Chapter 12

Define the terms chemical equilibrium and dynamic equilibrium.

If an equilibrium is product-favored, is its equilibrium constant large or small with respect to \(1 ?\) Explain.

List three characteristics that you would need to verify in order to determine that a chemical system is at equilibrium.

Decomposition of ammonium dichromate is shown in the designated series of photos. In a closed container this process reaches an equilibrium state. Write a balanced chemical equation for the equilibrium reaction. How is the equilibrium affected if (a) more ammonium dichromate is added to the equilibrium system? (b) more water vapor is added? (c) more chromium(III) oxide is added?

Indicate whether each statement below is true or false. If a statement is false, rewrite it to produce a closely related statement that is true. (a) For a given reaction, the magnitude of the equilibrium constant is independent of temperature. (b) If there is an increase in entropy and a decrease in enthalpy when reactants in their standard states are converted to products in their standard states, the equilibrium constant for the reaction must be negative. (c) The equilibrium constant for the reverse of a reaction is the reciprocal of the equilibrium constant for the reaction itself. (d) For the reaction $$ \mathrm{H}_{2} \mathrm{O}_{2}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\ell)+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) $$ the equilibrium constant is one half the magnitude of the equilibrium constant for the reaction $$ 2 \mathrm{H}_{2} \mathrm{O}_{2}(\ell) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{O}_{2}(\mathrm{~g}) $$

If the reaction quotient is larger than the equilibrium constant, in what direction does the reaction proceed as it approaches equilibrium? What will happen if \(Q \leq K\) ?

Think of an experiment you could do to demonstrate that the equilibrium $$ 2 \mathrm{NO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) $$ is a dynamic process in which the forward and reverse reactions continue to occur after equilibrium has been achieved. Describe how such an experiment might be carried out.

Discuss this statement: "No true chemical equilibrium can exist unless reactant molecules are constantly changing into product molecules, and vice versa."

The atmosphere consists of about \(80 \% \mathrm{~N}_{2}\) and \(20 \% \mathrm{O}_{2}\), yet there are many oxides of nitrogen that are stable and can be isolated in the laboratory. (a) Is the atmosphere at chemical equilibrium with respect to forming NO? (b) If not, why doesn't NO form? If so, how is it that \(\mathrm{NO}\) can be made and kept in the laboratory for long periods?

Consider the gas-phase reaction of \(\mathrm{N}_{2}+\mathrm{O}_{2}\) to give \(2 \mathrm{NO}\) and the reverse reaction of 2 NO to give \(\mathbf{N}_{2}+\mathrm{O}_{2},\) discussed in Section 12-2e. An equilibrium mixture of \(\mathrm{NO}\), \(\mathrm{N}_{2}\), and \(\mathrm{O}_{2}\) at \(5000 . \mathrm{K}\) that contains equal concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) has a concentration of NO about half as great. Make qualitatively correct plots of the concentrations of reactants and products versus time for these two processes, showing the initial state and the final dynamic equilibrium state. Assume a temperature of \(5000 . \mathrm{K}\). Don't do any calculations-just sketch how you think the plots should look.

Write equilibrium constant expressions for these reactions. For gases, use either pressures or concentrations. (a) \(3 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{O}_{3}(\mathrm{~g})\) (b) \(\mathrm{Fe}(\mathrm{s})+5 \mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{~g})\) (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\)

Write equilibrium constant expressions for these reactions: (a) \(\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(\mathrm{BaCO}_{3}(\mathrm{~s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\) (d) \(\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{HCl}(\mathrm{g}) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\)

Write the expression for \(K_{\mathrm{c}}\) for each reaction. (a) \(\mathrm{PCl}_{5}(\mathrm{~s}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (b) \(\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}(\mathrm{aq})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{CoCl}_{4}^{2-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{aq}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})\) (d) \(2 \mathrm{~F}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{OF}_{2}(\mathrm{~g})+2 \mathrm{HF}(\mathrm{g})\)

