Exercises

Complete the changes in concentrations for each of the following reactions:

(a) $\begin{array}{ccc}\text{AgI}(s)⟶& {\text{Ag}}^{\text{+}}(aq)& +{\text{I}}^{\text{−}}(aq)\\ \\ & x& \_\_\_\_\_\end{array}$

(b) $\begin{array}{ccc}{\text{CaCO}}_3(s)⟶& {\text{Ca}}^{\text{2+}}(aq)+& {\text{CO}}_3{}^{\text{2−}}(aq)\\ \\ & \_\_\_\_& x\end{array}$

(c) $\begin{array}{ccc}\text{Mg}{(\text{OH})}_2(s)⟶& {\text{Mg}}^{\text{2+}}(aq)+& 2{\text{OH}}^{\text{−}}(aq)\\ \\ & x& \_\_\_\_\_\end{array}$

(d) $\begin{array}{ccc}{\text{Mg}}_3({\text{PO}}_4{)}_2(s)⟶& 3{\text{Mg}}^{\text{2+}}(aq)+& 2{\text{PO}}_4{}^{\text{3−}}(aq)\\ \\ & & x\_\_\_\_\_\end{array}$

(e) $\begin{array}{cccc}{\text{Ca}}_5({\text{PO}}_4{)}_3\text{OH}(s)⟶& 5{\text{Ca}}^{\text{2+}}(aq)+& 3{\text{PO}}_4{}^{\text{3−}}(aq)+& {\text{OH}}^{\text{−}}(aq)\\ \\ & \_\_\_\_\_& \_\_\_\_\_& x\end{array}$

How do the concentrations of Ag⁺ and ${\text{CrO}}_4{}^{\text{2−}}$ in a saturated solution above 1.0 g of solid Ag₂CrO₄ change when 100 g of solid Ag₂CrO₄ is added to the system? Explain.

What additional information do we need to answer the following question: How is the equilibrium of solid silver bromide with a saturated solution of its ions affected when the temperature is raised?

Which of the following slightly soluble compounds has a solubility greater than that calculated from its solubility product because of hydrolysis of the anion present: AgCl, BaSO₄, CaF₂, Hg₂I₂, MnCO₃, ZnS, PbS?

Write the ionic equation for the dissolution and the K_sp expression for each of the following slightly soluble ionic compounds:

(a) LaF₃

(b) CaCO₃

(c) Ag₂SO₄

(d) Pb(OH)₂

The Handbook of Chemistry and Physics gives solubilities of the following compounds in grams per 100 mL of water. Because these compounds are only slightly soluble, assume that the volume does not change on dissolution and calculate the solubility product for each.

(a) BaSeO₄, 0.0118 g/100 mL

(b) Ba(BrO₃)₂·H₂O, 0.30 g/100 mL

(c) NH₄MgAsO₄·6H₂O, 0.038 g/100 mL

(d) La₂(MoO₄)₃, 0.00179 g/100 mL

Assuming that no equilibria other than dissolution are involved, calculate the molar solubility of each of the following from its solubility product:

(a) KHC₄H₄O₆

(b) PbI₂

(c) Ag₄[Fe(CN)₆], a salt containing the ${\text{Fe(CN)}}_4{}^{\text{−}}$ ion

(d) Hg₂I₂

Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that changes in the initial concentrations of the common ions can be neglected.

(a) AgCl(s) in 0.025 M NaCl

(b) CaF₂(s) in 0.00133 M KF

(c) Ag₂SO₄(s) in 0.500 L of a solution containing 19.50 g of K₂SO₄

(d) Zn(OH)₂(s) in a solution buffered at a pH of 11.45

Assuming that no equilibria other than dissolution are involved, calculate the concentration of all solute species in each of the following solutions of salts in contact with a solution containing a common ion. Show that it is not appropriate to neglect the changes in the initial concentrations of the common ions.

(a) TlCl(s) in 0.025 M TlNO₃

(b) BaF₂(s) in 0.0313 M KF

(c) MgC₂O₄ in 2.250 L of a solution containing 8.156 g of Mg(NO₃)₂

(d) Ca(OH)₂(s) in an unbuffered solution initially with a pH of 12.700

Explain why the changes in concentrations of the common ions in Exercise 15.18 cannot be neglected.

