Unit 4 Acid-Base and Solubility Equilibria

4.6 Exercises

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Section 4.6 Exercises

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

    (a) [latex]\begin{array}{lccc} \text{AgI}(s)\;{\longrightarrow}\; & \text{Ag}^{+}(aq) & + & \text{I}^{-}(aq) \\[0.5em] & +x & & \rule[0ex]{2.5em}{0.1ex} \end{array}[/latex]

    (b) [latex]\begin{array}{lccc} \text{CaCO}_3(s)\;{\longrightarrow} & \text{Ca}^{2+}(aq) & + & \text{CO}_3^{\;\;2-}(aq) \\[0.5em] & \rule[0ex]{2.5em}{0.1ex} & & +x \end{array}[/latex]

    (c) [latex]\begin{array}{lccc} \text{Mg(OH)}_2(s)\;{\longrightarrow} & \text{Mg}^{2+}(aq) & + & 2\text{OH}^{-}(aq) \\[0.5em] & +x & & \rule[0ex]{2.5em}{0.1ex} \end{array}[/latex]

    (d) [latex]\begin{array}{lccc} \text{Mg}_3(\text{PO}_4)_2(s)\;{\longrightarrow} & 3\text{Mg}^{2+}(aq) & + & 2\text{PO}_4^{\;\;3-}(aq) \\[0.5em] & \rule[0ex]{2.5em}{0.1ex} & & +2x \end{array}[/latex]

    (e) [latex]\begin{array}{lccccc} \text{Ca}_5(\text{PO}_4)_3\text{OH}(s)\;{\longrightarrow} & 5\text{Ca}^{2+}(aq) & + & 3\text{PO}_4^{\;\;3-}(aq) & + & \text{OH}^{-}(aq) \\[0.5em] & \rule[0ex]{2.5em}{0.1ex} & & \rule[0ex]{2.5em}{0.1ex} & & +x \end{array}[/latex]

  2. How do the concentrations of Ag+ and CrO42− in a saturated solution above 1.0 g of solid Ag2CrO4 change when 100 g of solid Ag2CrO4 is added to the system? Explain.
  3. 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?
  4. 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?
  5. Write the ionic equation for the dissolution and the Ksp expression for each of the following slightly soluble ionic compounds:

    (a) LaF3

    (b) CaCO3

    (c) Ag2SO4

    (d) Pb(OH)2

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

    (a) KHC4H4O6, a salt containing the anion HC4H4O6−

    (b) PbI2

    (c) Ag4[Fe(CN)6], a salt containing the Fe(CN)64− ion

    (d) Hg2I2, a salt containing the cation Hg22+

  7. 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

  8. 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. Check whether changes in the initial concentration of the ions can be neglected.

    (a) TlCl(s) in 0.025 M TlNO3

    (b) BaF2(s) in 0.313 M KF

    (c) MgC2O4 in 2.250 L of a solution containing 8.156 g of Mg2+

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

  9. Refer to the 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. Source: OpenStax Chemistry 2e
  10. Public Health Service standards for drinking water set a maximum of 250 mg/L (2.60 × 10–3 M) of SO42− because of its cathartic action (it is a laxative). Does natural water that is saturated with CaSO4 as a result or passing through soil containing gypsum, CaSO4·2H2O, meet these standards? What is [SO42−] in such water?
  11. What mass of CaSO4·2H2O will dissolve in 1.0 L of 0.010 M SO42−?  Check whether the change in initial ion concentrations can be ignored.
  12. Assuming that no equilibria other than dissolution are involved, calculate the concentrations of ions in a saturated solution of each of the following (see solubility products). Source: OpenStax Chemistry 2e

    (a) AgI

    (b) Ag2SO4

    (c) Mn(OH)2

    (d) Sr(OH)2·8H2O

    (e) the mineral brucite, Mg(OH)2

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

    (a) TlCl: [Tl+] = 1.21 × 10−2 M, [Cl−] = 1.2 × 10−2 M

    (b) Ce(IO3)4: [Ce4+] = 1.8 × 10−4 M, [IO3−] = 7.3 × 10−4 M

    (c) Gd2(SO4)3: [Gd3+] = 0.132 M, [SO42−] = 0.198 M

    (d) Ag2SO4: [Ag+] = 2.40 × 10−2 M, [SO42−] = 2.05 × 10−2 M

    (e) BaSO4: [Ba2+] = 0.500 M, [SO42−] = 2.16 × 10−10 M

  14. Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Ksp values.) Source: OpenStax Chemistry 2e