Write the equilibrium constant expression for each reaction. (a) The oxidation of ammonia with \(\mathrm{ClF}_{3}\) in a rocket motor $$ \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{ClF}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{HF}(\mathrm{g})+\frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g}) $$ (b) The simultaneous oxidation and reduction of a chlorite ion $$ \begin{aligned} 3 \mathrm{ClO}_{2}^{-}(\mathrm{aq}) \rightleftharpoons 2 \mathrm{ClO}_{3}^{-}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq}) \\ \text { (c) } \mathrm{IO}_{3}^{-}(\mathrm{aq})+6 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{Cl}_{2}(\mathrm{aq}) \rightleftharpoons & \\\ & \mathrm{IO}_{6}^{5-}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\ell) \end{aligned} $$

Write the equilibrium constant expression for each of these heterogeneous systems. (a) \(\mathrm{CaSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{CaSO}_{4} \cdot 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (b) \(\mathrm{SiF}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{SiO}_{2}(\mathrm{~s})+4 \mathrm{HF}(\mathrm{g})\) (c) \(\mathrm{LaCl}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{LaClO}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g})\)

Write the equilibrium constant expression for each of these heterogeneous systems. (a) \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})+\mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g})\) (b) \(\mathrm{C}(\mathrm{s})+2 \mathrm{~N}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{~N}_{2}(\mathrm{~g})\) (c) \(\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Write a chemical equation for an equilibrium system that would lead to each expression \((\mathrm{a}-\mathrm{c})\) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{H}_{2} \mathrm{~S}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}\) (b) \(K=\frac{\left(P_{\mathrm{F}_{2}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{\left(P_{\mathrm{IF}}\right)}\) (c) \(K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{Cl}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}\)

Consider this reaction at \(122^{\circ} \mathrm{C}\) : $$ 2 \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ (a) Write an equilibrium constant expression for the reaction and call the constant \(K_{1}\). (b) Write an equilibrium constant expression for the decomposition of \(1 \mathrm{~mol} \mathrm{SO}_{3}\) to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) and call the constant \(K_{2}\) (c) Relate \(K_{1}\) and \(K_{2}\).

Consider these two equilibria involving \(\mathrm{SO}_{2}(\mathrm{~g})\) and their corresponding equilibrium constants. $$ \begin{array}{cl} \mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g}) & K_{\mathrm{c}_{1}} \\ 2 \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) & K_{\mathrm{c}_{2}} \end{array} $$ Which of these expressions correctly relates \(K_{c_{1}}\) to \(K_{c_{2}} ?\) (a) \(K_{\mathrm{c}_{2}}=K_{\mathrm{c}_{1}}^{2}\) (b) \(K_{\mathrm{c}_{2}}^{2}=K_{\mathrm{c}_{1}}\) (c) \(K_{\mathrm{c}_{2}}=1 / K_{\mathrm{c}_{1}}\) (d) \(K_{\mathrm{c}_{2}}=K_{\mathrm{c}_{1}}\) (e) \(K_{\mathrm{c},}=1 / K_{\mathrm{c}}^{2}\)

The reaction of hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4},\) with chlorine trifluoride, \(\mathrm{ClF}_{3}\), has been used in experimental rocket motors. \(\mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{~g})+\frac{4}{3} \mathrm{ClF}_{3}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{HF}(\mathrm{g})+\mathrm{N}_{2}(\mathrm{~g})+\frac{2}{3} \mathrm{Cl}_{2}(\mathrm{~g})\) How is the equilibrium constant, \(K_{\mathrm{p}}\), for this reaction related to \(K_{\mathrm{p}}^{\prime}\) for the reaction written this way? $$ \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{~g})+4 \mathrm{ClF}_{3}(\mathrm{~g}) \rightleftharpoons 12 \mathrm{HF}(\mathrm{g})+3 \mathrm{~N}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ (a) \(K_{\mathrm{P}}=K_{\mathrm{P}}^{\prime}\) (b) \(K_{\mathrm{P}}=1 / K_{\mathrm{P}}^{\prime}\) (c) \(K_{\mathrm{p}}^{3}=K_{\mathrm{P}}^{\prime}\) (d) \(K_{\mathrm{P}}=\left(K_{\mathrm{P}}^{\prime}\right)^{3}\) (e) \(3 K_{\mathrm{p}}=K_{\mathrm{P}}^{\prime}\)

