Chapter 14

Define equilibrium. Give two examples of a dynamic equilibrium.

Explain the difference between physical equilibrium and chemical equilibrium. Give two examples of each.

What is the law of mass action?

Briefly describe the importance of equilibrium in the study of chemical reactions.

Define homogeneous equilibrium and heterogeneous equilibrium. Give two examples of each.

What do the symbols \(K_{\mathrm{c}}\) and \(K_{P}\) represent?

Write the expressions for the equilibrium constants \(K_{P}\) of the following thermal decomposition reactions: (a) \(2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons\) $$\mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ (b) \(2 \mathrm{CaSO}_{4}(s) \rightleftharpoons\) $$2 \mathrm{CaO}(s)+2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$

Write equilibrium constant expressions for \(K_{\mathrm{c}},\) and for \(K_{P}\), if applicable, for the following processes: (a) \(2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)\) (b) \(3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)\) (d) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) (e) \(\mathrm{HCOOH}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HCOO}^{-}(a q)\) (f) \(2 \mathrm{HgO}(s) \rightleftharpoons 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\)

Write the equilibrium constant expressions for \(K_{\mathrm{c}}\) and \(K_{P}\), if applicable, for the following reactions: (a) \(2 \mathrm{NO}_{2}(g)+7 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g)\) (c) \(\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)\) (d) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}(a q) \rightleftharpoons\) $$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-}(a q)+\mathrm{H}^{+}(a q)$$

Write the equation relating \(K_{\mathrm{c}}\) to \(K_{P}\), and define all the terms.

What is the rule for writing the equilibrium constant for the overall reaction involving two or more reactions?

Give an example of a multiple equilibria reaction.

The equilibrium constant \(\left(K_{\mathrm{c}}\right)\) for the reaction $$2 \mathrm{HCl}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)$$ is \(4.17 \times 10^{-34}\) at \(25^{\circ} \mathrm{C} .\) What is the equilibrium constant for the reaction $$\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)$$ at the same temperature?

Consider the following equilibrium process at \(700^{\circ} \mathrm{C}:\) $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)$$ Analysis shows that there are 2.50 moles of \(\mathrm{H}_{2}\), \(1.35 \times 10^{-5}\) mole of \(\mathrm{S}_{2}\), and 8.70 moles of \(\mathrm{H}_{2} \mathrm{~S}\) present in a 12.0-L flask. Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

Consider the following reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ If the equilibrium partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and NO are 0.15 atm, 0.33 atm, and 0.050 atm, respectively, at \(2200^{\circ} \mathrm{C},\) what is \(K_{P} ?\)

A reaction vessel contains \(\mathrm{NH}_{3}, \mathrm{~N}_{2},\) and \(\mathrm{H}_{2}\) at equilibrium at a certain temperature. The equilibrium concentrations are \(\left[\mathrm{NH}_{3}\right]=0.25 M,\left[\mathrm{~N}_{2}\right]=0.11 M\) and \(\left[\mathrm{H}_{2}\right]=1.91 \mathrm{M} .\) Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the synthesis of ammonia if the reaction is represented as (a) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) (b) \(\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{NH}_{3}(g)\)

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)$$ is \(3.8 \times 10^{-5}\) at \(727^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{c}}\) and \(K_{P}\) for the equilibrium $$2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g)$$ at the same temperature.

The equilibrium constant \(K_{P}\) for the reaction $$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ is 1.05 at \(250^{\circ} \mathrm{C}\). The reaction starts with a mixture of \(\mathrm{PCl}_{5}, \mathrm{PCl}_{3},\) and \(\mathrm{Cl}_{2}\) at pressures \(0.177 \mathrm{~atm},\) 0.223 atm, and 0.111 atm, respectively, at \(250^{\circ} \mathrm{C}\). When the mixture comes to equilibrium at that temperature, which pressures will have decreased and which will have increased? Explain why.

Consider the following reaction at \(1600^{\circ} \mathrm{C}\). $$\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)$$ When 1.05 moles of \(\mathrm{Br}_{2}\) are put in a 0.980 - \(\mathrm{L}\) flask, 1.20 percent of the \(\mathrm{Br}_{2}\) undergoes dissociation. Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

Pure phosgene gas \(\left(\mathrm{COCl}_{2}\right), 3.00 \times 10^{-2} \mathrm{~mol},\) was placed in a 1.50-L container. It was heated to \(800 \mathrm{~K}\), and at equilibrium the pressure of \(\mathrm{CO}\) was found to be 0.497 atm. Calculate the equilibrium constant \(K_{P}\) for the reaction $$\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g)$$

Consider the equilibrium $$2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g)$$ If nitrosyl bromide, \(\mathrm{NOBr},\) is 34 percent dissociated at \(25^{\circ} \mathrm{C}\) and the total pressure is 0.25 atm, calculate \(K_{P}\) and \(K_{\mathrm{c}}\) for the dissociation at this temperature.

