Exercises

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

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

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

Explain why an equilibrium between Br₂(l) and Br₂(g) would not be established if the container were not a closed vessel shown in Figure 13.4.

Among the solubility rules previously discussed is the statement: All chlorides are soluble except Hg₂Cl₂, AgCl, PbCl₂, and CuCl.

(a) Write the expression for the equilibrium constant for the reaction represented by the equation $\text{AgCl}(s)\rightleftharpoons {\text{Ag}}^{\text{+}}(aq)+{\text{Cl}}^{\text{−}}(aq).$ 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 ${\text{Pb}}^{\mathrm{2+}}(aq)+2{\text{Cl}}^{\text{−}}(aq)\rightleftharpoons {\text{PbCl}}_2(s).$ 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: $3{\text{C}}_2{\text{H}}_2(g)\rightleftharpoons {\text{C}}_6{\text{H}}_6(g).$ Which value of K_c would make this reaction most useful commercially? K_c ≈ 0.01, K_c ≈ 1, or K_c ≈ 10. Explain your answer.

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?

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) ${\text{CuSO}}_4\text{·}5{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{CuSO}}_4(s)+5{\text{H}}_2\text{O}(g)$

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.

$\begin{array}{cccc}\text{(a)}2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)\hfill & & & K_c=17;[{\text{NH}}_3]=0.20M,[{\text{N}}_2]=1.00M,[{\text{H}}_2]=1.00M\hfill \\ \text{(b)}2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)\hfill & & & K_P=6.8\times {10}^4;{\text{NH}}_3=3.0\text{atm},{\text{N}}_2=2.0\text{atm},{\text{H}}_2=1.0\text{atm}\hfill \\ \text{(c)}2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2\left(g\right)\hfill & & & K_c=0.230;[{\text{SO}}_3]=0.00M,[{\text{SO}}_2]=1.00M,[{\text{O}}_2]=1.00M\hfill \\ \text{(d)}2{\text{SO}}_3(g)\rightleftharpoons 2{\text{SO}}_2(g)+{\text{O}}_2(g)\hfill & & & K_P=16.5;{\text{SO}}_3=1.00\text{atm},{\text{SO}}_2=1.00\text{atm},{\text{O}}_2=1.00\text{atm}\hfill \\ \text{(e)}2\text{NO}(g)+{\text{Cl}}_2(g)\rightleftharpoons 2\text{NOCl}(g)\hfill & & & K_c=4.6\times {10}^4;[\text{NO}]=1.00M,[{\text{Cl}}_2]=1.00M,[\text{NOCl}]=0M\hfill \\ \text{(f)}{\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)\hfill & & & K_P=0.050;\text{NO}=10.0\text{atm},{\text{N}}_2={\text{O}}_2=\text{5 atm}\hfill \end{array}$

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(NH₃) = 93 atm, P(N₂) = 48 atm, and P(H₂) = 52 atm

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

For which of the reactions in Exercise 13.15 does K_c (calculated using concentrations) equal K_P (calculated using pressures)?

Convert the values of K_c to values of K_P or the values of K_P to values of K_c.

$\begin{array}{cccc}\text{(a)}{\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)\hfill & & & K_c=0.50\text{at}400\text{°C}\hfill \\ \text{(b)}{\text{H}}_2(g)+{\text{I}}_2(g)\rightleftharpoons 2\text{HI}(g)\hfill & & & K_c=50.2\text{at}448\text{°C}\hfill \\ \text{(c)}{\text{Na}}_2{\text{SO}}_4\text{·}10{\text{H}}_2\text{O}(s)\rightleftharpoons {\text{Na}}_2{\text{SO}}_4(s)+10{\text{H}}_2\text{O}(g)\hfill & & & K_P=4.08\times {10}^{\mathrm{-25}}\text{at}25\text{°C}\hfill \\ \text{(d)}{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\hfill & & & K_P=0.122\text{at}50\text{°C}\hfill \end{array}$

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 reaction quotient expression for the ionization of NH₃ in water.

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 CaCO₃ remains?

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 CH₄, O₂, CO₂, and H₂O established under these conditions? Explain your answer.

Suggest four ways in which the concentration of hydrazine, N₂H₄, could be increased in an equilibrium described by the following equation:
${\text{N}}_2(g)+2{\text{H}}_2(g)\rightleftharpoons {\text{N}}_2{\text{H}}_4(g)\text{Δ}H=95\text{kJ}$

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) $2{\text{NH}}_3(g)\rightleftharpoons {\text{N}}_2(g)+3{\text{H}}_2(g)\text{Δ}H=92\text{kJ}$

(b) ${\text{N}}_2(g)+{\text{O}}_2(g)\rightleftharpoons 2\text{NO}(g)\text{Δ}H=181\text{kJ}$

(c) $2{\text{O}}_3(g)\rightleftharpoons 3{\text{O}}_2(g)\text{Δ}H=\mathrm{-285}\text{kJ}$

(d) $\text{CaO}(s)+{\text{CO}}_2(g)\rightleftharpoons {\text{CaCO}}_3(s)\text{Δ}H=\mathrm{-176}\text{kJ}$

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
$2{\text{H}}_2(g)+\text{CO}(g)\rightleftharpoons {\text{CH}}_3\text{OH}(g)\text{Δ}H=\mathrm{-90.2}\text{kJ}$

(b) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if more H₂ is added?

