Chapter 15

When \(1.50 \mathrm{~mol} \mathrm{CO}_{2}\) and \(1.50 \mathrm{~mol} \mathrm{H}_{2}\) are placed in a 0.750-L container at \(395^{\circ} \mathrm{C}\), the following equilibrium is achieved: \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) .\) If \(K_{c}=0.802\), what are the concentrations of each substance in the equilibrium mixture?

The equilibrium constant \(K_{c}\) for \(\mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons\) \(2 \mathrm{CO}(g)\) is \(1.9\) at \(1000 \mathrm{~K}\) and \(0.133\) at \(298 \mathrm{~K}\). (a) If excess \(\mathrm{C}\) is allowed to react with \(25.0 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) in a \(3.00\) -L vessel at \(1000 \mathrm{~K}\), how many grams of \(\mathrm{CO}_{2}\) are produced? (b) How many grams of \(C\) are consumed? (c) If a smaller vessel is used for the reaction, will the yield of \(\mathrm{CO}\) be greater or smaller? (d) If the reaction is endothermic, how does increasing the temperature affect the equilibrium constant?

\(\mathrm{NiO}\) is to be reduced to nickel metal in an industrial process by use of the reaction $$ \mathrm{NiO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(s)+\mathrm{CO}_{2}(g) $$ At \(1600 \mathrm{~K}\) the equilibrium constant for the reaction is \(K_{p}=6.0 \times 10^{2}\). If a CO pressure of 150 torr is to be employed in the furnace and total pressure never exceeds 760 torr, will reduction occur?

At \(700 \mathrm{~K}\) the equilibrium constant for the reaction $$ \mathrm{CCl}_{4}(g) \rightleftharpoons \mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(g) $$ is \(K_{p}=0.76\). A flask is charged with \(2.00 \mathrm{~atm}\) of \(\mathrm{CCl}_{4}\), which then reaches equilibrium at \(700 \mathrm{~K}\). (a) What fraction of the \(\mathrm{CCl}_{4}\) is converted into \(\mathrm{C}\) and \(\mathrm{Cl}_{2} ?\) (b) What are the partial pressures of \(\mathrm{CCl}_{4}\) and \(\mathrm{Cl}_{2}\) at equilibrium?

The reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) has \(K_{p}=0.0870\) at \(300^{\circ} \mathrm{C}\). A flask is charged with \(0.50\) atm \(\mathrm{PCl}_{3}, 0.50 \mathrm{~atm} \mathrm{Cl}_{2}\), and \(0.20 \mathrm{~atm} \mathrm{PCl}_{5}\) at this tempera- ture. (a) Use the reaction quotient to determine the direction the reaction must proceed to reach equilibrium. (b) Calculate the equilibrium partial pressures of the gases. (c) What effect will increasing the volume of the system have on the mole fraction of \(\mathrm{Cl}_{2}\) in the equilibrium mixture? (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of \(\mathrm{Cl}_{2}\) in the equilibrium mixture?

Consider the hypothetical reaction \(\mathrm{A}(g)+2 \mathrm{~B}(g) \rightleftharpoons\) \(2 \mathrm{C}(\mathrm{g})\), for which \(K_{c}=0.25\) at some temperature. A 1.00-L reaction vessel is loaded with \(1.00 \mathrm{~mol}\) of compound \(\mathrm{C}\), which is allowed to reach equilibrium. Let the variable \(x\) represent the number of \(\mathrm{mol} / \mathrm{L}\) of compound A present at equilibrium. (a) In terms of \(x\), what are the equilibrium concentrations of compounds \(B\) and \(C\) ? (b) What limits must be placed on the value of \(x\) so that all concentrations are positive? (c) By putting the equilibrium concentrations (in terms of \(x\) ) into the equilibriumconstant expression, derive an equation that can be solved for \(x\). (d) The equation from part (c) is a cubic equation (one that hasthe form \(a x^{3}+b x^{2}+c x+d=0\) ). In general, cubic equations cannot be solved in closed form. However, you can estimate the solution by plotting the cubic equation in the allowed range of \(x\) that you specified in part (b). The point at which the cubic equation crosses the \(x\) -axis is the solution. (e) From the plot in part (d), estimate the equilibrium concentrations of \(\mathrm{A}, \mathrm{B}\), and \(\mathrm{C}\). (Hint: You can check the accuracy of your answer by substituting these concentrations into the equilibrium expression.)

