Chapter 15

Based on these descriptions, write a balanced equation and the corresponding \(K_{c}\) expression for each reversible reaction. (a) Carbonyl fluoride, \(\mathrm{COF}_{2}(\mathrm{g}),\) decomposes into gaseous carbon dioxide and gaseous carbon tetrafluoride. (b) Copper metal displaces silver(I) ion from aqueous solution, producing silver metal and an aqueous solution of copper(II) ion. (c) Peroxodisulfate ion, \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\), oxidizes iron(II) ion to iron(III) ion in aqueous solution and is itself reduced to sulfate ion.

Based on these descriptions, write a balanced equation and the corresponding \(K_{\mathrm{p}}\) expression for each reversible reaction. (a) Oxygen gas oxidizes gaseous ammonia to gaseous nitrogen and water vapor. (b) Hydrogen gas reduces gaseous nitrogen dioxide to gaseous ammonia and water vapor. (c) Nitrogen gas reacts with the solid sodium carbonate and carbon to produce solid sodium cyanide and carbon monoxide gas.

Write equilibrium constant expressions, \(K_{\mathrm{c}},\) for the reactions (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\) (b) \(\mathrm{Zn}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Zn}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})\) (c) \(\mathrm{Mg}(\mathrm{OH})_{2}(\mathrm{s})+\mathrm{CO}_{3}^{2-}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{MgCO}_{3}(\mathrm{s})+2 \mathrm{OH}^{-}(\mathrm{aq})\)

Write equilibrium constant expressions, \(K_{\mathrm{p}},\) for the reactions (a) \(\mathrm{CS}_{2}(\mathrm{g})+4 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) (b) \(\mathrm{Ag}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons 2 \mathrm{Ag}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})\) (c) \(2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Write an equilibrium constant, \(K_{c},\) for the formation from its gaseous elements of \((a) 1\) mol \(\mathrm{HF}(\mathrm{g})\) (b) \(2 \mathrm{mol} \mathrm{NH}_{3}(\mathrm{g}) ;(\mathrm{c}) 2 \mathrm{mol} \mathrm{N}_{2} \mathrm{O}(\mathrm{g}) ;(\mathrm{d}) 1 \mathrm{mol} \mathrm{ClF}_{3}(1)\)

Write an equilibrium constant, \(K_{\mathrm{p}},\) for the formation from its gaseous elements of (a) 1 mol \(\mathrm{NOCl}(\mathrm{g})\) (b) \(2 \mathrm{mol} \mathrm{ClNO}_{2}(\mathrm{g}) ;\) (c) \(1 \mathrm{mol} \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{g}) ;\) (d) \(1 \mathrm{mol}\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\)

Determine values of \(K_{c}\) from the \(K_{p}\) values given. (a) \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) \(K_{\mathrm{p}}=2.9 \times 10^{-2} \mathrm{at} 303 \mathrm{K}\) (b) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g})\) \(K_{\mathrm{p}}=1.48 \times 10^{4} \mathrm{at} 184^{\circ} \mathrm{C}\) (c) \(\mathrm{Sb}_{2} \mathrm{S}_{3}(\mathrm{s})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{Sb}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) \(K_{\mathrm{p}}=0.429\) at \(713 \mathrm{K}\)

Determine \(K_{c}\) for the reaction $$\frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{Br}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NOBr}(\mathrm{g})$$ from the following information (at \(298 \mathrm{K}\) ). $$\begin{aligned} 2 \mathrm{NO}(\mathrm{g}) & \rightleftharpoons \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) K_{\mathrm{c}}=2.1 \times 10^{30} \\ \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{Br}_{2}(\mathrm{g}) & \rightleftharpoons \mathrm{NOBr}(\mathrm{g}) \quad K_{\mathrm{c}}=1.4 \end{aligned}$$

