Consider the following equilibrium systems:

Define equilibrium. Give two examples of a dynamic equilibrium.

Write \(K_{c}\) and \(K_{p}\) for the decomposition of dinitrogen pentoxide: \(2 \mathrm{N}_{2} \mathrm{O}_{5}(g)\ \leftrightharpoons\ 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\)

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

Carbonyl chloride \(\left(\mathrm{COCl}_2\right)\), also called phosgene, was used in World War I as a poisonous gas. The equilibrium concentrations for the reaction between carbon monoxide and molecular chlorine to form carbonyl chloride \(\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_2(\mathrm{~g}) \rightleftharpoons \mathrm{COCl}_2(\mathrm{~g})\) at \(74^{\circ} \mathrm{C}\) are \([\mathrm{CO}]=1.2 \times 10^{-2} M\), \(\left[\mathrm{Cl}_2\right]=0.054 \mathrm{M}\), and \(\left[\mathrm{COCl}_2\right]=0.14 \mathrm{M}\). Calculate the equilibrium constant \(\left(K_{\mathrm{c}}\right)\).

You are given the equilibrium constant for the reaction \(N_{2}(g)+O_{2}(g)\ \leftrightharpoons\ 2 N O(g)\) Suppose you want to calculate the equilibrium constant for the reaction \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(g)\) What additional equilibrium constant value (for another reaction) would you need for this calculation? Assume all the equilibria are studied at the same temperature.

What is the law of mass action?

The equilibrium constant \(K_{p}\) for the reaction \(2 \mathrm{NO}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) Is 158 at 1000 K. Calculate \(P_{O_{2}}\) if \(P_{NO_{2}}=0.400\ \mathrm{atm}\) and \(P_{\mathrm{NO}}=0.270\ \mathrm{atm}\).

From the following equilibrium constant expression, write a balanced chemical equation for the gas-phase reaction. \(K_{c}=\frac{\left[\mathrm{NH}_{3}\right]^{2}\left[\mathrm{H}_{2} \mathrm{O}\right]^{4}}{\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{H}_{2}\right]^{7}}\)

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

The equilibrium constant \(\left(K_{c}\right)\) for reaction \(A\ \leftrightharpoons\ B+C\) is \(4.8 \times 10^{-2}\) at \(80^{\circ} \mathrm{C}\). If the forward rate constant is \(3.2 \times 10^{2}\ \mathrm{s}^{-1}\), calculate the reverse rate constant.

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

Write equilibrium constant expressions for \(K_{c}\) and \(K_{p}\) for the formation of nickel tetracarbonyl, which is used to separate nickel from other impurities: \(N i(s)+4 C O(g)\ \leftrightharpoons\ N i(C O)_{4}(g)\)

The equilibrium constant \(\left(K_{c}\right)\) for the \(A_{2}+B_{2}\ \leftrightharpoons\ 2 A B\) reaction is 3 at a certain temperature. Which of the diagrams shown here corresponds to the reaction at equilibrium? For those mixtures that are not at equilibrium, will the net reaction move in the forward or reverse direction to reach equilibrium?

What do the symbols \(K_{C}\) and \(K_{p}\) represent?

Consider the following equilibrium at 395 K: \(\mathrm{NH}_{4} \mathrm{HS}(s)\ \leftrightharpoons\ \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g)\) The partial pressure of each gas is 0.265 atm. Calculate \(K_{p}\) and \(K_{c}\) for the reaction.

The diagram here shows the gaseous reaction \(2 A\ \leftrightharpoons\ A_{2}\) at equilibrium. If the pressure is decreased by increasing the volume at constant temperature, how would the concentrations of A and \(A_{2}\) change when a new equilibrium is established?

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

Problem 7RC Write the equilibrium expression (Kc) for each of the following reactions and show how they are related to each other ________________

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

The equilibrium constant \(\left(K_{c}\right)\) for the formation of nitrosyl chloride, an orange-yellow compound, from nitric oxide and molecular chlorine \(2 N O(g)+C l_{2}(g)\ \leftrightharpoons\ 2 N O C l(g)\) is \(6.5 \times 10^{4}\) at \(35^{\circ} \mathrm{C}\). In a certain experiment, \(2.0 \times 10^{-2} \text { mole }\) of NO, \(8.3 \times 10^{-3} \text { mole }\) of \(\mathrm{Cl}_{2}\), and 6.8 moles of NOCI are mixed in a 2.0-L flask. In which direction will the system proceed to reach equilibrium?

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

Consider the reaction in Example 14.9. Starting with a concentration of 0.040 M for HI, calculate the concentrations of HI, \(\mathrm{H}_{2}\), and \(I_{2}\) at equilibrium.

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

At \(1280^{\circ} \mathrm{C}\) the equilibrium constant \(\left(K_{c}\right)\) for the reaction \(B r_{2}(g)\ \leftrightharpoons\ 2 B r(g)\) is \(1.1 \times 10^{-3}\). If the initial concentrations are \(\left[B r_{2}\right]=6.3 \times 10^{-2}\ M\) and \([B r]=1.2 \times 10^{-2}\ M\), calculate the concentrations of these species at equilibrium.

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

At \(430^{\circ} \mathrm{C}\), the equilibrium constant \(\left(K_{p}\right)\) for the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(g)\) is \(1.5 \times 10^{5}\). In one experiment, the initial pressures of NO, \(O_{2}\), and \(\mathrm{NO}_{2}\) are \(2.1 \times 10^{-3}\ \mathrm{atm}\),\(1.1 \times 10^{-2}\ \mathrm{atm}\), and 0.14 atm, respectively. Calculate \(Q_{p}\) and predict the direction that the net reaction will shift to reach equilibrium.

Give an example of a multiple equilibria reaction.

Consider the equilibrium reaction involving nitrosyl chloride, nitric oxide, and molecular chlorine \(2 \mathrm{NOCl}(g)\ \leftrightharpoons\ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\) Predict the direction of the net reaction as a result of decreasing the pressure (increasing the volume) on the system at constant temperature.

The equilibrium constant for the reaction \(A\ \leftrightharpoons\ B\) is \(K_{C}=10\) at a certain temperature. (1) Starting with only reactant A, which of the diagrams shown here best represents the system at equilibrium? (2) Which of the diagrams best represents the system at equilibrium if \(K_{C}=0.10\)? Explain why you can calculate \(K_{C}\) in each case without knowing the volume of the container. The gray spheres represent the A molecules and the green spheres represent the B molecules.

