Chapter 12

The following data are for the system $$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$$ $$\begin{array}{lcccccc}\hline \text { Time (s) } & 0 & 20 & 40 & 60 & 80 & 100 \\ P_{\mathrm{A}} \text { (atm) } & 1.00 & 0.83 & 0.72 & 0.65 & 0.62 & 0.62 \\ P_{B} \text { (atm) } & 0.00 & 0.34 & 0.56 & 0.70 & 0.76 & 0.76 \\\\\hline\end{array}$$ (a) How long does it take the system to reach equilibrium? (b) How does the rate of the forward reaction compare with the rate of the reverse reaction after 30 s? After 90 s?

The following data are for the system $$\mathrm{A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$$ $$\begin{array}{ccccccc}\hline \text { Time (s) } & 0 & 30 & 45 & 60 & 75 & 90 \\\ P_{\mathrm{A}} \text { (atm) } & 0.500 & 0.390 & 0.360 & 0.340 & 0.325 & 0.325 \\\ P_{\text {B }} \text { (atm) } & 0.000 & 0.220 & 0.280 & 0.320 & 0.350 & 0.350 \\\\\hline\end{array}$$ (a) How long does it take the system to reach equilibrium? (b) How does the rate of the forward reaction compare with the rate of the reverse reaction after 45 s? After 90 s?

Write equilibrium constant \((K)\) expressions for the following reactions: (a) \(\mathrm{I}_{2}(g)+5 \mathrm{~F}_{2}(g) \rightleftharpoons 2 \mathrm{IF}_{5}(g)\) (b) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(l)\) (c) \(2 \mathrm{H}_{2} \mathrm{~S}+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{SO}_{2}(g)\) (d) \(\mathrm{SnO}_{2}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{Sn}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\)

WEB Write equilibrium constant \((K)\) expressions for the following reactions: (a) \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)\) (d) \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s)\)

Write equilibrium constant expressions ( \(K\) ) for the following reactions: (a) \(2 \mathrm{NO}_{3}^{-}(a q)+8 \mathrm{H}^{+}(a q)+3 \mathrm{Cu}(s) \rightleftharpoons\) \(2 \mathrm{NO}(g)+3 \mathrm{Cu}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(2 \mathrm{PbS}(s)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{PbO}(s)+2 \mathrm{SO}_{2}(g)\) (c) \(\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s)\)

Given the following descriptions of reversible reactions, write a balanced equation (simplest whole-number coefficients) and the equilibrium constant expression \((K)\) for each. (a) Nitrogen gas reacts with solid sodium carbonate and solid carbon to produce carbon monoxide gas and solid sodium cyanide. (b) Solid magnesium nitride reacts with water vapor to form magnesium hydroxide solid and ammonia gas. (c) Ammonium ion in aqueous solution reacts with a strong base at \(25^{\circ} \mathrm{C}\), giving aqueous ammonia and water. (c) Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) bubbled into an aqueous solution of lead(II) ions produces lead sulfide precipitate and hydrogen ions.

Given the following descriptions of reversible reactions, write a balanced net ionic equation (simplest whole-number coefficients) and the equilibrium constant expression \((K)\) for each. (a) Liquid acetone \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\) is in equilibrium with its vapor. (b) Hydrogen gas reduces nitrogen dioxide gas to form ammonia and steam. (c) Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) bubbled into an aqueous solution of lead(II) ions produces lead sulfide precipitate and hydrogen ions.

Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{CO}_{2}}\right)^{3}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{4}}{\left(P_{\mathrm{C}, \mathrm{H}_{4}}\right)\left(P_{\mathrm{O}_{2}}\right)^{5}}\) (b) \(K=\frac{P_{\mathrm{C}_{0} \mathrm{H}_{12}}}{\left(P_{\mathrm{C}, \mathrm{H}_{6}}\right)^{2}}\) (c) \(K=\frac{\left[\mathrm{PO}_{4}^{3-}\right]\left[\mathrm{H}^{+}\right]^{3}}{\left[\mathrm{H}_{3} \mathrm{PO}_{4}\right]}\) (d) \(K=\frac{\left(P_{\mathrm{CO}_{2}}\right)\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)}{\left[\mathrm{CO}_{3}^{2-}\right]\left[\mathrm{H}^{+}\right]^{2}}\)

