Chapter 17

Write equilibrium constant expressions for these equilibria. \begin{equation} \begin{array}{l}{\text { a. } N_{2} O_{4}(g) \rightleftharpoons 2 N O_{2}(g)} \\\ {\text { b. } 2 \mathrm{H}_{2} \mathrm{S}(9) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{S}_{2}(\mathrm{g}) \\ \text { c. } \mathrm{CO}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { d. } 4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { e. } \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \rightleftharpoons \mathrm{CS}_{2}(\mathrm{g})+4 \mathrm{H}_{2}(\mathrm{g}) }\end{array} \end{equation}

Challenge Write the chemical equation that has the equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{CO}]^{2}\left[\mathrm{O}_{2}\right]}{\left[\mathrm{CO}_{2}\right]^{2}}\).

Write equilibrium constant expressions for these heterogeneous equilibria. \begin{equation} \begin{array}{l}{\text { a. } C_{10} \mathrm{H}_{8}(\mathrm{s}) \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{8}(\mathrm{g})} \\ {\text { b. } \mathrm{H}_{2} \mathrm{O}(1) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { c. } \mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})} \\\ {\text { d. } \mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})} \\\ {\text { e. } \mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightleftharpoons \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})}\end{array} \end{equation}

Challenge Solid iron reacts with chlorine gas to form solid iron(llI) chloride \(\left(\mathrm{FeCl}_{3}\right)\). Write the balanced equation and the equilibrium constant expression for the reaction.

Challenge The reaction \(\mathrm{COCl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) reaches equilibrium at 900 \(\mathrm{K}\). \(K_{\mathrm{eq}}\) is \(8.2 \times 10^{-2} .\) If the equilibrium concentrations of \(\mathrm{CO}\) and \(\mathrm{Cl}_{2}\) are \(0.150 \mathrm{M},\) what is the equilibrium concentration of \(\mathrm{COCl}_{2} ?\)

Explain how the size of the equilibrium constant relates to the amount of product formed at equilibrium.

List three characteristics a reaction mixture must have if is to attain a state of chemical equilibrium.

Calculate Determine the value of \(K_{\text { eq at }} 400\) K for this equation: \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\) \(\mathrm{Cl}_{2}(\mathrm{g})\) if \(\left[\mathrm{PCl}_{5}\right]=0.135 \mathrm{mol} / \mathrm{L}\), \(\left[\mathrm{PCl}_{3}\right]=0.550 \mathrm{mol} / \mathrm{L}\), and \(\left[\mathrm{Cl}_{2}\right]=0.550 \mathrm{mol} / \mathrm{L}\)

Explain how a system at equilibrium responds to a stress and list factors that can be stresses on an equilibrium system.

Explain how decreasing the volume of the reaction vessel affects each equilibrium. \begin{equation} \text { a. } 250_{2}(g)+0_{2}(g) \rightleftharpoons 250_{3}(g) \quad \text { b. } H_{2}(g)+C I_{2}(g) \rightleftharpoons 2 H C l(g) \end{equation}

Decide whether higher or lower temperatures will produce more \(\mathrm{CH}_{3} \mathrm{CH} 0\) in the following equilibrium. \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CHO}(\mathrm{g}) \Delta H^{\circ}=-151 \mathrm{kJ}\)

Challenge In a generic reaction \(A+B \rightleftharpoons C+D, 1.00\) mol of \(A\) and 1.00 mol of \(B\) are allowed to react in a \(1-L\) flask until equilibrium is established. If the equilibrium concentration of \(A\) is 0.450 \(\mathrm{m} / \mathrm{L}\) , what is the equilibrium concentration of each of the other substances? What is \(K_{\text { eq }} ?\)

Challenge The \(K_{s p}\) of lead carbonate \(\left(P b C O_{3}\right)\) is \(7.40 \times 10^{-14}\) at 298 K What is the solubility of lead carbonate in \(g / L ?\)

Calculate the solubility of $$\mathrm{Ag}_{3} \mathrm{PO}_{4}\left(K_{\mathrm{sp}}=2.6 \times 10^{-18}\right)$$

Challenge The solubility of silver chloride \((\mathrm{AgCl})\) is \(1.86 \times 10^{-4} \mathrm{g} / 100 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}\) at 298 \(\mathrm{K}\) Calculate the \(K_{\mathrm{sp}}\) for AgCl.