Given the equilibrium constant values $$\begin{aligned} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) & \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(\mathrm{g}) \quad K_{\mathrm{c}}=2.7 \times 10^{-18} \\ \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) & \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) K_{\mathrm{c}}=4.6 \times 10^{-3} \\ \frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) & \rightleftharpoons \mathrm{NO}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=4.1 \times 10^{-9} \end{aligned}$$ Determine a value of \(K_{\mathrm{c}}\) for the reaction $$ 2 \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) $$

Use the following data to estimate a value of \(K_{\mathrm{p}}\) at \(1200 \mathrm{K}\) for the reaction \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) $$\begin{array}{l} \text { C(graphite) }+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g}) \quad K_{\mathrm{c}}=0.64 \\ \quad \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \quad K_{\mathrm{c}}=1.4 \\ \text { C(graphite) }+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g}) \quad K_{\mathrm{c}}=1 \times 10^{8} \end{array}$$

Determine \(K_{c}\) for the reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})+\) \(\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NOCl}(\mathrm{g}),\) given the following data at \(298 \mathrm{K}\) $$\frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=1.0 \times 10^{-9}$$ $$\operatorname{NOCl}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \quad K_{\mathrm{p}}=1.1 \times 10^{2}$$ $$\mathrm{NO}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \quad K_{\mathrm{p}}=0.3$$

An important environmental and physiological reaction is the formation of carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}(\mathrm{aq})\) from carbon dioxide and water. Write the equilibrium constant expression for this reaction in terms of activities. Convert that expression into an equilibrium constant expression containing concentrations and pressures.

Rust, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s}),\) is caused by the oxidation of iron by oxygen. Write the equilibrium constant expression first in terms of activities, and then in terms of concentration and pressure.

\(1.00 \times 10^{-3} \mathrm{mol} \mathrm{PCl}_{5}\) is introduced into a \(250.0 \mathrm{mL}\) flask, and equilibrium is established at \(284^{\circ} \mathrm{C}\) : \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) .\) The quantity of \(\mathrm{Cl}_{2}(\mathrm{g})\) present at equilibrium is found to be \(9.65 \times 10^{-4} \mathrm{mol}\) What is the value of \(K_{c}\) for the dissociation reaction at \(284^{\circ} \mathrm{C} ?\)

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(1.06 \mathrm{g} \mathrm{H}_{2} \mathrm{S}\) in a 0.500 Lflask comes to equilibrium at \(1670 \mathrm{K}: 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{S}_{2}(\mathrm{g}) \rightleftharpoons\) \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) .\) The equilibrium amount of \(\mathrm{S}_{2}(\mathrm{g})\) found is \(8.00 \times 10^{-6}\) mol. Determine the value of \(K_{p}\) at 1670 K.

The two common chlorides of phosphorus, \(\mathrm{PCl}_{3}\) and \(\mathrm{PCl}_{5},\) both important in the production of other phosphorus compounds, coexist in equilibrium through the reaction $$ \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{5}(\mathrm{g}) $$ At \(250^{\circ} \mathrm{C},\) an equilibrium mixture in a \(2.50 \mathrm{L}\) flask contains \(0.105 \mathrm{g} \mathrm{PCl}_{5}, 0.220 \mathrm{g} \mathrm{PCl}_{3},\) and \(2.12 \mathrm{g} \mathrm{Cl}_{2}\) What are the values of (a) \(K_{c}\) and (b) \(K_{\mathrm{p}}\) for this reaction at \(250^{\circ} \mathrm{C} ?\)

Write the equilibrium constant expression for the following reaction, $$\begin{array}{r} \mathrm{Fe}(\mathrm{OH})_{3}+3 \mathrm{H}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ K=9.1 \times 10^{3} \end{array}$$ and compute the equilibrium concentration for \(\left[\mathrm{Fe}^{3+}\right]\) at \(\left.\mathrm{pH}=7 \text { (i.e., }\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-7}\right)\)

Write the equilibrium constant expression for the dissolution of ammonia in water: $$\mathrm{NH}_{3}(\mathrm{g}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{aq}) \quad K=57.5$$ Use this equilibrium constant expression to estimate the partial pressure of \(\mathrm{NH}_{3}(\mathrm{g})\) over a solution containing \(5 \times 10^{-9} \mathrm{M} \mathrm{NH}_{3}(\text { aq }) .\) These are conditions similar to that found for acid rains with a high ammonium ion concentration.