    (a) CaCO3: [Ca2+] = 0.003 M, [CO32−] = 0.003 M

    (b) Co(OH)2: [Co2+] = 0.01 M, [OH–] = 1 × 10−7M

    (c) CaHPO4: [Ca2+] = 0.01 M, [HPO42−] = 2 × 10−6 M

    (d) Pb3(PO4)2: [Pb2+] = 0.01 M, [PO43−] = 1 × 10−13 M

  15. Calculate the concentration of sulfate ion when BaSO4 just begins to precipitate from a solution that is 0.0758 M in Ba2+.
  16. Calculate the concentration of PO43− when Ag3PO4 starts to precipitate from a solution that is 0.0125 M in Ag+.
  17. Calculate the concentration of Ag+ required to begin precipitation of Ag2CO3 in a solution that is 2.50 × 10−6 M in CO32−.
  18. What [F–] is required to reduce [Ca2+] to 1.0 × 10–4 M by precipitation of CaF2?
  19. 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 (Ksp = 1.36 × 10−7).

    (b) If the NiCO3 were a contaminant in a sample of CoCO3 (Ksp = 1.4 × 10−13), what mass of CoCO3 would have been lost? Keep in mind that both NiCO3 and CoCO3 dissolve in the same solution.  Hint:  Check that the change in initial ion concentrations can be ignored for CoCO3.

  20. 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?  Try calculating the solubility product quotient (Qsp) for CdS.
  21. 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: When the Ksp of a salt is not listed, the salt is likely very soluble in water or we may refer to a table of solubility guidelines (e.g. all nitrates and nearly all Group 1 and ammonium salts are very soluble in water).  Consider the Ksp values. Source: OpenStax Chemistry 2e

    (a) Hg22+ and Cu2+

    (b) SO42− and Cl–

    (c) Hg2+ and Co2+

    (d) Mn2+ and Sr2+

    (e) Ba2+ and Mg2+

    (f) CO32− and OH–

  22. 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?  For simplicity, assume that the Ksp at 25oC can be used for calcium phosphate under physiological conditions.
  23. 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:

    [latex]\text{Mg}^{2+}(aq)\;+\;\text{Ca(OH)}_2(aq)\;{\longrightarrow}\;\text{Mg(OH)}_2(s)\;+\;\text{Ca}^{2+}(aq)[/latex]

    [latex]\text{Mg(OH)}_2(s)\;+\;2\text{HCl}(aq)\;{\longrightarrow}\;\text{MgCl}_2(s)\;+\;2\text{H}_2\text{O}(l)[/latex]

    [latex]\text{MgCl}_2(l)\;{\xrightarrow{\text{electrolysis}}}\;\text{Mg}(s)\;+\;\text{Cl}_2(g)[/latex]

    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 × 103 L of sea water?

  24. 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 × 10−3 mol/L. Find the Ksp.

    (b) Find the concentration of iodate ions in a saturated solution of Cu(IO3)2 (Ksp = 7.4 × 10−8).

  25. How many grams of Pb(OH)2 will dissolve in 500 mL of a 0.010-M PbCl2 solution (Ksp = 1.2 × 10−15)?
  26. How many grams of Milk of Magnesia, Mg(OH)2 (s) (58.3 g/mol), would be soluble in 200 mL of water. Include the ionic reaction and the expression for Ksp in your answer. (Kw = 1.0 × 10−14 = [H3O+][OH–])
  27. Which of the following carbonates will form first? Which of the following will form last? Explain.

    (a) [latex]\text{MgCO}_3\;\;\;\;\;\;\;K_{\text{sp}} = 3.5\;\times\;10^{-8}[/latex]

    (b) [latex]\text{CaCO}_3\;\;\;\;\;\;\;K_{\text{sp}} = 4.2\;\times\;10^{-7}[/latex]

    (c) [latex]\text{SrCO}_3\;\;\;\;\;\;\;K_{\text{sp}} = 3.9\;\times\;10^{-9}[/latex]

    (d) [latex]\text{BaCO}_3\;\;\;\;\;\;\;K_{\text{sp}} = 4.4\;\times\;10^{-5}[/latex]

    (e) [latex]\text{MnCO}_3\;\;\;\;\;\;\;K_{\text{sp}} = 5.1\;\times\;10^{-9}[/latex]