At \(627{ }^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.76\) for the reaction $$ 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) $$ Calculate \(K_{\mathrm{c}}\) at \(627{ }^{\circ} \mathrm{C}\) for (a) synthesis of 1 mol sulfur trioxide gas. (b) decomposition of \(2 \mathrm{~mol} \mathrm{SO}_{3}\)

At \(450^{\circ} \mathrm{C}\), the equilibrium constant \(K_{\mathrm{c}}\) for the HaberBosch synthesis of ammonia is 0.16 for the reaction written as $$ 3 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{N}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) $$ Calculate the value of \(K_{\mathrm{c}}\) for the same reaction written as $$ \frac{3}{2} \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{~g}) $$

Given these data at a certain temperature, $$ \begin{array}{cc} 2 \mathrm{~N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~N}_{2} \mathrm{O}(\mathrm{g}) & K=1.2 \times 10^{-35} \\ \mathrm{~N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) & K=4.6 \times 10^{-3} \\ \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{NO}_{2}(\mathrm{~g}) & K=4.1 \times 10^{-9} \end{array} $$ calculate \(K\) for the reaction between 1 mol dinitrogen oxide gas and oxygen gas to give dinitrogen tetraoxide gas.

The vapor pressure of water at \(80 .{ }^{\circ} \mathrm{C}\) is \(0.467 \mathrm{~atm} .\) Determine the value of \(K_{\mathrm{c}}\) for the process $$ \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ at this temperature.

The value of \(K_{\mathrm{c}}\) for the reaction $$\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) $$ is 2.00 at \(400,{ }^{\circ} \mathrm{C}\). Determine the value of \(K_{\mathrm{p}}\) for this reaction at this temperature using bars as pressure units.

At elevated temperatures, \(\mathrm{BrF}_{5}\) establishes this equilibrium. $$ 2 \mathrm{BrF}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{Br}_{2}(\mathrm{~g})+5 \mathrm{~F}_{2}(\mathrm{~g}) $$ The equilibrium concentrations of the gases at \(1500 \mathrm{~K}\) are \(0.0064 \mathrm{~mol} / \mathrm{L}\) for \(\mathrm{BrF}_{5}, 0.0018 \mathrm{~mol} / \mathrm{L}\) for \(\mathrm{Br}_{2},\) and \(0.0090 \mathrm{~mol} / \mathrm{L}\) for \(\mathrm{F}_{2}\). Calculate \(K_{c}\)

This reaction was examined at \(250^{\circ} \mathrm{C}\). $$ \begin{array}{c} \mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \\ \text { At equilibrium, }\left[\mathrm{PCl}_{5}\right]=4.2 \times 10^{-5} \mathrm{M},\left[\mathrm{PCl}_{3}\right]= \end{array} $$ \(1.3 \times 10^{-2} \mathrm{M},\) and \(\left[\mathrm{Cl}_{2}\right]=3.9 \times 10^{-3} \mathrm{M} .\) Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

At high temperature, hydrogen and carbon dioxide react to give water and carbon monoxide. $$ \mathrm{H}_{2 (\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) $$ Laboratory measurements at \(986^{\circ} \mathrm{C}\) show that there is \(0.11 \mathrm{~mol}\) each of \(\mathrm{CO}\) and water vapor and \(0.087 \mathrm{~mol}\) each of \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) at equilibrium in a sealed 1.0 - \(\mathrm{L}\) container. Calculate the equilibrium constant \(K_{\mathrm{p}}\) for the reac- $$ \text { tion at } 986^{\circ} \mathrm{C} \text { . } $$

Carbon dioxide reacts with carbon to give carbon monoxide according to the equation $$ \mathrm{C}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g}) $$ At \(700 .{ }^{\circ} \mathrm{C},\) a \(2.0-\mathrm{L}\) sealed flask at equilibrium contains $$ 0.10 \mathrm{~mol} \mathrm{CO}, 0.20 \mathrm{~mol} \mathrm{CO}_{2}, \text { and } 0.40 \mathrm{~mol} \mathrm{C} . \text { Calculate } $$ the equilibrium constant \(K_{\mathrm{P}}\) for this reaction at the specified temperature.

