Chapter 15

Write equilibrium constant expressions for the following reactions. For gases, use either pressures or concentrations. (a) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\) (b) \(\mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})\) (c) \(\mathrm{C}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g})\) (d) \(\mathrm{NiO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Ni}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\)

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

\(K_{c}=5.6 \times 10^{-12}\) at \(500 \mathrm{K}\) for the dissociation of iodine molecules to iodine atoms. $$ \mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g})$$ A mixture has \(\left|\mathrm{I}_{2}\right|=0.020 \mathrm{mol} / \mathrm{L}\) and \(|\mathrm{I}|=\) \(2.0 \times 10^{-8} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilibrium (at \(500 \mathrm{K}\) )? If not, which way must the reaction proceed to reach equilibrium?

The reaction $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) $$ has an equilibrium constant, \(K_{c}\) of 170 at \(25^{\circ} \mathrm{C}\). If \(2.0 \times 10^{-3}\) mol of \(\mathrm{NO}_{2}\) is present in a \(10 .\) -L. flask along with \(1.5 \times 10^{-3}\) mol of \(\mathrm{N}_{2} \mathrm{O}_{4}\), is the system at equilibrium? If it is not at equilibrium, does the concentration of \(\mathrm{NO}_{2}\) increase or decrease as the system proceeds to equilibrium?

A mixture of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at \(1000 \mathrm{K}\) contains the gases at the following concentrations: \(\left|\mathrm{SO}_{2}\right|=\) $$5.0 \times 10^{-3} \mathrm{mol} / \mathrm{L},\left|\mathrm{O}_{2}\right|=1.9 \times 10^{-3} \mathrm{mol} / \mathrm{L}, \text { and } $$ \(\left[\mathrm{SO}_{3}\right]=6.9 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilibrium? If not, which way will the reaction proceed to reach equilibrium?$$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) K_{c}=279 $$

The equilibrium constant, \(K_{c}\) for the reaction $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ is \(3.9 \times 10^{-3}\) at \(300^{\circ} \mathrm{C} .\) A mixture contains the gases at the following concentrations: \(|\mathrm{NOCl}|=\) \(5.0 \times 10^{-3} \mathrm{mol} / \mathrm{L}_{\alpha}[\mathrm{NO}]=2.5 \times 10^{-3} \mathrm{mol} / \mathrm{L}_{u}\) and \(\left[\mathrm{Cl}_{2}\right]=2.0 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilibrium at \(300^{\circ} \mathrm{C} ?\) If not, in which direction does the reaction proceed to come to equilibrium?

The reaction $$ \mathrm{PCl}_{3}(\mathrm{g}) \rightleftharpoons \mathrm{PC}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ was examined at \(250^{\circ} \mathrm{C}\). At equilibrium, \(\left|\mathrm{PCl}_{5}\right|=\) \(4.2 \times 10^{-5} \mathrm{mol} / \mathrm{L},\left[\mathrm{PCl}_{3}\right]=1.3 \times 10^{-2} \mathrm{mol} / \mathrm{L}_{-}\) and \(\left[\mathrm{Cl}_{2}\right]=3.9 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\epsilon}\) for the reaction.

An equilibrium mixture of \(\mathrm{SO}_{2}, \mathrm{O}_{2},\) and \(\mathrm{SO}_{3}\) at a high temperature contains the gases at the following concentrations: \(\left[\mathrm{SO}_{2}\right]=3.77 \times 10^{-3} \mathrm{mol} / \mathrm{L}\) \(\left[\mathrm{O}_{2}\right]=4.30 \times 10^{-3} \mathrm{mol} / \mathrm{L},\) and \(\left[\mathrm{SO}_{3}\right]=4.13 \times\) \(10^{-3} \mathrm{mol} / \mathrm{L} .\) Calculate the equilibrium constant, \(K_{c}\) for the reaction. $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) $$

