Chapter 9

Predict whether each of the following equilibria will shift toward products or reactants with a temperature increase. (a) \(\mathrm{CH}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g})\), \(\Delta H^{\circ}=+206 \mathrm{~kJ}\) (b) \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})=\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\), \(\Delta H^{2}=-41 \mathrm{~kJ}\) (c) \(2 \mathrm{SO}_{2}\) (g) \(+\mathrm{O}_{2}\) (g) \(=2 \mathrm{SO}_{3}\) (g), \(\Delta H^{\circ}=-198 \mathrm{~kJ}\)

A mixture consisting of \(2.23 \times 10^{-3} \mathrm{~mol} \mathrm{~N}_{2}\) and \(6.69 \times 10^{-3} \mathrm{~mol} \mathrm{H}_{2}\) in a \(500-\mathrm{ml}\). container was heated to \(600 \mathrm{~K}\) and allowed to reach equilibrium. Will more ammonia be formed if that equilibrium mixture is then heated to \(700 \mathrm{~K}\) ? For \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g})=\) \(2 \mathrm{NH}_{3}(\mathrm{~g}), K=1.7 \times 10^{-3}\) at \(600 \mathrm{~K}\) and \(7.8 \times 10^{-5}\) at \(700 \mathrm{~K}\).

A mixture consisting of \(1.1 \mathrm{mmol} \mathrm{SO}_{2}\) and \(2.2 \mathrm{mmol} \mathrm{O}_{2}\) in a \(250-\mathrm{mL}\) container was heated to \(500 \mathrm{~K}\) and allowed to reach equilibrium. Will more sulfur trioxide be formed if that equilibrium mixture is cooled to \(25^{\circ} \mathrm{C}\) ? For the reaction \(2 \mathrm{SO}_{2}(\mathrm{~g})+\) \(\mathrm{O}_{2}(\mathrm{~g})=2 \mathrm{SO}_{3}(\mathrm{~g}), \mathrm{K}=2.5 \times 10^{10}\) at \(500 \mathrm{~K}\) and \(4.0 \times 10^{24}\) at \(25^{\circ} \mathrm{C}\).

The value of the equilibrium constant \(K\) for the reaction \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) is \(3.0 \times 10^{4}\) at \(700 \mathrm{~K}\). Determine the value of \(K_{c}\) for the reactions (a) \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) and \((\mathrm{b}) \mathrm{SO}_{3}(\mathrm{~g}) \rightleftharpoons\) \(\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g})\)

\( \mathrm{Ar} 500^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.061\) for \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons\) \(2 \mathrm{NH}_{3}(\mathrm{~g}) .\) Calculate the value of \(K_{\varepsilon}\) at \(500^{\circ} \mathrm{C}\) for the following reactions. (a) \(\frac{1}{6} \mathrm{~N}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \frac{1}{3} \mathrm{NH}_{3}(\mathrm{~g})\) (b) \(\mathrm{NH}_{3}(g)=\frac{1}{2} \mathrm{~N}_{2}(g)+\frac{1}{2} \mathrm{H}_{2}(g)\) (c) \(4 \mathrm{~N}_{2}(\mathrm{~g})+12 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 8 \mathrm{NH}_{3}(\mathrm{~g})\)

At \(500^{\circ} \mathrm{C}, K_{c}=0.061\) for \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons\) \(2 \mathrm{NH}_{3}(\mathrm{~g})\). If analysis shows that the composition is \(3.00 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~N}_{2}, 2.00 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{H}_{2}\) and \(0.500 \mathrm{~mol} \cdot \mathrm{L}^{-1}\) \(\mathrm{NH}_{3}\), is the reaction at equilibrium? If not, in which direction does the reaction tend to proceed to reach equilibrium?

At \(2500 \mathrm{~K}, K_{e}=20\) for the reaction \(\mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{ClF}(\mathrm{g}) .\) An analysis of a reaction vessel at \(2500 \mathrm{~K}\) revealed the presence of \(0.18 \mathrm{~mol} \cdot \mathrm{L}^{-1}\) \(\mathrm{Cl}_{2}, 0.31 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{~F}_{2}\), and \(0.92 \mathrm{~mol} \cdot \mathrm{L}^{-1} \mathrm{ClF}\). Will \(\mathrm{ClF}\) tend to form or to decompose as the reaction proceeds toward cquilibrium?

The equilibrium constant \(K=3.5 \times 10^{4}\) for the reaction \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})=\mathrm{PCl}_{5}(\mathrm{~g})\) at \(760^{\circ} \mathrm{C}\). At equilibrium, the partial pressure of \(\mathrm{PCl}_{5}\) was \(2.2 \times\) \(10^{4}\) bar and that of \(\mathrm{PCl}_{3}\) was \(1.33\) bar. What was the equilibrium partial pressure of \(\mathrm{Cl}_{2}\) ?

A reaction mixture consisting of \(2.00 \mathrm{~mol} \mathrm{CO}\) and \(3.00 \mathrm{~mol} \mathrm{H}_{2}\) is placed into a \(10.0-\mathrm{L}\) reaction vessel and heated to \(1200 \mathrm{~K}\). At cquilibrium, \(0.478 \mathrm{~mol} \mathrm{CH}_{4}\) was present in the system. Determine the value of \(K_{c}\) for the reaction \(\mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{~g})+\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\).

A mixture consisting of \(1.000 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) and \(1.000 \mathrm{~mol} \mathrm{CO}(\mathrm{g})\) is placed in a \(10.00-\mathrm{L}\) reaction vessel at \(800 \mathrm{~K}\). At equilibrium, \(0.665 \mathrm{~mol} \mathrm{CO}_{2}(\mathrm{~g})\) is present as a result of the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})=\) \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})\). What are (a) the equilibrium concentrations for all substances and (b) the value of \(K_{e}\) ?