A 2.50 -mole quantity of \(\mathrm{NOCl}\) was initially in a \(1.50-\mathrm{L}\) reaction chamber at \(400^{\circ} \mathrm{C}\). After equilibrium was established, it was found that 28.0 percent of the NOCl had dissociated: $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$ Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

The following equilibrium constants have been determined for hydrosulfuric acid at \(25^{\circ} \mathrm{C}\) $$\begin{array}{l}\mathrm{H}_{2} \mathrm{~S}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HS}^{-}(a q) \\\\\qquad \begin{aligned}K_{\mathrm{c}}^{\prime} &=9.5 \times 10^{-8} \\\\\mathrm{HS}^{-}(a q) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q) \\\K_{\mathrm{c}}^{\prime \prime}=1.0 \times 10^{-19}\end{aligned}\end{array}$$ Calculate the equilibrium constant for the following reaction at the same temperature: $$\mathrm{H}_{2} \mathrm{~S}(a q) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+\mathrm{S}^{2-}(a q)$$

The following equilibrium constants have been determined for oxalic acid at \(25^{\circ} \mathrm{C}\) : $$\begin{array}{l}\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \\\\\qquad \begin{array}{r}K_{\mathrm{c}}^{\prime}=6.5 \times 10^{-2} \\\\\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \\\K_{\mathrm{c}}^{\prime \prime}=6.1 \times 10^{-5}\end{array}\end{array}$$ Calculate the equilibrium constant for the following reaction at the same temperature: $$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q)$$

The following equilibrium constants were determined at \(1123 \mathrm{~K}\) $$\begin{array}{ll}\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) & K_{P}^{\prime}=1.3 \times 10^{14} \\\\\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) & K_{P}^{\prime \prime}=6.0 \times 10^{-3}\end{array}$$ Write the equilibrium constant expression \(K_{P}\), and calculate the equilibrium constant at \(1123 \mathrm{~K}\) for $$\mathrm{C}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{COCl}_{2}(g)$$

At a certain temperature the following reactions have the constants shown: $$\begin{array}{ll}\mathrm{S}(s)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g) & K_{\mathrm{c}}^{\prime}=4.2 \times 10^{52} \\ 2 \mathrm{~S}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) & K_{\mathrm{c}}^{\prime \prime}=9.8 \times 10^{128}\end{array}$$ Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the following reaction at that temperature: $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$

Based on rate constant considerations, explain why the equilibrium constant depends on temperature.

Explain why reactions with large equilibrium constants, such as the formation of rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right),\) may have very slow rates.

Consider the following reaction, which takes place in a single elementary step: $$2 \mathrm{~A}+\mathrm{B} \underset{k_{-1}}{\frac{k_{1}}{\longrightarrow}} \mathrm{A}_{2} \mathrm{~B}$$ If the equilibrium constant \(K_{\mathrm{c}}\) is 12.6 at a certain temperature and if \(k_{\mathrm{r}}=5.1 \times 10^{-2} \mathrm{~s}^{-1},\) calculate the value of \(k_{\mathrm{f}}\).

Define reaction quotient. How does it differ from equilibrium constant?

Outline the steps for calculating the concentrations of reacting species in an equilibrium reaction.

The equilibrium constant \(K_{P}\) for the reaction $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$ is \(5.60 \times 10^{4}\) at \(350^{\circ} \mathrm{C}\). The initial pressures of \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) in a mixture are 0.350 atm and 0.762 atm, respectively, at \(350^{\circ} \mathrm{C}\). When the mixture equilibrates, is the total pressure less than or greater than the sum of the initial pressures \((1.112 \mathrm{~atm}) ?\)

For the synthesis of ammonia $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)$$ the equilibrium constant \(K_{\mathrm{c}}\) at \(375^{\circ} \mathrm{C}\) is \(1.2 .\) Starting with \(\left[\mathrm{H}_{2}\right]_{0}=0.76 M,\left[\mathrm{~N}_{2}\right]_{0}=0.60 M,\) and \(\left[\mathrm{NH}_{3}\right]_{0}=\) \(0.48 M\), which gases will have increased in concentration and which will have decreased in concentration when the mixture comes to equilibrium?

For the reaction $$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$$ at \(700^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.534 .\) Calculate the number of moles of \(\mathrm{H}_{2}\) that are present at equilibrium if a mixture of 0.300 mole of \(\mathrm{CO}\) and \(0.300 \mathrm{~mole}\) of \(\mathrm{H}_{2} \mathrm{O}\) is heated to \(700^{\circ} \mathrm{C}\) in a 10.0 -L container.

At \(1000 \mathrm{~K},\) a sample of pure \(\mathrm{NO}_{2}\) gas decomposes: $$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$ The equilibrium constant \(K_{P}\) is \(158 .\) Analysis shows that the partial pressure of \(\mathrm{O}_{2}\) is 0.25 atm at equilibrium. Calculate the pressure of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) in the mixture.