List the information you would need in order to calculate the concentration of a product in a reaction mixture at equilibrium.

Explain how to use the solubility product constant to calculate the solubility of a sparingly soluble ionic compound.

Describe how the presence of a common ion reduces the solubility of an ionic compound.

Calculate The \(K_{\text { sp }}\) of magnesium carbonate \(\left(\mathrm{Mg} \mathrm{CO}_{3}\right)\) is \(2.6 \times 10^{-9} .\) What is the solubility of Mg CO \(_{3}\) in pure water?

Describe an equilibrium in everyday life that illustrates a state of balance between two opposing processes.

Given the fact that the concentrations of reactants and products are not changing, why is the word dynamic used to describe chemical equilibrium?

Explain how a person bailing out a row boat with a leak could represent a state of physical equilibrium.

Does the following equation represent a homogeneous equilibrium or a heterogeneous equilibrium? Explain. your answer. $$ \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(1) $$

Why should you pay attention to the physical states of reactants and products when writing equilibrium constant expressions?

Why does a numerically large \(K\) eq mean that the products are favored in an equilibrium system?

What happens to \(K_{\mathrm{eq}}\) for an equilibrium system if the equation for the reaction is rewritten in the reverse?

How can an equilibrium system contain small and unchanging amounts of products yet have large amounts of reactants? What can you say about the relative size of \(K_{\mathrm{eq}}\) for such an equilibrium?

A system, which contains only molecules as reactants and products, is at equilibrium. Describe what happens to the concentrations of the reactants and products and what happens to individual reactant and product molecules.

Write equilibrium constant expressions for these homogeneous equilibria. \begin{equation} \begin{array}{l}{\text { a. } 2 \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{g})+2 \mathrm{NO}_{2}(\mathrm{g}) \rightleftharpoons 3 \mathrm{N}_{2}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})} \\ {\text { b. } 2 \mathrm{NbCl}_{4}(\mathrm{g}) \rightleftharpoons \mathrm{NbCl}_{3}(\mathrm{g})+\mathrm{NbCl}_{5}(\mathrm{g})}\end{array} \end{equation}

Write equilibrium constant expressions for these heterogeneous equilibria. \begin{equation} \begin{array}{l}{\text { a. } 2 \mathrm{NaHCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})} \\ {\text { b. } \mathrm{C}_{6} \mathrm{H}_{6}(1) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(\mathrm{g})}\end{array} \end{equation}

Heating limestone \(\left(\mathrm{CaCO}_{3}(\mathrm{s})\right)\) forms quicklime \((\mathrm{CaO}(\mathrm{s}))\) and carbon dioxide gas. Write the equilibrium constant expression for this reversible reaction.

When steam is passed over iron filings, solid iron(III) oxide and gaseous hydrogen are produced in a reversible reaction. Write the balanced chemical equation and the equilibrium constant expression for the reaction, which yields iron(III) oxide and hydrogen gas.

How does Le Chatelier's principle describe an equilibrium's response to a stress?

When an equilibrium shifts to the right, what happens to each of the following? \begin{equation} \begin{array}{l}{\text { a. the concentration of the reactants }} \\ {\text { b. the concentration of the products }}\end{array} \end{equation}

Carbonated Beverages Use Le Chatelier's principle to explain how a shift in the equilibrium \(\mathrm{H}_{2} \mathrm{CO}_{3}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g})\) causes a soft drink to go flat when its container is left open.

