an enzyme.) (Note: That is not a mistake in the equation - the products of the reaction, glucose and fructose, have the same molecular formulas, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},$ but differ in the arrangement of the atoms in their molecules). The equilibrium constant for the reaction is $1.36 \times 10^{5}$ at $27^{\circ} \mathrm{C}$ . What are the concentrations of glucose, fructose, and sucrose after a 0.150 $\mathrm{M}$ aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.

MH
Matthew H.
Numerade Educator

Problem 98

The density of trifluoroacetic acid vapor was determined at $118.1^{\circ} \mathrm{C}$ and 468.5 torr, and found to be 2.784 $\mathrm{g} / \mathrm{L}$ . Calculate $K_{c}$ for the association of the acid.

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Problem 99

Liquid $\mathrm{N}_{2} \mathrm{O}_{3}$ is dark blue at low temperatures, but the color fades and becomes greenish at higher temperatures as the compound decomposes to NO and $\mathrm{NO}_{2}$ . At $25^{\circ} \mathrm{C}$ , a value of $K_{P}=1.91$ has been established for this decomposition. If 0.236 moles of $\mathrm{N}_{2} \mathrm{O}_{3}$ are placed in a $1.52-\mathrm{L}$ vessel at $25^{\circ} \mathrm{C},$ calculate the equilibrium partial pressures of $\mathrm{N}_{2} \mathrm{O}_{3}(g), \mathrm{NO}_{2}(g),$ and $\mathrm{NO}(g)$

MH
Matthew H.
Numerade Educator

Problem 100

A $1.00-\mathrm{L}$ vessel at $400^{\circ} \mathrm{C}$ contains the following equilibrium concentrations: $\mathrm{N}_{2}, 1.00 \mathrm{M} ; \mathrm{H}_{2}, 0.50 \mathrm{M} ;$ and $\mathrm{NH}_{3}, 0.25 \mathrm{M}$ . How many moles of hydrogen must be removed from the vessel to increase the concentration of nitrogen to 1.1 $\mathrm{M}$ ?

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Problem 101

A 0.010 M solution of the weak acid HA has an osmotic pressure (see chapter on solutions and colloids) of 0.293 atm at $25^{\circ} \mathrm{C} .$ A 0.010 M solution of the weak acid HB has an osmotic pressure of 0.345 atm under the same conditions.
(a) Which acid has the larger equilibrium constant for ionization
HA $\left[\mathrm{HA}(a q) \rightleftharpoons \mathrm{A}^{-}(a q)+\mathrm{H}^{+}(a q)\right]$ or HB $\left[\mathrm{HB}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{B}^{-}(a q)\right]$ ?
(b) What are the equilibrium constants for the ionization of these acids?
(Hint: Remember that each solution contains three dissolved species: the weak acid (HA or HB), the conjugate base $\left(\mathrm{A}^{-} \text { or } \mathrm{B}^{-}\right)$and the hydrogen ion $\left(\mathrm{H}^{+}\right) .$ Remember that osmotic pressure (like all colligative properties) is related to the total number of solute particles. Specifically for osmotic pressure, those concentrations are described by molarities.)

MH
Matthew H.
Numerade Educator