Chapter 14

An 8.00-L reaction vessel at \(491^{\circ} \mathrm{C}\) contains \(0.650\) mole of \(\mathrm{H}_{2}, 0.275\) mole of \(\mathrm{I}_{2}\), and \(3.00\) moles of HI. Assuming that the reaction is at equilibrium, determine the value of \(K_{\text {eq }}\) and comment on where the equilibrium lies. The reaction is: \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)\)

How would the value of the equilibrium constant for a one-step reaction calculated as \(k_{\mathrm{f}} / k_{\mathrm{r}}\) compare with the value calculated from the concentrations of all substances present at equilibrium?

Suppose a reaction is at equilibrium and you then disturb the equilibrium by adding reactants. What happens to the value of \(K_{\text {eq }}\) ? Explain your answer.

State Le Châtelier's principle using the words undo and partially.

Suppose we have an equilibrium mixture of reactants and products for the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g)\) Predict the direction in which the reaction will shift when: (a) Chlorine \(\left(\mathrm{Cl}_{2}\right)\) gas is added. (b) Chlorine gas is removed. (c) \(\mathrm{PCl}_{5}\) is added. (d) \(\mathrm{PCl}_{3}\) is removed. (e) \(\mathrm{H}_{2}\) gas is added. (Assume the \(\mathrm{H}_{2}\) does not react with any reactant or product.)

Consider the gas-phase reaction \(3 \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{O}_{3}(g) .\) Suppose \(K_{\mathrm{eq}}\) for this reaction is \(\sim 1\) (it is not, but assume it is for this problem). Suppose you want pure ozone \(\left(\mathrm{O}_{3}\right)\) that is uncontaminated with oxygen \(\left(\mathrm{O}_{2}\right)\). (a) Why can't you simply remove the oxygen from the reaction vessel once the reaction has come to equilibrium to obtain pure ozone? (b) In fact, \(K_{\text {eq }}\) for this reaction at room temperature is \(2.5 \times 10^{-29}\). Knowing this, how important would you say Le Châtelier's principle is for this reaction when it comes to influencing the amount of ozone present at equilibrium? Explain.

When a reaction at equilibrium is disturbed by the addition of products, (a) Which way will the reaction shift? (b) After the reaction is done shifting, will the product concentration be the same as before the disturbance, greater than before the disturbance, or less than before the disturbance? Explain your answer. (c) Repeat part (b) but for the reactant concentration.

Consider the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftarrows \mathrm{PCl}_{5}(g)\) Use forward and reverse rate meters to represent the forward and reverse reaction rates for: (a) The initial equilibrium (b) Moments after you disturb the equilibrium by adding \(\mathrm{PCl}_{5}\) (c) The restored equilibrium (d) Which way did the reaction shift to get from the initial equilibrium, part (a), to the restored equilibrium, part (c)?

One way of preparing hydrogen is by decomposition of water: \(2 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \quad \Delta E_{\mathrm{rxn}}=484 \mathrm{~kJ}\) (a) Would you expect the decomposition to be more complete at equilibrium when it is run at high temperature or when it is run at low temperature? Explain. (b) According to your answer to (a), would the reaction speed up, slow down, or occur at the same rate as before the temperature was changed? Explain.

Suppose you are making ammonia \(\left(\mathrm{NH}_{3}\right)\) by the Haber reaction, at \(472{ }^{\circ} \mathrm{C}\) : \(3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g) K_{\mathrm{eq}}=0.105\) (a) Describe qualitatively where the equilibrium lies for this reaction. (b) On the face of it, would this reaction be a good one for isolating pure ammonia? (c) What would happen if you could keep feeding \(\mathrm{H}_{2}\) and \(\mathrm{N}_{2}\) into the reaction vessel while at the same time removing \(\mathrm{NH}_{3}\) ?

The equilibrium constant for the synthesis of methanol, $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{CH}_{3} \mathrm{OH}(g) $$ Methanol is \(4.3\) at \(250{ }^{\circ} \mathrm{C}\) and \(1.8\) at \(275^{\circ} \mathrm{C}\). (a) Does this reaction shift to the left or to the right when the reaction mixture is heated? Explain how you know. (b) Is this reaction endothermic or exothermic? Explain how you know. (c) Rewrite the equation for the reaction, including heat on the appropriate side.