Consider the equilibrium between molecular oxygen and ozone \(3 \mathrm{O}_{2}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{O}_{3}(\mathrm{g})\) \(\Delta H^{\circ}=284\ \mathrm{kJ} / \mathrm{mol}\) What would be the effect of (a) increasing the pressure on the system by decreasing the volume, (b) adding \(\mathrm{O}_{2}\) to the system at constant volume, (c) decreasing the temperature, and (d) adding a catalyst?

The following diagrams represent the equilibrium state for three different reactions of the type \(A+X\ \leftrightharpoons\ A X\ (X=B, C, \text { or } D)\): (a) Which reaction has the largest equilibrium constant? (b) Which reaction has the smallest equilibrium constant?

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

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

What is \(K_{P}\) at \(1273^{\circ} \mathrm{C}\) for the reaction \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{CO}_{2}(g)\) if \(K_{C}\) is \(2.24 \times 10^{22}\) at the same temperature?

The equilibrium constant \(K_{P}\) for the reaction \(2 \mathrm{SO}_{3}(g)\ \leftrightharpoons\ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)\) is \(1.8 \times 10^{-5}\) at \(350^{\circ} \mathrm{C}\). What is \(K_{C}\) for this reaction?

Consider the following reaction: \(N_{2}(g)+O_{2}(g)\ \leftrightharpoons\ 2 N O(g)\) If the equilibrium partial pressures of \(N_{2}\), \(\mathrm{O}_{2}\), 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 \(\left[N H_{3}\right]=0.25\ \mathrm{M}\), \(\left[N_{2}\right]=0.11\ M\), and \(\left[H_{2}\right]=1.91\ \mathrm{M}\). Calculate the equilibrium constant \(K_{C}\) for the synthesis of ammonia if the reaction is represented as (a) \(N_{2}(g)+3 H_{2}(g)\ \leftrightharpoons\ 2 N H H_{3}(g)\) (b) \(\frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g)\ \leftrightharpoons\ N H_{3}(g)\)

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

At equilibrium, the pressure of the reacting mixture \(\mathrm{CaCO}_{3}(s)\ \leftrightharpoons\ \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) is 0.105 atm at \(350^{\circ} \mathrm{C}\). Calculate \(K_{P}\) and \(K_{C}\) for this reaction.

The equilibrium constant \(K_{P}\) for the reaction \(P C l_{5}(g)\ \leftrightharpoons\ P C l_{3}(g)+C l_{2}(g)\) 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 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.

Ammonium carbamate, \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\), decomposes as follows: \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s)\ \leftrightharpoons\ 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)\) Starting with only the solid, it is found that at \(40^{\circ} \mathrm{C}\) the total gas pressure (\(\mathrm{NH}_{3}\) and \(\mathrm{CO}_{2}\)) is 0.363 atm. Calculate the equilibrium constant \(K_{P}\).

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

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

Consider the equilibrium \(2 N O B r(g)\ \leftrightharpoons\ 2 N O(g)+B r_{2}(g)\) If nitrosyl bromide, NOBr, is 34 percent dissociated at \(25^{\circ} \mathrm{C}\) and the total pressure is 0.25 atm, calculate \(K_{P}\) and \(K_{C}\) for the dissociation at this temperature.

A 2.50-mole quantity of NOCI was initially in a 1.50-L reaction chamber at \(400^{\circ} \mathrm{C}\). After equilibrium was established, it was found that 28.0 percent of the NOCI had dissociated: \(2 \mathrm{NOCl}(g)\ \leftrightharpoons\ 2 N O(g)+\mathrm{Cl}_{2}(g)\) Calculate the equilibrium constant \(K_{C}\) for the reaction.

The following equilibrium constants have been determined for hydrosulfuric acid at \(25^{\circ} \mathrm{C}\): \(H_{2} S(a q)\ \leftrightharpoons\ H^{+}(a q)+H S^{-}(a q)\) \(K_{c}^{\prime}=9.5 \times 10^{-8}\) \(H S^{-}(a q)\ \leftrightharpoons\ H^{+}(a q)+S^{2-}(a q)\) \(K_{c}^{\prime \prime}=1.0 \times 10^{-19}\) Calculate the equilibrium constant for the following reaction at the same temperature: \(H_{2} S(a q)\ \leftrightharpoons\ 2 H^{+}(a q)+S^{2-}(a q)\)

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

The following equilibrium constants were determined at 1123 K: \(C(s)+\mathrm{CO}_{2}(g)\ \leftrightharpoons\ 2 C O(g)\ \ \ \ \ \ \ \ \quad K_{p}^{\prime}=1.3 \times 10^{14}\) \(C O(g)+C_{2}(g)\ \leftrightharpoons\ C O C l_{2}(g)\ \ \ \ \ \ \ \ \ \ \ \quad K_{p}^{\prime \prime}=6.0 \times 10^{-3}\) Write the equilibrium constant expression \(K_{p}\), and calculate the equilibrium constant at 1123 K for \(C(s)+\mathrm{CO}_{2}(g)+2 \mathrm{Cl}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{COCl}_{2}(g)\)

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

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.

Water is a very weak electrolyte that undergoes the following ionization (called autoionization): \(H_{2}O(l)\ \xrightarrow[{k_{-1}}]{{k_{1}}}\ H^{+}(aq)+OH^{-}(aq)\) (a) If \(k_{1}=2.4 \times 10^{-5}\ s^{-1}\) and \(k_{-1}=1.3 \times 10^{11} / M \cdot s\), calculate the equilibrium constant K where \(K=\left[H^{+}\right]\left[\mathrm{OH}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{O}\right]\). (b) Calculate the product \(\left[H^{+}\right]\left[O H^{-}\right]\) and \(\left[H^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\).

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

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

The equilibrium constant \(K_{P}\) for the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{SO}_{3}(g)\) 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 atm)?

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

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

At 1000 K, a sample of pure \(\mathrm{NO}_{2}\) gas decomposes: \(2 \mathrm{NO}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) 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 NO and \(\mathrm{NO}_{2}\) in the mixture.