How would each of the following changes affect the equilibrium position of the system used to produce methanol from carbon monoxide and hydrogen? $$\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+ heat $$ \(\begin{array}{l}{\text { a. adding CO to the system }} \\ {\text { b. cooling the system }} \\ {\text { c. adding a catalyst to the system }} \\\ {\text { d. removing } \mathrm{CH}_{3} \mathrm{OH} \text { from the system }} \\\ {\text { e. decreasing the volume of the system }}\end{array}\)

Explain how a temperature increase would affect the equilibrium represented by the following equation. $$\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+ heat$$

A liquid solvent for chlorine is poured into a flask in which the following reaction is at equilibrium: \(\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+\) heat. How is the equilibrium affected when some of the chlorine gas dissolves?

Given two reactions at equilibrium: \begin{equation} \begin{array}{l}{\text { a. } \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})} \\\ {\text { b. } \mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{HCl}(\mathrm{g}),}\end{array} \end{equation} explain why changing the volume of the systems alters the equilibrium position of a but has no effect on b.

Would you expect the numerical value of \(K_{\mathrm{eq}}\)for the following equilibrium to increase or decrease with increasing temperature? Explain your answer. $$\mathrm{PCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})+ heat$$

Explain how you would regulate the pressure to favor the products in the following equilibrium system. $$\mathrm{MgCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$$

What does it mean to say that two solutions have a common ion? Give an example.

Why are compounds such as sodium chloride usually not given \(K_{s p}\) values?

Xrays Why is barium sulfate a better choice than barium chloride for adding definition to X rays? At \(26^{\circ} \mathrm{C}\) 37.5 \(\mathrm{g}\) of \(\mathrm{BaCl}_{2}\) can be dissolved in 100 \(\mathrm{mL}\) of water.

Explain why a common ion lowers the solubility of an ionic compound.

Describe the solution that results when two solutions are mixed and \(Q_{s p}\) is found to equal \(K_{\mathrm{sp}}\). Does a precipitate form?

Write the \(K_{s p}\) expression for lead chromate \(\left(\mathrm{PbCrO}_{4}\right),\) and calculate its solubility in mol/L. \(K_{\mathrm{sp}}=2.3 \times 10^{-13}\)

At \(350^{\circ} \mathrm{C}, K_{\mathrm{eq}}=1.67 \times 10^{-2}\) for the reversible reaction \(2 \mathrm{HI}(\mathrm{g}) \rightleftharpoons \mathrm{H}^{2}(\mathrm{g})+\mathrm{I}^{2}(\mathrm{g}) .\) What is the concentration of HI at equilibrium if \(\left[\mathrm{H}^{2}\right]\) is \(2.44 \times 10^{-3} M\) and \(\left[\mathrm{I}^{2}\right]\) is \(7.18 \times 10^{-5} \mathrm{M}\) ?

\(K_{\mathrm{sp}}\) for scandium fluoride \(\left(\mathrm{ScF}_{3}\right)\) at 298 \(\mathrm{K}\) is \(4.2 \times 10^{-18}\). Write the chemical equation for the solubility equilibrium of scandium fluoride in water. What concentration of \(S c^{3+}\) ions is required to cause a precipitate to form if the fluoride-ion concentration is 0.076\(M ?\)

Manufacturing Ethyl acetate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}\right), \mathrm{a}\) solvent used in making varnishes and lacquers, can be produced by the reaction between ethanol and acetic acid. The equilibrium system is described by the equation $$\begin{array}{c}{\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} \rightleftharpoons} \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad {\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}+\mathrm{H}_{2} \mathrm{O}}\end{array}$$ Calculate \(K_{\mathrm{eq}}\) using these equilibrium concentrations: \(\left[\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}\right]=2.90 \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=0.316 \mathrm{M}\) \(\left[\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right]=0.313 M,\) and \(\left[\mathrm{H}_{2} \mathrm{O}\right]=0.114 \mathrm{M}\)