Write a chemical equation for an equilibrium system that would lead to the following expressions (a-d) for \(K\). (a) \(K=\frac{\left(P_{\mathrm{H}_{2}}\right)^{2}\left(P_{\mathrm{O}_{2}}\right)^{3}}{\left(P_{\mathrm{SO}_{2}}\right)^{2}\left(P_{\mathrm{H}_{2} \mathrm{O}}\right)^{2}}\) (b) \(K=\frac{\left(P_{\mathrm{F}_{1}}\right)^{1 / 2}\left(P_{\mathrm{I}_{2}}\right)^{1 / 2}}{P_{\mathrm{IF}}}\) (c) \(K=\frac{\left[\mathrm{Cl}^{-}\right]^{2}}{\left(P_{\mathrm{C}_{2}}\right)\left[\mathrm{Br}^{-}\right]^{2}}\) (d) \(K=\frac{\left(P_{\mathrm{NO}}\right)^{2}\left(P_{\mathrm{H}_{3} \mathrm{O}}\right)^{4}\left[\mathrm{Cu}^{2+}\right]^{3}}{\left[\mathrm{NO}_{3}^{-}\right]^{2}\left[\mathrm{H}^{+}\right]^{8}}\)

Consider the following reaction at \(250^{\circ} \mathrm{C}\) : $$\mathrm{A}(s)+2 \mathrm{~B}(g) \rightleftharpoons \mathrm{C}(s)+2 \mathrm{D}(g)$$ (a) Write an equilibrium constant expression for the reaction. Call the equilibrium constant \(K_{1}\). (b) Write an equilibrium constant expression for the formation of one mole of \(\mathrm{B}(\mathrm{g})\) and call the equilibrium constant \(K_{2}\). (c) Relate \(K_{1}\) and \(K_{2}\).

WEB Consider the following reaction at \(122^{\circ} \mathrm{C}\) : $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ (a) Write an equilibrium constant expression for the reaction and call the constant \(K_{1}\). (b) Write an equilibrium constant expression for the decomposition of one mole of \(\mathrm{SO}_{3}\) to \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) and call the constant \(K_{2}\). (c) Relate \(K_{1}\) and \(K_{2}\).

At \(25^{\circ} \mathrm{C}, K=2.2 \times 10^{-3}\) for the reaction $$\mathrm{ICl}(g) \rightleftharpoons \frac{1}{2} \mathrm{I}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g)$$ Calculate \(K\) at \(25^{\circ} \mathrm{C}\) for (a) the decomposition of ICl into one mole of iodine and chlorine. (b) the formation of two moles of \(\operatorname{ICl}(g)\).

At \(627^{\circ} \mathrm{C}, K=0.76\) for the reaction $$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$ Calculate \(K\) at \(627^{\circ} \mathrm{C}\) for (a) the synthesis of one mole of sulfur trioxide gas. (b) the decomposition of two moles of \(\mathrm{SO}_{3}\).

Given the following reactions and their equilibrium constants, $$\begin{array}{lr}\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) & K=1.6 \\ \mathrm{FeO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Fe}(s)+\mathrm{CO}_{2}(g) & K=0.67 \end{array}$$ calculate \(K\) for the reaction$$\mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{FeO}(s)+\mathrm{H}_{2}(g)$$

Given the following reactions and their equilibrium constants, $$\begin{array}{cl}\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) & K=2.4 \times 10^{-9} \\ \mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) & K=8.8 \times 10^{-13} \end{array}$$ calculate \(K\) for the reaction $$\mathrm{C}(s)+\mathrm{CO}_{2}(g)+2 \mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{COCl}_{2}(g)$$

Given the following data at \(25^{\circ} \mathrm{C}\), $$\begin{array}{cl}2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) & K=1 \times 10^{-30} \\ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) & K=8 \times 10^{1} \end{array}$$ calculate \(K\) for the formation of one mole of NOBr from its elements in the gaseous state at \(25^{\circ} \mathrm{C}\).

When carbon monoxide reacts with hydrogen gas, methane and steam are formed. $$\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ At \(1127^{\circ} \mathrm{C}\), analysis at equilibrium shows that \(P_{\mathrm{CO}}=0.921 \mathrm{~atm}\), \(P_{\mathrm{H}_{2}}=1.21 \mathrm{~atm}, P_{\mathrm{CH}_{4}}=0.0391 \mathrm{~atm}\), and \(P_{\mathrm{H}_{2} \mathrm{O}}=0.0124 \mathrm{~atm} .\) What is the equilibrium constant, \(K\), for the reaction at \(1127^{\circ} \mathrm{C}\) ?