The equilibrium constant \(K_{c}\) for the reaction \(H_{2}(g)+B r_{2}(g)\ \leftrightharpoons\ 2 H B r(g)\) is \(2.18 \times 10^{6}\) at \(730^{\circ} \mathrm{C}\). Starting with 3.20 moles of HBr in a 12.0-L reaction vessel, calculate the concentrations of \(\mathrm{H}_{2}\), \(B r_{2}\), and HBr at equilibrium.

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

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

Consider the following equilibrium process at \(686^{\circ} \mathrm{C}\): \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\ \leftrightharpoons\ C O(g)+\mathrm{H}_{2} O(g)\) The equilibrium concentrations of the reacting species are \([\mathrm{CO}]=0.050 \mathrm{M},\ \left[\mathrm{H}_{2}\right]=0.0450 \mathrm{M},\ \left[\mathrm{CO}_{2}\right]=0.086 \mathrm{M},\ \text { and }\left[\mathrm{H}_{2} \mathrm{O}\right]=0.040 \mathrm{M}\). (a) Calculate \(K_{c}\) for the reaction at \(686^{\circ} \mathrm{C}\). (b) If we add \(\mathrm{CO}_{2}\) to increase its concentration to 0.50 mol/L, what will the concentrations of all the gases be when equilibrium is reestablished?

Consider the heterogeneous equilibrium process: \(C(s)+\mathrm{CO}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{CO}(g)\) 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 CO.

The equilibrium constant \(K_{c}\) for the reaction \(\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)\) is 4.2 at \(1650^{\circ} \mathrm{C}\). Initially 0.80 mol \(H_{2}\) and 0.80 mol \(\mathrm{CO}_{2}\) are injected into a 5.0-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.

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

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?

Consider the following equilibrium system involving \(\mathrm{SO}_{2},\ \mathrm{Cl}_{2},\ \text { and } \mathrm{SO}_{2} \mathrm{Cl}_{2}\) (sulfuryl dichloride): \(\mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\ \leftrightharpoons\ \mathrm{SO}_{2} \mathrm{Cl}_{2}(g)\) 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: \(2 \mathrm{NaHCO}_{3}(s)\ \leftrightharpoons\ \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}_{2}(g)\) 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) \(A\ \leftrightharpoons\ 2 B\ \ \ \ \ \ \ \ \ \ \ \quad \Delta H^{\circ}=20.0\ \mathrm{kJ} / \mathrm{mol}\) (b) \(A+B\ \leftrightharpoons\ C\ \ \ \ \ \ \ \ \ \ \ \quad \Delta H^{\circ}=-5.4\ \mathrm{kJ} / \mathrm{mol}\) (c) \(A\ \leftrightharpoons\ B\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \quad \Delta H^{\circ}=0.0\ \mathrm{kJ} / \mathrm{mol}\) Predict the change in the equilibrium constant \(K_{c}\) 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) \(A(s)\ \leftrightharpoons\ 2 B(s)\) (b) \(2 A(l)\ \leftrightharpoons\ B(l)\) (c) \(A(s)\ \leftrightharpoons\ B(g)\) (d) \(A(g)\ \leftrightharpoons\ B(g)\) (e) \(A(g)\ \leftrightharpoons\ 2 B(g)\)

Consider the equilibrium \(2 I(g)\ \leftrightharpoons\ I_{2}(g)\) 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 12 to the reaction mixture; and (c) decreasing the temperature at constant volume?

Consider the following equilibrium process: \(P C l_{5}(g)\ \leftrightharpoons\ P C l_{3}(g)+C l_{2}(g)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \quad \Delta H^{\circ}=92.5\ \mathrm{kJ} / \mathrm{mol}\) 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 \(2 \mathrm{SO}_2(g)+\mathrm{O}_2(g) \leftrightharpoons 2 \mathrm{SO}_3(g)\) \(\Delta H^{\circ}=-198.2 \mathrm{~kJ} / \mathrm{mol}\) 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.

In the uncatalyzed reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(\mathrm{g})\) the pressure of the gases at equilibrium are \(P_{N_{2} O_{4}}=0.377\ \mathrm{atm}\) and \(P_{\mathrm{NO}_{2}}=1.56\ \mathrm{atm}\) at \(100^{\circ} \mathrm{C}\). What would happen to these pressures if a catalyst were added to the mixture?

Consider the gas-phase reaction \(2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{CO}_{2}(\mathrm{g})\) Predict the shift in the equilibrium position when helium gas is added to the equilibrium mixture (a) at constant pressure and (b) at constant volume.

Consider the following equilibrium reaction in a closed container: \(\mathrm{CaCO}_{3}(s)\ \leftrightharpoons\ \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) What will happen if (a) the volume is increased; (b) some CaO is added to the mixture; (c) some \(\mathrm{CaCO}_{3}\) is removed; (d) some \(\mathrm{CO}_{2}\) is added to the mixture; (e) a few drops of a NaOH solution are added to the mixture; (f) a few drops of a HCl solution are added to the mixture (ignore the reaction between \(\mathrm{CO}_{2}\) and water); (g) temperature is increased?

Consider the statement: "The equilibrium constant of a reacting mixture of solid \(\mathrm{NH}_{4} \mathrm{Cl}\) and gaseous \(\mathrm{NH}_{3}\) and HCl is 0.316." List three important pieces of information that are missing from this statement.

Pure nitrosyl chloride (NOCI) gas was heated to \(240^{\circ} \mathrm{C}\) in a 1.00-L container. At equilibrium the total pressure was 1.00 atm and the NOCI pressure was 0.64 atm. \(2 \mathrm{NOCl}(g)\ \leftrightharpoons\ 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)\) (a) Calculate the partial pressures of NO and \(\mathrm{Cl}_{2}\) in the system. (b) Calculate the equilibrium constant \(K_{p}\).

Determine the initial and equilibrium concentrations of HI if the initial concentrations of \(\mathrm{H}_{2}\) and \(I_{2}\) are both 0.16 M and their equilibrium concentrations are both 0.072 M at \(430^{\circ} \mathrm{C}\). The equilibrium constant \(\left(K_{c}\right)\) for the reaction \(\mathrm{H}_{2}(g)+I_{2}(g)\ \leftrightharpoons\ 2 H I(g)\) is 54.2 at \(430^{\circ} \mathrm{C}\).