The amount of nitrogen dioxide formed by dissociation of dinitrogen tetroxide, \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)\) increases as the temperature rises. (a) Is the reaction exothermic or endothermic? Explain how you know. (b) Does \(K_{\text {eq }}\) increase or decrease as the temperature rises?

Diamond and graphite are two forms of elemental carbon. Under the appropriate conditions they will be in equilibrium with each other: \(C_{\text {diamond }} \rightleftarrows C_{\text {graphite }}\) If graphite is subjected to very high pressure and temperature, it will convert into the diamond form. (a) Is the above equilibrium reaction exothermic or endothermic? Explain how you know. (b) Which form, graphite or diamond, has the higher density? (Hint: Think about what increasing the pressure of a gas does to its density. It works the same for the solid and liquid phases as well.)

Suppose you have an endothermic reaction with \(K_{\text {eq }}\) approximately equal to \(1 \times 10^{3}\). How could you adjust the temperature of this reaction to drive it to completion? Explain your answer.

Will \(K_{\text {eq }}\) for an exothermic reaction increase or decrease when the reaction mixture is (a) heated and (b) cooled? Explain your answer.

Will \(K_{\text {eq }}\) for an endothermic reaction increase or decrease when the reaction mixture is (a) heated and (b) cooled? Explain your answer.

Cooling an exothermic reaction for which \(K_{\text {eq }}\) is very low shifts the reaction to the right, so that more product is formed, but there is a trade-off. What is the downside of cooling such a reaction, as far as forming product is concerned?

What effect does a catalyst have on: (a) The position of equilibrium for a reaction? (b) The value of the equilibrium constant? (c) The ratio of \(k_{\mathrm{f}} / k_{\mathrm{r}} ?\) 14.86 What does a catalyst do to the time it takes for a reaction to reach equilibrium? Explain how it does this.

What does a catalyst do to the time it takes for a reaction to reach equilibrium? Explain how it does this.

As noted in the chapter, the value of \(K_{\mathrm{eq}}\) for the reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)\) is \(0.0017\) at \(2027^{\circ} \mathrm{C}\) and \(2.3 \times 10^{-9}\) at \(25^{\circ} \mathrm{C}\). (a) Judging from the values of \(K_{\text {eq }}\), does this reaction shift to the left or to the right when the reaction mixture is heated? Explain your answer. (b) Is this reaction endothermic or exothermic? Explain your answer.

What is a heterogeneous chemical reaction? Where does a heterogeneous reaction occur?

Write the equilibrium constant expression for (a) \(2 \mathrm{FeCl}_{3}(s)+3 \mathrm{H}_{2} \mathrm{O}(g) \rightleftarrows \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) \(+6 \mathrm{HCl}(g)\) (b) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \rightleftarrows 2 \mathrm{Fe}(l)+3 \mathrm{CO}_{2}(g)\) (c) \(\mathrm{PbSO}_{4}(s) \rightleftarrows \mathrm{Pb}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q)\) (d) \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{H}_{2} \mathrm{CO}_{3}(a q)\)

Write the equilibrium constant expression for (a) \(\mathrm{SnO}_{2}(s)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{Sn}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \rightleftarrows \mathrm{PO}_{4}^{3-}(a q)\) (c) \(\mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q) \rightleftarrows \mathrm{PbI}_{2}(s)\) (d) \(\mathrm{Ca}^{2+}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\) \(\stackrel{\mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{3} \mathrm{O}^{+}(a q)}\)

What allows us to incorporate the concentrations of pure solids and liquids into \(K_{\text {eq }}\) instead of writing these concentrations explicitly in the equilibrium constant expression?