Equilibrium is established at \(1000 \mathrm{K},\) where \(K_{\mathrm{c}}=281\) for the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) .\) The equilibrium amount of \(\mathrm{O}_{2}(\mathrm{g})\) in a \(0.185 \mathrm{L}\) flask is 0.00247 mol. What is the ratio of \(\left[\mathrm{SO}_{2}\right]\) to \(\left[\mathrm{SO}_{3}\right]\) in this equilibrium mixture?

For the dissociation of \(\mathrm{I}_{2}(\mathrm{g})\) at about \(1200^{\circ} \mathrm{C}\) \(\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{I}(\mathrm{g}), K_{\mathrm{c}}=1.1 \times 10^{-2} .\) What volume flask should we use if we want 0.37 mol I to be present for every \(1.00 \mathrm{mol} \mathrm{I}_{2}\) at equilibrium?

In the Ostwald process for oxidizing ammonia, a variety of products is possible- \(\mathrm{N}_{2}, \mathrm{N}_{2} \mathrm{O}, \mathrm{NO},\) and \(\mathrm{NO}_{2}-\) depending on the conditions. One possibility is $$\begin{aligned} \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{4} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g}) &+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ K_{\mathrm{p}} &=2.11 \times 10^{19} \mathrm{at} 700 \mathrm{K} \end{aligned}$$ For the decomposition of \(\mathrm{NO}_{2}\) at \(700 \mathrm{K}\) $$\mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=0.524$$ (a) Write a chemical equation for the oxidation of \(\mathrm{NH}_{3}(\mathrm{g})\) to \(\mathrm{NO}_{2}(\mathrm{g})\) (b) Determine \(K_{\mathrm{p}}\) for the chemical equation you have written.

At \(2000 \mathrm{K}, K_{c}=0.154\) for the reaction \(2 \mathrm{CH}_{4}(\mathrm{g}) \rightleftharpoons\) \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) .\) If a \(1.00 \mathrm{L}\) equilibrium mixture at \(2000 \mathrm{K}\) contains \(0.10 \mathrm{mol}\) each of \(\mathrm{CH}_{4}(\mathrm{g})\) and \(\mathrm{H}_{2}(\mathrm{g})\) (a) what is the mole fraction of \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})\) present? (b) Is the conversion of \(\mathrm{CH}_{4}(\mathrm{g})\) to \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})\) favored at high or low pressures? (c) If the equilibrium mixture at \(2000 \mathrm{K}\) is transferred from a 1.00 L flask to a 2.00 L flask, will the number of moles of \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})\) increase, decrease, or remain unchanged?

An equilibrium mixture at 1000 K contains an equilibrium mixter \(0.276\ \mathrm{mol}\ \mathrm{H}_{2}, 0.276 \mathrm{mol}\ \mathrm{CO}_{2}, 0.224\ \mathrm{mol}\ \mathrm{CO},\) and \(0.224\ \mathrm{mol}\ \mathrm{H}_{2} \mathrm{O}\) $$\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ (a) Show that for this reaction, \(K_{\mathrm{c}}\) is independent of the reaction volume, \(V\) (b) Determine the value of \(K_{\mathrm{c}}\) and \(K_{\mathrm{p}}\)