Calculate \(K\) for the formation of methyl alcohol at \(100^{\circ} \mathrm{C}\) : $$\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$$ given that at equilibrium, the partial pressures of the gases are \(P_{\mathrm{CO}}=0.814 \mathrm{~atm}, P_{\mathrm{H}_{2}}=0.274 \mathrm{~atm}\), and \(P_{\mathrm{CH}_{3} \mathrm{OH}}=0.0512 \mathrm{~atm} .\)

Ammonium carbamate solid \(\left(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\right)\) decomposes at \(313 \mathrm{~K}\) into ammonia and carbon dioxide gases. At equilibrium, analysis shows that there are \(0.0451\) atm of \(\mathrm{CO}_{2}, 0.0961\) atm of ammonia, and \(0.159 \mathrm{~g}\) of ammonium carbamate. (a) Write a balanced equation for the decomposition of one mole of \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\) (b) Calculate \(K\) at \(313 \mathrm{~K}\).

WEB At \(1123 \mathrm{~K}\), methane and hydrogen sulfide gases react to form carbon disulfide and hydrogen gases. At equilibrium the concentrations of methane, hydrogen sulfide, carbon disulfide, and hydrogen gas are \(0.00142 M, 6.14 \times 10^{-4} M, 0.00266 M\), and \(0.00943 M\), respectively. (a) Write a balanced equation for the formation of one mole of carbon disulfide gas. (b) Calculate \(K\) for the reaction at \(1123 \mathrm{~K}\).

Consider the decomposition of ammonium hydrogen sulfide: $$\mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)$$ In a sealed flask at \(25^{\circ} \mathrm{C}\) are \(10.0 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{HS}\), ammonia with a partial pressure of \(0.692 \mathrm{~atm}\), and \(\mathrm{H}_{2} \mathrm{~S}\) with a partial pressure of \(0.0532 \mathrm{~atm}\). When equilibrium is established, it is found that the partial pressure of ammonia has increased by 12.4\%. Calculate \(K\) for the decomposition of \(\mathrm{NH}_{4} \mathrm{HS}\) at \(25^{\circ} \mathrm{C}\).

A sealed flask has \(0.541\) atm of \(\mathrm{SO}_{3}\) at \(1000 \mathrm{~K}\). The following equilibrium is established. $$2 \mathrm{SO}_{3}(g) \rightleftharpoons 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g)$$ At equilibrium, the partial pressure of oxygen is measured to be \(0.216\) atm. Calculate \(K\) for the decomposition of \(\mathrm{SO}_{3}\) at \(1000 \mathrm{~K}\).

For the system $$\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ \(K\) is 26 at \(300^{\circ} \mathrm{C}\). In a 5.0-L flask, a gaseous mixture consists of all three gases with partial pressures as follows: \(P_{\mathrm{PCl}_{5}}=0.012 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.45 \mathrm{~atm}\), \(P_{\mathrm{PCl}_{3}}=0.90 \mathrm{~atm} .\) (a) Is the mixture at equilibrium? Explain. (b) If it is not at equilibrium, which way will the system shift to establish equilibrium?

The reversible reaction between hydrogen chloride gas and one mole of oxygen gas produces steam and chlorine gas: $$4 \mathrm{HCl}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \quad K=0.79$$ Predict the direction in which the system will move to reach equilibrium if one starts with (a) \(P_{\mathrm{H}_{2} \mathrm{O}}=P_{\mathrm{HCl}}=P_{\mathrm{O}_{2}}=0.20 \mathrm{~atm}\) (b) \(P_{\mathrm{HCl}}=0.30 \mathrm{~atm}, P_{\mathrm{H}_{2} \mathrm{O}}=0.35 \mathrm{~atm}, P_{\mathrm{Cl}_{2}}=0.2 \mathrm{~atm}, P_{\mathrm{O}_{2}}=0.15 \mathrm{~atm}\)