Solutions

  1. (a) [latex]\begin{array}{lccc} \text{AgI}(s)\;{\rightleftharpoons}\; & \text{Ag}^{+}(aq) & + & \text{I}^{-}(aq) \\[0.5em] & +x & & \rule[-0.25ex]{0.5em}{0.1ex}\hspace{-0.5em}+x \end{array}[/latex]
    (b) [latex]\begin{array}{lccc} \text{CaCO}_3(s)\;{\rightleftharpoons} & \text{Ca}^{2+}(aq) & + & \text{CO}_3^{\;\;2-}(aq) \\[0.5em] & \rule[-0.25ex]{0.5em}{0.1ex}\hspace{-0.5em}+x & & +x \end{array}[/latex]
    (c) [latex]\begin{array}{lccc} \text{Mg(OH)}_2(s)\;{\rightleftharpoons} & \text{Mg}^{2+}(aq) & + & 2\text{OH}^{-}(aq) \\[0.5em] & +x & & \rule[-0.25ex]{1em}{0.1ex}\hspace{-1em}+2x \end{array}[/latex]
    (d) [latex]\begin{array}{lccc} \text{Mg}_3(\text{PO}_4)_2(s)\;{\rightleftharpoons} & 3\text{Mg}^{2+}(aq) & + & 2\text{PO}_4^{\;\;3-}(aq) \\[0.5em] & \rule[-0.25ex]{1em}{0.1ex}\hspace{-1em}+3x & & +2x \end{array}[/latex]
    (e) [latex]\begin{array}{lccccc} \text{Ca}_5(\text{PO}_4)_3\text{OH}(s)\;{\rightleftharpoons} & 5\text{Ca}^{2+}(aq) & + & 3\text{PO}_4^{\;\;3-}(aq) & + & \text{OH}^{-}(aq) \\[0.5em] & \rule[-0.25ex]{1em}{0.1ex}\hspace{-1em}+5x & & \rule[-0.25ex]{1em}{0.1ex}\hspace{-1em}+3x & & +x \end{array}[/latex]
  2. There is no change. A solid has an activity of 1 whether there is a little or a lot.
  3. The solubility of silver bromide at the new temperature must be known. Normally the solubility increases and some of the solid silver bromide will dissolve.  Le Châtelier’s Principle could predict whether solubility will increase or decrease depending on whether the forward reaction is endothermic or exothermic.
  4. CaF2, MnCO3, ZnS, and PbS
  5. (a) [latex]\text{LaF}_3(s)\;{\rightleftharpoons}\;\text{La}^{3+}(aq)\;+\;3\text{F}^{-}(aq)\;\;\;\;\;\;\;K_{\text{sp}} = [\text{La}^{3+}][\text{F}^{-}]^3[/latex];
    (b) [latex]\text{CaCO}_3(s)\;{\rightleftharpoons}\;\text{Ca}^{2+}(aq)\;+\;\text{CO}_3^{\;\;2-}(aq)\;\;\;\;\;\;\;K_{\text{sp}} = [\text{Ca}^{2+}][\text{CO}_3^{\;\;2-}][/latex];
    (c) [latex]\text{Ag}_2\text{SO}_4(s)\;{\rightleftharpoons}\;2\text{Ag}^{+}(aq)\;+\;\text{SO}_4^{\;\;2-}(aq)\;\;\;\;\;\;\;K_{\text{sp}} = [\text{Ag}^{+}]^2[\text{SO}_4^{\;\;2-}][/latex];
    (d) [latex]\text{Pb(OH)}_2(s)\;{\rightleftharpoons}\;\text{Pb}^{2+}(aq)\;+\;2\text{OH}^{-}(aq)\;\;\;\;\;\;\;K_{\text{sp}} = [\text{Pb}^{2+}][\text{OH}^{-}]^2[/latex]
  6. (a) 2 × 10–2 M; (b) 1.5 × 10–3 M; (c) 2.27 × 10–9 M; (d) 2.2 × 10–10 M
  7. (a) 6.4 × 10−9 M = [Ag+], [Cl−] = 0.025 M
    Check: [latex]\frac{6.4\;\times\;10^{-9}\;M}{0.025\;M}\;\times\;100\% = 2.6\;\times\;10^{-5}\;\%[/latex],an insignificant change;
    (b) 2.4 × 10−5 M = [Ca2+], [F−] = 0.0133 M + 2x = 0.00138 M
    Check: [latex]\frac{4.8\;\times\;10^{-5}\;M}{0.0133\;M}\;\times\;100\% = 0.36\%[/latex]. This value is less than 5% and can be ignored.
    (c) [SO42−] = 0.2238 M, [Ag+] = 7.4 × 10–3 M
    Check: [latex]\frac{3.7\;\times\;10^{-3}}{0.2238}\;\times\;100\% = 1.64\;\times\;10^{-2}\%[/latex]; the condition is satisfied.
    (d) [OH–] = 2.8 × 10–3 M, 5.7 × 10−12 M = [Zn2+]
    Check: [latex]\frac{5.7\;\times\;10^{-12}}{2.8\;\times\;10^{-3}}\;\times\;100\% = 2.0\;\times\;10^{-7}\%[/latex]; x is less than 5% of [OH–] and is, therefore, negligible.
  8. (a) estimate [Cl–] = 6.8 × 10−3 M
    Check: [latex]\frac{6.8\;\times\;10^{-3}}{0.025}\;\times\;100\% = 27\%[/latex]