Diagram (a) shows the reaction \(\mathrm{A}_2(\mathrm{~g})+\) \(\mathrm{B}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{AB}(\mathrm{g})\) at equilibrium at a certain temperature, where the blue spheres represent A and the yellow spheres represent B. If each sphere represents 0.020 mole and the volume of the container is 1.0 L, calculate the concentration of each species when the reaction in (b) reaches equilibrium.

The equilibrium constant \(\left(K_p\right)\) for the formation of the air pollutant nitric oxide (NO) in an automobile engine at \(530^{\circ} \mathrm{C}\) is \(2.9 \times 10^{-11}\) \(N_2(g)+O_2(g) \leftrightharpoons 2 N O(g)\) (a) Calculate the partial pressure of NO under these conditions if the partial pressures of nitrogen and oxygen are 3.0 atm and 0.012 atm, respectively. (b) Repeat the calculation for atmospheric conditions where the partial pressures of nitrogen and oxygen are 0.78 atm and 0.21 atm and the temperature is \(25^{\circ} \mathrm{C}\). (The \(K_p\) for the reaction is \(4.0 \times 10^{-31}\) at this temperature.) (c) Is the formation of NO endothermic or exothermic? (d) What natural phenomenon promotes the formation of NO? Why?

Baking soda (sodium bicarbonate) undergoes thermal decomposition as follows: \(2 \mathrm{NaHCO}_{3}\ \leftrightharpoons\ \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) Would we obtain more \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) by adding extra baking soda to the reaction mixture in (a) a closed vessel or (b) an open vessel?

Consider the following reaction at equilibrium: \(A(g)\ \leftrightharpoons\ 2 B(g)\) From the data shown here, calculate the equilibrium constant (both \(K_{p} \text { and } K_{c}\)) at each temperature. Is the reaction endothermic or exothermic?

The equilibrium constant \(K_{p}\) for the reaction \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) is \(2 \times 10^{-42}\) at \(25^{\circ} \mathrm{C}\). (a) What is \(K_{c}\) for the reaction at the same temperature? (b) The very small value of \(K_{p}\) (and \(K_{c}\)) indicates that the reaction overwhelmingly favors the formation of water molecules. Explain why, despite this fact, a mixture of hydrogen and oxygen gases can be kept at room temperature without any change.

Consider the following reacting system: \(2 N O(g)+\mathrm{Cl}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NOCl}(\mathrm{g})\) What combination of temperature and pressure (high or low) would maximize the yield of nitrosyl chloride (NOCI)? [Hint: \(\Delta H_{f}^{\circ}\)(NOCI) = 51.7 kJ/mol. You will also need to consult Appendix 3.]

At a certain temperature and a total pressure of 1.2 atm, the partial pressures of an equilibrium mixture \(2 A(g)\ \leftrightharpoons\ B(g)\) are \(P_{A}=0.60\ \mathrm{atm}\) and \(P_{B}=0.60\ \mathrm{atm}\). (a) Calculate the \(K_{p}\) for the reaction at this temperature. (b) If the total pressure were increased to 1.5 atm, what would be the partial pressures of A and B at equilibrium?

The decomposition of ammonium hydrogen sulfide \(\mathrm{NH}_{4} \mathrm{HS}(\mathrm{s})\ \leftrightharpoons\ \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) is an endothermic process. A 6.1589-g sample of the solid is placed in an evacuated 4.000-L vessel at exactly \(24^{\circ} \mathrm{C}\). After equilibrium has been established, the total pressure inside is 0.709 atm. Some solid \(\mathrm{NH}_{4} \mathrm{HS}\) remains in the vessel. (a) What is the \(K_{p}\) for the reaction? (b) What percentage of the solid has decomposed? (c) If the volume of the vessel were doubled at constant temperature, what would happen to the amount of solid in the vessel?

When heated, ammonium carbamate decomposes as follows: \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s)\ \leftrightharpoons\ 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)\) At a certain temperature the equilibrium pressure of the system is 0.318 atm. Calculate \(K_{p}\) for the reaction.

When heated at high temperatures, iodine vapor dissociates as follows: \(I_{2}(g)\ \leftrightharpoons\ 2 I(g)\) In one experiment, a chemist finds that when 0.054 mole of \(I_{2}\) was placed in a flask of volume 0.48 L at 587 K, the degree of dissociation (that is, the fraction of \(I_{2}\) dissociated) was 0.0252. Calculate \(K_{c}\) and \(K_{p}\) for the reaction at this temperature.

Eggshells are composed mostly of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) formed by the reaction \(\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q)\ \leftrightharpoons\ \mathrm{CaCO}_{3}(s)\) The carbonate ions are supplied by carbon dioxide produced as a result of metabolism. Explain why eggshells are thinner in the summer when the rate of panting by chickens is greater. Suggest a remedy for this situation.

At room temperature, solid iodine is in equilibrium with its vapor through sublimation and deposition (see p. 504). Describe how you would use radioactive iodine, in either solid or vapor form, to show that there is a dynamic equilibrium between these two phases.

A mixture containing 3.9 moles of NO and 0.88 mole of \(\mathrm{CO}_{2}\) was allowed to react in a flask at a certain temperature according to the equation \(\mathrm{NO}(g)+\mathrm{CO}_{2}(g)\ \leftrightharpoons\ \mathrm{NO}_{2}(g)+\mathrm{CO}(g)\) At equilibrium, 0.11 mole of \(\mathrm{CO}_{2}\) was present. Calculate the equilibrium constant \(K_{c}\) of this reaction.

When heated, a gaseous compound A dissociates as follows: \(A(g)\ \leftrightharpoons\ B(g)+C(g)\) In an experiment. A was heated at a certain temperature until its equilibrium pressure reached 0.14P where P is the total pressure. Calculate the equilibrium constant \(K_{p}\) of this reaction.

When a gas was heated under atmospheric conditions, its color deepened. Heating above \(150^{\circ} \mathrm{C}\) caused the color to fade, and at \(550^{\circ} \mathrm{C}\) the color was barely detectable. However, at \(550^{\circ} \mathrm{C}\), the color was partially restored by increasing the pressure of the system. Which of the following best fits the above description? Justify your choice. (a) A mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color and nitrogen dioxide is a brown gas. The other gases are colorless.)

