Chapter 15

Write the expressions for the thermodynamic equilibrium constant \(K \text { for the following reactions. (Section } 15.1)\) (a) \(\quad 4 \mathrm{NH}_{3}(\mathrm{g})+7 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 4 \mathrm{NO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{f})\) (b) \(\mathrm{HCN}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{CN}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})\) (c) \(\quad \mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) (d) \(3 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{O}_{3}(\mathrm{g})\) (e) \(2 \mathrm{H}_{2} \mathrm{O}() \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{*}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq})\) (f) \(3 \operatorname{Zn}(s)+2 F e^{3+}(a q) \rightleftharpoons 2 F e(s)+3 \operatorname{Zn}^{2}+(a q)\)

The solubility of silver chloride in water at \(25^{\circ} \mathrm{C}\) is \(1.27 \times 10^{-5} \mathrm{moldm}^{-3}\). Calculate (a) the solubility product of AgCl (b) the solubility of AgCl in 0.01 moldm \(^{-3}\) aqueous sodium chloride solution. (Section \(15.1)\)

The equilibrium constants for two gas phase reactions at \(1000^{\circ} \mathrm{C}\) are shown. \\[ \begin{array}{l} \mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad \mathrm{K}_{1}=9.1 \times 10^{-12} \\ \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \quad K_{2}=7.1 \times 10^{-12} \end{array} \\] Use these data to find the equilibrium constant at the same temperature for the reaction: \\[ \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\] (Section \(15.1)\)

The equilibrium constant for the following reaction is \\[ \begin{array}{l} K=1.5 \times 10^{4} \\ \qquad \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{COCl}_{2}(\mathrm{g}) \end{array} \\] In a reaction vessel, the partial pressures of the reaction mixture are: \(\mathrm{COCl}_{2} 0.050 \mathrm{bar}, \mathrm{CO} 0.0010 \mathrm{bar},\) and \(\mathrm{Cl}_{2} 0.0001 \mathrm{bar}\). (a) Calculate the value for the reaction quotient, \(Q\), for this mixture. (b) What will happen to the composition of the reaction mixture as it moves to equilibrium? (Section 15.2 )

An important reaction in the formation of smog is: \\[ \mathrm{O}_{3}(\mathrm{g})+\mathrm{NO}(\mathrm{g}) \rightleftharpoons \mathrm{O}_{2}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \\] Under certain conditions, the equilibrium constant for this reaction is \(K=6.0 \times 10^{34}\). If the partial pressures of each gas in the air over your home town were \(1.0 \times 10^{-6} \mathrm{bar} \mathrm{O}_{3}\) \(1.0 \times 10^{-5} \mathrm{bar} \mathrm{NO}, 2.5 \times 10^{-4} \mathrm{bar} \mathrm{NO}_{2},\) and \(8.2 \times 10^{-3} \mathrm{bar} \mathrm{O}_{2}\) what could you say about the course of the reaction as it moves to equilibrium? (Section 15.2 )

Calculate the equilibrium constant, \(K\), at \(298 \mathrm{K}\) for the reaction \\[ \mathrm{H}_{2} \mathrm{O}\left(\mathrm{m} \rightleftharpoons \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})\right. \\] The standard Gibbs energy change of formation of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{j})\) at \\[ 298 \mathrm{K} \text { is }-237.1 \mathrm{kJmol}^{-1} \text {. (Section } 15.3 \text { ) } \\]

2.0 mol of carbon disulfide and \(4.0 \mathrm{mol}\) of chlorine react at constant temperature according to this equation \\[ \mathrm{CS}_{2}(\mathrm{g})+3 \mathrm{Cl}_{2}(\mathrm{g}) \rightleftarrows \mathrm{S}_{2} \mathrm{Cl}_{2}(\mathrm{g})+\mathrm{CCl}_{4}(\mathrm{g}) \\] At equilibrium, \(0.30 \mathrm{mol}\) of tetrachloromethane are formed. How much of each of the other components is present in this equilibrium mixture? (Section 15.4 )

Nitrosy chloride (NOCI) decomposes to nitric oxide and chlorine when heated \\[ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \\] In a mixture of all three gases at \(600 \mathrm{K}\), the partial pressure of NOCl is 0.88 bar, that of \(\mathrm{NO}\) is 0.06 bar, and the partial pressure of chlorine is 0.03 bar. At \(600 \mathrm{K}\), the equilibrium constant, \(K,\) is \(0.060 .\) (Section 15.2 and several others) (a) What is the value of the reaction quotient for this mixture? Is the mixture at equilibrium? (b) In which direction will the system move to reach equilibrium? (c) What will happen if an additional amount of NOCl(g) is injected into the reaction?