For the reaction $$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$ \(K\) at a certain temperature is \(0.50\). Predict the direction in which the system will move to reach equilibrium if one starts with (a) \(P_{\mathrm{O}_{2}}=P_{\mathrm{NO}}=P_{\mathrm{NO}_{2}}=0.10 \mathrm{~atm}\) (b) \(P_{\mathrm{NO}_{2}}=0.0848 \mathrm{~atm}, P_{\mathrm{O}_{2}}=0.0116 \mathrm{~atm}\) (c) \(P_{\mathrm{NO}_{2}}=0.20 \mathrm{~atm}, P_{\mathrm{O}_{2}}=0.010 \mathrm{~atm}, P_{\mathrm{NO}}=0.040 \mathrm{~atm}\)

A compound, \(\mathrm{X}\), decomposes at \(131^{\circ} \mathrm{C}\) according to the following equation: $$2 \mathrm{X}(g) \rightleftharpoons \mathrm{A}(g)+3 \mathrm{C}(g) \quad K=1.1 \times 10^{-3}$$ If a flask initially contains \(\mathrm{X}, \mathrm{A}\), and \(\mathrm{C}\), all at partial pressures of \(0.250 \mathrm{~atm}\), in which direction will the reaction proceed?

At a certain temperature, \(K\) is \(1.3 \times 10^{5}\) for the reaction $$2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{~S}(g)$$ What is the equilibrium pressure of hydrogen sulfide if those of hydrogen and sulfur gases are \(0.103\) atm and \(0.417\) atm, respectively?

At a certain temperature, \(K\) is \(0.040\) for the decomposition of two moles of bromine chloride gas (BrCl) to its elements. An equilibrium mixture at this temperature contains bromine and chlorine gases at equal partial pressures of \(0.0493\) atm. What is the equilibrium partial pressure of bromine chloride?

For the reaction $$\mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g)$$ \(K\) is \(1.54 \times 10^{-3}\). When equilibrium is established, the partial pressure of nitrogen is \(0.168 \mathrm{~atm}\), and that of \(\mathrm{NO}\) is \(0.225 \mathrm{~atm}\). The total pressure of the system at equilibrium is \(1.87 \mathrm{~atm}\). What are the equilibrium partial pressures of hydrogen and steam?

WEB Nitrogen dioxide can decompose to nitrogen oxide and oxygen. $$2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)$$ \(K\) is \(0.87\) at a certain temperature. A 5.0-L flask at equilibrium is determined to have a total pressure of \(1.25\) atm and oxygen to have a partial pressure of \(0.515\) atm. Calculate \(P_{\mathrm{NO}}\) and \(P_{\mathrm{NO}}\), at equilibrium.

Carbonyl fluoride, \(\mathrm{COF}_{2}\), is an important intermediate for organic fluorine compounds. It can be prepared by the following reaction: $$\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{CF}_{4}(g) \rightleftharpoons 2 \mathrm{COF}_{2}(g)$$ At \(1000^{\circ} \mathrm{C}, K\) for this reaction is \(0.50 .\) What are the partial pressures of all the gases at equilibrium when the initial partial pressures of \(\mathrm{CO}_{2}\) and \(\mathrm{CF}_{4}\) are \(0.713 \mathrm{~atm} ?\)

. Consider the equilibrium $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)$$ At a certain temperature, the equilibrium constant for the reaction is \(0.0255\). What are the partial pressures of all gases at equilibrium if the initial partial pressure of the gases (both reactants and products) is \(0.300 \mathrm{~atm} ?\)

The reaction $$\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)$$ has an equilibrium constant of \(1.30\) at \(650^{\circ} \mathrm{C}\). Carbon monoxide and steam both have initial partial pressures of \(0.485 \mathrm{~atm}\), while hydrogen and carbon dioxide start with partial pressures of \(0.159\) atm. (a) Calculate the partial pressure of each gas at equilibrium. (b) Compare the total pressure initially with the total pressure at equilibrium. Would that relation be true of all gaseous systems?

At \(460^{\circ} \mathrm{C}\), the reaction $$\mathrm{SO}_{2}(g)+\mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{NO}(g)+\mathrm{SO}_{3}(g)$$ has \(K=84.7\). All gases are at an initial pressure of \(1.25\) atm. (a) Calculate the partial pressure of each gas at equilibrium. (b) Compare the total pressure initially with the total pressure at equilibrium. Would that relation be true of all gaseous systems?