Consider a saturated aqueous solution of \(\mathrm{AgCl}\), a salt that is only sparingly soluble in water. What happens to this solution if a saturated solution of NaCl (a water-soluble salt) is added to it? (Hint: If \(\left[\mathrm{Ag}^{+}(a q)\right] \times\left[\mathrm{Cl}^{-}(a q)\right]>K_{\mathrm{sp}^{\prime}}\), precipitation will occur.)

Consider the reaction \(\mathrm{SnO}_{2}(s)+2 \mathrm{H}_{2}(g) \rightleftarrows \mathrm{Sn}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\) run in an explosion-proof sealed vessel. (a) Running the reaction in a sealed vessel allows equilibrium to be established. Explain why. (b) Express the concentration of \(\mathrm{H}_{2}(g)\) in terms of \(K_{\text {eq }}\) (c) The equilibrium constant for this reaction decreases as the reaction mixture is heated. Which way does the equilibrium shift? (d) Is the reaction exothermic or endothermic? Explain. (e) A new employee at a chemical company adds additional \(\mathrm{SnO}_{2}(s)\) to the reaction in order to drive its position of equilibrium further to the right. Will this get her a promotion or get her fired? Explain.

What is "dynamic" about the equilibrium that is established when a sparingly soluble salt is added to water?

At \(25^{\circ} \mathrm{C}\), the solubility of \(\mathrm{Al}(\mathrm{OH})_{3}\) in water is \(2.86 \times 10^{-9} \mathrm{M}\). What are the equilibrium concentrations of the cation and the anion in a saturated solution?

At \(25^{\circ} \mathrm{C}\), the solubility of \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) in water is \(2.60 \times 10^{-6} \mathrm{M}\). What are the equilibrium concentrations of the cation and the anion in a saturated solution?

At \(25^{\circ} \mathrm{C}\), the solubility in water of the moderately soluble salt silver acetate, \(\mathrm{AgC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) is \(10.6 \mathrm{~g} / \mathrm{L}\). (a) Write the chemical equation for the dissolving of silver acetate in water. (b) Write the \(K_{\mathrm{sp}}\) expression for silver acetate. (c) Calculate the value of \(K_{\mathrm{sp}}\) (show your work).

At \(25^{\circ} \mathrm{C}\), the solubility of calcium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4}\), in water is \(6.1 \mathrm{mg} / \mathrm{L}\). (a) What are the equilibrium molar concentrations of \(\mathrm{Ca}^{2+}(a q)\) and \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) ?\) (b) Calculate \(K_{\mathrm{sp}}\) for calcium oxalate.

At \(25^{\circ} \mathrm{C}\), the solubility of iron(III) hydroxide in water is \(4.49 \times 10^{-10} \mathrm{M}\). (a) What is the solubility in grams per liter? (b) What is the molar equilibrium concentration of each ion? (c) How many grams of iron(III) hydroxide could you dissolve in a 20,000-gallon swimming pool?

Phosphorus pentachloride gas decomposes to \(\mathrm{PCl}_{3}(\mathrm{~g})\) and \(\mathrm{Cl}_{2}(\mathrm{~g}) .\) At equilibrium, the concentrations of the decomposition products are \(5.50 \times 10^{-3} \mathrm{M}\) for \(\mathrm{PCl}_{3}(\mathrm{~g})\) and \(0.125 \mathrm{M}\) for \(\mathrm{Cl}_{2}(g)\). What is the equilibrium concentration of \(\mathrm{PCl}_{5}\) ? The equilibrium constant for this reaction is \(7.50 \times 10^{-2}\).

In the Haber process, nitrogen gas reacts with hydrogen gas to form gaseous ammonia (see Problem 14.76). (a) Write the equilibrium expression for the reaction. (b) The equilibrium constant at a certain temperature is \(1.5 \times 10^{-2}\). If the equilibrium concentrations of hydrogen and nitrogen are both \(0.20 \mathrm{M}\) at this temperature, what is the equilibrium concentration of ammonia?

