### 13.1 Chemical Equilibria

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

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

### 13.2 Equilibrium Constants

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.

Explain why an equilibrium between Br_{2}(*l*) and Br_{2}(*g*) would not be established if the container were not a closed vessel shown in Figure 13.4.

If you observe the following reaction at equilibrium, is it possible to tell whether the reaction started with pure NO_{2} or with pure N_{2}O_{4}?

$2{\text{NO}}_{2}(g)\rightleftharpoons {\text{N}}_{2}{\text{O}}_{4}(g)$

Among the solubility rules previously discussed is the statement: All chlorides are soluble except Hg_{2}Cl_{2}, AgCl, PbCl_{2}, and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation $\text{AgCl}(s)\rightleftharpoons {\text{Ag}}^{\text{+}}(aq)+{\text{Cl}}^{\text{\u2212}}(aq).$ Is *K _{c}* > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation ${\text{Pb}}^{\mathrm{2+}}(aq)+2{\text{Cl}}^{\text{\u2212}}(aq)\rightleftharpoons {\text{PbCl}}_{2}(s).$ Is *K _{c}* > 1, < 1, or ≈ 1? Explain your answer.

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 ${\text{CaCO}}_{3}(s)\rightleftharpoons {\text{Ca}}^{\mathrm{2+}}(aq)+{\text{CO}}_{3}{}^{\mathrm{2-}}(\text{aq}).$ Is *K _{c}* > 1, < 1, or ≈ 1? Explain your answer.

(b) Write the expression for the equilibrium constant for the reaction represented by the equation $3{\text{Ba}}^{\mathrm{2+}}(aq)+2{\text{PO}}_{4}{}^{\mathrm{3-}}(aq)\rightleftharpoons {\text{Ba}}_{3}{\left({\text{PO}}_{4}\right)}_{2}(s).$ Is *K _{c}* > 1, < 1, or ≈ 1? Explain your answer.

Benzene is one of the compounds used as octane enhancers in unleaded gasoline. It is manufactured by the catalytic conversion of acetylene to benzene: $3{\text{C}}_{2}{\text{H}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}{\text{C}}_{6}{\text{H}}_{6}(g).$ Which value of *K _{c}* would make this reaction most useful commercially?

*K*≈ 0.01,

_{c}*K*≈ 1, or

_{c}*K*≈ 10. Explain your answer.

_{c}Show that the complete chemical equation, the total ionic equation, and the net ionic equation for the reaction represented by the equation $\text{KI}(aq)+{\text{I}}_{2}(aq)\rightleftharpoons {\text{KI}}_{3}(aq)$ give the same expression for the reaction quotient. KI_{3} is composed of the ions K^{+} and ${\text{I}}_{3}{}^{\text{\u2212}}.$

For a titration to be effective, the reaction must be rapid and the yield of the reaction must essentially be 100%. Is *K _{c}* > 1, < 1, or ≈ 1 for a titration reaction?

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 ≈ 1 for a useful precipitation reaction?

Write the mathematical expression for the reaction quotient, *Q _{c}*, for each of the following reactions:

(a) ${\text{CH}}_{4}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons {\text{CH}}_{3}\text{Cl}(g)+\text{HCl}(g)$

(b) ${\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)$

(c) $2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{SO}}_{3}(g)$

(d) ${\text{BaSO}}_{3}(s)\rightleftharpoons \text{BaO}(s)+{\text{SO}}_{2}(g)$

(e) ${\text{P}}_{4}(g)+5{\text{O}}_{2}(g)\rightleftharpoons {\text{P}}_{4}{\text{O}}_{10}(s)$

(f) ${\text{Br}}_{2}(g)\rightleftharpoons 2\text{Br}(g)$

(g) ${\text{CH}}_{4}(g)+2{\text{O}}_{2}(g)\rightleftharpoons {\text{CO}}_{2}(g)+2{\text{H}}_{2}\text{O}(l)$

(h) ${\text{CuSO}}_{4}\text{\xb7}5{\text{H}}_{2}\text{O}(s)\rightleftharpoons {\text{CuSO}}_{4}(s)+5{\text{H}}_{2}\text{O}(g)$

Write the mathematical expression for the reaction quotient, *Q _{c}*, for each of the following reactions:

(a) ${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)$

(b) $4{\text{NH}}_{3}(g)+5{\text{O}}_{2}(g)\rightleftharpoons 4\text{NO}(g)+6{\text{H}}_{2}\text{O}(g)$

(c) ${\text{N}}_{2}{\text{O}}_{4}(g)\rightleftharpoons 2{\text{NO}}_{2}(g)$

(d) ${\text{CO}}_{2}(g)+{\text{H}}_{2}(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_{2}\text{O}(g)$

(e) ${\text{NH}}_{4}\text{Cl}(s)\rightleftharpoons {\text{NH}}_{3}(g)+\text{HCl}(g)$

(f) $2\text{Pb}{\left({\text{NO}}_{3}\right)}_{2}(s)\rightleftharpoons 2\text{PbO}(s)+4{\text{NO}}_{2}(g)+{\text{O}}_{2}(g)$

(g) $2{\text{H}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{H}}_{2}\text{O}(l)$

(h) ${\text{S}}_{8}(g)\rightleftharpoons 8\text{S}(g)$

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.