The reaction $$ \mathrm{C}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g}) $$ occurs at high temperatures. At \(700^{\circ} \mathrm{C},\) a 200.0 - \(\mathrm{L}\) tank contains 1.0 mol of \(\mathrm{CO}, 0.20\) mol of \(\mathrm{CO}_{2}\), and 0.40 mol of \(\mathrm{C}\) at equilibrium. (a) Calculate \(K_{c}\) for the reaction at \(700^{\circ} \mathrm{C}\) (b) Calculate \(K_{c}\) for the reaction, also at \(700^{\circ} \mathrm{C},\) if the amounts at equilibrium in the 200.0 -L tank are 1.0 mol of \(\mathrm{CO}, 0.20\) mol of \(\mathrm{CO}_{2}\), and \(0.80 \mathrm{mol}\) of \(\mathrm{C}\) (c) Compare the results of (a) and (b). Does the quantity of carbon affect the value of \(K_{c} ?\) Explain.

Hydrogen and carbon dioxide react at a high temperature to give water and carbon monoxide. $$ \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) $$ (a) Laboratory measurements at \(986^{\circ} \mathrm{C}\) show that there are 0.11 mol each of \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\) vapor and 0.087 mol each of \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) at equilibrium in a 50.0 -L container. Calculate the equilibrium constant for the reaction at \(986^{\circ} \mathrm{C}\) (b) Suppose 0.010 mol each of \(\mathrm{H}_{2}\) and \(\mathrm{CO}_{2}\) are placed in a 200.0 -L. container. When equilibrium is achieved at \(986^{\circ} \mathrm{C},\) what amounts of \(\mathrm{CO}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}),\) in moles, would be present? [Use the value of \(K_{c}\) from part (a).]

A mixture of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) is placed in a reaction flask: \(|\mathrm{CO}|=0.0102 \mathrm{mol} / \mathrm{L}\) and \(\left|\mathrm{Cl}_{2}\right|=\) \(0.00609 \mathrm{mol} / \mathrm{L} .\) When the reaction $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) $$ has come to equilibrium at \(600 \mathrm{R},\left[\mathrm{Cl}_{2}\right]=\) \(0.00301 \mathrm{mol} / \mathrm{L}\) (a) Calculate the concentrations of \(\mathrm{CO}\) and \(\mathrm{COCl}_{2}\) at equilibrium. (b) Calculate \(K_{\mathrm{r}}\)

You place 0.0300 mol of pure \(\mathrm{SO}_{3}\) in an \(8.00-\mathrm{L}\) flask at \(1150 \mathrm{K}\). At equilibrium, 0.0058 mol of \(\mathrm{O}_{2}\) has been formed. Calculate \(K_{c}\) for the reaction at \(1150 \mathrm{K}\) $$ 2 \mathrm{sO}_{3}(\mathrm{g}) \rightleftharpoons 2 \mathrm{sO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) $$

The equilibrium constant for the dissociation of iodine molecules to iodine atoms $$ \mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g}) $$ is \(3.76 \times 10^{-3}\) at 1000 K. Suppose 0.105 mol of \(\mathrm{I}_{2}\) is placed in a 12.3 -L flask at 1000 K. What are the concentrations of \(\mathrm{I}_{2}\) and I when the system comes to equilibrium?

The equilibrium constant, \(K_{c}\), for the reaction $$ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) $$ at \(25^{\circ} \mathrm{C}\) is \(5.9 \times 10^{-3} .\) Suppose \(15.6 \mathrm{g}\) of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is placed in a 5.000 -L flask at \(25^{\circ}\) C. Calculate the following: (a) the amount of \(\mathrm{NO}_{2}\) (mol) present at equilibrium; (b) the percentage of the original \(\mathrm{N}_{2} \mathrm{O}_{4}\) that is dissociated.