Refer to Appendix J for solubility products for calcium salts. Determine which of the calcium salts listed is most soluble in moles per liter and which is most soluble in grams per liter.

Public Health Service standards for drinking water set a maximum of 250 mg/L (2.60 $\times$ 10^–3 M) of ${\text{SO}}_4{}^{\text{2−}}$ because of its cathartic action (it is a laxative). Does natural water that is saturated with CaSO₄ (“gyp” water) as a result or passing through soil containing gypsum, CaSO₄·2H₂O, meet these standards? What is the concentration of ${\text{SO}}_4{}^{\text{2−}}$ in such water?

The solubility product of CaSO₄·2H₂O is 2.4 $\times$ 10^–5. What mass of this salt will dissolve in 1.0 L of 0.010 M ${\text{SO}4}_{}{}^{\text{2−}}?$

Assuming that no equilibria other than dissolution are involved, calculate the concentrations of ions in a saturated solution of each of the following (see Appendix J for solubility products):

(a) AgI

(b) Ag₂SO₄

(c) Mn(OH)₂

(d) Sr(OH)₂·8H₂O

(e) the mineral brucite, Mg(OH)₂

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K_sp for each of the slightly soluble solids indicated:

(a) TlCl: [Tl⁺] = 1.21 $\times$ 10^–2 M, [Cl^–] = 1.2 $\times$ 10^–2 M

(b) Ce(IO₃)₄: [Ce⁴⁺] = 1.8 $\times$ 10^–4 M, $[{\text{IO}}_3{}^{\text{−}}]$ = 2.6 $\times$ 10^–13 M

(c) Gd₂(SO₄)₃: [Gd³⁺] = 0.132 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 0.198 M

(d) Ag₂SO₄: [Ag⁺] = 2.40 $\times$ 10^–2 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 2.05 $\times$ 10^–2 M

(e) BaSO₄: [Ba²⁺] = 0.500 M, $[{\text{SO}}_{\text{4}}{}^{\text{2−}}]$ = 2.16 $\times$ 10^–10 M

Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Appendix J for K_sp values.)

(a) CaCO₃: [Ca²⁺] = 0.003 M, $[{\text{CO}}_{\text{3}}{}^{\text{2−}}]$ = 0.003 M

(b) Co(OH)₂: [Co²⁺] = 0.01 M, [OH^–] = 1 $\times$ 10^–7 M

(c) CaHPO₄: [Ca²⁺] = 0.01 M, $[{\text{HPO}}_{\text{4}}{}^{\text{2−}}]$ = 2 $\times$ 10^–6 M

(d) Pb₃(PO₄)₂: [Pb²⁺] = 0.01 M, $[{\text{PO}}_{\text{4}}{}^{\text{3−}}]$= 1 $\times$ 10^–13 M

Calculate the concentration of sulfate ion when BaSO₄ just begins to precipitate from a solution that is 0.0758 M in Ba²⁺.

Calculate the concentration of ${\text{PO}}_4{}^{\text{3−}}$ when Ag₃PO₄ starts to precipitate from a solution that is 0.0125 M in Ag⁺.

Calculate the concentration of Ag⁺ required to begin precipitation of Ag₂CO₃ in a solution that is 2.50 $\times$ 10^–6 M in ${\text{CO}}_3{}^{\text{2−}}.$

What [F^–] is required to reduce [Ca²⁺] to 1.0 $\times$ 10^–4 M by precipitation of CaF₂?

Perform these calculations for nickel(II) carbonate. (a) With what volume of water must a precipitate containing NiCO₃ be washed to dissolve 0.100 g of this compound? Assume that the wash water becomes saturated with NiCO₃ (K_sp = 1.36 $\times$ 10^–7).

(b) If the NiCO₃ were a contaminant in a sample of CoCO₃ (K_sp = 1.0 $\times$ 10^–12), what mass of CoCO₃ would have been lost? Keep in mind that both NiCO₃ and CoCO₃ dissolve in the same solution.

A solution is 0.010 M in both Cu²⁺ and Cd²⁺. What percentage of Cd²⁺ remains in the solution when 99.9% of the Cu²⁺ has been precipitated as CuS by adding sulfide?

What reagent might be used to separate the ions in each of the following mixtures, which are 0.1 M with respect to each ion? In some cases it may be necessary to control the pH. (Hint: Consider the K_sp values given in Appendix J.)