The equilibrium constant \(K_{c}\) for the following reaction is 1.2 at \(375^{\circ} \mathrm{C}\). \(N_{2}(g)+3 H_{2}(g)\ \leftrightharpoons\ 2 N H_{3}(g)\) (a) What is the value of \(K_{p}\) for this reaction? (b) What is the value of the equilibrium constant \(K_{c}\) for \(2 \mathrm{NH}_{3}(g)\ \leftrightharpoons\ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) (c) What is the value of \(K_{c}\) for \(\frac{1}{2} N_{2}(g)+\frac{3}{2} H_{2}(g)\ \leftrightharpoons\ N H_{3}(g)\)? (d) What are the values of \(K_{p}\) for the reactions described in (b) and (c)?

Industrially, sodium metal is obtained by electrolyzing molten sodium chloride. The reaction at the cathode is \(\mathrm{Na}^{+}+e^{-}\ \rightarrow\ N a\). We might expect that potassium metal would also be prepared by electrolyzing molten potassium chloride. However, potassium metal is soluble in molten potassium chloride and therefore is hard to recover. Furthermore, potassium vaporizes readily at the operating temperature, creating hazardous conditions. Instead, potassium is prepared by the distillation of molten potassium chloride in the presence of sodium vapor at \(892^{\circ} \mathrm{C}\): \(N a(g)+K C l(l)\ \leftrightharpoons\ N a C l(l)+K(g)\) In view of the fact that potassium is a stronger reducing agent than sodium, explain why this approach works. (The boiling points of sodium and potassium are \(892^{\circ} \mathrm{C}\) and \(770^{\circ} \mathrm{C}\), respectively.)

About 75 percent of hydrogen for industrial use is produced by the steam-reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at \(800^{\circ} \mathrm{C}\) to give hydrogen and carbon monoxide: \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)\ \leftrightharpoons\ \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)\) \(\Delta H^{\circ}=260\ \mathrm{kJ} / \mathrm{mol}\) The secondary stage is carried out at about \(1000^{\circ} \mathrm{C}\), in the presence of air, to convert the remaining methane to hydrogen: \(\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\ \leftrightharpoons\ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)\) \(\Delta H^{\circ}=35.7\ \mathrm{kJ} / \mathrm{mol}\) (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stage? (b) The equilibrium constant \(K_{c}\) for the primary stage is 18 at \(800^{\circ} \mathrm{C}\). (i) Calculate \(K_{p}\) for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?

At \(25^{\circ} \mathrm{C}\), the equilibrium partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) are 0.15 atm and 0.20 atm, respectively. If the volume is doubled at constant temperature, calculate the partial pressures of the gases when a new equilibrium is established.

In 1899 the German chemist Ludwig Mond developed a process for purifying nickel by converting it to the volatile nickel tetracarbonyl \(\left[\mathrm{Ni}(\mathrm{CO})_4\right]\) (b.p. \(=42.2^{\circ} \mathrm{C}\) ) \(\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \leftrightharpoons \mathrm{Ni}(\mathrm{CO})_4(\mathrm{~g})\) (a) Describe how you can separate nickel and its solid impurities. (b) How would you recover nickel? \(\Delta \mathrm{H}_f^{\circ}\) for \(\mathrm{Ni}(\mathrm{CO})_4\) is - \(602.9 \mathrm{~kJ} / \mathrm{mol}\).]

The forward and reverse rate constants for the reaction \(A(g)+B(g)\ \leftrightharpoons\ C(g)\) are \(3.6 \times 10^{-3} / M \cdot s\) and \(8.7 \times 10^{-4}\ \mathrm{s}^{-1}\), respectively, at 323 K. Calculate the equilibrium pressures of all the species starting at \(P_{A}=1.6\ \mathrm{atm}\) and \(P_{B}=0.44\ \mathrm{atm}\).

The "boat" form and "chair" form of cyclohexane \(\left(C_{6} H_{12}\right)\) interconverts as shown here: In this representation, the H atoms are omitted and a C atom is assumed to be at each intersection of two lines (bonds). The conversion is first order in each direction. The activation energy for the chair \(\rightarrow\) boat conversion is 41 kJ/mol. If the frequency factor is \(1.0 \times 10^{12}\ \mathrm{s}^{-1}\), what is k at 298 K? The equilibrium constant \(K_{c}\) for the reaction is \(9.83 \times 10^{3}\) at 298 K.

Iodine is sparingly soluble in water but much more so in carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\). The equilibrium constant, also called the partition coefficient, for the distribution of \(I_{2}\) between these two phases \(I_{2}(a q)\ \leftrightharpoons\ I_{2}\left(C C l_{4}\right)\) is 83 at \(20^{\circ} \mathrm{C}\). (a) A student adds 0.030 L of \(\mathrm{CCl}_{4}\) to 0.200 L of an aqueous solution containing 0.032 g \(I_{2}\). The mixture is shaken and the two phases are then allowed to separate. Calculate the fraction of \(I_{2}\) remaining in the aqueous phase. (b) The student now repeats the extraction of \(I_{2}\) with another 0.030 L of \(\mathrm{CCl}_{4}\). Calculate the fraction of the \(I_{2}\) from the original solution that remains in the aqueous phase. (c) Compare the result in (b) with a single extraction using 0.060 L of \(\mathrm{CCl}_{4}\). Comment on the difference.

The equilibrium constant \(\left(K_{p}\right)\) for the reaction \(I_{2}(g)\ \rightarrow\ 2 I(g)\) is \(1.8 \times 10^{-4}\) at 872 K and 0.048 at 1173 K. From these data, estimate the bond enthalpy of \(I_{2}\). (Hint: See van't Hoff's equation in Problem 14.119.)

For the reaction \(N_{2}(g)+3 H_{2}(g)\ \leftrightharpoons\ 2 N H H_{3}(g)\) \(K_{p}\) is \(4.3 \times 10^{-4}\) at \(375^{\circ} \mathrm{C}\). Calculate \(K_{c}\) for the reaction.