The equilibrium constant \(K\) for the reaction $$ \mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) $$ is \(6.66 \times 10^{-12}\) at 1000 K. Calculate \(K\) for the reaction $$ 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}_{2}(\mathrm{g}) $$

Calculate \(K\) for the reaction $$ \mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Sn}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) $$ given the following information: $$\begin{array}{c} \mathrm{SnO}_{2}(\mathrm{s})+2 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{Sn}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \quad K=8.12 \\\ \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \quad K=0.771 \end{array}$$

Calculate \(K\) for the reaction $$ \mathrm{Fe}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{FeO}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g}) $$ given the following information: $$\begin{array}{ll} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) & K=1.6 \\ \mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) & \mathrm{K}=0.67 \end{array}$$

Relationship of \(K_{c}\) and \(K_{\mathrm{p}}\) (a) \(K_{\mathrm{p}}\) for the following reaction is 0.16 at \(25^{\circ} \mathrm{C}\) What is the value of \(K_{c} ?\) $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ (b) The equilibrium constant, \(K_{c}\) for the following reaction is 1.05 at 350 K. What is the value of \(K_{\mathrm{p}} ?\) $$ 2 \mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CCl}_{4}(\mathrm{g}) $$

Dinitrogen trioxide decomposes to \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) in an endothermic process \(\left(\Delta_{r} H^{\circ}=40.5 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\right)\) $$ \mathrm{N}, \mathrm{O}_{3}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) $$ Predict the effect of the following changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of the following changes is made. (a) adding more \(\mathrm{N}_{2} \mathrm{O}_{3}(\mathrm{g})\) (b) adding more \(\mathrm{NO}_{2}(\mathrm{g})\) (c) increasing the volume of the reaction flask (d) lowering the temperature

\(K_{p}\) for the following reaction is 0.16 at \(25^{\circ} \mathrm{C}\) $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ The enthalpy change for the reaction at standard conditions is \(+16.3 \mathrm{kJ} / \mathrm{mol}\) -ran. Predict the effect of the following changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of the following changes is made. (a) adding more \(\mathrm{Br}_{2}(\mathrm{g})\) (b) removing some \(\mathrm{NOBr}(\mathrm{g})\) (c) decreasing the temperature (d) increasing the container volume

Consider the isomerization of butane with an equilibrium constant of \(K=2.5 .\) (See Study Question \(13 .\) The system is originally at equilibrium with [butane] \(=1.0 \mathrm{M}\) and [isobutane] \(=2.5 \mathrm{M}\) (a) If 0.50 mol/L. of isobutane is suddenly added and the system shifts to a new equilibrium position, what is the equilibrium concentration of each gas? (b) If 0.50 mol/L of butane is added to the original equilibrium mixture and the system shifts to a new equilibrium position, what is the equilibrium concentration of each gas?

The decomposition of \(\mathrm{NH}_{4} \mathrm{HS}\) $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ is an endothermic process. Using Le Chatelier's principle, explain how increasing the temperature would affect the equilibrium. If more \(\mathrm{NH}_{4} \mathrm{HS}\) is added to a flask in which this equilibrium exists, how is the equilibrium affected? What if some additional \(\mathrm{NH}_{3}\) is placed in the flask? What will happen to the pressure of \(\mathrm{NH}_{3}\) if some \(\mathrm{H}_{2} \mathrm{S}\) is removed from the flask?

Suppose 0.086 mol of Bra is placed in a 1.26-L. flask and heated to \(1756 \mathrm{K}\), a temperature at which the halogen 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 \(K_{c}\)

The equilibrium constant for the reaction $$ \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}) $$ is \(1.7 \times 10^{-3}\) at \(2300 K\) (a) What is \(K\) for the reaction when written as follows? $$ 1 / 2 \mathrm{N}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) $$ (b) What is \(K\) for the following reaction? $$ 2 \mathrm{NO}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) $$

\(K_{\mathrm{p}}\) for the formation of phosgene, \(\mathrm{COCl}_{2},\) is \(6.5 \times 10^{11}\) at \(25^{\circ} \mathrm{C}\) $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) $$ What is the value of \(K_{p}\) for the dissociation of phosgene? $$ \mathrm{COCl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$

The equilibrium constant, \(K_{c}\) for the following reaction is 1.05 at \(350 \mathrm{K}\). $$ 2 \mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CCl}_{4}(\mathrm{g}) $$ If an equilibrium mixture of the three gases at \(350 \mathrm{K}\) contains \(0.0206 \mathrm{M} \mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{g})\) and \(0.0163 \mathrm{M}\) \(\mathrm{CH}_{4},\) what is the equilibrium concentration of \(\mathrm{CCl}_{4} ?\)

Equal numbers of moles of \(\mathrm{H}_{2}\) gas and \(\mathrm{I}_{2}\) vapor are mixed in a flask 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 \(\mathrm{I}_{2}\) is consumed 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.

