Chapter 14

Carbon Monoxide Poisoning Patients suffering from carbon monoxide poisoning are treated with pure oxygen to remove CO from the hemoglobin (Hb) in their blood. The two relevant equilibria are $$ \begin{aligned} \mathrm{Hb}+4 \mathrm{CO}(g) & \rightleftharpoons \mathrm{Hb}(\mathrm{CO}) \\ \mathrm{Hb}+4 \mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4} \end{aligned} $$ The value of the equilibrium constant for CO binding to Hb is greater than that for \(\mathrm{O}_{2}\). How, then, does this treatment work?

Is the equilibrium constant \(K_{\mathrm{p}}\) for the reaction $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) $$ in air the same in Los Angeles as in Denver if the atmospheric pressure in Denver is lower but the temperature is the same?

Henry's law (Chapter 10 ) predicts that the solubility of a gas in a liquid increases with its partial pressure. Explain Henry's law in relation to Le Chatelicr's principle.

For the reaction $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$ why does adding an inert gas such as argon to an equilibrium mixture of \(\mathrm{CO}, \mathrm{O}_{2},\) and \(\mathrm{CO}_{2}\) in a sealed vessel increase the total pressure of the system but not affect the position of the equilibrium?

Which of the following equilibria will shift toward formation of more products if an equilibrium mixture is compressed into half its volume? a. \(2 \mathrm{N}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)\) b. \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g)\) c. \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) d. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)\)

Which of the following equilibria will shift toward formation of more products if the volume of a reaction mixture at equilibrium increases by a factor of \(2 ?\) a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) b. \(\mathrm{NO}(g)+\mathrm{O}_{3}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) c. \(2 \mathrm{N}_{2} \mathrm{O}_{5}(g) \rightleftharpoons 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\)

How will the changes listed affect the position of the following equilibrium? $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{NO}(g)+\mathrm{NO}_{3}(\mathrm{g}) $$ a. The concentration of \(\mathrm{NO}\) is increased. b. The concentration of \(\mathrm{NO}_{2}\) is increased. c. The volume of the system is allowed to cxpand to 5 times its initial value.

How would reducing the partial pressure of \(\mathrm{O}_{2}(g)\) affect the position of the equilibrium in the following reaction? $$ 2 \mathrm{sO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$

Ammonia is added to a gaseous reaction mixture containing \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) that is at chemical equilibrium. How will the addition of ammonia affect the relative concentrations of \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) if the cquilibrium constant of reaction 2 is much greater than the cquilibrium constant of reaction \(1 ?\) (1) \(\quad \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) $$ \text { (2) } \quad \mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s) $$

In which of the following hypothetical equilibria does the product yield increase with increasing temperature? a. \(A+2 B \rightleftharpoons C \quad \Delta H>0\) b. \(A+2 B \rightleftarrows C \quad \Delta H=0\) c. \(A+2 B \rightleftharpoons C \quad \Delta H<0\)

In which of the following hypothetical cquilibria docs the product yield decrease with increasing temperature? a. \(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H>0\) b. \(2 X+Y \rightleftharpoons Z \quad \Delta H=0\) c. \(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H<0\)

Could the quadratic equation be used to solve for the equilibrium concentration of \(\mathrm{NO}_{2}\) in the following reaction? $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$

Consider the following reaction: \(\operatorname{PCl}_{5}(g) \rightleftharpoons \operatorname{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \quad K_{\mathrm{p}}=23.6 \mathrm{at} 500 \mathrm{K}\) a. Calculate the equilibrium partial pressures of the reactants and products if the initial pressures are \(P_{\mathrm{RC}_{5}}=0.560\) atm and \(P_{\mathrm{PC}_{2}}=0.500 \mathrm{atm}\) b. If more chlorine is added after cquilibrium is reached, how will the concentrations of \(\mathrm{PCl}_{5}\) and \(\mathrm{PCl}_{3}\) change?