For the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\) \(\mathrm{H}_{2}(\mathrm{g}), K_{\mathrm{p}}=23.2\) at \(600 \mathrm{K} .\) Explain which of the fol- lowing situations might equilibrium: (a) \(\quad P_{\mathrm{CO}}=P_{\mathrm{H}_{2} \mathrm{O}}=P_{\mathrm{CO}_{2}}=P_{\mathrm{H}_{2}} ; \quad\) (b) \(\quad P_{\mathrm{H}_{2}} / P_{\mathrm{H}_{2} \mathrm{O}}=\) \(P_{\mathrm{CO}_{2}} / P_{\mathrm{CO}} ; \quad(\mathrm{c}) \quad\left(P_{\mathrm{CO}_{2}}\right)\left(P_{\mathrm{H}_{2}}\right)=\left(P_{\mathrm{CO}}\right)\left(P_{\mathrm{H}_{2} \mathrm{O}}^{2}\right)\) (d) \(P_{\mathrm{CO}_{2}} / P_{\mathrm{H}_{2} \mathrm{O}}=P_{\mathrm{H}_{2}} / P_{\mathrm{CO}}\)

Can a mixture of \(2.2 \mathrm{mol} \mathrm{O}_{2}, 3.6 \mathrm{mol} \mathrm{SO}_{2},\) and \(1.8 \mathrm{mol}\) \(\mathrm{SO}_{3}\) be maintained indefinitely in a \(7.2 \mathrm{L}\) flask at a temperature at which \(K_{\mathrm{c}}=100\) in this reaction? Explain. $$ 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) $$

Is a mixture of \(0.0205 \mathrm{mol} \mathrm{NO}_{2}(\mathrm{g})\) and \(0.750 \mathrm{mol}\) \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})\) in a \(5.25 \mathrm{L}\) flask at \(25^{\circ} \mathrm{C},\) at equilibrium? If not, in which direction will the reaction proceed toward products or reactants? $$\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=4.61 \times 10^{-3} \mathrm{at} 25^{\circ} \mathrm{C}$$

In the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}), 0.455\) \(\mathrm{mol} \mathrm{SO}_{2}, 0.183 \mathrm{mol} \mathrm{O}_{2},\) and \(0.568 \mathrm{mol} \mathrm{SO}_{3}\) are introduced simultaneously into a 1.90 L vessel at \(1000 \mathrm{K}\). (a) If \(K_{c}=2.8 \times 10^{2},\) is this mixture at equilibrium? (b) If not, in which direction will a net change occur?

In the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\) \(\mathrm{H}_{2}(\mathrm{g}), K=31.4\) at \(588 \mathrm{K} .\) Equal masses of each reactant and product are brought together in a reaction vessel at \(588 \mathrm{K}\). (a) Can this mixture be at equilibrium? (b) If not, in which direction will a net change occur?

A mixture consisting of \(0.150 \mathrm{mol} \mathrm{H}_{2}\) and \(0.150 \mathrm{mol} \mathrm{I}_{2}\) is brought to equilibrium at \(445^{\circ} \mathrm{C},\) in a 3.25 L flask. What are the equilibrium amounts of \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and HI? $$\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) \quad K_{\mathrm{c}}=50.2\ \mathrm\ {at}\ 445^{\circ} \mathrm{C}$$

Starting with \(0.280 \mathrm{mol} \mathrm{SbCl}_{3}\) and \(0.160 \mathrm{mol} \mathrm{Cl}_{2},\) how many moles of \(\mathrm{SbCl}_{5}, \mathrm{SbCl}_{3},\) and \(\mathrm{Cl}_{2}\) are present when equilibrium is established at \(248^{\circ} \mathrm{C}\) in a 2.50 L flask? $$\begin{aligned} \mathrm{SbCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{SbCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) & \\ K_{\mathrm{c}}=& 2.5 \times 10^{-2} \mathrm{at} \ 248^{\circ} \mathrm{C} \end{aligned}$$

Starting with \(0.3500 \mathrm{mol} \mathrm{CO}(\mathrm{g})\) and \(0.05500 \mathrm{mol}\) \(\mathrm{COCl}_{2}(\mathrm{g})\) in a \(3.050 \mathrm{L}\) flask at \(668 \mathrm{K},\) how many moles of \(\mathrm{Cl}_{2}(\mathrm{g})\) will be present at equilibrium? $$\begin{aligned} \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) & \\ K_{\mathrm{c}} &=1.2 \times 10^{3} \mathrm{at} \ 668 \mathrm{K} \end{aligned}$$

