Chapter 14

Increasing the concentration of a reactant shifts the position of chemical equilibrium toward formation of more products. What effect does adding a reactant have on the rates of the forward and reverse reactions?

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 $$\begin{aligned} \mathrm{Hb}(a q)+4 \mathrm{CO}(g) & \rightleftharpoons \mathrm{Hb}(\mathrm{CO})_{4}(a q) \\ \mathrm{Hb}(a q)+4 \mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4}(a q) \end{aligned}$$ 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? Explain your answer.

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

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 shift the following equilibrium? $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{CO}_{2}(g) $$

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. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)\) d. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\)

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. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)\)

How will the changes listed affect the equilibrium concentrations of reactants and products in the following reaction? $$ 2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g) $$ a. \(\mathrm{O}_{3}\) is added to the system. b. \(\mathrm{O}_{2}\) is added to the system. c. The mixture is compressed to one-tenth its initial volume.

How will the changes listed affect the position of the following equilibrium? $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{NO}_{3}(g) $$ 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 expand to 5 times its initial value.

How will reducing the partial pressure of \(\mathrm{O}_{2}\) 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 equilibrium constant of reaction 2 is much greater than the equilibrium constant of reaction \(1 ?\) (1) \(\quad \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) (2) \(\quad \mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)\)

In which of the following equilibria does an increase in temperature produce a shift toward the formation of more product? a.\(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) \quad \quad \Delta H^{\circ}<0\) b. \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}>0\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \Delta H^{\circ}<0\)

In which of the following equilibria does an increase in temperature produce a shift toward the formation of more product? a. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \quad \Delta H^{\circ}<0\) b. \(2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}>0\) c. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(g) \quad \Delta H^{\circ}<0\)

Why are calculations based on \(K\) often simpler when the value of \(K\) is very small?

The following reaction is carried out in a sealed, rigid vessel at constant temperature. $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g) $$ a. If the change in the partial pressure of \(\mathrm{O}_{2}\) is \(-x,\) what are the changes in the partial pressures of \(\mathrm{NO}\) and \(\mathrm{NO}_{2} ?\) b. As the reaction proceeds, what happens to the total pressure in the reaction vessel?

Enough \(\mathrm{NO}_{2}\) gas is injected into a cylindrical vessel to produce a partial pressure, \(P_{\mathrm{NO}_{2}},\) 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 $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) \quad K_{\mathrm{p}}=4 \text { at } 298 \mathrm{K} $$

The value of \(K_{\mathrm{c}}\) 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 at \(25^{\circ} \mathrm{C}\) if the starting concentrations of both reactants are \(0.00432 M\) and no HOCl is present.

The value of \(K_{\mathrm{p}}\) 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 \(648 \mathrm{K}\)

The value of \(K_{\mathrm{p}}\) for the reaction $$ \mathrm{NO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g) $$ is \(1.5 \times 10^{6}\) at \(25^{\circ} \mathrm{C} .\) At equilibrium, what is the ratio of \(P_{\mathrm{NO}_{2}}\) to \(P_{\mathrm{NO}}\) in air at \(25^{\circ} \mathrm{C} ?\) Assume that \(P_{\mathrm{O}_{2}}=0.21 \mathrm{atm}\) and does not change.

Passing steam over hot carbon produces a mixture of carbon monoxide and hydrogen known as water gas: $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$ The value of \(K_{\mathrm{c}}\) 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 at \(1000^{\circ} \mathrm{C}\) if \(P_{\mathrm{H}_{2} \mathrm{O}}=0.442\) 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 sufficient \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) are added to the equilibrium mixture in part (a) to initially increase the partial pressures of both gases by 0.075 atm.

Ammonium hydrogen sulfide (NH_4SH) has been detected in the atmosphere of Jupiter. The equilibrium between ammonia, hydrogen sulfide, and \(\mathrm{NH}_{4} \mathrm{SH}\) is described by the following equation: $$ \mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{S}(g) $$ The value of \(K_{\mathrm{p}}\) 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 \(24^{\circ} \mathrm{C} .\) 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 \(\mathrm{NO}_{2}\) was heated to \(1000 \mathrm{K},\) a temperature at which the value of \(K_{\mathrm{p}}\) for the decomposition of \(\mathrm{NO}_{2}\) is 158 $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ 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?

In a study of the formation of \(\mathrm{NO}_{x}\) in 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 \(2200^{\circ} \mathrm{C} ?\) $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$

The equilibrium constant \(K_{\mathrm{p}}\) for the thermal decomposition of \(\mathrm{NO}_{2}\) $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ is \(6.5 \times 10^{-6}\) at \(450^{\circ} \mathrm{C} .\) If a reaction vessel at this temperature initially contains only 0.500 atm \(\mathrm{NO}_{2},\) what will be the partial pressures of \(\mathrm{NO}_{2}, \mathrm{NO},\) and \(\mathrm{O}_{2}\) in the vessel when equilibrium has been attained?

The value of \(K_{\mathrm{c}}\) for the thermal decomposition of hydrogen sulfide $$ 2 \mathrm{H}_{2} \mathrm{S}(g) \rightleftharpoons 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) $$ is \(2.2 \times 10^{-4}\) at \(1400 \mathrm{K} .\) A sample of gas in which \(\left[\mathrm{H}_{2} \mathrm{S}\right]\) \(=6.00 M\) is heated to \(1400 \mathrm{K}\) in a sealed high-pressure vessel. After chemical equilibrium has been achieved, what is the value of \(\left[\mathrm{H}_{2} \mathrm{S}\right]\) ? Assume that no \(\mathrm{H}_{2}\) or \(\mathrm{S}_{2}\) was present in the original sample.

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

Phosgene, \(\mathrm{COCl}_{2},\) gained notoriety as a chemical weapon in World War I. Phosgene is produced by the reaction of carbon monoxide with chlorine $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$ The value of \(K_{\mathrm{c}}\) for this reaction is 5.0 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 \(P_{\mathrm{CO}}=P_{\mathrm{Cl}_{2}}=0.265\) atm and there is no \(\mathrm{COCl}_{2} ?\)

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

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

Ammonia decomposes at high temperatures. In an experiment to explore this behavior, 2.00 moles of gaseous \(\mathrm{NH}_{3}\) is sealed in a rigid 1 -liter vessel. The vessel is heated at \(800 \mathrm{K}\) and some of the \(\mathrm{NH}_{3}\) decomposes in the following reaction: $$ 2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(\mathrm{g}) $$ The system eventually reaches equilibrium and is found to contain 1.74 moles of \(\mathrm{NH}_{3} .\) What are the values of \(K_{\mathrm{p}}\) and \(K_{\mathrm{c}}\) for the decomposition reaction at \(800 \mathrm{K} ?\)

Elements of group 16 form hydrides with the generic formula \(\mathrm{H}_{2} \mathrm{X}\). At a certain temperature, when gaseous \(\mathrm{H}_{2} \mathrm{X}\) is bubbled through a solution containing \(0.3 \mathrm{M}\) 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.

A 100 -mL reaction vessel initially contains \(2.60 \times 10^{-2} \mathrm{mol}\) of \(\mathrm{NO}\) and \(1.30 \times 10^{-2} \mathrm{mol}\) of \(\mathrm{H}_{2} . \mathrm{At}\) equilibrium, the concentration of NO in the vessel is \(0.161 M .\) The vessel also contains \(\mathrm{N}_{2}, \mathrm{H}_{2} \mathrm{O},\) and \(\mathrm{H}_{2}\) at equilibrium. What is the value of the equilibrium constant \(K_{\mathrm{c}}\) for the following reaction? $$ 2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g) $$