Enough \(\mathrm{NO}_{2}\) gas is injected into a cylindrical vessel to produce a partial pressure, \(P_{\mathrm{NO},},\) of 0.900 atm at \(298 \mathrm{K}\) Calculate the equilibrium partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4},\) given $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) \quad K_{\mathrm{p}}=4.0 \mathrm{at} 298 \mathrm{K} $$

The valuc of \(K_{c}\) for the reaction between water vapor and dichlorine monoxide $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g) $$ is 0.0900 at \(25^{\circ} \mathrm{C} .\) Determine the equilibrium concentrations of all three compounds if the starting concentrations of both reactants are \(0.00432 M\) and no \(\mathrm{HOCl}\) is present.

The value of \(K_{p}\) for the reaction $$ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.3 \times 10^{-4}\) at \(648 \mathrm{K}\). Determine the equilibrium partial pressure of \(\mathrm{NH}_{3}\) in a reaction vessel that initially contained 0.900 atm \(\mathrm{N}_{2}\) and 0.500 atm \(\mathrm{H}_{2}\) at \(648 \mathrm{K}\)

Making Hydrogen Gas Passing steam over hot carbon produces a mixture of carbon monoxide and hydrogen: $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$ The valuc of \(K_{c}\) for the reaction at \(1000^{\circ} \mathrm{C}\) is \(3.0 \times 10^{-2}\) a. Calculate the equilibrium partial pressures of the products and reactants if \(P_{11,0}=0.442\) atm and \(P_{\mathrm{CO}}=5.0\) atm at the start of the reaction. Assume that the carbon is in excess. b. Determine the equilibrium partial pressures of the reactants and products after sufficicnt CO and \(\mathrm{H}_{2}\) are added to the cquilibrium mixture in part (a) to initially increase the partial pressures of both gascs by 0.075 atm.

Jupiter's Atmosphere Ammonium hydrogen sulfide \(\left(\mathrm{NH}_{4} \mathrm{SH}\right)\) has been detected in the atmosphere of Jupiter, where it probably exists in equilibrium with ammonia and hydrogen sulfide: $$ \mathrm{NH}_{1} \mathrm{SH}(j) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) $$ The value of \(K_{p}\) for the reaction at \(24^{\circ} \mathrm{C}\) is \(0.126 .\) Suppose a sealed flask contains an equilibrium mixture of \(\mathrm{NH}_{4} \mathrm{SH}\), \(\mathrm{NH}_{3},\) and \(\mathrm{H}_{2} \mathrm{S}\). At equilibrium, the partial pressure of \(\mathrm{H}_{2} \mathrm{S}\) is 0.355 atm. What is the partial pressure of \(\mathrm{NH}_{3} ?\)

A flask containing pure \(\mathrm{NO}_{2}\) is heated to \(1000 \mathrm{K},\) a temperature at which \(K_{p}=158\) for the decomposition of \(\mathrm{NO}_{2}\) $$ 2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) $$ The partial pressure of \(\mathrm{O}_{2}\) at equilibrium is 0.136 atm. a. Calculate the partial pressures of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\). b. Calculate the total pressure in the flask at equilibrium.

The equilibrium constant \(K_{\mathrm{p}}\) of the reaction $$ 2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) $$ is 7.69 at \(830^{\circ} \mathrm{C} .\) If a vessel at this temperature initially contains pure \(\mathrm{SO}_{3}\) and if the partial pressure of \(\mathrm{SO}_{3}\) at equilibrium is 0.100 atm, what is the partial pressure of \(\mathrm{O}_{2}\) in the flask at equilibrium?

NO, Pollution \(\ln\) a study of the formation of \(\mathrm{NO}_{x}\) air pollution, a chamber heated to \(2200^{\circ} \mathrm{C}\) was filled with air \(\left(0.79 \mathrm{atm} \mathrm{N}_{2}, 0.21 \mathrm{atm} \mathrm{O}_{2}\right) .\) What are the equilibrium partial pressures of \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{NO}\) if \(K_{\mathrm{p}}=0.050\) for the following reaction at \(2200^{\circ} \mathrm{C} ?\) $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$

Urban Air On a very smoggy day, the cquilibrium concentration of \(\mathrm{NO}_{2}\) in the air over an urban arca reaches \(2.2 \times 10^{-7} M .\) If the temperature of the air is \(25^{\circ} \mathrm{C},\) what is the concentration of the dimer \(\mathrm{N}_{2} \mathrm{O}_{4}\) in the air? $$ \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad K_{e}=6.1 \times 10^{-3} $$