$\begin{array}{cccc}\text{(a)}\phantom{\rule{0.2em}{0ex}}2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\hfill & & & {K}_{c}=17;[{\text{NH}}_{3}]=0.20\phantom{\rule{0.2em}{0ex}}M,[{\text{N}}_{2}]=1.00\phantom{\rule{0.2em}{0ex}}M,[{\text{H}}_{2}]=1.00\phantom{\rule{0.2em}{0ex}}M\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\hfill & & & {K}_{P}=6.8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};{\text{NH}}_{3}=3.0\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{N}}_{2}=2.0\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{H}}_{2}=1.0\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{3}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}\left(g\right)\hfill & & & {K}_{c}=0.230;[{\text{SO}}_{3}]=0.00\phantom{\rule{0.2em}{0ex}}M,[{\text{SO}}_{2}]=1.00\phantom{\rule{0.2em}{0ex}}M,[{\text{O}}_{2}]=1.00\phantom{\rule{0.2em}{0ex}}M\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\hfill & & & {K}_{P}=16.5;{\text{SO}}_{3}=1.00\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{SO}}_{2}=1.00\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{O}}_{2}=1.00\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill \\ \text{(e)}\phantom{\rule{0.2em}{0ex}}2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)\hfill & & & {K}_{c}=4.6\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};[\text{NO}]=1.00\phantom{\rule{0.2em}{0ex}}M,[{\text{Cl}}_{2}]=1.00\phantom{\rule{0.2em}{0ex}}M,[\text{NOCl}]=0\phantom{\rule{0.2em}{0ex}}M\hfill \\ \text{(f)}\phantom{\rule{0.2em}{0ex}}{\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\hfill & & & {K}_{P}=0.050;\text{NO}=10.0\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{N}}_{2}={\text{O}}_{2}=\text{5 atm}\hfill \end{array}$

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.

$\begin{array}{cccc}\text{(a)}\phantom{\rule{0.2em}{0ex}}2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\hfill & & & {K}_{c}=17;[{\text{NH}}_{3}]=0.50\phantom{\rule{0.2em}{0ex}}M,[{\text{N}}_{2}]=0.15\phantom{\rule{0.2em}{0ex}}M,[{\text{H}}_{2}]=0.12\phantom{\rule{0.2em}{0ex}}M\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\hfill & & & {K}_{P}=6.8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};{\text{NH}}_{3}=2.00\phantom{\rule{0.2em}{0ex}}\text{atm},{\text{N}}_{2}=\text{10.00 atm},{\text{H}}_{2}=\text{10.00 atm}\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\hfill & & & {K}_{c}=0.230;[{\text{SO}}_{3}]=2.00\phantom{\rule{0.2em}{0ex}}M,[{\text{SO}}_{2}]=2.00\phantom{\rule{0.2em}{0ex}}M,[{\text{O}}_{2}]=2.00\phantom{\rule{0.2em}{0ex}}M\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\hfill & & & {K}_{P}=6.5\phantom{\rule{0.2em}{0ex}}\text{atm};{\text{SO}}_{2}=\text{1.00 atm},{\text{O}}_{2}=\text{1.130 atm},{\text{SO}}_{3}=\text{0 atm}\hfill \\ \text{(e)}\phantom{\rule{0.2em}{0ex}}2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)\hfill & & & {K}_{P}=2.5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3};\text{NO}=\text{1.00 atm},{\text{Cl}}_{2}=\text{1.00 atm},\text{NOCl}=\text{0 atm}\hfill \\ \text{(f)}\phantom{\rule{0.2em}{0ex}}{\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\hfill & & & {K}_{c}=0.050;[{\text{N}}_{2}]=0.100\phantom{\rule{0.2em}{0ex}}M,[{\text{O}}_{2}]=0.200\phantom{\rule{0.2em}{0ex}}M,[\text{NO}]=1.00\phantom{\rule{0.2em}{0ex}}M\hfill \end{array}$

The following reaction has *K _{P}* = 4.50 $\times $ 10

^{−5}at 720 K.

${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)$

If a reaction vessel is filled with each gas to the partial pressures listed, in which direction will it shift to reach equilibrium? *P*(NH_{3}) = 93 atm, *P*(N_{2}) = 48 atm, and *P*(H_{2}) = 52 atm

Determine if the following system is at equilibrium. If not, in which direction will the system need to shift to reach equilibrium?

${\text{SO}}_{2}{\text{Cl}}_{2}(g)\rightleftharpoons {\text{SO}}_{2}(g)+{\text{Cl}}_{2}(g)$

[SO_{2}Cl_{2}] = 0.12 *M*, [Cl_{2}] = 0.16 *M* and [SO_{2}] = 0.050 *M*. *K _{c}* for the reaction is 0.078.

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

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

For which of the reactions in Exercise 13.15 does *K _{c}* (calculated using concentrations) equal

*K*(calculated using pressures)?

_{P}For which of the reactions in Exercise 13.16 does *K _{c}* (calculated using concentrations) equal

*K*(calculated using pressures)?

_{P}Convert the values of *K _{c}* to values of

*K*or the values of

_{P}*K*to values of

_{P}*K*.

_{c}$\begin{array}{cccc}\text{(a)}\phantom{\rule{0.2em}{0ex}}{\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)\hfill & & & {K}_{c}=0.50\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}400\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}(g)+{\text{I}}_{2}(g)\rightleftharpoons 2\text{HI}(g)\hfill & & & {K}_{c}=50.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}448\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}{\text{Na}}_{2}{\text{SO}}_{4}\text{\xb7}10{\text{H}}_{2}\text{O}(s)\rightleftharpoons {\text{Na}}_{2}{\text{SO}}_{4}(s)+10{\text{H}}_{2}\text{O}(g)\hfill & & & {K}_{P}=4.08\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-25}}\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)\hfill & & & {K}_{P}=0.122\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}50\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \end{array}$

Convert the values of *K _{c}* to values of

*K*or the values of

_{P}*K*to values of

_{P}*K*.

