Chapter 9

Write the equilibrium expressions \(K\) for the following reactions. (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{NO}_{2}(\mathrm{~g})\) (b) \(\mathrm{SbCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{SbCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+2 \mathrm{H}_{2}(\mathrm{~g}) \Rightarrow \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{~g})\)

Determine \(K_{c}\) from the value of \(K\) for cach of the following equilibria. (a) \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{SO}_{3}(\mathrm{~g}), K=3.4\) at \(1000 \mathrm{~K}\) (b) \(\mathrm{NH}_{4} \mathrm{HS}(\mathrm{s})=\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g}), K=9.4 \times 10^{-2}\) at \(24^{\circ} \mathrm{C}\)

A \(0.10-\mathrm{mol}\) sample of pure czone, \(\mathrm{O}_{3}\), is placed in a sealed \(1.0\) - L container and the reaction \(2 \mathrm{O}_{3}(\mathrm{~g}) \rightarrow 3 \mathrm{O}_{2}(\mathrm{~g})\) is allowed to reach equilihrium. A \(0.50-\mathrm{mol}\) sample of pure ozone is placed in a second 1.0-L container at the same temperature and allowed to reach equilibrium. Without doing any calculations, predict which of the following will be different in the two containers at equilibrium. Which will be the same? Explain each of your answers: (a) amount of \(\mathrm{O}_{2}\); (b) concentration of \(\mathrm{O}_{2}\); (c) the ratio \(\left[\mathrm{O}_{2}\right] /\left[\mathrm{O}_{3}\right]\); (d) the ratio \(\left.\left[\mathrm{O}_{2}\right]^{3} / \mathrm{O}_{3}\right]^{2} ;\) (e) the ratio \(\left|\mathrm{O}_{3}\right|^{2} /\left[\mathrm{O}_{2}\right]^{3}\).

For the reaction \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})=2 \mathrm{NH}_{3}(\mathrm{~g})\) at \(400 \mathrm{~K}, K=41\). Find the value of \(\mathrm{K}\) for each of the following reactions at the same temperature. (a) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(\frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{3}{2} \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{~g})\) (c) \(2 \mathrm{~N}_{2}(\mathrm{~g})+6 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{NH}_{3}(\mathrm{~g})\)

The equilibrium constant for the reaction \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{SO}_{3}(\mathrm{~g})\) has the value \(K=2.5 \times 10^{10}\) at \(500 \mathrm{~K}\). Find the value of \(K\) for each of the following reactions at the same temperature. (a) \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})=\mathrm{SO}_{3}(\mathrm{~g})\) (b) \(\mathrm{SO}_{3}(\mathrm{~g})=\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\) (c) \(3 \mathrm{SO}_{2}(\mathrm{~g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{SO}_{3}(\mathrm{~g})\)

Explain why the following cquilibria are heterogeneous and write the reaction quotient \(Q\) for each one. (a) \(2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{FcCl}_{3}(\mathrm{~s})\) (b) \(\mathrm{NH}_{4}\left(\mathrm{NH}_{2} \mathrm{CO}_{2}\right)(\mathrm{s}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})\) (c) \(2 \mathrm{KNO}_{3}\) (s) \(\rightleftharpoons 2 \mathrm{KNO}_{2}\) (s) \(+\mathrm{O}_{2}\) (g)

Explain why the following equilibria are heterogencous and write the reaction quoticnt \(Q\) for each one. (a) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})=\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{HCl}(\mathrm{g})\) (b) \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot \mathrm{OH}_{2} \mathrm{O}\) (s) \(\rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s})+10 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(2 \mathrm{KCO}_{3}\) (s) \(\Rightarrow 2 \mathrm{KCl}\) (s) \(+3 \mathrm{O}_{2}\) (g)

Write the reaction quotients \(Q_{c}\) for (a) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{CuCl}_{2}(\mathrm{~s})\) (b) \(\mathrm{NH}_{4} \mathrm{NO}_{2}\) (s) \(\rightarrow \mathrm{N}_{2} \mathrm{O}\) (g) \(+2 \mathrm{H}_{2} \mathrm{O}\) (g) (c) \(\mathrm{MgCO}_{3}(\mathrm{~s}) \rightarrow \mathrm{MgO}\) (s) \(+\mathrm{CO}_{2}\) (g)

Write the reaction quotients \(Q_{c}\) for (a) \(\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{~s}) \rightarrow \mathrm{Fe}^{3}(\mathrm{aq})+3 \mathrm{OH}^{-}(\mathrm{aq})\) (b) \(\mathrm{CuSO}_{4}(\mathrm{~s})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) (s) (c) \(\mathrm{ZnO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Zn}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\)

For the reaction \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{I}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g})\), \(K_{\mathrm{c}}=160\) at \(500 \mathrm{~K}\). An analysis of a reaction mixture at \(500 \mathrm{~K}\) showed that it had the composition \(4.8 \times 10^{-3} \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{H}_{2}, 2.4 \times 10^{-3} \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{I}_{2}\), and \(2.4 \times 10^{-3} \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{HI}\). (a) Calculate the reaction quoticnt. (b) Is the reaction mixture at equilibrium? (c) If not, is there a tendency to form more reactants or more products?