Chemical Weapon Phosgene, \(\mathrm{COCl}_{2}\), gained notoricty as a chemical weapon in World War I. Phosgene is produced by the reaction of carbon monoxide with chlorine: $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$ \(K_{c}=5.0\) for this reaction at \(600 \mathrm{K} .\) What are the equilibrium partial pressures of the three gases if a reaction vessel initially contains a mixture of the reactants in which \(P_{\mathrm{CO}}=P_{\mathrm{Cl}_{1}}=0.265\) atm and \(P_{\mathrm{COC}_{1}}=0.000\) atm?

At \(2000^{\circ} \mathrm{C}, K_{\epsilon}=1.0\) for the following reaction: $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$ What is the ratio of \([\mathrm{CO}]\) to \(\left[\mathrm{CO}_{2}\right]\) in an atmosphere in which \(\left[\mathrm{O}_{2}\right]=0.0045 M ?\)

The water-gas shift reaction is an important source of hydrogen. The valuc of \(K_{c}\) for the reaction $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$ at \(700 \mathrm{K}\) is \(5.1 .\) Calculate the equilibrium concentrations of the four gases if the initial concentration of cach of them is \(0.050 \bar{M}\)

Sulfur dioxide reacts with \(\mathrm{NO}_{2},\) forming \(\mathrm{SO}_{3}\) and \(\mathrm{NO}\) : $$ \mathrm{SO}_{2}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{g})+\mathrm{NO}(\mathrm{g}) $$ If \(K_{c}=2.50\) for the reaction, what are the equilibrium concentrations of the products if the reaction mixture was initially \(0.50 \mathrm{M} \mathrm{SO}_{2}, 0.50 \mathrm{M} \mathrm{NO}_{2}, 0.0050 \mathrm{M} \mathrm{SO}_{3},\) and \(0.0050 M \mathrm{NO} ?\)

For the decomposition of \(\mathrm{HI}(g)\) into \(\mathrm{H}_{2}(g)\) and \(\mathrm{I}_{2}(g)\) at \(400^{\circ} \mathrm{C}, K_{c}=0.0183\) $$ 2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) $$ If \(80.0 \mathrm{g}\) of \(\mathrm{HI}(g)\) is placed in a 2.5 I. chamber at \(400^{\circ} \mathrm{C}\) what are the concentrations of all species when the system comes to cquilibrium?

Do all reactions with equilibrium constants \(<1\) have values of \(\Delta G^{\circ}>0 ?\)

The equation \(\Delta G^{\circ}=-R T\) ln \(K\) relates the valuc of \(K_{\mathrm{p}},\) not \(K_{\mathrm{c}},\) to the change in standard free energy for a reaction in the gas phasc. Explain why.

Starting with pure reactants, in which dircction will an equilibrium shift if \(\Delta G^{*}<0 ?\)

Starting with pure products, in which direction will an equilibrium shift if \(\Delta G^{*}<0 ?\)

Which of the following reactions has the largest cquilibrium constant at \(25^{\circ} \mathrm{C} ?\) a. \(\mathrm{Cl}_{2}(\mathrm{g})+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{ClF}(g) \quad \Delta G^{*}=115.4 \mathrm{kJ}\) b. \(\mathrm{Cl}_{2}(\mathrm{g})+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{ClBr}(g) \quad \Delta G^{*}=-2.0 \mathrm{kJ}\) c. \(\mathrm{Cl}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 21 \mathrm{Cl}(g) \quad \Delta G^{*}=-27.9 \mathrm{kJ}\)

The value of \(\Delta G^{*}\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ is \(68.9 \mathrm{kJ} .\) What is the value of the equilibrium constant for this reaction at \(298 \mathrm{K} ?\)

At a temperature of \(1000 \mathrm{K}, \mathrm{SO}_{2}(g)\) combines with oxygen to make \(\mathrm{SO}_{3}(\mathrm{g})\) $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ Under these conditions, \(K_{p}=3.4\) a. Use the appropriate thermodynamic data in Appendix 4 to calculate the value of \(\Delta H_{\mathrm{ren}}^{\circ}\) for this reaction. b. What is the value of \(K_{p}\) for this reaction at \(298 \mathrm{K}\) ? c. Use the answer from part (b) to calculate the value of \(\Delta G_{\max }^{*}\) at \(298 \mathrm{K},\) and compare it to the value you obtaincd using the \(\Delta G_{\mathrm{f}}^{s}\) valucs in Appendix 4.