_{c}$\begin{array}{cccc}\text{(a)}\phantom{\rule{0.2em}{0ex}}{\text{Cl}}_{2}(g)+{\text{Br}}_{2}(g)\rightleftharpoons 2\text{BrCl}(g)\hfill & & & {K}_{c}=4.7\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-2}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{SO}}_{3}(g)\hfill & & & {K}_{P}=48.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}500\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}{\text{CaCl}}_{2}\text{\xb7}6{\text{H}}_{2}\text{O}(s)\rightleftharpoons {\text{CaCl}}_{2}(s)+6{\text{H}}_{2}\text{O}(g)\hfill & & & {K}_{P}=5.09\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-44}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}{\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)\hfill & & & {K}_{P}=0.196\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}60\phantom{\rule{0.2em}{0ex}}\text{\xb0C}\hfill \end{array}$

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

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

What is the approximate value of the equilibrium constant *K _{P}* for the change ${\text{C}}_{2}{\text{H}}_{5}{\text{OC}}_{2}{\text{H}}_{5}(l)\rightleftharpoons {\text{C}}_{2}{\text{H}}_{5}{\text{OC}}_{2}{\text{H}}_{5}(g)$ at 25 °C. (The equilibrium vapor pressure for this substance is 570 torr at 25 °C.)

### 13.3 Shifting Equilibria: Le Châtelier’s Principle

The following equation represents a reversible decomposition:

${\text{CaCO}}_{3}(s)\rightleftharpoons \text{CaO}(s)+{\text{CO}}_{2}(g)$

Under what conditions will decomposition in a closed container proceed to completion so that no CaCO_{3} remains?

Explain how to recognize the conditions under which changes in volume will affect gas-phase systems at equilibrium.

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

The following reaction occurs when a burner on a gas stove is lit:

${\text{CH}}_{4}(g)+2{\text{O}}_{2}(g)\rightleftharpoons {\text{CO}}_{2}(g)+2{\text{H}}_{2}\text{O}(g)$

Is an equilibrium among CH_{4}, O_{2}, CO_{2}, and H_{2}O established under these conditions? Explain your answer.

A necessary step in the manufacture of sulfuric acid is the formation of sulfur trioxide, SO_{3}, from sulfur dioxide, SO_{2}, and oxygen, O_{2}, shown here. At high temperatures, the rate of formation of SO_{3} is higher, but the equilibrium amount (concentration or partial pressure) of SO_{3} is lower than it would be at lower temperatures.

$2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}2{\text{SO}}_{3}(g)$

(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?

Suggest four ways in which the concentration of hydrazine, N_{2}H_{4}, could be increased in an equilibrium described by the following equation:

${\text{N}}_{2}(g)+2{\text{H}}_{2}(g)\rightleftharpoons {\text{N}}_{2}{\text{H}}_{4}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=95\phantom{\rule{0.2em}{0ex}}\text{kJ}$

Suggest four ways in which the concentration of PH_{3} could be increased in an equilibrium described by the following equation:

${\text{P}}_{4}(g)+6{\text{H}}_{2}(g)\rightleftharpoons 4{\text{PH}}_{3}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=110.5\phantom{\rule{0.2em}{0ex}}\text{kJ}$

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) $2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=92\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(b) ${\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=181\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(c) $2{\text{O}}_{3}(g)\rightleftharpoons 3{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=\mathrm{-285}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(d) $\text{CaO}(s)+{\text{CO}}_{2}(g)\rightleftharpoons {\text{CaCO}}_{3}(s)\phantom{\rule{5em}{0ex}}\text{\Delta}H=\mathrm{-176}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

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) $2{\text{H}}_{2}\text{O}(g)\rightleftharpoons 2{\text{H}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=484\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(b) ${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=\mathrm{-92.2}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(c) $2\text{Br}(g)\rightleftharpoons {\text{Br}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=\mathrm{-224}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(d) ${\text{H}}_{2}(g)+{\text{I}}_{2}(s)\rightleftharpoons 2\text{HI}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=53\phantom{\rule{0.2em}{0ex}}\text{kJ}$

Methanol can be prepared from carbon monoxide and hydrogen at high temperature and pressure in the presence of a suitable catalyst.

(a) Write the expression for the equilibrium constant (*K _{c}*) for the reversible reaction

$2{\text{H}}_{2}(g)+\text{CO}(g)\rightleftharpoons {\text{CH}}_{3}\text{OH}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=\mathrm{-90.2}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(b) What will happen to the concentrations of H_{2}, CO, and CH_{3}OH at equilibrium if more H_{2} is added?

(c) What will happen to the concentrations of H_{2}, CO, and CH_{3}OH at equilibrium if CO is removed?

(d) What will happen to the concentrations of H_{2}, CO, and CH_{3}OH at equilibrium if CH_{3}OH is added?

(e) What will happen to the concentrations of H_{2}, CO, and CH_{3}OH at equilibrium if the temperature of the system is increased?

Nitrogen and oxygen react at high temperatures.

(a) Write the expression for the equilibrium constant (*K _{c}*) for the reversible reaction

${\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=181\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(b) What will happen to the concentrations of N_{2}, O_{2}, and NO at equilibrium if more O_{2} is added?

(c) What will happen to the concentrations of N_{2}, O_{2}, and NO at equilibrium if N_{2} is removed?

(d) What will happen to the concentrations of N_{2}, O_{2}, and NO at equilibrium if NO is added?

(e) What will happen to the concentrations of N_{2}, O_{2}, and NO at equilibrium if the volume of the reaction vessel is decreased?