(a) ${\text{Hg}}_2{}^{\text{2+}}$ and Cu²⁺

(b) ${\text{SO}}_4{}^{\text{2−}}$ and Cl^–

(c) Hg²⁺ and Co²⁺

(d) Zn²⁺ and Sr²⁺

(e) Ba²⁺ and Mg²⁺

(f) ${\text{CO}}_3{}^{\text{2−}}$ and OH^–

A solution contains 1.0 $\times$ 10^–2 mol of KI and 0.10 mol of KCl per liter. AgNO₃ is gradually added to this solution. Which forms first, solid AgI or solid AgCl?

About 50% of urinary calculi (kidney stones) consist of calcium phosphate, Ca₃(PO₄)₂. The normal mid range calcium content excreted in the urine is 0.10 g of Ca²⁺ per day. The normal mid range amount of urine passed may be taken as 1.4 L per day. What is the maximum concentration of phosphate ion that urine can contain before a calculus begins to form?

Magnesium metal (a component of alloys used in aircraft and a reducing agent used in the production of uranium, titanium, and other active metals) is isolated from sea water by the following sequence of reactions:

${\text{Mg}}^{\text{2+}}(aq)+{\text{Ca(OH)}}_2(aq)⟶{\text{Mg(OH)}}_2(s)+{\text{Ca}}^{\text{2+}}(aq)$

${\text{Mg(OH)}}_2(s)+\text{2HCl(}aq)⟶{\text{MgCl}}_2(s)+{\text{2H}}_2\text{O}(l)$

${\text{MgCl}}_2(l)\stackrel{\text{electrolysis}}{\to }\text{Mg}(s)+{\text{Cl}}_2(g)$

Sea water has a density of 1.026 g/cm³ and contains 1272 parts per million of magnesium as Mg²⁺(aq) by mass. What mass, in kilograms, of Ca(OH)₂ is required to precipitate 99.9% of the magnesium in 1.00 $\times$ 10³ L of sea water?

Perform the following calculations involving concentrations of iodate ions:

(a) The iodate ion concentration of a saturated solution of La(IO₃)₃ was found to be 3.1 $\times$ 10^–3 mol/L. Find the K_sp.

(b) Find the concentration of iodate ions in a saturated solution of Cu(IO₃)₂ (K_sp = 7.4 $\times$ 10^–8).

How many grams of Pb(OH)₂ will dissolve in 500 mL of a 0.050-M PbCl₂ solution (K_sp = 1.2 $\times$ 10^–15)?

How many grams of Milk of Magnesia, Mg(OH)₂ (s) (58.3 g/mol), would be soluble in 200 mL of water. K_sp = 7.1 $\times$ 10^–12. Include the ionic reaction and the expression for K_sp in your answer. (K_w = 1 $\times$ 10^–14 = [H₃O⁺][OH^–])

Which of the following carbonates will form first? Which of the following will form last? Explain.

(a) ${\text{MgCO}}_3{K}_{\text{sp}}=3.5\times 10^{-8}$

(b) ${\text{CaCO}}_3{K}_{\text{sp}}=4.2\times 10^{-7}$

(c) ${\text{SrCO}}_3{K}_{\text{sp}}=3.9\times 10^{-9}$

(d) ${\text{BaCO}}_3{K}_{\text{sp}}=4.4\times 10^{-5}$

(e) ${\text{MnCO}}_3{K}_{\text{sp}}=5.1\times 10^{-9}$

Under what circumstances, if any, does a sample of solid AgCl completely dissolve in pure water?

Calculate the cadmium ion concentration, [Cd²⁺], in a solution prepared by mixing 0.100 L of 0.0100 M Cd(NO₃)₂ with 1.150 L of 0.100 NH₃(aq).