(c) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CO is removed?

(d) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if CH₃OH is added?

(e) What will happen to the concentrations of H₂, CO, and CH₃OH at equilibrium if the temperature of the system is increased?

Water gas, a mixture of H₂ 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
$\text{C}(s)+{\text{H}}_2\text{O}(g)\rightleftharpoons \text{CO}(g)+{\text{H}}_2(g)\text{Δ}H=131.30\text{kJ}$

(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 H₂O 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?

Ammonia is a weak base that reacts with water according to this equation:
${\text{NH}}_3(aq)+{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{NH}}_4{}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)$

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 NH₄Cl

Suggest two ways in which the equilibrium concentration of Ag⁺ can be reduced in a solution of Na⁺, Cl⁻, Ag⁺, and ${\text{NO}}_3{}^{\text{−}},$ in contact with solid AgCl.
${\text{Na}}^{\text{+}}(aq)+{\text{Cl}}^{\text{−}}(aq)+{\text{Ag}}^{\text{+}}(aq)+{\text{NO}}_3{}^{\text{−}}(aq)\rightleftharpoons \text{AgCl}(s)+{\text{Na}}^{\text{+}}(aq)+{\text{NO}}_3{}^{\text{−}}(aq)$
$\text{Δ}H=\mathrm{-65.9}\text{kJ}$

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.

A reaction is represented by this equation: $\text{A}(aq)+2\text{B}(aq)\rightleftharpoons 2\text{C}(aq)K_c=1\times {10}^3$

(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.

What is the value of the equilibrium constant at 500 °C for the formation of NH₃ according to the following equation?

${\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)$

An equilibrium mixture of NH₃(g), H₂(g), and N₂(g) at 500 °C was found to contain 1.35 M H₂, 1.15 M N₂, and 4.12 $\times$ 10⁻¹ M NH₃.

A 0.72-mol sample of PCl₅ is put into a 1.00-L vessel and heated. At equilibrium, the vessel contains 0.40 mol of PCl₃(g) and 0.40 mol of Cl₂(g). Calculate the value of the equilibrium constant for the decomposition of PCl₅ to PCl₃ and Cl₂ at this temperature.

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; Cl₂, 0.30 atm; NOCl, 1.2 atm.

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 NH₃(g) was found to be 1.75 atm. What is the value of the equilibrium constant K_P for the decomposition at this temperature?

Complete the following partial ICE tables.

(a)

$\begin{array}{lllll}& 2{\text{SO}}_3(g)\hfill & \rightleftharpoons \hfill & 2{\text{SO}}_2(g)+\hfill & {\text{O}}_2(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & & \text{\_\_\_}\hfill & +x\hfill \end{array}$

(b)

$\begin{array}{llllll}& 4{\text{NH}}_3(g)\hfill & +3{\text{O}}_2(g)\hfill & \rightleftharpoons \hfill & 2{\text{N}}_2(g)+\hfill & 6{\text{H}}_2\text{O}(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & +x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(c)

$\begin{array}{lllll}& 2{\text{CH}}_4(g)\hfill & \rightleftharpoons \hfill & {\text{C}}_2{\text{H}}_2(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{change}& \text{\_\_\_}\hfill & & +x\hfill & \text{\_\_\_}\hfill \end{array}$

(d)

$\begin{array}{llllll}& {\text{CH}}_4(g)+\hfill & {\text{H}}_2\text{O}(g)\hfill & \rightleftharpoons \hfill & \text{CO}(g)+\hfill & 3{\text{H}}_2(g)\hfill \\ \text{change}\hfill & \text{\_\_\_}& +x\hfill & & \text{\_\_\_}\hfill & \text{\_\_\_}\hfill \end{array}$

(e)

$\begin{array}{lllll}& {\text{NH}}_4\text{Cl}(s)\hfill & \rightleftharpoons \hfill & {\text{NH}}_3(g)+\hfill & \text{HCl}(g)\hfill \\ \text{change}& & +x\hfill & \text{\_\_\_}\hfill \end{array}$

(f)

$\begin{array}{ccccc}& \text{Ni}(s)+\hfill & 4\text{CO}(g)\hfill & \rightleftharpoons \hfill & \text{Ni}{(\text{CO})}_4(g)\hfill \\ \text{change}& +x\hfill & & \text{\_\_\_}\hfill \end{array}$

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

Analysis of the gases in a sealed reaction vessel containing NH₃, N₂, and H₂ at equilibrium at 400 °C established the concentration of N₂ to be 1.2 M and the concentration of H₂ to be 0.24 M.

${\text{N}}_2(g)+3{\text{H}}_2(g)\rightleftharpoons 2{\text{NH}}_3(g)K_c=0.50\text{at}400\text{°}\text{C}$

Calculate the equilibrium molar concentration of NH₃.