(f) What will happen to the concentrations of N_{2}, O_{2}, and NO at equilibrium if the temperature of the system is increased?

Water gas, a mixture of H_{2} and CO, 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

$\text{C}(s)+{\text{H}}_{2}\text{O}(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=131.30\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(b) What will happen to the concentration of each reactant and product at equilibrium if more C is added?

(c) What will happen to the concentration of each reactant and product at equilibrium if H_{2}O is removed?

(d) What will happen to the concentration of each reactant and product at equilibrium if 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?

Pure iron metal can be produced by the reduction of iron(III) oxide with hydrogen gas.

(a) Write the expression for the equilibrium constant (*K _{c}*) for the reversible reaction

${\text{Fe}}_{2}{\text{O}}_{3}(s)+3{\text{H}}_{2}(g)\rightleftharpoons 2\text{Fe}(s)+3{\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=98.7\phantom{\rule{0.2em}{0ex}}\text{kJ}$

(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 H_{2}O is removed?

(d) What will happen to the concentration of each reactant and product at equilibrium if H_{2} is added?

(e) What will happen to the concentration of each reactant and product at equilibrium if the volume of the reaction vessel is decreased?

(f) What will happen to the concentration of each reactant and product at equilibrium if the temperature of the system is increased?

Ammonia is a weak base that reacts with water according to this equation:

${\text{NH}}_{3}(aq)+{\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{NH}}_{4}{}^{\text{+}}(aq)+{\text{OH}}^{\text{\u2212}}(aq)$

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 NH_{4}Cl

Acetic acid is a weak acid that reacts with water according to this equation:

${\text{CH}}_{3}{\text{CO}}_{2}\text{H}(aq)+{\text{H}}_{2}\text{O}(aq)\rightleftharpoons {\text{H}}_{3}{\text{O}}^{\text{+}}(aq)+{\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{\u2212}}(aq)$

Will any of the following increase the percent of acetic acid that reacts and produces ${\text{CH}}_{3}{\text{CO}}_{2}{}^{\text{\u2212}}$ ion?

(a) Addition of HCl

(b) Addition of NaOH

(c) Addition of NaCH_{3}CO_{2}

Suggest two ways in which the equilibrium concentration of Ag^{+} can be reduced in a solution of Na^{+}, Cl^{−}, Ag^{+}, and ${\text{NO}}_{3}{}^{\text{\u2212}},$ in contact with solid AgCl.

${\text{Na}}^{\text{+}}(aq)+{\text{Cl}}^{\text{\u2212}}(aq)+{\text{Ag}}^{\text{+}}(aq)+{\text{NO}}_{3}{}^{\text{\u2212}}(aq)\rightleftharpoons \text{AgCl}(s)+{\text{Na}}^{\text{+}}(aq)+{\text{NO}}_{3}{}^{\text{\u2212}}(aq)$

$\text{\Delta}H=\mathrm{-65.9}\phantom{\rule{0.2em}{0ex}}\text{kJ}$

How can the pressure of water vapor be increased in the following equilibrium?

${\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}H=41\phantom{\rule{0.2em}{0ex}}\text{kJ}$

A solution is saturated with silver sulfate and contains excess solid silver sulfate:

${\text{Ag}}_{2}{\text{SO}}_{4}(s)\rightleftharpoons 2{\text{Ag}}^{\text{+}}(aq)+{\text{SO}}_{4}{}^{\mathrm{2-}}(aq)$

A small amount of solid silver sulfate containing a radioactive isotope of silver is added to this solution. Within a few minutes, a portion of the solution phase is sampled and tests positive for radioactive Ag^{+} ions. Explain this observation.

When equal molar amounts of HCl and HOCl are dissolved separately in equal amounts of water, the solution of HCl freezes at a lower temperature. Which compound has the larger equilibrium constant for acid ionization?

(a) HCl

(b) H
^{+}
+ Cl
^{–}

(c) HOCl

(d) H
^{+}
+ OCl
^{–}

### 13.4 Equilibrium Calculations

A reaction is represented by this equation: $\text{A}(aq)+2\text{B}(aq)\rightleftharpoons 2\text{C}(aq)\phantom{\rule{5em}{0ex}}{K}_{c}=1\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations ≤1 *M*, identify two sets of concentrations that describe a mixture of A, B, and C at equilibrium.

A reaction is represented by this equation: $2\text{W}(aq)\rightleftharpoons \text{X}(aq)+2\text{Y}(aq)\phantom{\rule{5em}{0ex}}{K}_{c}=5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-4}}$

(a) Write the mathematical expression for the equilibrium constant.

(b) Using concentrations of ≤1 *M*, identify two sets of concentrations that describe a mixture of W, X, and Y at equilibrium.

What is the value of the equilibrium constant at 500 °C for the formation of NH_{3} according to the following equation?

${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)$

An equilibrium mixture of NH_{3}(*g*), H_{2}(*g*), and N_{2}(*g*) at 500 °C was found to contain 1.35 *M* H_{2}, 1.15 *M* N_{2}, and 4.12 $\times $ 10^{−1} *M* NH_{3}.

Hydrogen is prepared commercially by the reaction of methane and water vapor at elevated temperatures.

${\text{CH}}_{4}(g)+{\text{H}}_{2}\text{O}(g)\rightleftharpoons 3{\text{H}}_{2}(g)+\text{CO}(g)$

What is the equilibrium constant for the reaction if a mixture at equilibrium contains gases with the following concentrations: CH_{4}, 0.126 *M*; H_{2}O, 0.242 *M*; CO, 0.126 *M*; H_{2} 1.15 *M*, at a temperature of 760 °C?