Sometimes equilibria for complex ions are described in terms of dissociation constants, K_d. For the complex ion ${\text{AlF}}_6{}^{\text{3−}}$ the dissociation reaction is:

${\text{AlF}}_6{}^{\text{3−}}\rightleftharpoons {\text{Al}}^{\text{3+}}+6{\text{F}}^{\text{−}}$ and $K_{\text{d}}=\frac{[{\text{Al}}^{\text{3+}}]{[{\text{F}}^{\text{−}}]}^6}{[{\text{AlF}}_6{}^{\text{3−}}]}=2\times {10}^{-24}$

Calculate the value of the formation constant, K_f, for ${\text{AlF}}_{\text{6}}{}^{\text{3−}}.$

Using the dissociation constant, K_d = 7.8 $\times$ 10^–18, calculate the equilibrium concentrations of Cd²⁺ and CN^– in a 0.250-M solution of $\text{Cd}{(\text{CN})}_4{}^{\text{2−}}.$

Using the dissociation constant, K_d = 2.2 $\times$ 10^–34, calculate the equilibrium concentrations of Co³⁺ and NH₃ in a 0.500-M solution of $\text{Co}{({\text{NH}}_3)}_6{}^{\text{3+}}.$

Calculate the mass of potassium cyanide ion that must be added to 100 mL of solution to dissolve 2.0 $\times$ 10^–2 mol of silver cyanide, AgCN.

A roll of 35-mm black and white photographic film contains about 0.27 g of unexposed AgBr before developing. What mass of Na₂S₂O₃·5H₂O (sodium thiosulfate pentahydrate or hypo) in 1.0 L of developer is required to dissolve the AgBr as $\text{Ag}{({\text{S}}_2{\text{O}}_3)}_2{}^{\text{3−}}$ (K_f = 4.7 $\times$ 10¹³)?

Write the Lewis structures of the reactants and product of each of the following equations, and identify the Lewis acid and the Lewis base in each:

(a) ${\text{CO}}_2+{\text{OH}}^{\text{−}}⟶{\text{HCO}}_3{}^{\text{−}}$

(b) $\text{B}{(\text{OH})}_3+{\text{OH}}^{\text{−}}⟶\text{B}{(\text{OH})}_4{}^{\text{−}}$

(c) ${\text{I}}^{\text{−}}+{\text{I}}_2⟶{\text{I}}_3{}^{\text{−}}$

(d) ${\text{AlCl}}_3+{\text{Cl}}^{\text{−}}⟶{\text{AlCl}}_4{}^{\text{−}}$ (use Al-Cl single bonds)

(e) ${\text{O}}^{\text{2−}}+{\text{SO}}_3⟶{\text{SO}}_4{}^{\text{2−}}$

Using Lewis structures, write balanced equations for the following reactions:

(a) $\text{HCl}(g)+{\text{PH}}_3(g)⟶$

(b) ${\text{H}}_3{\text{O}}^{\mathrm{+}}+{\text{CH}}_3{}^{\text{−}}⟶$

(c) $\text{CaO}+{\text{SO}}_3⟶$

(d) ${\text{NH}}_4{}^{\mathrm{+}}+{\text{C}}_2{\text{H}}_5{\text{O}}^{\text{−}}⟶$

In a titration of cyanide ion, 28.72 mL of 0.0100 M AgNO₃ is added before precipitation begins. [The reaction of Ag⁺ with CN^– goes to completion, producing the $\text{Ag}{(\text{CN})}_2{}^{\text{−}}$ complex.] Precipitation of solid AgCN takes place when excess Ag⁺ is added to the solution, above the amount needed to complete the formation of $\text{Ag}{(\text{CN})}_2{}^{\text{−}}.$ How many grams of NaCN were in the original sample?

In dilute aqueous solution HF acts as a weak acid. However, pure liquid HF (boiling point = 19.5 °C) is a strong acid. In liquid HF, HNO₃ acts like a base and accepts protons. The acidity of liquid HF can be increased by adding one of several inorganic fluorides that are Lewis acids and accept F^– ion (for example, BF₃ or SbF₅). Write balanced chemical equations for the reaction of pure HNO₃ with pure HF and of pure HF with BF₃.

Boric acid, H₃BO₃, is not a Brønsted-Lowry acid but a Lewis acid.

(a) Write an equation for its reaction with water.

(b) Predict the shape of the anion thus formed.

(c) What is the hybridization on the boron consistent with the shape you have predicted?

Calculate the equilibrium concentration of Ni²⁺ in a 1.0-M solution [Ni(NH₃)₆](NO₃)₂.

Calculate the equilibrium concentration of Cu²⁺ in a solution initially with 0.050 M Cu²⁺ and 1.00 M NH₃.

Calculate the Fe³⁺ equilibrium concentration when 0.0888 mole of K₃[Fe(CN)₆] is added to a solution with 0.0.00010 M CN^–.