Suppose the reaction \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftarrows 2 \mathrm{AB}\) proceeds via a one-step mechanism involving a collision between one \(\mathrm{A}_{2}\) molecule and one \(\mathrm{B}_{2}\) molecule. Suppose also that this reaction is reversible, and that the forward reaction is inherently much faster than the reverse reaction. (a) Does the equilibrium lie to the left or to the right? Explain your choice in terms of the reactant and product concentrations necessary to establish equal forward and reverse rates. (b) Does an analysis in terms of the relationship \(K_{\mathrm{eq}}=k_{\mathrm{f}} / k_{\mathrm{r}}\) yield the same answer as in (a)? Explain.

When the reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)\) is run at \(2000^{\circ} \mathrm{C}\), appreciable amounts of reactants and product are present at equilibrium. (a) A sealed 2.00-L container at \(2000{ }^{\circ} \mathrm{C}\) is filled with \(1.00\) mole of \(\mathrm{NO}(g)\) and nothing else. At that moment, which reaction is faster, forward or reverse? Justify your answer. (b) At equilibrium, the concentration of \(\mathrm{NO}(g)\) is \(0.0683 \mathrm{M}\) and the concentration of \(\mathrm{N}_{2}(g)\) is \(0.2159 \mathrm{M}\). What is the value of \(K_{\mathrm{eq}}\) at \(2000^{\circ} \mathrm{C} ?\)

For the reaction \(2 \mathrm{NO}_{2}(g) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(K_{\text {eq }}=0.500\). What is the equilibrium molar concentration of \(\mathrm{NO}_{2}(g)\) if \(\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.248 \mathrm{M}\) ?

For an endothermic reaction, will the equilibrium constant increase, decrease, or stay the same as the temperature of the reaction mixture increases? Explain your answer.

Write the equilibrium constant expression for: (a) \(\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(g)\) \(\rightleftarrows \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)\) (b) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CO}_{2}(g) \rightleftarrows \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{MnO}_{2}(s)+4 \mathrm{H}^{+}(a q)+2 \mathrm{Cl}^{-}(a q)\) \(\rightleftarrows \mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{I}_{2}(s) \rightleftarrows \mathrm{I}_{2}(g)\) (e) \(\mathrm{TiCl}_{4}(g)+2 \mathrm{Mg}(s) \rightleftarrows \mathrm{Ti}(s)+2 \mathrm{MgCl}_{2}(s)\) (f) \(\mathrm{Ni}(\mathrm{OH})_{2}(s) \rightleftarrows \mathrm{Ni}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\)

After the reaction \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g)\) is run, an equilibrium mixture at \(300^{\circ} \mathrm{C}\) is \(0.25 \mathrm{M}\) in \(\mathrm{N}_{2}(g), 0.15 \mathrm{M}\) in \(\mathrm{H}_{2}(g)\), and \(0.090 \mathrm{M}\) in \(\mathrm{NH}_{3}(g)\). (a) What is the value of \(K_{\text {eq }}\) ? (b) Which way does the equilibrium shift when \(\mathrm{H}_{2}(g)\) is added? (c) What happens to the value of \(K_{\text {eq }}\) when \(\mathrm{H}_{2}(g)\) is added? (d) Suppose we write this reaction as: \(2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2}(g) \rightleftarrows 4 \mathrm{NH}_{3}(g)\) Now what is the value of \(K_{\text {eq }} ?\) (e) The equilibrium shifts to the right when the reaction mixture is cooled. Is this reaction exothermic or endothermic? Justify your choice.

Hydrochloric acid is added to an aqueous solution of silver nitrate. (a) What precipitate forms? (b) The equilibrium concentration of \(\mathrm{Cl}^{-}(a q)\) is \(2.0 \times 10^{-3} \mathrm{M}\). What is the equilibrium concentration of \(\mathrm{Ag}^{+}(a q) ?\)

The solubility of silver acetate in water at \(20{ }^{\circ} \mathrm{C}\) is \(10.5 \mathrm{~g} / \mathrm{L}\) of solution. Calculate \(\mathrm{K}_{\mathrm{sp}}\) for silver acetate.

The solubility of \(\mathrm{PbI}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(1.52 \times 10^{-3}\) M. How many grams of \(\mathrm{PbI}_{2}\) will dissolve in \(2.50 \times 10^{6}\) gallons of water at \(25^{\circ} \mathrm{C}\) ?