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

At 1 atm and 25 °C, NO_{2} with an initial concentration of 1.00 *M* is 0.0033% decomposed into NO and O_{2}. Calculate the value of the equilibrium constant for the reaction.

$2{\text{NO}}_{2}(g)\rightleftharpoons 2\text{NO}(g)+{\text{O}}_{2}(g)$

Calculate the value of the equilibrium constant *K _{P}* for the reaction $2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)$ from these equilibrium pressures: NO, 0.050 atm; Cl

_{2}, 0.30 atm; NOCl, 1.2 atm.

When heated, iodine vapor dissociates according to this equation:

${\text{I}}_{2}(g)\rightleftharpoons 2\text{I}(g)$

At 1274 K, a sample exhibits a partial pressure of 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 K.

A sample of ammonium chloride was heated in a closed container.

${\text{NH}}_{4}\text{Cl}(s)\rightleftharpoons {\text{NH}}_{3}(g)+\text{HCl}(g)$

At equilibrium, the pressure of NH_{3}(*g*) was found to be 1.75 atm. What is the value of the equilibrium constant *K _{P}* for the decomposition at this temperature?

At a temperature of 60 °C, the vapor pressure of water is 0.196 atm. What is the value of the equilibrium constant *K _{P}* for the vaporization equilibrium at 60 °C?

${\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)$

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

$\begin{array}{llll}2{\text{SO}}_{3}(g)\hfill & \rightleftharpoons \hfill & 2{\text{SO}}_{2}(g)+\hfill & {\text{O}}_{2}(g)\hfill \\ \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & +x\hfill \\ \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & 0.125\phantom{\rule{0.2em}{0ex}}M\hfill \end{array}$

(b)

$\begin{array}{lllll}4{\text{NH}}_{3}(g)\hfill & +\phantom{\rule{0.2em}{0ex}}3{\text{O}}_{2}(g)\hfill & \rightleftharpoons \hfill & 2{\text{N}}_{2}(g)+\hfill & 6{\text{H}}_{2}\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & 3x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & 0.24\phantom{\rule{0.2em}{0ex}}M\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(c) Change in pressure:

$\begin{array}{llll}2{\text{CH}}_{4}(g)\hfill & \rightleftharpoons \hfill & {\text{C}}_{2}{\text{H}}_{2}(g)+\hfill & 3{\text{H}}_{2}(g)\hfill \\ \text{\_\_\_}\hfill & & x\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & & 25\phantom{\rule{0.2em}{0ex}}\text{torr}\hfill & \text{\_\_\_}\hfill \end{array}$

(d) Change in pressure:

$\begin{array}{lllll}{\text{CH}}_{4}(g)+\hfill & {\text{H}}_{2}\text{O}(g)\hfill & \rightleftharpoons \hfill & \text{CO}(g)+\hfill & 3{\text{H}}_{2}(g)\hfill \\ \text{\_\_\_}\hfill & x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ \text{\_\_\_}\hfill & 5\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(e)

$\begin{array}{llll}{\text{NH}}_{4}\text{Cl}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_{3}(g)+\hfill & \text{HCl}(g)\hfill \\ & & x\hfill & \text{\_\_\_}\hfill \\ & & \hfill 1.03\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-4}}\phantom{\rule{0.2em}{0ex}}M\hfill & \text{\_\_\_}\hfill \end{array}$

(f) change in pressure:

$\begin{array}{cccc}\text{Ni}(s)+\hfill & 4\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Ni}{(\text{CO})}_{4}(g)\hfill \\ & 4x\hfill & & \text{\_\_\_}\hfill \\ & \hfill 0.40\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & & \text{\_\_\_}\hfill \end{array}$

Complete the changes in concentrations (or pressure, if requested) for each of the following reactions.

(a)

$\begin{array}{cccc}2{\text{H}}_{2}(g)+\hfill & {\text{O}}_{2}(g)\hfill & \rightleftharpoons \hfill & 2{\text{H}}_{2}\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & +2x\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & 1.50\phantom{\rule{0.2em}{0ex}}M\hfill \end{array}$

(b)

$\begin{array}{ccccc}{\text{CS}}_{2}(g)+\hfill & 4{\text{H}}_{2}(g)\hfill & \rightleftharpoons \hfill & {\text{CH}}_{4}(g)+\hfill & 2{\text{H}}_{2}\text{S}(g)\hfill \\ x\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \\ 0.020\phantom{\rule{0.2em}{0ex}}M\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(c) Change in pressure:

$\begin{array}{cccc}{\text{H}}_{2}(g)+\hfill & {\text{Cl}}_{2}(g)\hfill & \rightleftharpoons \hfill & 2\text{HCl}(g)\hfill \\ x\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill \\ 1.50\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill \end{array}$

(d) Change in pressure:

$\begin{array}{ccccc}2{\text{NH}}_{3}(g)\hfill & +\phantom{\rule{0.2em}{0ex}}2{\text{O}}_{2}(g)\hfill & \rightleftharpoons \hfill & {\text{N}}_{2}\text{O}(g)+\hfill & 3{\text{H}}_{2}\text{O}(g)\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & x\hfill \\ \text{\_\_\_}\hfill & \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & 60.6\phantom{\rule{0.2em}{0ex}}\text{torr}\hfill \end{array}$

(e)

$\begin{array}{cccc}{\text{NH}}_{4}\text{HS}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_{3}(g)+\hfill & {\text{H}}_{2}\text{S}(g)\hfill \\ & & x\hfill & \text{\_\_\_}\hfill \\ & & 9.8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-6}}\phantom{\rule{0.2em}{0ex}}M\hfill & \text{\_\_\_}\hfill \end{array}$

(f) Change in pressure:

$\begin{array}{cccc}\text{Fe}(s)+\hfill & 5\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Fe}{(\text{CO})}_{5}(g)\hfill \\ & \text{\_\_\_}\hfill & & x\hfill \\ & \text{\_\_\_}\hfill & & 0.012\phantom{\rule{0.2em}{0ex}}\text{atm}\hfill \end{array}$

Why are there no changes specified for Ni in Exercise 13.60, part (f)? What property of Ni does change?

