## Exercises

### 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 13.5.

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: $3{\text{C}}_{2}{\text{H}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{C}}_{6}{\text{H}}_{6}(g).$ 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.

(a) $2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=17;$ [NH_{3}] = 0.20 *M*, [N_{2}] = 1.00 *M*, [H_{2}] = 1.00 *M*

(b) $2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=6.8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};$ initial pressures: NH_{3} = 3.0 atm, N_{2} = 2.0 atm, H_{2} = 1.0 atm

(c) $2{\text{SO}}_{3}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}\left(g\right)\phantom{\rule{5em}{0ex}}{K}_{c}=0.230;$ [SO_{3}] = 0.00 *M*, [SO_{2}] = 1.00 *M*, [O_{2}] = 1.00 *M*

(d) $2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=16.5;$ initial pressures: SO_{3} = 1.00 atm, SO_{2} = 1.00 atm, O_{2} = 1.00 atm

(e) $2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=4.6\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};$ [NO] = 1.00 *M*, [Cl_{2}] = 1.00 *M*, [NOCl] = 0 *M*

(f) ${\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=0.050;$ initial pressures: NO = 10.0 atm, N_{2} = O_{2} = 5 atm

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) $2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=17;$ [NH_{3}] = 0.50 *M*, [N_{2}] = 0.15 *M*, [H_{2}] = 0.12 *M*

(b) $2{\text{NH}}_{3}(g)\rightleftharpoons {\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=6.8\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4};$ initial pressures: NH_{3} = 2.00 atm, N_{2} = 10.00 atm, H_{2} = 10.00 atm

(c) $2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.230;$ [SO_{3}] = 2.00 *M*, [SO_{2}] = 2.00 *M*, [O_{2}] = 2.00 *M*

(d) $2{\text{SO}}_{3}(g)\rightleftharpoons 2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=6.5\phantom{\rule{0.2em}{0ex}}\text{atm;}$ initial pressures: SO_{2} = 1.00 atm, O_{2} = 1.130 atm, SO_{3} = 0 atm

(e) $2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=2.5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3};$ initial pressures: NO = 1.00 atm, Cl_{2} = 1.00 atm, NOCl = 0 atm

(f) ${\text{N}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2\text{NO}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.050;$ [N_{2}] = 0.100 *M*, [O_{2}] = 0.200 *M*, [NO] = 1.00 *M*

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

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 give homogeneous equilibria? Which give heterogeneous equilibria?

Which of the systems described in Exercise 13.16 give homogeneous equilibria? Which give 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}(a) ${\text{N}}_{2}(g)+3{\text{H}}_{2}(g)\rightleftharpoons 2{\text{NH}}_{3}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.50\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}400\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

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

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

(d) ${\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=0.122\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}50\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

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

*K*or the values of

_{P}*K*to values of

_{P}*K*.

_{c}(a) ${\text{Cl}}_{2}(g)+{\text{Br}}_{2}(g)\rightleftharpoons 2\text{BrCl}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=4.7\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-2}}\text{at}\phantom{\rule{0.2em}{0ex}}25\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

(b) $2{\text{SO}}_{2}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{SO}}_{3}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=48.2\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}500\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

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

(d) ${\text{H}}_{2}\text{O}(l)\rightleftharpoons {\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=0.196\phantom{\rule{0.2em}{0ex}}\text{at}\phantom{\rule{0.2em}{0ex}}60\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

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. (Vapor pressure was described in the previous chapter on liquids and solids; refer back to this chapter to find the relevant information needed to solve this problem.)

### 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 pressure would affect 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?

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.

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

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: ${\text{H}}_{2}\text{O}(g)+\text{C}(s)\rightleftharpoons {\text{H}}_{2}(g)+\text{CO}(g).$ 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 (*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?

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

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 pressure on the system is increased by reducing the volume of the reaction vessel?

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

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

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 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?

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?

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

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.

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

Which of the following will occur?