\(1.00 \mathrm{g}\) each of \(\mathrm{CO}, \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{H}_{2}\) are sealed in a \(1.41 \mathrm{L}\) vessel and brought to equilibrium at 600 K. How many grams of \(\mathrm{CO}_{2}\) will be present in the equilibrium mixture? $$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=23.2$$

Equilibrium is established in a 2.50 L flask at \(250^{\circ} \mathrm{C}\) for the reaction $$\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \quad K_{\mathrm{c}}=3.8 \times 10^{-2}$$ How many moles of \(\mathrm{PCl}_{5}, \mathrm{PCl}_{3},\) and \(\mathrm{Cl}_{2}\) are present at equilibrium, if (a) 0.550 mol each of \(\mathrm{PCl}_{5}\) and \(\mathrm{PCl}_{3}\) are initially introduced into the flask? (b) \(0.610 \mathrm{mol} \mathrm{PCl}_{5}\) alone is introduced into the flask?

For the following reaction, \(K_{\mathrm{c}}=2.00\) at \(1000^{\circ} \mathrm{C}\) $$2 \operatorname{COF}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{CF}_{4}(\mathrm{g})$$ If a \(5.00 \mathrm{L}\) mixture contains \(0.145 \mathrm{mol} \mathrm{COF}_{2}, 0.262 \mathrm{mol}\) \(\mathrm{CO}_{2},\) and \(0.074 \mathrm{mol} \mathrm{CF}_{4}\) at a temperature of \(1000^{\circ} \mathrm{C}\) (a) Will the mixture be at equilibrium? (b) If the gases are not at equilibrium, in what direction will a net change occur? (c) How many moles of each gas will be present at equilibrium?

Formamide, used in the manufacture of pharmaceuticals, dyes, and agricultural chemicals, decomposes at high temperatures. $$\begin{array}{r} \mathrm{HCONH}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \\ K_{\mathrm{c}}=4.84 \text { at } 400 \mathrm{K} \end{array}$$ If \(0.186 \mathrm{mol} \mathrm{HCONH}_{2}(\mathrm{g})\) dissociates in a 2.16 Lflask at 400 K, what will be the total pressure at equilibrium?

A mixture of \(1.00 \mathrm{mol} \mathrm{NaHCO}_{3}(\mathrm{s})\) and \(1.00 \mathrm{mol}\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})\) is introduced into a \(2.50 \mathrm{L}\) flask in which the partial pressure of \(\mathrm{CO}_{2}\) is 2.10 atm and that of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is \(715 \mathrm{mmHg} .\) When equilibrium is established at \(100^{\circ} \mathrm{C},\) will the partial pressures of \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) be greater or less than their initial partial pressures? Explain. $$\begin{array}{r} 2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ K_{\mathrm{p}}=0.23 \mathrm{at} 100^{\circ} \mathrm{C} \end{array}$$

Cadmium metal is added to \(0.350 \mathrm{L}\) of an aqueous solution in which \(\left[\mathrm{Cr}^{3+}\right]=1.00 \mathrm{M} .\) What are the concentrations of the different ionic species at equilibrium? What is the minimum mass of cadmium metal required to establish this equilibrium? $$\begin{array}{r} 2 \mathrm{Cr}^{3+}(\mathrm{aq})+\mathrm{Cd}(\mathrm{s}) \rightleftharpoons 2 \mathrm{Cr}^{2+}(\mathrm{aq})+\mathrm{Cd}^{2+}(\mathrm{aq}) \\ K_{\mathrm{c}}=0.288 \end{array}$$

