Chapter 9

A mixture of \(0.0560 \mathrm{~mol} \mathrm{O}_{2}\) and \(0.0200 \mathrm{~mol}\) \(\mathrm{N}_{2} \mathrm{O}\) is placed in a \(1.00-\mathrm{L}\) reaction vessel at \(25^{\circ} \mathrm{C}\). When the reaction \(2 \mathrm{~N}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{~g})=4 \mathrm{NO}_{2}(\mathrm{~g})\) is at equilibrium, \(0.0200\) mol \(\mathrm{NO}_{2}\) is present. (a) What are the equilibrium concentrations? (b) What is the value of \(K_{c}\) ?

A 30.1-g sample of NOCl is placed into a \(200-\mathrm{mL}\) reaction vessel and heated to \(500 \mathrm{~K}\). The value of \(K\) for the decomposition of NOCl at \(500 \mathrm{~K}\) in the reaction \(2 \mathrm{NOCl}(\mathrm{g})=2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g})\) is \(1.13 \times 10^{-3}\). (a) What are the equilibrium partial pressures of \(\mathrm{NOCl}, \mathrm{NO}\), and \(\mathrm{Cl}_{2}\) ? (b) What is the percentage decomposition of NOCl at this temperature?

The photosynthesis reaction is \(6 \mathrm{CO}_{2}(\mathrm{~g})+\) \(6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{C}_{\mathrm{g}} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})+6 \mathrm{O}_{2}(\mathrm{~g})\), and \(\Delta H^{\circ}=+2802 \mathrm{~kJ}\). Suppose that the reaction is at cquilibrium. State the effect (tend to shift toward the formation of reactants, tend to shift toward the formation of products, or have no effect) that each of the following changes will have on the equilibrium composition: (a) the partial pressure of \(\mathrm{O}_{2}\) is increased; (b) the system is compressed; (c) the amount of \(\mathrm{CO}_{2}\) is increased; (d) the temperature is increased; (c) some of the \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is removed; \((f)\) water is added; \((g)\) the partial pressure of \(\mathrm{CO}_{2}\) is decreased.

Use Le Chatelier's principle to predict the effect that the change given in the first column of the following table has on the quantity in the second column for the following equilibrium system: $$ \begin{gathered} 5 \mathrm{CO}(\mathrm{g})+\mathrm{I}_{2} \mathrm{O}_{5}(\mathrm{~s}) \rightleftharpoons \mathrm{I}_{2}(\mathrm{~g})+5 \mathrm{CO}_{2}(\mathrm{~g}) \\\ \Delta H^{\circ}=-1175 \mathrm{~kJ} \end{gathered} $$

\( \mathrm{~A} 3.00-\mathrm{L}\) reaction vessel is filled with \(0.150 \mathrm{~mol}\) \(\mathrm{CO}, 0.0900 \mathrm{~mol} \mathrm{H}_{2}\), and \(0.180 \mathrm{~mol} \mathrm{CH}_{3} \mathrm{OH}\). Equilibrium is reached in the presence of a zinc oxidechromium(III) oxide catalyst; and at \(300^{\circ} \mathrm{C}, K_{c}=\) \(1.1 \times 10^{-2}\) for the reaction, \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons\) \(\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\). (a) As the reaction approaches equilibrium, will the molar concentration of \(\mathrm{CH}_{3} \mathrm{OH}\) increase, decrease, or remain unchanged? (b) What is the equilibrium composition of the mixture?

At \(1565 \mathrm{~K}\), the equilibrium constants for the reactions (1) \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})\) and \((2)\) \(2 \mathrm{CO}_{2}(\mathrm{~g})=2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g})\) are \(1.6 \times 10^{-11}\) and \(1.3 \times 10^{-10}\), respectively. (a) What is the equilibrium constant for the reaction (3) \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g})=\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g})\) at that temperature? (b) Show that the manner in which equilibrium constants are calculated is consistent with the manner in which the \(\Delta G_{1}^{\circ}\) values are calculated when combining two or more equarions by determining \(\Delta G_{e}{ }^{\circ}\) for \((1)\) and \((2)\) and using those values to calculare \(\Delta G,{ }^{\circ}\) and \(K_{3}\) for reaction (3).

Let \(\alpha\) be the fraction of \(\mathrm{PCl}_{5}\) molecules that have decomposed to \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\) in the reaction \(\mathrm{PCl}_{5}(\mathrm{~g})=\) \(\mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\) in a constant- volume container, so that the amount of \(\mathrm{PCl}_{5}\) at equilibrium is \(n(1-\alpha)\), where \(n\) is the pressure present initially. Derive an equation for \(K\) in terms of \(\alpha\) and the total pressure \(P\), and solve it for \(\alpha\) in terms of \(P\). Calculate the fraction decomposed at \(556 \mathrm{~K}\), at which temperature \(K=4.96\), and the total pressure is (a) \(0.50\) har; (b) \(1.00\) bar.

The temperature dependence of the equilibrium constant of the reaction \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\), which makes an important contribution to atmospheric nitrogen oxides, can be expressed as \(\ln K=2.5-\) \((21700 \mathrm{~K}) \cdot T^{-1}\). What is the standard enthalpy of the forward reaction?