For which of the following reactions is \(K_{c}\) equal to \(K_{p}\)? (a) \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g})\ \leftrightharpoons\ 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (b) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(a q)\ \leftrightharpoons\ 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g})\) (c) \(\mathrm{PCl}_{3}(g)+3 \mathrm{NH}_{3}(\mathrm{g})\ \leftrightharpoons\ 3 \mathrm{HCl}(\mathrm{g})+\mathrm{P}\left(\mathrm{NH}_{2}\right)_{3}(g)\)

Write the equilibrium expression \(\left(K_{c}\right)\) for each of the following reactions and show how they are related to each other: (a) \(3 O_{2}(g)\ \leftrightharpoons\ 2 O_{3}(g)\), (b) \(O_{2}(g)\ \leftrightharpoons\ \frac{2}{3} O_{3}(g)\).

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

Consider the reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(g)\) At \(430^{\circ} \mathrm{C}\), an equilibrium mixture consists of 0.020 mole of \(O_{2}\), 0.040 mole of NO, and 0.96 mole of \(\mathrm{NO}_{2}\). Calculate \(K_{p}\) for the reaction, given that the total pressure is 0.20 atm.

A mixture of 0.47 mole of \(H_{2}\) and 3.59 moles of HCI is heated to \(2800^{\circ} \mathrm{C}\). Calculate the equilibrium partial pressures of \(H_{2}\), \(\mathrm{Cl}_{2}\), and HCl if the total pressure is 2.00 atm. For the reaction \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{HCl}(g)\) \(K_{p}\) is 193 at \(2800^{\circ} \mathrm{C}\).

One mole of \(N_{2}\) and three moles of \(\mathrm{H}_{2}\) are placed in a flask at \(375^{\circ} \mathrm{C}\). Calculate the total pressure of the system at equilibrium if the mole fraction of \(\mathrm{NH}_{3}\) is 0.21. The \(K_{p}\) for the reaction is \(4.31 \times 10^{-4}\).

At \(1130^{\circ} \mathrm{C}\) the equilibrium constant \(\left(K_{c}\right)\) for the reaction \(2 \mathrm{H}_{2} \mathrm{S}(g)\ \leftrightharpoons\ 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)\) is \(2.25 \times 10^{-4}\). If \(\left[H_{2} S\right]=4.84 \times 10^{-3}\ M\) and \(\left[H_{2}\right]=1.50 \times 10^{-3}\ M\), calculate \(\left[S_{2}\right]\).

A quantity of 6.75 g of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) was placed in a 2.00-L flask. At 648 K, there is 0.0345 mole of \(\mathrm{SO}_{2}\) present. Calculate \(K_{c}\) for the reaction \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)\ \leftrightharpoons\ \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\)

The formation of \(\mathrm{SO}_{3}\) from \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) is an intermediate step in the manufacture of sulfuric acid, and it is also responsible for the acid rain phenomenon. The equilibrium constant \(K_{p}\) for the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{SO}_{3}(g)\) is 0.13 at \(830^{\circ} \mathrm{C}\). In one experiment 2.00 mol \(\mathrm{SO}_{2}\) and 2.00 mol \(\mathrm{O}_{2}\) were initially present in a flask. What must the total pressure at equilibrium be in order to have an 80.0 percent yield of \(\mathrm{SO}_{3}\)?

Consider the dissociation of iodine: \(I_{2}(g)\ \leftrightharpoons\ 2 I(g)\) A 1.00-g sample of I, is heated to \(1200^{\circ} \mathrm{C}\) in a 500-ml flask. At equilibrium the total pressure is 1.51 atm. Calculate \(K_{p}\) for the reaction. (Hint: Use the result in 14.117(a). The degree of dissociation \(\alpha\) can be obtained by first calculating the ratio of observed pressure over calculated pressure, assuming no dissociation.)

The equilibrium constant \(K_{p}\) for the following reaction is \(4.31 \times 10^{-4}\) at \(375^{\circ} \mathrm{C}\): \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{NH}_{3}(g)\) In a certain experiment a student starts with 0.862 atm of \(N_{2}\) and 0.373 atm of \(\mathrm{H}_{2}\) in a constant-volume vessel at \(375^{\circ} \mathrm{C}\). Calculate the partial pressures of all species when equilibrium is reached.

A quantity of 0.20 mole of carbon dioxide was heated to a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: \(C(s)+\mathrm{CO}_2(g) \leftrightharpoons 2 \mathrm{CO}(g)\) Under these conditions, the average molar mass of the gases was 35 g / mol. (a) Calculate the mole fractions of CO and CO \(\mathrm{CO}_2\). (b) What is \(K_p\) if the total pressure is 11 atm ? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.)

When dissolved in water, glucose (corn sugar) and fructose (fruit sugar) exist in equilibrium as follows: \(\text { fructose }\ \leftrightharpoons\ \text { glucose }\) A chemist prepared a 0.244 M fructose solution at \(25^{\circ} C\). At equilibrium, it was found that its concentration had decreased to 0.113 M. (a) Calculate the equilibrium constant for the reaction. (b) At equilibrium, what percentage of fructose was converted to glucose?

At \(1024^{\circ} \mathrm{C}\), the pressure of oxygen gas from the decomposition of copper(II) oxide (CuO) is 0.49 atm: \(4 \mathrm{CuO}(\mathrm{s})\ \leftrightharpoons\ 2 \mathrm{Cu}_{2} \mathrm{O}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g})\) (a) What is \(K_{p}\) for the reaction? (b) Calculate the fraction of CuO that will decompose if 0.16 mole of it is placed in a 2.0-L flask at \(1024^{\circ} \mathrm{C}\). (c) What would the fraction be if a 1.0 mole sample of Cuo were used? (d) What is the smallest amount of Cuo (in moles) that would establish the equilibrium?

The equilibrium constant \(K_{c}\) for the reaction \(H_{2}(g)+I_{2}(g)\ \leftrightharpoons\ 2 H I(g)\) is 54.3 at \(430^{\circ} \mathrm{C}\). At the start of the reaction there are 0.714 mole of \(\mathrm{H}_{2}\), 0.984 mole of \(I_{2}\)., and 0.886 mole of HI in a 2.40-L reaction chamber. Calculate the concentrations of the gases at equilibrium.