The equilibrium constant for the butane \(\rightleftarrows\) isobutane isomerization reaction is 2.5 at \(25^{\circ} \mathrm{C}\). If 1.75 mol of butane and 1.25 mol of isobutane are mixed, is the system at equilibrium? If not, when it proceeds to equilibrium, which reagent increases in concentration? Calculate the concentrations of the two compounds when the system reaches equilibrium.

At 2300 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 shows that the concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are both \(0.25 \mathrm{M},\) and that of \(\mathrm{NO}\) is \(0.0042 \mathrm{M}\) under certain conditions. Is the system at equilibrium? (b) If the system is not at equilibrium, in which direction does the reaction proceed? (c) When the system is at equilibrium, what are the equilibrium concentrations?

Consider the following equilibrium: \(\operatorname{COBr}_{2}(g) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=0.190\) at \(73^{\circ} \mathrm{C}\) (a) \(A\) 0.50 mol sample of \(\operatorname{COBr}_{2}\) is transferred to a 9.50-L. flask and heated until equilibrium is attained. Calculate the equilibrium concentrations of each species. (b) The volume of the container is decreased to 4.5 L and the system allowed to return to equilibrium. Calculate the new equilibrium concentrations. (Hint: The calculation will be easier if you view this as a new problem with 0.5 mol of \(\mathrm{COBr}_{2}\) transferred to a 4.5 -L flask. (c) What is the effect of decreasing the container volume from 9.50 L. to 4.50 L?

Heating a metal carbonate leads to decomposition. $$ \mathrm{BaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{BaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ Predict the effect on the equilibrium of each change listed below. Answer by choosing (i) no change, (ii) shifts left, or (iii) shifts right. (a) add \(\mathrm{BaCO}_{3}\) (c) add BaO (b) add \(\mathrm{CO}_{2}\) (d) raise the temperature (e) increase the volume of the flask containing the reaction

Carbonyl bromide decomposes to carbon monoxide and bromine. $$ \mathrm{COBr}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ \(K_{c}\) is 0.190 at \(73^{\circ} \mathrm{C}\). Suppose you place \(0.500 \mathrm{mol}\) of \(\mathrm{COBr}_{2}\) in a 2.00 -L. flask and heat it to \(73^{\circ} \mathrm{C}\) (see Study Question 17 ). After equilibrium has been achieved, you add an additional 2.00 mol of CO. (a) How is the equilibrium mixture affected by adding more CO? (b) When equilibrium is reestablished, what are the new equilibrium concentrations of \(\mathrm{COBr}_{2}\) \(\mathrm{CO},\) and \(\mathrm{Br}_{2} ?\) (c) How has the addition of CO affected the percentage of \(\mathrm{COBr}_{2}\) that decomposed?

Ammonium hydrogen sulfide decomposes on heating. $$ \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) $$ If \(K_{\mathrm{p}}\) for this reaction is 0.11 at \(25^{\circ} \mathrm{C}\) (when the partial pressures are measured in atmospheres), what is the total pressure in the flask at equilibrium?

Ammonium iodide dissociates reversibly to ammonia and hydrogen iodide if the salt is heated to a sufficiently high temperature. $$ \mathrm{NH}_{4}\left[(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{HI}(\mathrm{g})\right. $$ Some ammonium iodide is placed in a flask, which is then heated to \(400^{\circ} \mathrm{C}\). If the total pressure in the flask when equilibrium has been achieved is \(705 \mathrm{mm} \mathrm{Hg},\) what is the value of \(K_{\mathrm{p}}\) (when partial pressures are in atmospheres)?