    This value is too large to drop x. Therefore solve by using the quadratic equation:
    [Ti+] = 3.1 × 10–2 M, [Cl–] = 5.6 × 10–3 M
    (b) estimate [Ba2+] = 0.000245 M
    Check: [latex]\frac{2\times2.5\;\times\;10^{-4}}{0.313}\;\times\;100\% = 0.16\%[/latex]
    Therefore, the condition is satisfied.
    [Ba2+] = 2.5 × 10−4 M, [F–] = 0.313 M
    (c) [Mg2+] = 0.1491 M, [C2O42−] = 5 × 10−6 M
    Check: [latex]\frac{5\;\times\;10^{-6}}{0.14911}\;\times\;100\% = 0.003\%[/latex]
    The condition is satisfied; the above value is less than 5%.
    [Mg2+] = 0.1491 M, [C2O42−] = 5 × 10−6 M
    (d) [OH–] = 0.0501 M, [Ca2+] = 5.2 × 10–4 M
    Check: [latex]\frac{2\times 5.2\;\times\;10^{-4}}{0.0501}\;\times\;100\% = 2.1\%[/latex]
    The condition is satisfied; the above value is less than 5%.
    [OH–] = 0.051 M, [Ca2+] = 5.2 × 10–4 M
  9. CaSO4∙2H2O is the most soluble Ca salt in mol/L, and it is also the most soluble Ca salt in g/L.  CaSO4·2H2O has the highest solubility for all listed salts with the formula CaX, where X2− is an anion, since it has the largest Ksp.  Ksp is equal to x2, and x is the molar solubility, 0.0078 mol/L.  Ca(OH)2 has higher solubility than CaF2 since it has larger Ksp.  Ksp = 4x3 gives a molar solubility of 0.0069 mol/L.  The molar solubility of Ca3(PO4)2 is 1.6 × 10−7 mol/L.  The molar mass of CaSO4·2H2O exceeds that of Ca(OH)2.  Thus, the solubility in g/L is also the highest.
  10. 7.8 × 10–3 M = [SO42−] = [Ca2+]; Since this concentration is higher than 2.60 × 10–3 M, gypsum-containing water does not meet the standards.
  11. Mass (CaSO4·2H2O) = 0.72 g/L.  Initial check x = 0.0061 M, 61% > 5%.  It is necessary to use the quadratic formula to solve for x so that x = 0.0043 M.
  12. (a) [Ag+] = [I–] = 1.2 × 10–8 M; (b) [Ag+] = 2.88 × 10–2 M, [SO42−] = 1.44 × 10–2 M; (c) [Mn2+] = 3.7 × 10–5 M, [OH–] = 7.4 × 10–5 M; (d) [Sr2+] = 4.3 × 10–2 M, [OH–] = 8.6 × 10–2 M; (e) [Mg2+] = 1.3 × 10–4 M, [OH–] = 2.6 × 10–4 M.
  13. (a) 2.0 × 10–4; (b) 5.1 × 10–17; (c) 1.35 × 10–4; (d) 1.18 × 10–5; (e) 1.08 × 10–10
  14. (a) CaCO3 does precipitate.
    (b) The compound does not precipitate.
    (c) The compound does not precipitate.
    (d) The compound precipitates.
  15. 3.0 × 10−7 M
  16. 9.2 × 10−13 M
  17. [Ag+] = 1.8 × 10–3 M
  18. 6.3 × 10–4 M
  19. (a) 2.25 L; (b) 1.0 × 10–7 g, check 1.0 × 10–4% << 5%
  20. Qsp = (0.010)(8.5 × 10-40) = 8.5 × 10-38 < 1.0 × 10-28, 100% of it is dissolved
  21. (a) Hg22+ and Cu2+: Add SO42−.
    (b) SO42− and Cl–: Add Ba2+.
    (c) Hg2+ and Co2+: Add S2–.
    (d) Mn2+ and Sr2+: Add OH– until [OH–] = 0.050 M.
    (e) Ba2+ and Mg2+: Add SO42−.
    (f) CO32− and OH–: Add Ba2+.
  22. 1.5 × 10−12 M
  23. 3.99 kg.  This is a difficult question!  The full solutions is available.
  24. (a) 3.1 × 10–11; (b) [Cu2+] = 2.6 × 10–3; [IO3−] = 5.3 × 10–3
  25. 2.1 × 10–5 g Pb(OH)2
  26. [latex]\text{Mg(OH)}_2(s)\;{\rightleftharpoons}\;\text{Mg}^{2+}(aq)\;+\;2\text{OH}^{-}(aq)\;\;\;\;\;\;\;K_{\text{sp}} = [\text{Mg}^{2+}(aq)][\text{OH}^{-}(aq)]^2[/latex]
    1.5 × 10−3 g Mg(OH)2
  27. SrCO3 will form first, since it has the smallest Ksp value it is the least soluble. BaCO3 will be the last to precipitate, it has the largest Ksp value.

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