In this chapter we learned that a catalyst has no effect on the position of an equilibrium because it speeds up both the forward and reverse rates to the same extent. To test this statement, consider a situation in which an equilibrium of the type \(2 A(g)\ \leftrightharpoons\ B(g)\) is established inside a cylinder fitted with a weightless piston. The piston is attached by a string to the cover of a box containing a catalyst. When the piston moves upward (expanding against atmospheric pressure), the cover is lifted and the catalyst is exposed to the gases. When the piston moves downward, the box is closed. Assume that the catalyst speeds up the forward reaction \((2 A\ \rightarrow\ B)\) but does not affect the reverse process \((B\ \rightarrow\ 2 A)\). Suppose the catalyst is suddenly exposed to the equilibrium system as shown here. Describe what would happen subsequently. How does this “thought" experiment convince you that no such catalyst can exist?

A sealed glass bulb contains a mixture of \(\mathrm{NO}_2\) and \(\mathrm{N}_2 \mathrm{O}_4\) gasses. Describe what happens to the following properties of the gasses when the bulb is heated from \(20^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\) : (a) color, (b) pressure, (c) average molar mass, (d) degree of dissociation (from \(\mathrm{N}_2 \mathrm{O}_4\) to \(\mathrm{NO}_2\) ), (e) density. Assume that volume remains constant. (Hint: \(\mathrm{NO}_2\) is a brown gas; \(\mathrm{N}_2 \mathrm{O}_4\) is colorless.)

At \(20^{\circ} \mathrm{C}\), the vapor pressure of water is 0.0231 atm. Calculate \(K_{p}\) and \(K_{c}\) for the process \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\ \leftrightharpoons\ \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

In the gas phase, nitrogen dioxide is actually a mixture of nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\) and dinitrogen tetroxide \(\left(\mathrm{N}_{2} \mathrm{O}_{4}\right)\). If the density of such a mixture is 2.3 g/L at \(74^{\circ} \mathrm{C}\) and 1.3 atm, calculate the partial pressures of the gases and \(K_{p}\) for the dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\).

The equilibrium constant for the reaction \(A+2 B\ \leftrightharpoons\ 3 C\) is 0.25 at a certain temperature. Which diagram shown here corresponds to the system at equilibrium? If the system is not at equilibrium, predict the direction of the net reaction to reach equilibrium. Each molecule represents 0.40 mole and the volume of the container is 2.0 L. The color codes are A = green, B = red, C = blue.

The equilibrium constant for the reaction \(4 X+Y\ \leftrightharpoons\ 3 Z\) is 33.3 at a certain temperature. Which diagram shown here corresponds to the system at equilibrium? If the system is not at equilibrium, predict the direction of the net reaction to reach equilibrium. Each molecule represents 0.20 mole and the volume of the container is 1.0 L. The color codes are X = blue, Y = green, and Z = red.

Photosynthesis can be represented by \(6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\ \leftrightharpoons\ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{s})+6 \mathrm{O}_{2}(g)\) \(\Delta H^{\circ}=2801\ \mathrm{kJ} / \mathrm{mol}\) Explain how the equilibrium would be affected by the following changes: (a) partial pressure of \(\mathrm{CO}_{2}\) is increased, (b) \(\mathrm{O}_{2}\) is removed from the mixture, (c) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (glucose) is removed from the mixture, (d) more water is added, (e) a catalyst is added, (f) temperature is decreased.

Consider the decomposition of ammonium chloride at a certain temperature: \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\ \leftrightharpoons\ \mathrm{NH}_{3}(\mathrm{g})+\mathrm{HCl}(\mathrm{g})\) Calculate the equilibrium constant \(K_{p}\) if the total pressure is 2.2 atm at that temperature.

Consider the equilibrium reaction described in Problem 14.23. A quantity of 2.50 g of \(\mathrm{PCl}_{5}\) is placed in an evacuated 0.500-L flask and heated to \(250^{\circ} \mathrm{C}\). (a) Calculate the pressure of \(\mathrm{PCl}_{5}\), assuming it does not dissociate. (b) Calculate the partial pressure of \(\mathrm{PCl}_{5}\) at equilibrium. (c) What is the total pressure at equilibrium? (d) What is the degree of dissociation of \(\mathrm{PCl}_{5}\)? (The degree of dissociation is given by the fraction of \(\mathrm{PCl}_{5}\) that has undergone dissociation.)

Consider the equilibrium system \(3 A\ \leftrightharpoons\ B\). Sketch the changes in the concentrations of A and B over time for the following situations: (a) initially only A is present; (b) initially only B is present; (c) initially both A and B are present (with A in higher concentration). In each case, assume that the concentration of B is higher than that of A at equilibrium.

The vapor pressure of mercury is 0.0020 mmHg at \(26^{\circ} \mathrm{C}\). (a) Calculate \(K_{c}\) and \(K_{p}\) for the process \(H g(l)\ \leftrightharpoons\ H g(g)\). (b) A chemist breaks a thermometer and spills mercury onto the floor of a laboratory measuring 6.1 m long, 5.3 m wide, and 3.1 m high. Calculate the mass of mercury (in grams) vaporized at equilibrium and the concentration of mercury vapor in \(m g / m^{3}\). Does this concentration exceed the safety limit of \(0.05\ \mathrm{mg} / \mathrm{m}^{3}\)? (Ignore the volume of furniture and other objects in the laboratory.)

At \(25^{\circ} \mathrm{C}\), a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) gases are in equilibrium in a cylinder fitted with a movable piston. The concentrations are \(\left[\mathrm{NO}_{2}\right]\) = 0.0475 M and \(\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]\) = 0.487 M. The volume of the gas mixture is halved by pushing down on the piston at constant temperature. Calculate the concentrations of the gases when equilibrium is reestablished. Will the color become darker or lighter after the change? [Hint: \(K_{c}\) for the dissociation of \(\mathrm{N}_{2} \mathrm{O}_{4}\) to \(\mathrm{NO}_{2}\) is \(4.63 \times 10^{-3}\). \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) is colorless and \(\mathrm{NO}_{2}(g)\) has a brown color.]

A student placed a few ice cubes in a drinking glass with water. A few minutes later she noticed that some of the ice cubes were fused together. Explain what happened.

Consider the potential energy diagrams for two types of reactions \(A \leftrightharpoons B\). In each case, answer the following questions for the system at equilibrium. (a) How would a catalyst affect the forward and reverse rates of the reaction? (b) How would a catalyst affect the energies of the reactant and product? (c) How would an increase in temperature affect the equilibrium constant? (d) If the only effect of a catalyst is to lower the activation energies for the forward and reverse reactions, show that the equilibrium constant remains unchanged if a catalyst is added to the reacting mixture.