Carbon tetrachloride can be produced by this reaction: $$ \mathrm{CS}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{S}_{2} \mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{CCl}_{4}(\mathrm{~g}) $$ Suppose \(1.2 \mathrm{~mol} \mathrm{CS}_{2}\) and \(3.6 \mathrm{~mol} \mathrm{Cl}_{2}\) are placed in a 1.00-L flask and the flask is sealed. After equilibrium has been achieved, the mixture contains \(0.90 \mathrm{~mol} \mathrm{CCl}_{4} \cdot\) Calculate \(K_{\mathrm{c}}\).

Assume you place \(0.010 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{4}(\mathrm{~g})\) in a sealed \(2.0-\mathrm{L}\) flask at \(50 .{ }^{\circ} \mathrm{C}\). After the system reaches equilibrium, \(\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.00090 \mathrm{M} .\) Calculate the value of \(K_{\mathrm{c}}\) for this reaction. $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) $$

Nitrosyl chloride, NOCl, decomposes to \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) at high temperatures. $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ Suppose you place \(2.00 \mathrm{~mol} \mathrm{NOCl}\) in a \(1.00-\mathrm{L}\) flask, seal it, and raise the temperature to \(462^{\circ} \mathrm{C}\). When equilibrium has been established, \(0.66 \mathrm{~mol} \mathrm{NO}\) is present. Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the decomposition reaction from these data.

Suppose \(0.086 \mathrm{~mol} \mathrm{Br}_{2}\) is placed in a 1.26-L flask. The flask is sealed and heated to \(1756 \mathrm{~K}\), a temperature at which the \(\mathrm{Br}_{2}\) dissociates to atoms $$ \mathrm{Br}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Br}(\mathrm{g}) $$ If \(\mathrm{Br}_{2}\) is \(3.7 \%\) dissociated at this temperature, calculate \(K_{c}\)

\(\mathrm{H}_{2}\) gas and \(\mathrm{I}_{2}\) vapor are mixed in a flask. The flask is sealed and heated to \(700^{\circ} \mathrm{C}\). The initial concentration of each gas is \(0.0088 \mathrm{~mol} / \mathrm{L},\) and \(78.6 \%\) of the \(\mathrm{I}_{2}\) has reacted when equilibrium is achieved according to the equation $$ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) $$ Calculate \(K_{c}\) for this reaction.

Chemists carried out a study of the high temperature reaction of sulfur dioxide with oxygen in which a sealed reactor initially contained \(0.0076-\mathrm{M} \mathrm{SO}_{2}, 0.0036-\mathrm{M} \mathrm{O}_{2}\), and no \(\mathrm{SO}_{3}\). After equilibrium was achieved, the \(\mathrm{SO}_{2}\) concentration decreased to \(0.0032 \mathrm{M}\). Calculate \(K_{\mathrm{c}}\) at this temperature for $$ 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g}) $$

On the basis of the equilibrium constant values, choose the reactions in which the reactants are favored. (a) \(\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}\) (aq) \(\quad K=1.0 \times 10^{-14}\) (b) \(\left[\mathrm{AlF}_{6}\right]^{3-}(\mathrm{aq}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+6 \mathrm{~F}^{-}\) (aq) \(\quad K=2 \times 10^{-24}\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{~s}) \rightleftharpoons 3 \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{PO}_{4}^{3-}(\mathrm{aq})\) \(K=1 \times 10^{-25}\) (d) \(2 \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{~S}^{2-}(\mathrm{aq}) \rightleftharpoons \mathrm{Fe}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \quad K=1 \times 10^{88}\)

The equilibrium constants for dissolving silver sulfate and silver sulfide in water are \(1.7 \times 10^{-5}\) and \(6 \times 10^{-30}\), respectively. (a) Write the balanced dissociation reaction equation and the associated equilibrium constant expression for each process. (b) Which compound is more soluble? Explain your answer. (c) Which compound is less soluble? Explain your answer.