The equilibrium constant for the reaction ${\text{Hg}}^{\text{2+}}(aq)+2{\text{Cl}}^{\text{−}}(aq)\rightleftharpoons {\text{HgCl}}_2(aq)$ is 1.6 $\times$ 10¹³. Is HgCl₂ a strong electrolyte or a weak electrolyte? What are the concentrations of Hg²⁺ and Cl^– in a 0.015-M solution of HgCl₂?

Calculate the molar solubility of Al(OH)₃ in a buffer solution with 0.100 M NH₃ and 0.400 M ${\text{NH}}_4{}^{\mathrm{+}}.$

What is the molar solubility of BaSO₄ in a 0.250-M solution of NaHSO₄? K_a for ${\text{HSO}}_4{}^{\text{−}}$ = 1.2 $\times$ 10^–2.

What is the molar solubility of Pb(OH)₂ in a 0.138-M solution of CH₃NH₂?

A 0.125-M solution of Mn(NO₃)₂ is saturated with H₂S ([H₂S] = 0.10 M). At what pH does MnS begin to precipitate?

$\text{MnS}(s)\rightleftharpoons {\text{Mn}}^{\text{2+}}(aq)+{\text{S}}^{\text{2−}}(aq)K_{\text{sp}}=4.3\times {10}^{\text{−22}}$

${\text{H}}_2\text{S}(aq)+2{\text{H}}_2\text{O}(l)\rightleftharpoons 2{\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{S}}^{\text{2−}}(aq)K=1.0\times {10}^{\text{−26}}$

Calculate the molar solubility of CdCO₃ in a buffer solution containing 0.115 M Na₂CO₃ and 0.120 M NaHCO₃

Calculate the concentration of Cd²⁺ resulting from the dissolution of CdCO₃ in a solution that is 0.250 M in CH₃CO₂H, 0.375 M in NaCH₃CO₂, and 0.010 M in H₂CO₃.

Calculate the volume of 1.50 M CH₃CO₂H required to dissolve a precipitate composed of 350 mg each of CaCO₃, SrCO₃, and BaCO₃.

What mass of NaCN must be added to 1 L of 0.010 M Mg(NO₃)₂ in order to produce the first trace of Mg(OH)₂?

The following question is taken from a Chemistry Advanced Placement Examination and is used with the permission of the Educational Testing Service.

Solve the following problem:

${\text{MgF}}_2(s)\rightleftharpoons {\text{Mg}}^{\text{2+}}(aq)+2{\text{F}}^{\text{−}}(aq)$

In a saturated solution of MgF₂ at 18 °C, the concentration of Mg²⁺ is 1.21 $\times$ 10^–3 M. The equilibrium is represented by the preceding equation.

(a) Write the expression for the solubility-product constant, K_sp, and calculate its value at 18 °C.

(b) Calculate the equilibrium concentration of Mg²⁺ in 1.000 L of saturated MgF₂ solution at 18 °C to which 0.100 mol of solid KF has been added. The KF dissolves completely. Assume the volume change is negligible.

(c) Predict whether a precipitate of MgF₂ will form when 100.0 mL of a 3.00 $\times$ 10^–3-M solution of Mg(NO₃)₂ is mixed with 200.0 mL of a 2.00 $\times$ 10^–3-M solution of NaF at 18 °C. Show the calculations to support your prediction.

(d) At 27 °C the concentration of Mg²⁺ in a saturated solution of MgF₂ is 1.17 $\times$ 10^–3 M. Is the dissolving of MgF₂ in water an endothermic or an exothermic process? Give an explanation to support your conclusion.

Which of the following compounds, when dissolved in a 0.01-M solution of HClO₄, has a solubility greater than in pure water: AgBr, BaF₂, Ca₃(PO₄)₂, ZnS, PbI₂? Explain your answer.

What is the effect on the amount of CaHPO₄ that dissolves and the concentrations of Ca²⁺ and ${\text{HPO}}_4{}^{\text{−}}$ when each of the following are added to a mixture of solid CaHPO₄ and water at equilibrium?

(a) CaCl₂

(b) HCl

(c) KClO₄

(d) NaOH

(e) CaHPO₄

A volume of 50 mL of 1.8 M NH₃ is mixed with an equal volume of a solution containing 0.95 g of MgCl₂. What mass of NH₄Cl must be added to the resulting solution to prevent the precipitation of Mg(OH)₂?