(a) Ag^{+} or ${\text{SO}}_{4}{}^{\mathrm{2-}}$ 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 ${\text{SO}}_{4}{}^{\mathrm{2-}}$ ions combine.

(d) The Ag^{+} ion concentration will increase and the ${\text{SO}}_{4}{}^{\mathrm{2-}}$ ion concentration will decrease.

The amino acid alanine has two isomers, α-alanine and β-alanine. When equal masses of these two compounds are dissolved in equal amounts of a solvent, the solution of α-alanine freezes at the lowest temperature. Which form, α-alanine or β-alanine, has the larger equilibrium constant for ionization $(\text{HX}\rightleftharpoons {\text{H}}^{\text{+}}+{\text{X}}^{\text{\u2212}})$?

### 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*, make up 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*, make up 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 3.3 $\times $ 10^{−3}% 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 transformation 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 13.61, part (f)? What property of Ni does change?

Why are there no changes specified for NH_{4}HS in Exercise 13.62, 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.

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

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}?

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:

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

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) Show 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) Show 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) Show 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?

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

What are the concentrations of PCl_{5}, PCl_{3}, and Cl_{2} in an equilibrium mixture produced by the decomposition of a sample of pure PCl_{5} with [PCl_{5}] = 2.00 *M*?

${\text{PCl}}_{5}(g)\rightleftharpoons {\text{PCl}}_{3}(g)+{\text{Cl}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=0.0211$

Calculate the pressures of all species at equilibrium in a mixture of NOCl, NO, and Cl_{2} produced when a sample of NOCl with a pressure of 10.0 atm comes to equilibrium according to this reaction:

$\text{2NOCl}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}\text{2NO}(g)+{\text{Cl}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=4.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\text{\u22124}}$

Calculate the equilibrium concentrations of NO, O_{2}, and NO_{2} in a mixture at 250 °C that results from the reaction of 0.20 *M* NO and 0.10 *M* O_{2}. (Hint: *K* is large; assume the reaction goes to completion then comes back to equilibrium.)

$2\text{NO}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{NO}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=2.3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{5}\text{at}\phantom{\rule{0.2em}{0ex}}250\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$

Calculate the equilibrium concentrations that result when 0.25 *M* O_{2} and 1.0 *M* HCl react and come to equilibrium.

$4\text{HCl}(g)+{\text{O}}_{2}(g)\rightleftharpoons 2{\text{Cl}}_{2}(g)+2{\text{H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{c}=3.1\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{13}$

One of the important reactions in the formation of smog is represented by the equation

${\text{O}}_{3}(g)+\text{NO}(g)\rightleftharpoons {\text{NO}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=6.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{34}$

What is the pressure of O_{3} remaining after a mixture of O_{3} with a pressure of 1.2 $\times $ 10^{−8} atm and NO with a pressure of 1.2 $\times $ 10^{−8} atm comes to equilibrium? (Hint: *K _{P}* is large; assume the reaction goes to completion then comes back to equilibrium.)

Calculate the pressures of NO, Cl_{2}, and NOCl in an equilibrium mixture produced by the reaction of a starting mixture with 4.0 atm NO and 2.0 atm Cl_{2}. (Hint: *K _{P}* is small; assume the reverse reaction goes to completion then comes back to equilibrium.)

$2\text{NO}(g)+{\text{Cl}}_{2}(g)\rightleftharpoons 2\text{NOCl}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=2.5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}$

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 0.050 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.

At 25 °C and at 1 atm, the partial pressures in an equilibrium mixture of N_{2}O_{4} and NO_{2} are ${\text{P}}_{{\text{N}}_{2}{\text{O}}_{4}}=0.70\phantom{\rule{0.2em}{0ex}}\text{atm}$ and ${\text{P}}_{{\text{NO}}_{2}}=0.30\phantom{\rule{0.2em}{0ex}}\text{atm.}$

(a) Predict how the pressures of NO_{2} and N_{2}O_{4} will change if the total pressure increases to 9.0 atm. Will they increase, decrease, or remain the same?