The equilibrium constant \(K_{c}\) for the reaction \(2 \mathrm{NH}_{3}(g)\ \leftrightharpoons\ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\) is 0.83 at \(375^{\circ} \mathrm{C}\). A 14.6-g sample of ammonia is placed in a 4.00-L flask and heated to \(375^{\circ} \mathrm{C}\). Calculate the concentrations of all the gases when equilibrium is reached.

A quantity of 1.0 mole of \(\mathrm{N}_{2} \mathrm{O}_{4}\) was introduced into an evacuated vessel and allowed to attain equilibrium at a certain temperature \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(g)\) The average molar mass of the reacting mixture was 70.6 g/mol. (a) Calculate the mole fractions of the gases. (b) Calculate \(K_{p}\) for the reaction if the total pressure was 1.2 atm. (c) What would be the mole fractions if the pressure were increased to 4.0 atm by reducing the volume at the same temperature?

The equilibrium constant \(\left(K_{p}\right)\) for the reaction \(C(s)+\mathrm{CO}_{2}(g)\ \leftrightharpoons\ 2 \mathrm{CO}(g)\) is 1.9 at \(727^{\circ} \mathrm{C}\). What total pressure must be applied to the reacting system to obtain 0.012 mole of \(\mathrm{CO}_{2}\) and 0.025 mole of CO?

The equilibrium constant \(\left(K_{p}\right)\) for the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)\ \leftrightharpoons\ \mathrm{PCl}_{5}(g)\) is 2.93 at \(127^{\circ} \mathrm{C}\). Initially there were 2.00 moles of \(\mathrm{PCl}_{3}\) and 1.00 mole of \(\mathrm{Cl}_{2}\) present. Calculate the partial pressures of the gases at equilibrium if the total pressure is 2.00 atm.

Consider the reaction between \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) in a closed container: \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(g)\) Initially, 1 mole of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is present. At equilibrium, a mole of \(\mathrm{N}_{2} \mathrm{O}_{4}\) has dissociated to form \(\mathrm{NO}_{2}\). (a) Derive an expression for \(K_{p}\) in terms of \(\alpha\) and P, the total pressure. (b) How does the expression in (a) help you predict the shift in equilibrium due to an increase in P? Does your prediction agree with Le Châtelier's principle?

The dependence of the equilibrium constant of a reaction on temperature is given by the van't Hoff equation: \(\ln K=-\frac{\Delta H^{\circ}}{R T}+C\) where C is a constant. The following table gives the equilibrium constant \(\left(K_P\right)\) for the reaction at various temperatures \(2 \mathrm{NO}(g)+\mathrm{O}_2(g) \rightleftharpoons 2 \mathrm{NO}_2(g)\) Determine graphically the \(\Delta H^{\circ}\) for the reaction.

(a) Use the van't Hoff equation in Problem 14.118 to derive the following expression, which relates the equilibrium constants at two different temperatures \(\ln \frac{K_{1}}{K_{2}}=\frac{\Delta H^{0}}{R}\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)\) How does this equation support the prediction based on Le Châtelier's principle about the shift in equilibrium with temperature? (b) The vapor pressures of water are 31.82 mmHg at \(30^{\circ} \mathrm{C}\) and 92.51 mmHg at \(50^{\circ} \mathrm{C}\). Calculate the molar heat of vaporization of water.

The \(K_{p}\) for the reaction \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(g)\ \leftrightharpoons\ \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g)\) is 2.05 at 648 K. A sample of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a container and heated to 648 K while the total pressure is kept constant at 9.00 atm. Calculate the partial pressures of the gases at equilibrium.

Consider the following reaction at a certain temperature \(A_{2}+B_{2}\ \leftrightharpoons\ 2 A B\) The mixing of 1 mole of \(A_{2}\) with 3 moles of \(B_{2}\) gives rise to x mole of AB at equilibrium. The addition of 2 more moles of \(A_{2}\) produces another x mole of AB. What is the equilibrium constant for the reaction?

Consider the following equilibrium system: \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\ \leftrightharpoons\ 2 \mathrm{NO}_{2}(\mathrm{g})\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \quad \Delta H^{\circ}=58.0 \mathrm{kJ} / \mathrm{mol}\) (a) If the volume of the reacting system is changed at constant temperature, describe what a plot of P versus 1/V would look like for the system. (Hint: See Figure 5.7.) (b) If the temperature of the reacting system is changed at constant pressure, describe what a plot of V versus T would look like for the system. (Hint: See Figure 5.9.)

At \(1200^{\circ} \mathrm{C}\), the equilibrium constant \(\left(K_{c}\right)\) for the reaction \(I_{2}(g)\ \leftrightharpoons\ 2 I(g)\) is \(2.59 \times 10^{-3}\). Calculate the concentrations of \(I_{2}\) and I after the stopcock is opened and the system reestablishes equilibrium at the same temperature.

Estimate the vapor pressure of water at \(60^{\circ} \mathrm{C}\) (see Problem 14.119).

A compound \(X Y_{2}(s)\) decomposes to form X(g) and Y(g) according to the following chemical equation: \(X Y_{2}(s)\ \rightarrow\ X(g)+2 Y(g)\) A 0.01-mol sample of \(X Y_{2}(s)\) was placed in a 1-L vessel, which was sealed and heated to \(500^{\circ} \mathrm{C}\). The reaction was allowed to reach equilibrium, at which point some \(X Y_{2}(s)\) remained in the vessel. The experiment was repeated, this time using a 2-L vessel, and again some \(X Y_{2}(s)\) remained in the vessel after equilibrium was established. This process was repeated, each time doubling the volume of the vessel, until finally a 16-L vessel was used, at which point heating the vessel and its contents to 500°C resulted in decomposition of the entire 0.01 mole of XY(s) according to the above reaction. Estimate \(K_{c}\) and \(K_{p}\) for the reaction at \(500^{\circ} \mathrm{C}\).

Using the simplified chemical equilibrium given in the Chemistry in Action on p. 653, by how much would the concentration of hemoglobin, Hb, in a person's blood need to increase if she moved to an altitude of 2 km above sea level, in order to give the same concentration of \(\mathrm{HbO}_{2}\) as when she was living at sea level?