Solid ammonium carbamate, \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\), decomposes at \(25^{\circ} \mathrm{C}\) to ammonia and carbon dioxide. $$\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(g)$$ The equilibrium constant for the decomposition at \(25^{\circ} \mathrm{C}\) is \(2.3 \times 10^{-4}\), At \(25^{\circ} \mathrm{C}, 7.50 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\) is sealed in a \(10.0\) - \(\mathrm{L}\) flask and allowed to decompose. (a) What is the total pressure in the flask when equilibrium is established? (b) What percentage of \(\mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}\) decomposed? (c) Can you state from the data calculated that the decomposition took place slowly?

Solid ammonium iodide decomposes to ammonia and hydrogen iodide gases at sufficiently high temperatures. $$\mathrm{NH}_{4} \mathrm{I}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HI}(g)$$ The equilibrium constant for the decomposition at \(673 \mathrm{~K}\) is \(0.215\). Fifteen grams of ammonium iodide are sealed in a \(5.0\) -L flask and heated to \(673 \mathrm{~K}\). (a) What is the total pressure in the flask at equilibrium? (b) How much ammonium iodide decomposes?

Hydrogen cyanide, a highly toxic gas, can decompose to cyanogen and hydrogen gases, $$2 \mathrm{HCN}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{~N}_{2}(g)+\mathrm{H}_{2}(g)$$ At a certain temperature, \(K\) for this decomposition is \(0.17\). What are the partial pressures of all gases at equilibrium if initially the partial pressures are \(P_{\mathrm{C}_{2} \mathrm{~N}_{2}}=P_{\mathrm{H}_{2}}=0.32 \mathrm{~atm}, P_{\mathrm{HCN}}=0.45 \mathrm{~atm} ?\)

. At \(800 \mathrm{~K}\), hydrogen iodide can decompose into hydrogen and iodine gases. $$2 \mathrm{HI}(g) \rightleftharpoons \mathrm{I}_{2}(g)+\mathrm{H}_{2}(g)$$ At this temperature, \(K=0.0169 .\) What are the partial pressures at equilibrium of the hydrogen and iodine if initially a sealed flask at \(800 \mathrm{~K}\) contains only HI at a pressure of \(0.200\) atm?

For the following reactions, predict whether the pressure of the reactants or products increases or remains the same when the volume of the reaction vessel is increased. (a) \(\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\)

Consider the system $$\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta H=98.9 \mathrm{~kJ}$$ (a) Predict whether the forward or reverse reaction will occur when the equilibrium is disturbed by (1) adding oxygen gas. (2) compressing the system at constant temperature. (3) adding argon gas. (4) removing \(\mathrm{SO}_{2}(g)\). (5) decreasing the temperature. (b) Which of the above factors will increase the value of \(K ?\) Which will decrease it?

Consider the system \(4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-1530.4 \mathrm{~kJ}\) (a) How will the amount of ammonia at equilibrium be affected by (1) removing \(\mathrm{O}_{2}(g)\) ? (2) adding \(\mathrm{N}_{2}(g)\) ? (3) adding water? (4) expanding the container at constant pressure? (5) increasing the temperature? (b) Which of the above factors will increase the value of \(K ?\) Which will decrease it?

Predict the direction in which each of the following equilibria will shift if the pressure on the system is increased by compression. (a) \(\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{C}(s) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) (b) \(\mathrm{SbCl}_{3}(g) \rightleftharpoons \mathrm{SbCl}_{3}(g)+\mathrm{Cl}_{2}(g)\) (c) \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g)\)

Predict the direction in which each of the following equilibria will shift if the pressure on the system is decreased by expansion. (a) \(\mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g)\) (b) \(\mathrm{CI} \mathrm{F}_{5}(g) \rightleftharpoons \mathrm{Cl} \mathrm{F}_{3}(g)+\mathrm{F}_{2}(g)\) (c) \(\mathrm{HBr}(g) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)\)

At a certain temperature, nitrogen and oxygen gases combine to form nitrogen oxide gas. $$\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(g)$$ When equilibrium is established, the partial pressures of the gases are: \(P_{\mathrm{N}_{2}}=\) \(1.2 \mathrm{~atm}, P_{\mathrm{O}_{2}}=0.80 \mathrm{~atm}, P_{\mathrm{NO}}=0.022 \mathrm{~atm} .\) (a) Calculate \(K\) at the temperature of the reaction. (b) After equilibrium is reached, more oxygen is added to make its partial pressure \(1.2\) atm. Calculate the partial pressure of all gases when equilibrium is reestablished.