(b) Calculate the partial pressures of NO_{2} and N_{2}O_{4} when they are at equilibrium at 9.0 atm and 25 °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 reaction between H_{2} and O_{2} at 1000 K

${\text{2H}}_{2}(g)+{\text{O}}_{2}(g)\phantom{\rule{0.2em}{0ex}}\rightleftharpoons \phantom{\rule{0.2em}{0ex}}{\text{2H}}_{2}\text{O}(g)\phantom{\rule{5em}{0ex}}{K}_{P}=\phantom{\rule{0.2em}{0ex}}\frac{{({P}_{{\text{H}}_{2}\text{O}})}^{\text{2}}}{({P}_{{\text{O}}_{2}}){({P}_{{\text{H}}_{2}})}^{\text{2}}}\phantom{\rule{0.2em}{0ex}}=1.33\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{20}$

If 0.500 atm of H_{2} and 0.500 atm of O_{2} are allowed to come to equilibrium at this temperature, what are the partial pressures of the components?

An equilibrium is established according to the following equation

${\text{Hg}}_{2}{}^{\mathrm{2+}}(aq)+{\text{NO}}_{3}{}^{\text{\u2212}}(aq)+3{\text{H}}^{\text{+}}(aq)\rightleftharpoons 2{\text{Hg}}^{\mathrm{2+}}(aq)+{\text{HNO}}_{2}(aq)+{\text{H}}_{2}\text{O}(l)\phantom{\rule{5em}{0ex}}{K}_{c}=4.6$

What will happen in a solution that is 0.20 *M* each in ${\text{Hg}}_{2}{}^{\mathrm{2+}},$ ${\text{NO}}_{3}{}^{\text{\u2212}},$ H^{+}, Hg^{2+}, and HNO_{2}?

(a) ${\text{Hg}}_{2}{}^{\mathrm{2+}}$ will be oxidized and ${\text{NO}}_{3}{}^{\text{\u2212}}$ reduced.

(b) ${\text{Hg}}_{2}{}^{\mathrm{2+}}$ will be reduced and ${\text{NO}}_{3}{}^{\text{\u2212}}$ oxidized.

(c) Hg^{2+} will be oxidized and HNO_{2} reduced.

(d) Hg^{2+} will be reduced and HNO_{2} oxidized.

(e) There will be no change because all reactants and products have an activity of 1.

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 a decrease in pressure (from 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.

The hydrolysis of the sugar sucrose to the sugars glucose and fructose follows a first-order rate equation for the disappearance of sucrose.

${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}(aq)+{\text{H}}_{2}\text{O}(l)\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}{\text{C}}_{6}{\text{H}}_{12}{\text{O}}_{6}(aq)+{\text{C}}_{6}{\text{H}}_{12}{\text{O}}_{6}(aq)$

Rate = *k*[C_{12}H_{22}O_{11}]

In neutral solution, *k* = 2.1 $\times $ 10^{−11}/s at 27 °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, C_{6}H_{12}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 °C. What are the concentrations of glucose, fructose, and sucrose after a 0.150 *M* aqueous solution of sucrose has reached equilibrium? Remember that the activity of a solvent (the effective concentration) is 1.

The density of trifluoroacetic acid vapor was determined at 118.1 °C and 468.5 torr, and found to be 2.784 g/L. Calculate *K _{c}* for the association of the acid.

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*?

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 °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 $[\text{HA}(aq)\rightleftharpoons {\text{A}}^{\text{\u2212}}(aq)+{\text{H}}^{\text{+}}(aq)]$ or HB $[\text{HB}(aq)\rightleftharpoons {\text{H}}^{\text{+}}(aq)+{\text{B}}^{\text{\u2212}}(aq)]$?

(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 (A^{−} or B^{−}), and the hydrogen ion (H^{+}). 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.)