Use the \(\Delta G^{*}\) data given here to calculate the value of \(K_{\mathrm{p}}\) at \(298 \mathrm{K}\) for the following reaction: $$ \begin{array}{c} \mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \\\ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad \Delta G^{*}=173.2 \mathrm{kJ} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad \Delta G^{*}=-69.7 \mathrm{kJ} \end{array} $$

Under the appropriate conditions, NO forms \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{NO}_{2}\) : $$ 3 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) $$ Use the values for \(\Delta G^{\circ}\) for the following reactions to calculate the value of \(K_{\mathrm{p}}\) for the preceding reaction at \(500^{\circ} \mathrm{C}\) $$ \begin{aligned} 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}_{2}(g) & \Delta G^{\circ} &=-69.7 \mathrm{kJ} \\ 2 \mathrm{N}_{2} \mathrm{O}(g) & \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{N}_{2}(g) & \Delta G^{\circ} &=-33.8 \mathrm{kJ} \\ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & \rightleftharpoons 2 \mathrm{NO}(g) & \Delta G^{*} &=173.2 \mathrm{kJ} \end{aligned} $$

The value of the equilibrium constant of a reaction decreases with increasing temperature. Is this reaction endothermic or exothcrmic?

The valuc of \(K_{p}\) for the water-gas shift reaction $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) $$ increases as the temperature decreases. Is the reaction exothermic or endothermic?

Does the value of \(K_{\mathrm{p}}\) for the reaction \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g) \quad \Delta H^{\circ}=206 \mathrm{kJ}\) increase, decrease, or remain unchanged as the temperature increases?

Air Pollution Automobiles and trucks pollute the air with NO. At \(2000^{\circ} \mathrm{C}, K_{c}\) for the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ is \(4.10 \times 10^{-4},\) and \(\Delta H^{*}=180.6 \mathrm{kJ} .\) What is the value of \(K_{c}\) at \(25^{\circ} \mathrm{C} ?\)

At \(400 \mathrm{K}\) the value of \(K_{\mathrm{p}}\) for the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(41,\) and \(\Delta H^{*}=-92.2 \mathrm{kJ} .\) What is the value of \(K_{\mathrm{p}}\) at \(700 \mathrm{K} ?\)

The value of \(K_{e}\) for the reaction \(A \rightleftharpoons B\) is 0.455 at \(50^{\circ} \mathrm{C}\) and 0.655 at \(100^{\circ} \mathrm{C}\). Calculate \(\Delta H^{*}\) for the reaction.

CO as a Fuel Is carbon dioxide a viable source of the fuel CO? Pure carbon dioxide \(\left(P_{\mathrm{CO}_{2}}=1 \text { atm }\right)\) decomposes at high temperatures. For the system $$ 2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) $$ the percentage of decomposition of \(\mathrm{CO}_{2}(g)\) changes with temperature as follows: $$\begin{array}{cc} \text { Temperature }(\mathrm{K}) & \text { Decomposition }(\%) \\ 1500 & 0.048 \\ \hline 2500 & 17.6 \\ \hline 3000 & 54.8 \\ \hline \end{array}$$ Is the reaction endothermic? Calculate the value of \(K_{\text {p at each temperature and discuss the results. Is the }}\) decomposition of \(\mathrm{CO}_{2}\) an antidote for global warming?

