Problem 1
Consider the equilibrium: \\[ \begin{aligned} 2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g}) & \\ \Delta_{\mathrm{r}} H^{\circ}(298 \mathrm{K})=-96 \mathrm{kJ} \text { per mole of } \mathrm{SO}_{3} \end{aligned} \\] What are the effects of (a) increasing the external pressure, and (b) lowering the external temperature?
Problem 2
For \(\mathrm{NO}_{2}(\mathrm{g}), \Delta_{\mathrm{f}} H^{\mathrm{o}}(298 \mathrm{K})=+34.2 \mathrm{kJ} \mathrm{mol}^{-1}\) (a) Write an equation for the reversible formation of \(\mathrm{NO}_{2}\) from its constituent elements. (b) What is the effect on this equilibrium of raising the external temperature? (c) If the external pressure is increased, how is the yield of \(\mathrm{NO}_{2}\) affected?
Problem 3
What is the effect on the following equilibrium of (a) adding propanoic acid, and (b) removing benzyl propanoate by distillation?$$\begin{array}{l} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H}+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH} \rightleftharpoons \\ \text { Propanoic acid } \quad \mathrm{Benzyl} \text { alcohol } \\ \qquad \begin{aligned} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{CH}_{2} \mathrm{C}_{6} \mathrm{H}_{5}+\mathrm{H}_{2} \mathrm{O} \\ \text { Benzyl propanoate } \end{aligned} \end{array}$$
Problem 4
Write down expressions for \(K\) in terms of the activities of the components present in the following gaseous equilibria: (a) \(2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3}\) (b) \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3}\) (c) \(\mathrm{Al}_{2} \mathrm{Cl}_{6} \rightleftharpoons 2 \mathrm{AlCl}_{3}\) (d) \(\mathrm{Cl}_{2} \rightleftharpoons 2 \mathrm{Cl}\) (e) \(\mathrm{H}_{2}+\mathrm{I}_{2} \rightleftharpoons 2 \mathrm{HI}\)
Problem 5
Write down expressions for \(K\) in terms of the concentrations of the components present in the following equilibria. What are the limitations of using concentrations instead of activities? (a) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons\) \\[ \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}(\mathrm{aq}) \\] (b) \(\left[\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}(\mathrm{aq})+6 \mathrm{CN}^{-}(\mathrm{aq}) \rightleftharpoons\) \\[ \left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(1) \\] (c) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq}) \rightleftharpoons 2 \mathrm{CrO}_{4}^{2-}(\mathrm{aq})+\)
Problem 6
\(\mathrm{I}_{2}\) is very sparingly soluble in water, and laboratory solutions are usually made up in aqueous KI in which the following equilibrium is established: \\[ \mathrm{I}_{2}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{I}_{3}^{-}(\mathrm{aq}) \\] \(2.54 \mathrm{g}\) of \(\mathrm{I}_{2}\) are added to \(1 \mathrm{dm}^{3}\) of a \(0.50 \mathrm{mol} \mathrm{dm}^{-3}\) aqueous solution of \(\mathrm{KI}\), and the solution is allowed to reach equilibrium. At this point, \(9.8 \times 10^{-3}\) moles of \(\left[\mathrm{I}_{3}\right]^{-}\) are present. Determine the equilibrium constant, assuming no change in solution volume on adding solid \(\mathrm{I}_{2}\)
Problem 8
The oxidation of \(\mathrm{SO}_{2}\) is a stage in the manufacture of sulfuric acid: \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) If 2.00 moles of \(\mathrm{SO}_{2}\) react with 0.50 moles of \(\mathrm{O}_{2}\) at \(1100 \mathrm{K}\) and 1.00 bar pressure and the system is left to establish equilibrium, the final mixture contains 0.24 moles of \(\mathrm{SO}_{3}\). Calculate \(K\) under these conditions.
Problem 9
Consider the equilibrium: \\[ \mathrm{H}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \\] At \(800 \mathrm{K}, K=0.29 .\) If 0.80 moles of \(\mathrm{H}_{2}\) and 0.60 moles of \(\mathrm{CO}_{2}\) react under a pressure of \(1.00 \mathrm{bar}\) how many moles of \(\mathrm{CO}_{2}\) will remain when the reaction mixture has reached equilibrium?
Problem 10
The formation of HCl could be considered in terms of the equilibria: \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{HCl}(\mathrm{g}) \quad K_{1}\) or \(\frac{1}{2} \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{HCl}(\mathrm{g}) \quad K_{2}\) What is the relationship between the values of the equilibrium constants for these equilibria?
Problem 11
Write equations to show the dissociation in aqueous solution of the following acids: (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H} ;(\mathrm{b}) \mathrm{HNO}_{3} ;(\mathrm{c}) \mathrm{H}_{2} \mathrm{SO}_{3} ;(\mathrm{d}) \mathrm{H}_{2} \mathrm{SO}_{4}\)