Why are there no changes specified for NH_{4}HS in Exercise 13.61, part (e)? What property of NH_{4}HS does change?

Analysis of the gases in a sealed reaction vessel containing NH_{3}, N_{2}, and H_{2} at equilibrium at 400 °C established the concentration of N_{2} to be 1.2 *M* and the concentration of H_{2} to be 0.24 *M*.

${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.50\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}400\phantom{\rule{0.2em}{0ex}}\text{\xb0}\text{C}$

Calculate the equilibrium molar concentration of NH_{3}.

Calculate the number of moles of HI that are at equilibrium with 1.25 mol of H_{2} and 1.25 mol of I_{2} in a 5.00−L flask at 448 °C.

${\text{H}}_{2}+{\text{I}}_{2}\rightleftharpoons 2\text{HI}\phantom{\rule{5em}{0ex}}{K}_{c}=50.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}448\phantom{\rule{0.2em}{0ex}}\text{\xb0}\text{C}$

What is the pressure of BrCl in an equilibrium mixture of Cl_{2}, Br_{2}, and BrCl if the pressure of Cl_{2} in the mixture is 0.115 atm and the pressure of Br_{2} in the mixture is 0.450 atm?

${\text{Cl}}_{2}(g)+{\text{Br}}_{2}(g)\rightleftharpoons 2\text{BrCl}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=4.7\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-2}}$

What is the pressure of CO_{2} in a mixture at equilibrium that contains 0.50 atm H_{2}, 2.0 atm of H_{2}O, and 1.0 atm of CO at 990 °C?

${\text{H}}_{2}(g)+{\text{CO}}_{2}(g)\rightleftharpoons {\text{H}}_{2}\text{O}(g)+\text{CO}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=1.6\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}990\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

Cobalt metal can be prepared by reducing cobalt(II) oxide with carbon monoxide.

$\text{CoO}(s)+\text{CO}(g)\rightleftharpoons \text{Co}(s)+{\text{CO}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=4.90\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{2}\text{at}\phantom{\rule{0.2em}{0ex}}550\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

What concentration of CO remains in an equilibrium mixture with [CO_{2}] = 0.100 *M*?

Carbon reacts with water vapor at elevated temperatures.

$\text{C}(s)+{\text{H}}_{2}\text{O}(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}1000\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

Assuming a reaction mixture initially contains only reactants, what is the concentration of CO in an equilibrium mixture with [H_{2}O] = 0.500 *M* at 1000 °C?

Sodium sulfate 10−hydrate, Na_{2}SO_{4}·10H_{2}O, dehydrates according to the equation

${\text{Na}}_{2}{\text{SO}}_{4}\text{\xb7}10{\text{H}}_{2}\text{O}(s)\rightleftharpoons {\text{Na}}_{2}{\text{SO}}_{4}(s)+10{\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=4.08\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-25}}\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

What is the pressure of water vapor at equilibrium with a mixture of Na_{2}SO_{4}·10H_{2}O and NaSO_{4}?

Calcium chloride 6−hydrate, CaCl_{2}·6H_{2}O, dehydrates according to the equation

${\text{CaCl}}_{\text{2}}\text{\xb7}6{\text{H}}_{2}\text{O}(s)\rightleftharpoons {\text{CaCl}}_{2}(s)+6{\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=5.09\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-44}}\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

What is the pressure of water vapor at equilibrium with a mixture of CaCl_{2}·6H_{2}O and CaCl_{2} at 25 °C?

A student solved the following problem and found the equilibrium concentrations to be [SO_{2}] = 0.590 *M*, [O_{2}] = 0.0450 *M*, and [SO_{3}] = 0.260 *M*. How could this student check the work without reworking the problem? The problem was: For the following reaction at 600 °C:

$2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{SO}}_{3}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=4.32$

What are the equilibrium concentrations of all species in a mixture that was prepared with [SO_{3}] = 0.500 *M*, [SO_{2}] = 0 *M*, and [O_{2}] = 0.350 *M*?

A student solved the following problem and found [N_{2}O_{4}] = 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 N_{2}O_{4} in a mixture formed from a sample of NO_{2} with a concentration of 0.10 *M*?

$2{\text{NO}}_{2}(g)\rightleftharpoons {\text{N}}_{2}{\text{O}}_{4}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=160$

Assume that the change in concentration of N_{2}O_{4} is small enough to be neglected in the following problem.

(a) Calculate the equilibrium concentration of both species in 1.00 L of a solution prepared from 0.129 mol of N_{2}O_{4} with chloroform as the solvent.

${\text{N}}_{2}{\text{O}}_{4}(g)\rightleftharpoons 2{\text{NO}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=1.07\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-5}}$ in chloroform

(b) Confirm that the change is small enough to be neglected.

Assume that the change in concentration of 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 COCl_{2} with an initial concentration of 0.3166 *M*.

${\text{COCl}}_{2}(g)\rightleftharpoons \text{CO}(g)+{\text{Cl}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=2.2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-10}}$

(b) Confirm that the change is small enough to be neglected.