Lead metal is added to \(0.100 \mathrm{M} \mathrm{Cr}^{3+}(\mathrm{aq}) .\) What are \(\left[\mathrm{Pb}^{2+}\right],\left[\mathrm{Cr}^{2+}\right],\) and \(\left[\mathrm{Cr}^{3+}\right]\) when equilibrium is established in the reaction? $$\begin{aligned} \mathrm{Pb}(\mathrm{s})+2 \mathrm{Cr}^{3+}(\mathrm{aq}) \rightleftharpoons \mathrm{Pb}^{2+}(\mathrm{aq})+2 \mathrm{Cr}^{2+}(\mathrm{aq}) & \\ K_{\mathrm{c}}=3.2 \times 10^{-10} & \end{aligned}$$

One important reaction in the citric acid cycle is citrate(aq) \(\rightleftharpoons\) aconitate \((\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \quad K=0.031\) Write the equilibrium constant expression for the above reaction. Given that the concentrations of \([\text { citrate }(\mathrm{aq})]=0.00128 \mathrm{M},[\text { aconitate }(\mathrm{aq})]=4.0 \times\) \(10^{-5} \mathrm{M},\) and \(\left[\mathrm{H}_{2} \mathrm{O}\right]=55.5 \mathrm{M},\) calculate the reaction quotient. Is this reaction at equilibrium? If not, in which direction will it proceed?

The following reaction is an important reaction in the citric acid cycle: citrate(aq) \(+\mathrm{NAD}_{\mathrm{ox}}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons\) \(\mathrm{CO}_{2}(\mathrm{aq})+\mathrm{NAD}_{\mathrm{red}}+\) oxoglutarate \((\mathrm{aq}) \quad K=0.387\) Write the equilibrium constant expression for the above reaction. Given the following data for this reaction, \([\text { citrate }]=0.00128 \mathrm{M},\left[\mathrm{NAD}_{\mathrm{ox}}\right]=0.00868,\left[\mathrm{H}_{2} \mathrm{O}\right]=\) \(55.5 \mathrm{M},\left[\mathrm{CO}_{2}\right]=0.00868 \mathrm{M},\left[\mathrm{NAD}_{\mathrm{red}}\right]=0.00132 \mathrm{M}\) and [oxoglutarate] \(=0.00868 \mathrm{M},\) calculate the reaction quotient. Is this reaction at equilibrium? If not, in which direction will it proceed?

Refer to Example \(15-4 . \mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) at \(747.6 \mathrm{mmHg}\) pressure and a \(1.85 \mathrm{g}\) sample of \(\mathrm{I}_{2}(\mathrm{s})\) are introduced into a \(725 \mathrm{mL}\) flask at \(60^{\circ} \mathrm{C} .\) What will be the total pressure in the flask at equilibrium? $$\begin{aligned} \mathrm{H}_{2} \mathrm{S}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{s}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})+\mathrm{S}(\mathrm{s}) & \\ K_{\mathrm{p}}=& 1.34 \times 10^{-5} \mathrm{at} 60^{\circ} \mathrm{C} \end{aligned}$$

A sample of \(\mathrm{NH}_{4} \mathrm{HS}(\mathrm{s})\) is placed in a \(2.58 \mathrm{L}\) flask containing 0.100 mol \(\mathrm{NH}_{3}(\mathrm{g}) .\) What will be the total gas pressure when equilibrium is established at \(25^{\circ} \mathrm{C} ?\) $$\begin{aligned} \mathrm{NH}_{4} \mathrm{HS}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{S}(\mathrm{g}) & \\ K_{\mathrm{p}} &=0.108 \text { at } 25^{\circ} \mathrm{C} \end{aligned}$$

The following reaction is used in some self-contained breathing devices as a source of \(\mathrm{O}_{2}(\mathrm{g})\) $$\begin{aligned} 4 \mathrm{KO}_{2}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{K}_{2} \mathrm{CO}_{3}(\mathrm{s}) &+3 \mathrm{O}_{2}(\mathrm{g}) \\\ K_{\mathrm{p}} &=28.5 \mathrm{at} 25^{\circ} \mathrm{C} \end{aligned}$$ Suppose that a sample of \(\mathrm{CO}_{2}(\mathrm{g})\) is added to an evacuated flask containing \(\mathrm{KO}_{2}(\mathrm{s})\) and equilibrium is established. If the equilibrium partial pressure of \(\mathrm{CO}_{2}(\mathrm{g})\) is found to be \(0.0721 \mathrm{atm},\) what are the equilibrium partial pressure of \(\mathrm{O}_{2}(\mathrm{g})\) and the total gas pressure?