\- When solid ammonium carbamate sublimes, it dissociates completely into ammonia and carbon dioxide according to the following equation: $$ \left(\mathrm{NH}_{4}\right)\left(\mathrm{H}_{2} \mathrm{NCO}_{2}\right)(\mathrm{s}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) $$ At \(25^{\circ} \mathrm{C},\) experiment shows that the total pressure of the gases in equilibrium with the solid is 0.116 atm. What is the equilibrium constant, \(K_{p} ?\)

Assume 3.60 mol of ammonia is placed in a 2.00 - \(L\) vessel and allowed to decompose to the elements at \(723 \mathrm{K}\) $$ 2 \mathrm{NH}_{3}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) $$ If the experimental value of \(K_{r}\) is 6.3 for this reaction at the temperature in the reactor, calculate the equilibrium concentration of each reagent. What is the total pressure in the flask?

The total pressure for a mixture of \(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\) is 0.15 atm. If \(K_{p}=7.1\) (at \(25^{\circ} \mathrm{C}\) ), calculate the partial pressure of each gas in the mixture. $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) $$

A \(\mathrm{COCl}_{2}\) decomposes to \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) at high temperatures. \(K_{c}\) at \(600 \mathrm{K}\) for the reaction is \(0.0071 .\) $$ \mathrm{COCl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ If 0.050 mol of \(\mathrm{COCl}_{2}\) is placed in a 12.5 -L. flask, what is the total pressure at equilibrium at \(600 \mathrm{K} ?\)

Lanthanum oxalate decomposes when heated to lanthanum(III) oxide, \(\mathrm{CO},\) and \(\mathrm{CO}_{2}\) \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}(\mathrm{s}) \rightleftharpoons \mathrm{La}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g})+3 \mathrm{CO}_{2}(\mathrm{g})\) (a) If, at equilibrium, the total pressure in a \(10.0-\mathrm{L}\) flask is 0.200 atm, what is the value of \(K_{p} ?\) (b) Suppose 0.100 mol of \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\) was originally placed in the 10.0-L. flask. What quantity of \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\) remains unreacted at equilibrium at \(373 \mathrm{K} ?\)

Sulfuryl chloride, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\), is used as a reagent in the synthesis of organic compounds. When heated to a sufficiently high temperature, it decomposes to \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=0.045\) at \(375^{\circ} \mathrm{C}\) (a) \(A\) 10.0-L. flask containing 6.70 g of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is heated to \(375^{\circ} \mathrm{C}\). What is the concentration of each of the compounds in the system when equilibrium is achieved? What fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) has dissociated? (b) What are the concentrations of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}, \mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\) at equilibrium in the 10.0 -L flask at \(375^{\circ} \mathrm{C}\) if you begin with a mixture of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) \((6.70 \mathrm{g})\) and \(\mathrm{Cl}_{2}(0.10 \mathrm{atm}) ?\) What fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) has dissociated? (c) Compare the fractions of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) in parts (a) and (b). Do they agree with your expectations based on Le Chatelier's principle?

Hemoglobin (Hb) can form a complex with both \(\mathrm{O}_{2}\) and \(\mathrm{CO}\). For the reaction $$ \mathrm{HbO}_{2}(\mathrm{aq})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{HbCO}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{g}) $$ at body temperature, \(K\) is about \(200 .\) If the ratio \(|\mathrm{HbCO}| /\left|\mathrm{HbO}_{2}\right|\) comes close to \(1,\) death is probable. What partial pressure of CO in the air is likely to be fatal? Assume the partial pressure of \(\mathbf{O}_{2}\) is \(0.20 \mathrm{atm}\)

A limestone decomposes at high temperatures. $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ At \(1000^{\circ} \mathrm{C}, K_{\mathrm{p}}=3.87 .\) If pure \(\mathrm{CaCO}_{3}\) is placed in a 5.00 -L flask and heated to \(1000^{\circ} \mathrm{C},\) what quantity of \(\mathrm{CaCO}_{3}\) must decompose to achieve the equilibrium pressure of \(\mathrm{CO}_{2} ?\)

At \(1800 \mathrm{K},\) oxygen dissociates very slightly into its atoms. $$ \mathbf{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{O}(\mathrm{g}) \quad K_{\mathrm{p}}=1.2 \times 10^{-10} $$ If you place 0.050 mol of \(\mathrm{O}_{2}\) in a \(10 .\) -L vessel and heat it to \(1800 \mathrm{K}\), how many \(\mathrm{O}\) atoms are present in the flask?