The following gas phase reaction is exothermic \\[ \mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g}) \\] What will be the effect of (a) increasing the pressure, (b) increasing the temperature, and (c) adding a catalyst on (i) the equilibrium constant, \(K\), and (ii) the yield of \(\mathrm{CO}_{2}\) ? (Section 15.5 )

For the gas phase reaction \\[ \mathrm{COCl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \\] at \(100^{\circ} \mathrm{C}\) and 2 bar pressure, the fraction, \(\alpha,\) of phosgene \(\left(\mathrm{COCl}_{2}\right)\) that reacts is \(6.3 \times 10^{-5}\). Calculate the equilibrium constant, \(K, \text { for the reaction. (Section } 15.4)\)

Bromine and chlorine react to produce bromine monochloride according to the equation \\[ \mathrm{Br}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{BrCl}(\mathrm{g}) \\] \(0.2 \mathrm{mol}\) of bromine gas and \(0.2 \mathrm{mol}\) of chlorine gas are introduced into a sealed flask with a volume of \(5.0 \mathrm{dm}^{3}\). Under the conditions of the experiment, \(K=36.0 .\) How much BrCl will be present at equilibrium? (Section 15.4 )

\(\mathrm{CO}_{2}\) decomposes into \(\mathrm{CO}\) and \(\mathrm{O}_{2}\) over a platinum catalyst \\[ 2 \mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \\] At 1 bar pressure, the fraction, \(\alpha,\) of \(\mathrm{CO}_{2}\) that reacts is 0.014 at \(1395 \mathrm{K}, 0.025\) at \(1443 \mathrm{K}\), and 0.047 at \(1498 \mathrm{K}\). (Section 15.5 ) (a) Calculate the equilibrium constant at \(1443 \mathrm{K}\) (b) Calculate \(\Delta_{r} H^{\theta}\) and \(\Delta_{r} S^{\theta}\) for the reaction.

For a general reaction \\[ \alpha A+\beta B \rightleftharpoons \gamma C+\delta D \\] derive the relationship between the Gibbs energy change of the reaction and the reaction quotient. Use the relationship to show that \(\left.\Delta_{r} G^{\ominus}=-R T \ln K . \text { (Section } 15.3\right)\)

For the following esterification reaction \\[ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\left(\mathrm{p}+\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{D}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\left(\mathrm{f}+\mathrm{H}_{2} \mathrm{O}(0)\right.\right. \\] the equilibrium constant at \(298 \mathrm{K}\) is \(3.8 .\) A mixture containing \(0.5 \mathrm{moldm}^{-3}\) each of ethanol and ethanoic acid was reacted in a sealed flask at \(298 \mathrm{K}\). After a certain time, the concentrations of each had changed to 0.39 moldm \(^{-3}\). (Section 15.3 ) (a) Had the reaction reached equilibrium? (b) If not, what would the concentration of \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}(\mathrm{aq})\) be at equilibrium? (c) In practice, the reaction is carried out so as to remove the water as it forms. Explain why this is done.

An equilibrium constant, \(K,\) is five times larger when a reaction is performed at \(200 \mathrm{K}\) than at \(150 \mathrm{K}\). Assuming the enthalpy change is constant over this temperature range, calculate \(\Delta_{N} H^{\circ}\) for the reaction. (Section 15.5 )

If the following reaction was at equilibrium in a closed vessel at a controlled temperature, what would be the effect of adding more \(\mathrm{H}_{2}\) to the reaction vessel and permitting the reaction to approach equilibrium again? (Section 15.5 ) \\[ \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \\]

Calculate the maximum quantity (in mol) of \(\mathrm{KIO}_{3}\) that can be added to \(250 \mathrm{cm}^{3}\) of a solution containing \(1.00 \times 10^{-3} \mathrm{mol} \mathrm{dm}^{-3}\) of \(\mathrm{Cu}^{2}\) ' (aq) without precipitating \(\mathrm{Cu}(\mathrm{IO} 3)_{2}(\mathrm{s}) . K_{\mathrm{sp}}=1.4 \times 10^{-7}\) for \(\mathrm{Cu}\left(\mathrm{IO}_{3}\right)_{2}(\mathrm{s})\).

For the reaction, \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{s}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}), \Delta_{r} \mathrm{G}^{0}=3.40 \mathrm{kJ} \mathrm{mor}^{-1}\) at \(298.15 \mathrm{K}\) (a) Calculate the equilibrium constant. (b) Does the reaction favour the products or reactants? (c) If additional \(\mathrm{H}_{2}(\mathrm{g})\) was added to the equilibrium mixture at the same temperature, predict what would happen to the position of equilibrium.

A student was investigating the following equilibrium reaction Which has an equilibrium constant of 0.220 at \(800^{\circ} \mathrm{C}\) \\[ \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \\] and did four experiments. (a) \(0.2 g\) of \(\mathrm{CaCO}_{3}(\mathrm{s})\) was heated to \(800^{\circ} \mathrm{C}\) in a \(1.0 \mathrm{dm}^{3}\) container (b) \(2.0 \mathrm{g}\) of \(\mathrm{CaCO}_{3}(\mathrm{s})\) was heated to \(800^{\circ} \mathrm{C}\) in a \(1.0 \mathrm{dm}^{3}\) container (c) \(0.2 g\) of \(\mathrm{CaCO}_{3}\) (s) was heated to \(800^{\circ} \mathrm{C}\) in a \(500 \mathrm{cm}^{3}\) container (d) \(2.0 g\) of \(\mathrm{CaCO}_{3}(\mathrm{s})\) was heated to \(800^{\circ} \mathrm{C}\) in a \(500 \mathrm{cm}^{3}\) container The pressure of \(\mathrm{CO}_{2}\) (g) measured in each case was ( 1 ) 0.18 bar, (ii) 0.22 bar, (iii) 0.22 bar, \((\text { iv) } 0.22\) bar. Explain these observations.