At \(1200 \mathrm{~K}\), the approximate temperature of automobile exhaust gases (Figure 15.16), \(K_{p}\) for the reaction $$ 2 \mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) $$ is about \(1 \times 10^{-13}\). Assuming that the exhaust gas (total pressure 1 atm) contains \(0.2 \%\) CO, \(12 \% \mathrm{CO}_{2}\), and \(3 \% \mathrm{O}_{2}\) by volume, is the system at equilibrium with respect to the above reaction? Based on your conclusion, would the CO concentration in the exhaust be decreased or increased by a catalyst that speeds up the reaction above?

Consider the equilibrium \(\mathrm{IO}_{4}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) \(\mathrm{H}_{4} \mathrm{IO}_{6}^{-}(a q), K_{c}=3.5 \times 10^{-2} .\) If you start with \(20.0 \mathrm{~mL}\) of a \(0.905 \mathrm{M}\) solution of \(\mathrm{NaIO}_{4}\), and then dilute it with water to \(250.0 \mathrm{~mL}\), what is the concentration of \(\mathrm{H}_{4} \mathrm{IO}_{6}^{-}\) at equilibrium?

Silver chloride, \(\mathrm{AgCl}(s)\), is an insoluble strong electrolyte. (a) Write the equation for the dissolution of \(\mathrm{AgCl}(s)\) in \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Write the expression for \(K_{c}\) for the reaction in part (a). (c) Based on the thermochemical data in Appendix \(\mathrm{C}\) and Le Châtelier's principle, predict whether the solubility of \(\mathrm{AgCl}\) in \(\mathrm{H}_{2} \mathrm{O}\) increases or decreases with increasing temperature.

At \(25^{\circ} \mathrm{C}\) the reaction $$ \mathrm{NH}_{4} \mathrm{HS}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g) $$ has \(K_{p}=0.120 .\) A \(5.00-\mathrm{L}\) flask is charged with \(0.300 \mathrm{~g}\) of pure \(\mathrm{H}_{2} \mathrm{~S}(g)\) at \(25^{\circ} \mathrm{C}\). Solid \(\mathrm{NH}_{4} \mathrm{HS}\) is then added until there is excess unreacted solid remaining. (a) What is the initial pressure of \(\mathrm{H}_{2} \mathrm{~S}(g)\) in the flask? (b) Why does no reaction occur until \(\mathrm{NH}_{4} \mathrm{HS}\) is added? (c) What are the partial pressures of \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{~S}\) at equilibrium? (d) What is the mole fraction of \(\mathrm{H}_{2} \mathrm{~S}\) in the gas mixture at equilibrium? (e) What is the minimum mass, in grams, of \(\mathrm{NH}_{4} \mathrm{HS}\) that must be added to the flask to achieve equilibrium?

Write the equilibrium-constant expression for the equilibrium $$ \mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) $$ The table included below shows the relative mole percentages of \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{CO}(\mathrm{g})\) at a total pressure of \(1 \mathrm{~atm}\) for several temperatures. Calculate the value of \(K_{p}\) at each temperature. Is the reaction exothermic or endothermic? Explain. $$ \begin{array}{lll} \hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & \mathrm{CO}_{2} \text { (mol \%) } & \text { CO (mol \%) } \\ \hline 850 & 6.23 & 93.77 \\ 950 & 1.32 & 98.68 \\ 1050 & 0.37 & 99.63 \\ 1200 & 0.06 & 99.94 \\ \hline \end{array} $$

Polyvinyl chloride (PVC) is one of the most commercially important polymers (Table 12.5). PVC is made by addition polymerization of vinyl chloride \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\right)\). Vinyl chloride is synthesized from ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) in a twostep process involving the following equilibria: Equilibrium 1: \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(g)\) Equilibrium 2: \(\quad \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}(g)+\mathrm{HCl}(g)\) The product of Equilibrium 1 is 1,2 -dichloroethane, a compound in which one \(\mathrm{Cl}\) atom is bonded to each \(\mathrm{C}\) atom. (a) Draw Lewis structures for \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\) and \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\). What are the \(\mathrm{C}-\mathrm{C}\) bond orders in these two compounds? (b) Use average bond enthalpies (Table 8.4) to estimate the enthalpy changes in the two equilibria. (c) How would the yield of \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\) in Equilibrium 1 vary with temperature and volume? (d) How would the yield of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\) in Equilibrium 2 vary with temperature and volume? (e) Look up the normal boiling points of 1,2 -dichloroethane and vinyl chloride in a sourcebook, such as the CRC Handbook of Chemistry and Physics. Based on these data, propose a reactor design (analogous to Figure 15.12) that could be used to maximize the amount of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\) produced by using the two equilibria.