Assume that the change in pressure of H_{2}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 H_{2}S with an initial pressure of 0.824 atm.

$2{\text{H}}_{2}\text{S}(g)\rightleftharpoons 2{\text{H}}_{2}(g)+{\text{S}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=2.2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-6}}$

(b) Confirm that the change is small enough to be neglected.

What are all concentrations after a mixture that contains [H_{2}O] = 1.00 *M* and [Cl_{2}O] = 1.00 *M* comes to equilibrium at 25 °C?

${\text{H}}_{2}\text{O}(g)+{\text{Cl}}_{2}\text{O}(g)\rightleftharpoons 2\text{HOCl}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.0900$

Calculate the number of grams of HI that are at equilibrium with 1.25 mol of H_{2} and 63.5 g of iodine at 448 °C.

${\text{H}}_{2}+{\text{I}}_{2}\rightleftharpoons 2\text{HI}\phantom{\rule{5em}{0ex}}{K}_{c}=50.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}448\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

Butane exists as two isomers, *n*−butane and isobutane.

*K _{P}* = 2.5 at 25 °C

What is the pressure of isobutane in a container of the two isomers at equilibrium with a total pressure of 1.22 atm?

What is the minimum mass of CaCO_{3} required to establish equilibrium at a certain temperature in a 6.50-L container if the equilibrium constant (*K _{c}*) is 0.50 for the decomposition reaction of CaCO

_{3}at that temperature?

${\text{CaCO}}_{3}(s)\rightleftharpoons \text{CaO}(s)+{\text{CO}}_{2}(g)$

The equilibrium constant (*K _{c}*) for this reaction is 1.60 at 990 °C:

${\text{H}}_{2}(g)+{\text{CO}}_{2}(g)\rightleftharpoons {\text{H}}_{2}\text{O}(g)+\text{CO}(g)$

Calculate the number of moles of each component in the final equilibrium mixture obtained from adding 1.00 mol of H_{2}, 2.00 mol of CO_{2}, 0.750 mol of H_{2}O, and 1.00 mol of CO to a 5.00-L container at 990 °C.

In a 3.0-L vessel, the following equilibrium partial pressures are measured: N_{2}, 190 torr; H_{2}, 317 torr; NH_{3}, 1.00 $\times $ 10^{3} torr.

${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)$

(a) How will the partial pressures of H_{2}, N_{2}, and NH_{3} change if 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.

The equilibrium constant (*K _{c}*) for this reaction is 5.0 at a given temperature.

$\text{CO}(g)+{\text{H}}_{2}\text{O}(g)\rightleftharpoons {\text{CO}}_{2}(g)+{\text{H}}_{2}(g)$

(a) On analysis, an equilibrium mixture of the substances present at the given temperature was found to contain 0.20 mol of CO, 0.30 mol of water vapor, and 0.90 mol of H_{2} in a liter. How many moles of CO_{2} were there in the equilibrium mixture?

(b) Maintaining the same temperature, additional 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 mol of CO, 0.30 mol of water vapor, and 1.2 mol of H_{2} in a liter. How many moles of 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.

Antimony pentachloride decomposes according to this equation:

${\text{SbCl}}_{5}(g)\rightleftharpoons {\text{SbCl}}_{3}(g)+{\text{Cl}}_{2}(g)$

An equilibrium mixture in a 5.00-L flask at 448 °C contains 3.85 g of SbCl_{5}, 9.14 g of SbCl_{3}, and 2.84 g of Cl_{2}. How many grams of each will be found if the mixture is transferred into a 2.00-L flask at the same temperature?

Consider the equilibrium

$4{\text{NO}}_{2}(g)+6{\text{H}}_{2}\text{O}(g)\rightleftharpoons 4{\text{NH}}_{3}(g)+7{\text{O}}_{2}(g)$

(a) What is the expression for the equilibrium constant (*K _{c}*) of the reaction?

(b) How must the concentration of 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 an increase in the volume of the reaction vessel affect the pressure of NO_{2}?

(d) If the change in the pressure of NO_{2} is 28 torr as a mixture of the four gases reaches equilibrium, how much will the pressure of O_{2} change?

The binding of oxygen by hemoglobin (Hb), giving oxyhemoglobin (HbO_{2}), is partially regulated by the concentration of H_{3}O^{+} and dissolved CO_{2} in the blood. Although the equilibrium is complicated, it can be summarized as

${\text{HbO}}_{2}(aq)+{\text{H}}_{3}{\text{O}}^{\text{+}}(aq)+{\text{CO}}_{2}(g)\rightleftharpoons {\text{CO}}_{2}\text{\u2212}\text{Hb}\text{\u2212}{\text{H}}^{\text{+}}+{\text{O}}_{2}(g)+{\text{H}}_{2}\text{O}(l)$

(a) Write the equilibrium constant expression for this reaction.

(b) Explain why the production of lactic acid and CO_{2} in a muscle during exertion stimulates release of O_{2} from the oxyhemoglobin in the blood passing through the muscle.

Liquid N_{2}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 NO_{2}. At 25 °C, a value of *K _{P}* = 1.91 has been established for this decomposition. If 0.236 moles of N

_{2}O

_{3}are placed in a 1.52-L vessel at 25 °C, calculate the equilibrium partial pressures of N

_{2}O

_{3}(

*g*), NO

_{2}(

*g*), and NO(

*g*).