The dissociation of molecular iodine into iodine atoms is represented as $$\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)$$ At \(1000 \mathrm{~K},\) the equilibrium constant \(K_{\mathrm{c}}\) for the reaction is \(3.80 \times 10^{-5}\). Suppose you start with 0.0456 mole of \(\mathrm{I}_{2}\) in a 2.30 -L flask at \(1000 \mathrm{~K}\). What are the concentrations of the gases at equilibrium?

The equilibrium constant \(K_{\mathrm{c}}\) for the decomposition of phosgene, \(\mathrm{COCl}_{2}\), is \(4.63 \times 10^{-3}\) at \(527^{\circ} \mathrm{C}\) : $$\mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g)$$ Calculate the equilibrium partial pressure of all the components, starting with pure phosgene at 0.760 atm.

Consider the heterogeneous equilibrium process: $$\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)$$ At \(700^{\circ} \mathrm{C},\) the total pressure of the system is found to be 4.50 atm. If the equilibrium constant \(K_{P}\) is 1.52, calculate the equilibrium partial pressures of \(\mathrm{CO}_{2}\) and \(\mathrm{CO}\).

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$$ is 4.2 at \(1650^{\circ} \mathrm{C}\). Initially \(0.80 \mathrm{~mol} \mathrm{H}_{2}\) and \(0.80 \mathrm{~mol}\) \(\mathrm{CO}_{2}\) are injected into a 5.0 - \(\mathrm{L}\) flask. Calculate the concentration of each species at equilibrium.

Explain Le Châtelier's principle. How can this principle help us maximize the yields of reactions?

Use Le Châtelier's principle to explain why the equilibrium vapor pressure of a liquid increases with increasing temperature.

List four factors that can shift the position of an equilibrium. Only one of these factors can alter the value of the equilibrium constant. Which one is it?

Does the addition of a catalyst have any effects on the position of an equilibrium?

Consider the following equilibrium system involving \(\mathrm{SO}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) (sulfuryl dichloride): $$\mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2} \mathrm{Cl}_{2}(g)$$ Predict how the equilibrium position would change if (a) \(\mathrm{Cl}_{2}\) gas were added to the system; (b) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) were removed from the system; (c) \(\mathrm{SO}_{2}\) were removed from the system. The temperature remains constant.

Heating solid sodium bicarbonate in a closed vessel establishes the following equilibrium: $$2 \mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)$$ What would happen to the equilibrium position if (a) some of the \(\mathrm{CO}_{2}\) were removed from the system; (b) some solid \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) were added to the system; (c) some of the solid \(\mathrm{NaHCO}_{3}\) were removed from the system? The temperature remains constant.

Consider the following equilibrium systems: (a) \(A \Longrightarrow 2 B\) \(\Delta H^{\circ}=20.0 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}\) \(\Delta H^{\circ}=-5.4 \mathrm{~kJ} / \mathrm{mol}\) (c) \(A \Longrightarrow B\) \(\Delta H^{\circ}=0.0 \mathrm{~kJ} / \mathrm{mol}\) Predict the change in the equilibrium constant \(K_{\mathrm{c}}\) that would occur in each case if the temperature of the reacting system were raised.

What effect does an increase in pressure have on each of the following systems at equilibrium? The temperature is kept constant and, in each case, the reactants are in a cylinder fitted with a movable piston. (a) \(\mathrm{A}(s) \rightleftharpoons 2 \mathrm{~B}(s)\) (b) \(2 \mathrm{~A}(l) \rightleftharpoons \mathrm{B}(l)\) (c) \(\mathrm{A}(s) \rightleftharpoons \mathrm{B}(g)\) (d) \(\mathrm{A}(g) \rightleftharpoons \mathrm{B}(g)\) (e) \(\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)\)

Consider the equilibrium $$2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g)$$ What would be the effect on the position of equilibrium of (a) increasing the total pressure on the system by decreasing its volume; (b) adding gaseous I \(_{2}\) to the reaction mixture; and (c) decreasing the temperature at constant volume?

Consider the following equilibrium process: $$\mathrm{PCl}_{5}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \quad \Delta H^{\circ}=92.5 \mathrm{~kJ} / \mathrm{mol}$$ Predict the direction of the shift in equilibrium when (a) the temperature is raised; (b) more chlorine gas is added to the reaction mixture; (c) some \(\mathrm{PCl}_{3}\) is removed from the mixture; (d) the pressure on the gases is increased; (e) a catalyst is added to the reaction mixture.

Consider the reaction $$\begin{array}{r}2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) \\\\\Delta H^{\circ}=-198.2 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ Comment on the changes in the concentrations of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at equilibrium if we were to (a) increase the temperature; (b) increase the pressure; (c) increase \(\mathrm{SO}_{2}\); (d) add a catalyst; (e) add helium at constant volume.