Ammonia decomposes at high temperatures. In an experiment to explore this behavior, 2.00 mol of gascous \(\mathrm{NH}_{3}\) is sealed in a rigid \(1.00 \mathrm{L}\) vessel. The vessel is heated to \(785 \mathrm{K}\) and some of the \(\mathrm{NH}_{3}\) decomposes in the following reaction: $$2 \mathrm{NH}_{3}(\mathrm{g}) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$$ The system eventually reaches equilibrium and is found to contain 0.0040 mol of \(\mathrm{NH}_{3}\). What are the values of \(K_{\mathrm{p}}\) and \(K_{c}\) for the decomposition reaction at \(785 \mathrm{K} ?\)

Flements of group 16 form hydrides with the generic formula \(\mathrm{H}_{2} \mathrm{X}\). When gaseous \(\mathrm{H}_{2} \mathrm{X}\) is bubbled through a solution containing \(0.3 M\) hydrochloric acid, the solution becomes saturated and \(\left[\mathrm{H}_{2} \mathrm{X}\right]=0.1 \mathrm{M} .\) The following equilibria exist in this solution: \(\mathrm{H}_{2} \mathrm{X}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{HX}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \quad K_{1}=8.3 \times 10^{-8}\) \(\mathrm{HX}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{X}^{2-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) \quad K_{2}=1 \times 10^{-14}\) Calculate the concentration of \(\mathrm{X}^{2-}\) in the solution.

Cobalt(11) oxide has been used for centuries as a glaxe for pottery because of its decp bluc color, which is known as cobalt bluc. The oxide can be decomposed into cobalt metal by reduction with CO: $$ \mathrm{CoO}(\mathrm{s})+\mathrm{CO}(g) \rightleftharpoons \mathrm{Co}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) $$ For this equilibrium at \(770 \mathrm{K}, K_{c}=4.90 \times 10^{2}\) a. What is the value of \(K_{\mathrm{p}}\) at \(770 \mathrm{K} ?\) b. If the total pressure in the reactor in which the oxide is being reduced is 15.8 atm, what are the partial pressures of \(\mathrm{CO}\) and \(\mathrm{CO}_{2} ?\)

Carbon disulfide is a foul-smelling solvent that dissolves sulfur and other nonpolar substances. It can be made by heating sulfur in an atmosphere of methane: $$4 \mathrm{CH}_{4}(g)+\mathrm{S}_{\mathrm{g}}(s) \longrightarrow 4 \mathrm{CS}_{2}(g)+8 \mathrm{H}_{2}(\mathrm{g})$$ Starting with the appropriate data in Appendix \(4,\) calculate the values of \(K_{\mathrm{p}}\) for the reaction at \(25^{\circ} \mathrm{C}\) and \(500^{\circ} \mathrm{C}\)

Making Hydrogen Debate continues on the practicality of using \(\mathrm{H}_{2}\) gas as a fucl for cars. The equilibrium constant \(K_{e}\) for the reaction $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)$$ is \(1.0 \times 10^{5}\) at \(25^{\circ} \mathrm{C} .\) Starting with this value, calculate the value of \(\Delta G_{r r n}^{\infty}\) at \(25^{\circ} \mathrm{C}\) and, without doing any calculations, guess the sign of \(\Delta H_{\text {rent }}\)

Air Pollution Control Calcium oxide is used to remove the pollutant \(\mathrm{SO}_{2}\) from smokestack gases. The \(\Delta G^{\circ}\) of the overall reaction $$\mathrm{CaO}(\mathrm{s})+\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CaSO}_{4}(\mathrm{s})$$ is \(-418.6 \mathrm{kJ} .\) What is \(P_{\mathrm{SO}},\) in equilibrium with air \(\left(P_{O_{2}}=0.21 \mathrm{atm}\right)\) and solid \(\mathrm{CaO}_{2}\)

Hydrogen Production The steam-methane reforming reaction plays a key role in producing hydrogen gas for use as a fuel and as a reactant in ammonia production. The equilibrium constant \(\left(K_{\mathrm{p}}\right)\) of the reaction: \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 3 \mathrm{H}_{2}(g)+\mathrm{CO}(g)\) is 13.0 at \(700^{\circ} \mathrm{C}\) a. Describe two advantages in running this endothermic \(\left(\Delta H_{r x n}=206 \mathrm{kJ}\right)\) reaction at \(700^{\circ} \mathrm{C}\) instead of \(100^{\circ} \mathrm{C}\) b. If the initial partial pressures of the two reactants are \(\operatorname{cach} 5.00\) atm at \(700^{\circ} \mathrm{C}\) and no products are present, what is the partial pressurc of \(\mathrm{H}_{2}\) gas after cquilibrium is achicved?