\(1.00 \mathrm{mol}\) each of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) are introduced into an evacuated 1.75 L flask, and the following equilibrium is established at \(668 \mathrm{K}\). $$ \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g}) \quad K_{\mathrm{p}}=22.5 $$ For this equilibrium, calculate (a) the partial pressure of \(\mathrm{COCl}_{2}(\mathrm{g}) ;\) (b) the total gas pressure.

Continuous removal of one of the products of a chemical reaction has the effect of causing the reaction to go to completion. Explain this fact in terms of Le Châtelier's principle.

We can represent the freezing of \(\mathrm{H}_{2} \mathrm{O}(1)\) at \(0^{\circ} \mathrm{C}\ \mathrm{as} \mathrm{H}_{2} \mathrm{O}\) \(\left(1, d=1.00 \mathrm{g} / \mathrm{cm}^{3}\right) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}\left(\mathrm{s}, d=0.92 \mathrm{g} / \mathrm{cm}^{3}\right) . \quad \mathrm{Ex}\) plain why increasing the pressure on ice causes it to melt. Is this the behavior you expect for solids in general? Explain.

Explain how each of the following affects the amount of \(\mathrm{H}_{2}\) present in an equilibrium mixture in the reaction \(3 \mathrm{Fe}(\mathrm{s})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}_{3} \mathrm{O}_{4}(\mathrm{s})+4 \mathrm{H}_{2}(\mathrm{g})\) $$ \Delta H^{\circ}=-150 \mathrm{kJ} $$ (a) Raising the temperature of the mixture; (b) introducing more \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) ;\) (c) doubling the volume of the container holding the mixture; (d) adding an appropriate catalyst.

In the gas phase, iodine reacts with cyclopentene \(\left(\mathrm{C}_{5} \mathrm{H}_{8}\right)\) by a free radical mechanism to produce cyclopentadiene \(\left(\mathrm{C}_{5} \mathrm{H}_{6}\right)\) and hydrogen iodide. Explain how each of the following affects the amount of \(\mathrm{HI}(\mathrm{g})\) present in the equilibrium mixture in the reaction \begin{array}{r} \mathrm{I}_{2}(\mathrm{g})+\mathrm{C}_{5} \mathrm{H}_{8}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{5} \mathrm{H}_{6}(\mathrm{g})+2 \mathrm{HI}(\mathrm{g}) \\ \Delta H^{\circ}=92.5 \mathrm{kJ} \end{array} (a) Raising the temperature of the mixture; (b) introducing more \(\mathrm{C}_{5} \mathrm{H}_{6}(\mathrm{g}) ;\) (c) doubling the volume of the container holding the mixture; (d) adding an appropriate catalyst; (e) adding an inert gas such as He to a constant-volume reaction mixture.

The reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}), \quad \Delta H^{\circ}=\) \(+181 \mathrm{kJ},\) occurs in high-temperature combustion processes carried out in air. Oxides of nitrogen produced from the nitrogen and oxygen in air are intimately involved in the production of photochemical smog. What effect does increasing the temperature have on (a) the equilibrium production of \(\mathrm{NO}(\mathrm{g})\) (b) the rate of this reaction?

If the volume of an equilibrium mixture of \(\mathrm{N}_{2}(\mathrm{g}), \mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{NH}_{3}(\mathrm{g})\) is reduced by doubling the pressure, will \(P_{\mathrm{N}_{2}}\) have increased, decreased, or remained the same when equilibrium is re established? Explain. $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})$$