The equilibrium constants for dissolving calcium carbonate, silver nitrate, and silver chloride in water are \(2.8 \times 10^{-9}, 2.0 \times 10^{2},\) and \(1.8 \times 10^{-10},\) respectively. (a) Write the balanced dissociation reaction equation and the associated equilibrium constant expression for each process. (b) Which compound is most soluble? Explain your answer. (c) Which compound is least soluble? Explain your answer.

The hydrocarbon \(\mathrm{C}_{4} \mathrm{H}_{10}\) can exist in two gaseous forms: butane and 2 -methylpropane. The value of \(K_{\mathrm{c}}\) for conversion of butane to 2 -methylpropane is 2.5 at \(25^{\circ} \mathrm{C}\). CCCCC=CC(C)(C)CO (a) Suppose that the initial concentrations of butane and 2-methylpropane are each \(0.100 \mathrm{~mol} / \mathrm{L}\). Make up a table of initial concentrations, change in concentrations, and equilibrium concentrations for this reaction. (b) Write the equilibrium constant expression in terms of \(x\), the change in the concentration of butane, and then solve for \(x\). (c) If you place 0.017 mol butane in a \(0.50-\mathrm{L}\) sealed flask at \(25^{\circ} \mathrm{C},\) calculate the equilibrium concentration of each isomer.

The hydrocarbon cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12},\) can isomerize, changing into methylcyclopentane, a compound with the same molecular formula but a different molecular structure. $$ \mathrm{C}_{6} \mathrm{H}_{12}(\mathrm{~g}) \rightleftharpoons \mathrm{C}_{5} \mathrm{H}_{9} \mathrm{CH}_{3}(\mathrm{~g}) $$ \(\begin{array}{l}\text { cyclohexane } & \text { methylcyclopentane }\end{array}\) The equilibrium constant \(K_{\mathrm{c}}\) has been estimated to be 0.12 at \(25^{\circ} \mathrm{C}\). If you place \(3.79 \mathrm{~g}\) cyclohexane in an empty \(2.80-\mathrm{L}\) flask and seal the flask, calculate the mass of cyclohexane that is present when equilibrium is established.

Consider the equilibrium $$ \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) $$ At \(2300 \mathrm{~K}\) the equilibrium constant \(K_{\mathrm{c}}=1.7 \times 10^{-3}\). If \(0.15 \mathrm{~mol} \mathrm{NO}(\mathrm{g})\) is placed into an empty, sealed \(10.0-\mathrm{L}\) flask and heated to \(2300 \mathrm{~K},\) calculate the equilibrium concentrations of all three substances at this temperature.

The equilibrium constant, \(K_{\mathrm{c}}\), for the reaction $$ \mathrm{Br}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{BrF}(\mathrm{g}) $$ is 55.3 . Calculate what the equilibrium concentrations of all these gases are if the initial concentrations of bromine and fluorine were both \(0.220 \mathrm{~mol} / \mathrm{L}\). (Assume constantvolume conditions.)

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) $$ has the value 50.0 at \(745 \mathrm{~K}\). (a) When \(1.00 \mathrm{~mol} \mathrm{I}_{2}\) and \(3.00 \mathrm{~mol} \mathrm{H}_{2}\) are allowed to come to equilibrium at \(745 \mathrm{~K}\) in a sealed 10.00 -L flask, calculate the amount (in moles) of HI produced. (b) Calculate the amount of HI produced in a 5.00-L flask. (c) Calculate the total amount of HI present at equilibrium if an additional \(3.00 \mathrm{~mol} \mathrm{H}_{2}\) is added to the \(10.00-\mathrm{L}\) flask.

The equilibrium constant \(K_{\mathrm{c}}\) for the cis-trans isomerization of gaseous 2 -butene has the value 1.50 at \(580 . \mathrm{K}\). C=CC(C)=C(C)C (a) Is the reaction product-favored at \(580 . \mathrm{K} ?\) Explain your answer. (b) Calculate the amount (in moles) of trans isomer produced when \(1 \mathrm{~mol}\) cis-2-butene is heated to \(580 . \mathrm{K}\) in the presence of a catalyst in a sealed, 1.00 - \(\mathrm{L}\) flask and reaches equilibrium. (c) What would the answer be if the flask had a volume of \(10.0 \mathrm{~L} ?\)

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) $$ has the value \(2.64 \times 10^{-3}\) at \(2300 . \mathrm{K}\). If a mixture of \(1.00 \mathrm{~mol} \mathrm{CO}\) and \(1.00 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) is allowed to come to equilibrium in a sealed, \(1.00-\mathrm{L}\) flask at \(2300 . \mathrm{K}\), (a) calculate the final concentrations of all four species: CO, \(\mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2}\) (b) calculate the equilibrium concentrations after an additional 1.00 mol each of \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) is added to the flask.