Boric acid and glycerin form a complex \(\mathrm{B}(\mathrm{OH})_{3}(\mathrm{aq})+\) glycerin \((\mathrm{aq}) \rightleftharpoons \mathrm{B}(\mathrm{OH})_{3} \cdot\) glycerin(aq) with an equilibrium constant of 0.90. If the concentration of boric acid is 0.10 M, how much glycerin should be added, per liter, so that \(60 . \%\) of the boric acid is in the form of the complex?

The dissociation of calcium carbonate has an equilibrium constant of \(K_{\mathrm{p}}=1.16\) at \(800^{\circ} \mathrm{C}\) $$ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ (a) What is \(K_{c}\) for the reaction? (b) If you place \(22.5 \mathrm{g}\) of \(\mathrm{CaCO}_{3}\) in a 9.56 -L container at \(800^{\circ} \mathrm{C},\) what is the pressure of \(\mathrm{CO}_{2}\) in the container? (c) What percentage of the original 22.5 -g sample of \(\mathrm{CaCO}_{3}\) remains undecomposed at equilibrium?

A sample of \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas with a pressure of 1.00 atm is placed in a flask. When equilibrium is achieved, \(20.0 \%\) of the \(\mathrm{N}_{2} \mathrm{O}_{4}\) has been converted to \(\mathrm{NO}_{2}\) gas. (a) Calculate \(K_{\mathrm{p}}\) (b) If the original pressure of \(\mathrm{N}_{2} \mathrm{O}_{4}\) is 0.10 atm, what is the percent dissociation of the gas? Is the result in agreement with Le Chatelier's principle?

Decide whether each of the following statements is true or false. If false, change the wording to make it true. (a) The magnitude of the equilibrium constant is always independent of temperature. (b) When two chemical equations are added to give a net equation, the equilibrium constant for the net equation is the product of the equilibrium constants of the summed equations. (c) The equilibrium constant for a reaction has the same value as \(K\) for the reverse reaction. (d) Only the concentration of \(\mathrm{CO}_{2}\) appears in the equilibrium constant expression for the reaction \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})\) (e) For the reaction \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\) \(\mathrm{CO}_{2}(\mathrm{g}),\) the value of \(K\) is numerically the same, whether the amount of \(\mathrm{CO}_{2}\) is expressed as moles/liter or as gas pressure.

Neither \(\mathrm{PbCl}_{2}\) nor \(\mathrm{PbF}_{2}\) is appreciably soluble in water. If solid \(\mathrm{PbCl}_{2}\) and solid \(\mathrm{PbF}_{2}\) are placed in equal amounts of water in separate beakers, in which beaker is the concentration of \(\mathrm{Pb}^{2+}\) greater? Equilibrium constants for these solids dissolving in water are as follows: $$\begin{aligned} \mathrm{PbCl}_{2}(\mathrm{s}) & \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq}) & & K_{c}=1.7 \times 10^{-5} \\ \mathrm{PbF}_{2}(\mathrm{s}) & \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{F}^{-}(\mathrm{aq}) & & K_{\mathrm{c}}=3.7 \times 10^{-8} \end{aligned}$$

Characterize each of the following as product- or reactant-favored at equilibrium. $$\begin{aligned} &\text { (a) } \mathrm{CO}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})\\\ &&K_{\mathrm{p}}=1.2 \times 10^{45} \end{aligned}$$ $$\begin{aligned} &\text { (b) } \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g})\\\ &&K_{\mathrm{p}}=9.1 \times 10^{-41} \end{aligned}$$ $$\begin{aligned} &\text { (c) } \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g})\\\ &&K_{\mathrm{p}}=6.5 \times 10^{11} \end{aligned}$$

The size of a flask containing colorless \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) and brown \(\mathrm{NO}_{2}(\mathrm{g})\) at equilibrium is rapidly reduced to half the original volume. $$\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \approx 2 \mathrm{NO}_{2}(\mathrm{g})$$ (a) What color change (if any) is observed immediately upon halving the flask size? (b) What color change (if any) is observed during the process in which equilibrium is reestablished in the flask?