A 1.00-L vessel at 400 °C contains the following equilibrium concentrations: N_{2}, 1.00 *M*; H_{2}, 0.50 *M*; and NH_{3}, 0.25 *M*. How many moles of hydrogen must be removed from the vessel to increase the concentration of nitrogen to 1.1 *M*? The equilibrium reaction is

${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of Δ*G*° given.

(a) ${\text{I}}_{2}(s)+{\text{Cl}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{2ICl}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}G\text{\xb0}=\text{\u221210.88 kJ}$

(b) ${\text{H}}_{2}(g)+{\text{I}}_{2}(s)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{2HI}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}G\text{\xb0}=\text{3.4 kJ}$

(c) ${\text{CS}}_{2}(g)+{\text{3Cl}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}(g)+{\text{S}}_{2}{\text{Cl}}_{2}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}G\text{\xb0}=\text{\u221239 kJ}$

(d) ${\text{2SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{2SO}}_{3}(g)\phantom{\rule{5em}{0ex}}\text{\Delta}G\text{\xb0}=\text{\u2212141.82 kJ}$

(e) ${\text{CS}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{CS}}_{2}(l)\phantom{\rule{5em}{0ex}}\text{\Delta}G\text{\xb0}=\text{\u22121.88 kJ}$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{O}}_{2}(g)+{\text{2F}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{2F}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}(\text{T}=100\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(b) ${\text{I}}_{2}(s)+{\text{Br}}_{2}(l)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{2IBr}(g)\phantom{\rule{5em}{0ex}}(\text{T}=0.0\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(c) $\text{2LiOH}(s)+{\text{CO}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{Li}}_{2}{\text{CO}}_{3}(s)+{\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}(\text{T}=575\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(d) ${\text{N}}_{2}{\text{O}}_{3}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{NO}(g)+{\text{NO}}_{2}(g)\phantom{\rule{5em}{0ex}}(\text{T}=\mathrm{-10.0}\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(e) ${\text{SnCl}}_{4}(l)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{SnCl}}_{4}(g)\phantom{\rule{5em}{0ex}}(\text{T}=200\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{I}}_{2}(s)+{\text{Cl}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{2ICl}(g)\phantom{\rule{5em}{0ex}}(\text{T}=100\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(b) ${\text{H}}_{2}(g)+{\text{I}}_{2}(s)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{2HI}(g)\phantom{\rule{5em}{0ex}}(\text{T}=0.0\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(c) ${\text{CS}}_{2}(g)+{\text{3Cl}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}(g)+{\text{S}}_{2}{\text{Cl}}_{2}(g)\phantom{\rule{5em}{0ex}}(\text{T}=125\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(d) ${\text{2SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{2SO}}_{3}(g)\phantom{\rule{5em}{0ex}}(\text{T}=675\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

(e) ${\text{CS}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{CS}}_{2}(l)\phantom{\rule{5em}{0ex}}(\text{T}=90\phantom{\rule{0.2em}{0ex}}\text{\xb0C})$

Consider the following reaction at 298 K:

${\text{N}}_{2}{\text{O}}_{4}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}{\text{2NO}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=0.142$

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.

Determine the normal boiling point (in kelvin) of dichloroethane, CH_{2}Cl_{2}. Find the actual boiling point using the Internet or some other source, and calculate the percent error in the temperature. Explain the differences, if any, between the two values.

Under what conditions is ${\text{N}}_{2}{\text{O}}_{3}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{NO}(g)+{\text{NO}}_{2}(g)$ spontaneous?

At room temperature, the equilibrium constant (*K _{w}*) for the self-ionization of water is 1.00 $\times $ 10

^{−14}. Using this information, calculate the standard free energy change for the aqueous reaction of hydrogen ion with hydroxide ion to produce water. (Hint: The reaction is the reverse of the self-ionization reaction.)

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction ${\text{2H}}_{2}\text{S}(g)+{\text{SO}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}\frac{3}{8}{\text{S}}_{8}(s,\phantom{\rule{0.2em}{0ex}}\text{rhombic})+{\text{2H}}_{2}\text{O}(l).$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

Consider the decomposition of CaCO_{3}(*s*) into CaO(*s*) and CO_{2}(*g*). What is the equilibrium partial pressure of CO_{2} at room temperature?

In the laboratory, hydrogen chloride (HCl(*g*)) and ammonia (NH_{3}(*g*)) often escape from bottles of their solutions and react to form the ammonium chloride (NH_{4}Cl(*s*)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH_{3} in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)

Benzene can be prepared from acetylene. ${\text{3C}}_{2}{\text{H}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}{\text{C}}_{6}{\text{H}}_{6}(g).$ Determine the equilibrium constant at 25 °C and at 850 °C. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?

Carbon dioxide decomposes into CO and O_{2} at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO_{2} was 1.15 atm?

Carbon tetrachloride, an important industrial solvent, is prepared by the chlorination of methane at 850 K.

${\text{CH}}_{4}(g)+{\text{4Cl}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{CCl}}_{4}(g)+\text{4HCl}(g)$

What is the equilibrium constant for the reaction at 850 K? Would the reaction vessel need to be heated or cooled to keep the temperature of the reaction constant?

Acetic acid, CH_{3}CO_{2}H, can form a dimer, (CH_{3}CO_{2}H)_{2}, in the gas phase.

${\text{2CH}}_{3}{\text{CO}}_{2}\text{H}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{({\text{CH}}_{3}{\text{CO}}_{2}\text{H})}_{2}(g)$

The dimer is held together by two hydrogen bonds with a total strength of 66.5 kJ per mole of dimer.

At 25 °C, the equilibrium constant for the dimerization is 1.3 $\times $ 10^{3} (pressure in atm). What is Δ*S*° for the reaction?