At \(503 \mathrm{~K}\) the equilibrium constant \(K_{\mathrm{c}}\) for the dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) $$ has the value 40.0 . (a) Calculate the fraction of \(\mathrm{N}_{2} \mathrm{O}_{4}\) left undissociated when \(1.00 \mathrm{~mol}\) of this gas is heated to \(503 \mathrm{~K}\) in a \(10.0-\mathrm{L}\) sealed container. (b) If the volume is now reduced to \(2.0 \mathrm{~L},\) calculate the new fraction of \(\mathrm{N}_{2} \mathrm{O}_{4}\) that is undissociated. (c) Calculate all three equilibrium concentrations.

Consider the equilibrium at \(25^{\circ} \mathrm{C}\) $$ 2 \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \quad K_{\mathrm{c}}=3.58 \times 10^{-3} $$ Suppose that \(0.15 \mathrm{~mol} \mathrm{SO}_{3}(\mathrm{~g}), 0.015 \mathrm{~mol} \mathrm{SO}_{2}(\mathrm{~g}),\) and \(0.0075 \mathrm{~mol} \mathrm{O}_{2}(\mathrm{~g})\) are placed into a \(10.0-\mathrm{L}\) flask at \(25^{\circ} \mathrm{C}\) and the flask is sealed. (a) Is the system at equilibrium? (b) If the system is not at equilibrium, in which direction must the reaction proceed to reach equilibrium? Explain your answer.

At \(2300 \mathrm{~K}\) the equilibrium constant for the formation of \(\mathrm{NO}(\mathrm{g})\) is \(1.7 \times 10^{-3}\) $$ \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) $$ (a) Analysis of the contents of a sealed flask at \(2300 \mathrm{~K}\) shows that the concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are both \(0.25 \mathrm{M}\) and that of \(\mathrm{NO}\) is \(0.0042 \mathrm{M}\). Determine if the system is at equilibrium. (b) If the system is not at equilibrium, in which direction does the reaction proceed? (c) Calculate all three equilibrium concentrations.

Consider the equilibrium $$ \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) $$ At \(2300 \mathrm{~K}\) the equilibrium constant \(K_{\mathrm{c}}=1.7 \times 10^{-3}\). Suppose that \(0.015 \mathrm{~mol} \mathrm{NO}(\mathrm{g}), 0.25 \mathrm{~mol} \mathrm{~N}_{2}(\mathrm{~g}),\) and \(0.25 \mathrm{~mol} \mathrm{O}_{2}(\mathrm{~g})\) are placed into a \(10.0-\mathrm{L}\) flask, sealed, and heated to \(2300 \mathrm{~K}\). (a) Determine whether the system is at equilibrium. (b) If not, in which direction must the reaction proceed to reach equilibrium? (c) Calculate the equilibrium concentrations of all three substances.

Consider the equilibrium $$ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) $$ At \(745 \mathrm{~K}\) the equilibrium constant \(K_{\mathrm{c}}=50.0 .\) Suppose that \(0.75 \mathrm{~mol} \mathrm{HI}(\mathrm{g}), 0.025 \mathrm{~mol} \mathrm{H}_{2}(\mathrm{~g})\), and \(0.025 \mathrm{~mol}\) \(\mathrm{I}_{2}(\mathrm{~g})\) are placed into a sealed 20.0 - \(\mathrm{L}\) flask and heated to \(745 \mathrm{~K}\) (a) Is the system at equilibrium? (b) If not, in which direction must the reaction proceed to reach equilibrium? (c) Calculate the equilibrium concentrations of all three substances.