(a) How would you prepare a saturated aqueous solution of copper(I) iodide at \(25^{\circ} \mathrm{C}\) ? (b) What is the mass in milligrams of CuI in \(400.0 \mathrm{~mL}\) of the saturated solution? (Hint: Begin with a \(K_{\mathrm{sp}}\) value from Table 14.1.) (c) Suppose you add some CuI* to this saturated solution, where \(\mathrm{I}^{*}\) is a radioactive form of iodide ion. A student says, "Because the solution is already saturated, the added CuI* won't dissolve and there's no danger of getting any radioactive iodide ion in solution." What is wrong with his thinking?

For the reaction \(4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{~N}_{2} \mathrm{O}_{5}(g)\) at \(25^{\circ} \mathrm{C}, K_{\mathrm{eq}}=0.150 .\) What is the equilibrium concentration of \(\mathrm{NO}_{2}(g)\) if \(\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=0.300 \mathrm{M}\) and \(\left[\mathrm{O}_{2}\right]=1.20 \mathrm{M} ?\)

Which of the following reactions is described by the equilibrium constant expression \(K_{\mathrm{eq}}=\frac{[\mathrm{A}]^{2} \times[\mathrm{B}]^{3}}{[\mathrm{C}]^{3} \times[\mathrm{D}]^{2}}\) (a) \(\mathrm{A}_{2}+\mathrm{B}_{3} \rightleftarrows \mathrm{C}_{3}+\mathrm{D}_{2}\) (b) \(2 \mathrm{~A}+3 \mathrm{~B} \rightleftarrows 3 \mathrm{C}+2 \mathrm{D}\) (c) \(3 \mathrm{C}+2 \mathrm{D} \rightleftarrows 2 \mathrm{~A}+3 \mathrm{~B}\) (d) \(A^{2}+B^{3} \rightleftarrows C^{3}+D^{2}\) (e) \(2 \mathrm{C}+3 \mathrm{D} \rightleftarrows 3 \mathrm{~A}+2 \mathrm{~B}\)

Would the solubility of \(\mathrm{PbI}_{2}(s)\) be greater in water or in an aqueous solution of NaI? Explain your answer. (Hint: If \(\left[\mathrm{Pb}^{2+}\right] \times\left[\mathrm{I}^{-}\right]^{2}>K_{\mathrm{sp}}\) ' precipitation will occur.)

In which direction does the reaction \(\mathrm{CaCO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\) \(\rightleftarrows \mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q)\) shift when: (a) \(\left[\mathrm{CO}_{2}\right]\) is increased? (b) The volume of the reaction vessel is decreased? (c) \(\mathrm{Ca}^{2+}(a q)\) is added? (d) \(\mathrm{CaCO}_{3}(s)\) is removed?

\(K_{\text {eq }}=3.9 \times 10^{-11}\) for the dissolution of calcium fluoride in water: \(\mathrm{CaF}_{2}(s) \rightleftarrows \mathrm{Ca}^{2+}(a q)+2 \mathrm{~F}^{-}(a q)\) (a) What is another name for \(K_{\mathrm{eq}}\) for this reaction? (b) If the equilibrium calcium ion concentration in a saturated aqueous solution of calcium fluoride is \(3.3 \times 10^{-4} \mathrm{M}\), what is the equilibrium fluoride ion concentration? (c) Which is larger, the rate constant for the forward reaction or the rate constant for the reverse reaction? (d) Which is larger, \(E_{a}\) for the forward reaction or \(E_{\mathrm{a}}\) for the reverse reaction? (e) Which is larger, the rate of the forward reaction or the rate of the reverse reaction? (f) For lithium carbonate, \(K_{\mathrm{sp}}=0.0011\). Write the balanced chemical equation and the equilibrium expression for the dissolution of \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) in water. (g) Which is more soluble in water, calcium fluoride or lithium carbonate?

Consider the two curves, one showing supply of tapes, the other showing demand for tapes. At what price per quantity is equilibrium established?