Problem 88
A mixture containing 3.9 moles of \(\mathrm{NO}\) and 0.88 mole of \(\mathrm{CO}_{2}\) was allowed to react in a flask at a certain temperature according to the equation: $$ \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{NO}_{2}(g)+\mathrm{CO}(g) $$ At equilibrium, 0.11 mole of \(\mathrm{CO}_{2}\) was present. Calculate the equilibrium constant \(K_{\mathrm{c}}\) of this reaction.
Problem 89
The equilibrium constant \(K_{\mathrm{c}}\) for the reaction: $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)$$ is 54.3 at \(430^{\circ} \mathrm{C}\). At the start of the reaction, there are \(0.714 \mathrm{~mol}\) of \(\mathrm{H}_{2}, 0.984 \mathrm{~mol}\) of \(\mathrm{I}_{2}\), and \(0.886 \mathrm{~mol}\) of HI in a 2.40-L reaction chamber. Calculate the concentrations of the gases at equilibrium.
Problem 90
When heated, a gaseous compound A dissociates as follows: $$ \mathrm{A}(g) \rightleftarrows \mathrm{B}(g)+\mathrm{C}(g) $$ In an experiment, A was heated at a certain temperature until its equilibrium pressure reached \(0.14 P\), where \(P\) is the total pressure. Calculate the equilibrium constant \(K_{P}\) of this reaction.
Problem 91
When a gas was heated under atmospheric conditions, its color deepened. Heating above \(150^{\circ} \mathrm{C}\) caused the color to fade, and at \(550^{\circ} \mathrm{C}\) the color was barely detectable. However, at \(550^{\circ} \mathrm{C},\) the color was partially restored by increasing the pressure of the system. Which of the following best fits the preceding description: (a) a mixture of hydrogen and bromine, (b) pure bromine, (c) a mixture of nitrogen dioxide and dinitrogen tetroxide. (Hint: Bromine has a reddish color, and nitrogen dioxide is a brown gas. The other gases are colorless.) Justify your choice.
Problem 93
A sealed glass bulb contains a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) gases. Describe what happens to the following properties of the gases when the bulb is heated from \(20^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}:\) (a) color, (b) pressure, (c) average molar mass, (d) degree of dissociation (from \(\mathrm{N}_{2} \mathrm{O}_{4}\) to \(\mathrm{NO}_{2}\) ), (e) density. Assume that volume remains constant. (Hint: \(\mathrm{NO}_{2}\) is a brown gas; \(\mathrm{N}_{2} \mathrm{O}_{4}\) is colorless.)
Problem 94
At \(20^{\circ} \mathrm{C},\) the vapor pressure of water is \(0.0231 \mathrm{~atm} .\) Calculate \(K_{P}\) and \(K_{\mathrm{c}}\) for the process: $$\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}_{2} \mathrm{O}(g)$$
Problem 95
A 2.50 -mol sample of \(\mathrm{NOCl}\) was initially in a \(1.50-\mathrm{L}\) reaction chamber at \(400^{\circ} \mathrm{C}\). After equilibrium was established, it was found that 28.0 percent of the \(\mathrm{NOCl}\) had dissociated: $$ 2 \mathrm{NOCl}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) $$ Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.
Problem 96
About 75 percent of hydrogen for industrial use is produced by the steam- reforming process. This process is carried out in two stages called primary and secondary reforming. In the primary stage, a mixture of steam and methane at about 30 atm is heated over a nickel catalyst at \(800^{\circ} \mathrm{C}\) to give hydrogen and carbon monoxide: \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=206 \mathrm{~kJ} / \mathrm{mol}\) The secondary stage is carried out at about \(1000^{\circ} \mathrm{C},\) in the presence of air, to convert the remaining methane to hydrogen: \(\mathrm{CH}_{4}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftarrows \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}=35.7 \mathrm{~kJ} / \mathrm{mol}\) (a) What conditions of temperature and pressure would favor the formation of products in both the primary and secondary stages? (b) The equilibrium constant \(K_{\mathrm{c}}\) for the primary stage is 18 at \(800^{\circ} \mathrm{C}\). (i) Calculate \(K_{P}\) for the reaction. (ii) If the partial pressures of methane and steam were both 15 atm at the start, what are the pressures of all the gases at equilibrium?
Problem 97
Water is a very weak electrolyte that undergoes the following ionization (called autoionization): $$ \mathrm{H}_{2} \mathrm{O}(l) \stackrel{k_{1}}{\stackrel{\mathrm{m}_{-1}}} \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ (a) If \(k_{1}=2.4 \times 10^{-5} \mathrm{~s}^{-1}\) and \(k_{-1}=1.3 \times 10^{11} / M \cdot \mathrm{s}\) calculate the equilibrium constant \(K\) where \(K=\left[\mathrm{H}^{+}\right]\) \(\left[\mathrm{OH}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{O}\right] .\) (b) Calculate the product \(\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right],\) \(\left[\mathrm{H}^{+}\right],\) and \(\left[\mathrm{OH}^{-}\right] .\) (Hint : Calculate the concentration of liquid water using its density, \(1.0 \mathrm{~g} / \mathrm{mL}\).)
Problem 98
Consider the following reaction, which takes place in a single elementary step: $$2 \mathrm{~A}+\mathrm{B} \underset{k_{-1}}{\stackrel{k_{1}}{\rightleftarrows}} \mathrm{A}_{2} \mathrm{~B}$$ If the equilibrium constant \(K_{\mathrm{c}}\) is 12.6 at a certain temperature and if \(k_{1}=5.1 \times 10^{-2} \mathrm{~s}^{-1},\) calculate the value of \(k_{-1}\).