A 1.0-L reaction vessel at \(90^{\circ} \mathrm{C}\) contains \(8.00 \mathrm{~g}\) of sulfur, hydrogen, and hydrogen sulfide gases with partial pressures of \(6.0 \mathrm{~atm}\) and \(0.40 \mathrm{~atm}\), respectively, at equilibrium: $$\mathrm{H}_{2}(g)+\mathrm{S}(s) \rightleftharpoons \mathrm{H}_{2} \mathrm{~S}(g)$$ (a) Calculate \(K\) for the reaction at equilibrium. (b) The mass of sulfur is increased to \(10.0\) grams. What are the partial pressures of \(\mathrm{H}_{2}\) and \(\mathrm{H}_{2} \mathrm{~S}\) when equilibrium is reestablished? (c) The pressure of \(\mathrm{H}_{2} \mathrm{~S}\) is increased to \(1.0 \mathrm{~atm}\). What are the partial pressures of \(\mathrm{H}_{2}\) and \(\mathrm{H}_{2} \mathrm{~S}\) when equilibrium is reestablished?

Iodine chloride decomposes at high temperatures to iodine and chlorine gases. $$2 \mathrm{ICl}(g) \rightleftharpoons \mathrm{I}_{2}(g)+\mathrm{Cl}_{2}(g)$$ Equilibrium is established at a certain temperature when the partial pressures of ICI, \(\mathrm{I}_{2}\), and \(\mathrm{Cl}_{2}\) are (in atm) \(0.43,0.16\), and \(0.27\), respectively. (a) Calculate \(K\). (b) If enough iodine condenses to decrease its partial pressure to \(0.10 \mathrm{~atm}\), in which direction will the reaction proceed? What is the partial pressure of iodine when equilibrium is re-established?

Carbonylbromide (COBr_2) can be formed by combining carbon monoxide and bromine gas. $$\mathrm{CO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons \operatorname{COBr}_{2}(g)$$ When equilibrium is established at \(346 \mathrm{~K}\), the partial pressures (in atm) of \(\mathrm{COBr}_{2}\), \(\mathrm{CO}\), and \(\mathrm{Br}_{2}\) are \(0.12,1.00\), and \(0.65\), respectively. (a) What is \(K\) at \(346 \mathrm{~K} ?\) (b) Enough bromine condenses to decrease its partial pressure to \(0.50\) atm. What are the equilibrium partial pressures of all gases after equilibrium is re-established?

Hemoglobin (Hb) binds to both oxygen and carbon monoxide. When the carbon monoxide replaces the oxygen in an organism, the following reaction occurs: $$\mathrm{HbO}_{2}(a q)+\mathrm{CO}(g) \rightleftharpoons \mathrm{HbCO}(a q)+\mathrm{O}_{2}(g)$$ At \(37^{\circ} \mathrm{C}, K\) is about 200 . When equal concentrations of \(\mathrm{HbO}_{2}\) and \(\mathrm{HbCO}\) are present, the effect of CO inhalation is fatal. Assuming \(\mathrm{P}_{\mathrm{O}_{2}}=0.21 \mathrm{~atm}\), what is \(\mathrm{P}_{\mathrm{CO}}\) when \(\left[\mathrm{HbO}_{2}\right]=[\mathrm{HbCO}] ?\)

At \(1800 \mathrm{~K}\), oxygen dissociates into gaseous atoms: $$\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}(g)$$ \(K\) for the system is \(1.7 \times 10^{-8} .\) If one mole of oxygen molecules is placed in a \(5.0\) -L flask and heated to \(1800 \mathrm{~K}\), what percentage by mass of the oxygen dissociates? How many \(\mathrm{O}\) atoms are in the flask?

For the decomposition of \(\mathrm{CaCO}_{3}\) at \(900^{\circ} \mathrm{C}, K=1.04\). $$\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{O}_{2}(g)$$ Find the smallest mass of \(\mathrm{CaCO}_{3}\) needed to reach equilibrium in a 5.00-L vessel at \(900^{\circ} \mathrm{C}\).