effect on equilibrium when a substance with an ion in common with the dissolved species is added to the solution; causes a decrease in the solubility of an ionic species, or a decrease in the ionization of a weak acid or base

solubility of a compound expressed in units of moles per liter (mol/L)

selective precipitation

process in which ions are separated using differences in their solubility with a given precipitating reagent

solubility product constant (K_sp)

equilibrium constant for the dissolution of an ionic compound

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Chemistry 2e · 15.1 Precipitation and Dissolution

Precipitation and Dissolution: practice problems

29 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 1
Complete the changes in concentrations for each of the following reactions:
(a)
$AgI (s) ⟶ Ag^{+} (a q) x + I^{-} (a q)_____$
(b)
$CaCO_{3} (s) ⟶ Ca^{2+} (a q) +____CO_{3}^{2-} (a q) x$
(c)
$Mg (OH)_{2} (s) ⟶ Mg^{2+} (a q) + x 2 OH^{-} (a q)_____$
(d)
$Mg_{3} (PO_{4})_{2} (s) ⟶ 3 Mg^{2+} (a q) + x 2 PO_{4}^{3-} (a q)_____$
(e)
$Ca_{5} (PO_{4})_{3} OH (s) ⟶ 5 Ca^{2+} (a q) +_____3 PO_{4}^{3-} (a q) +_____OH^{-} (a q) x$
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Exercises 3
How do the concentrations of Ag⁺ and $CrO_{4}^{2-}$ in a saturated solution above 1.0 g of solid Ag₂CrO₄ change when 100 g of solid Ag₂CrO₄ is added to the system? Explain.
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Exercises 5
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?
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Exercises 7
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, and ZnS?
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Exercises 9
Write the ionic equation for the dissolution and the K $_{s p}$ expression for each of the following slightly soluble ionic compounds:
(a) LaF₃
(b) CaCO₃
(c) Ag₂SO₄
(d) Pb(OH)₂
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Exercises 11
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
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Exercises 13
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 $Fe(CN)_{6}^{4-}$ ion
(d) Hg₂I₂
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Exercises 15
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
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Exercises 17
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. State whether or not it is 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 0.313 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
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Exercises 21
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.
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Exercises 23
Public Health Service standards for drinking water set a maximum of 250 mg/L (2.60 $\times$ 10–3 M) of $SO_{4}^{2-}$ 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 $SO_{4}^{2-}$ in such water?
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Exercises 25
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 $SO_{4}^{2-} ?$
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Exercises 27
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
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Exercises 29
The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K $_{s p}$ 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, $[IO_{3}^{-}]$ = 2.6 10–13
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Exercises 31
Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Appendix J for K $_{s p}$ values.)
(a) CaCO₃: [Ca²⁺] = 0.003 M, $[CO_{3}^{2-}]$ = 0.003 M
(b) Co(OH)₂: [Co²⁺] = 0.01 M, [OH–] = 1 $\times$ 10–7 M
(c) CaHPO₄: [Ca²⁺] = 0.01 M, = 2 10–6
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Exercises 33
Calculate the concentration of sulfate ion when BaSO₄ just begins to precipitate from a solution that is 0.0758 M in Ba²⁺.
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Exercises 35
Calculate the concentration of $PO_{4}^{3-}$ when Ag₃PO₄ starts to precipitate from a solution that is 0.0125 M in Ag⁺.
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Exercises 37
Calculate the concentration of Ag⁺ required to begin precipitation of Ag₂CO₃ in a solution that is 2.50 $\times$ 10–6 M in $CO_{3}^{2-} .$
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Exercises 39
What [F–] is required to reduce [Ca²⁺] to 1.0 $\times$ 10–4 M by precipitation of CaF₂?
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Exercises 41
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 $_{s p}$ = 1.36 $\times$ 10–7).
(b) If the NiCO₃ were a contaminant in a sample of CoCO₃ (K $_{s p}$ = 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.
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Exercises 43
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?
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Exercises 45
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 $_{s p}$ values given in Appendix J.)
(a) $Hg_{2}^{2+}$ and Cu²⁺
(b) $SO_{4}^{2-}$ and Cl–
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Exercises 47
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?
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Exercises 49
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?
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Exercises 51
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:
$Mg^{2+} (a q) + Ca(OH)_{2} (a q) ⟶ Mg(OH)_{2} (s) + Ca^{2+} (a q)$
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Exercises 53
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 $_{s p}$ .
(b) Find the concentration of iodate ions in a saturated solution of Cu(IO₃)₂ (K $_{s p}$ = 7.4 $\times$ 10–8).
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Exercises 55
How many grams of Pb(OH)₂ will dissolve in 500 mL of a 0.050-M PbCl₂ solution (K $_{s p}$ = 1.2 $\times$ 10–15)?
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Exercises 57
How many grams of Milk of Magnesia, Mg(OH)₂ (s) (58.3 g/mol), would be soluble in 200 mL of water. K $_{s p}$ = 7.1 $\times$ 10–12. Include the ionic reaction and the expression for K $_{s p}$ in your answer. (K $_{w}$ = 1 $\times$ 10–14 = [H₃O⁺][OH–])
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Exercises 59
The carbonate ion concentration is gradually increased in a solution containing equal concentrations of the divalent cations of magnesium, calcium, strontium, barium, and manganese. Which of the following carbonates will precipitate first? Which will precipitate last? Explain.
(a) $MgCO_{3} •3 H_{2} O K_{sp} = 1 \times 1 0^{- 5}$
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Key terms · 4

common ion effect: effect on equilibrium when a substance with an ion in common with the dissolved species is added to the solution; causes a decrease in the solubility of an ionic species, or a decrease in the ionization of a weak acid or base
molar solubility: solubility of a compound expressed in units of moles per liter (mol/L)
selective precipitation: process in which ions are separated using differences in their solubility with a given precipitating reagent
solubility product constant (K_sp): equilibrium constant for the dissolution of an ionic compound

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Precipitation and Dissolution: practice problems

29 problems from the book, with its answers. Check your working, or have any of them explained to you on the whiteboard.

Exercises 1

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

(a)

$AgI (s) ⟶ Ag^{+} (a q) x + I^{-} (a q)_____$

(b)

$CaCO_{3} (s) ⟶ Ca^{2+} (a q) +____CO_{3}^{2-} (a q) x$

(c)

$Mg (OH)_{2} (s) ⟶ Mg^{2+} (a q) + x 2 OH^{-} (a q)_____$

(d)

$Mg_{3} (PO_{4})_{2} (s) ⟶ 3 Mg^{2+} (a q) + x 2 PO_{4}^{3-} (a q)_____$

(e)

$Ca_{5} (PO_{4})_{3} OH (s) ⟶ 5 Ca^{2+} (a q) +_____3 PO_{4}^{3-} (a q) +_____OH^{-} (a q) x$

Exercises 3

How do the concentrations of Ag⁺ and $CrO_{4}^{2-}$ in a saturated solution above 1.0 g of solid Ag₂CrO₄ change when 100 g of solid Ag₂CrO₄ is added to the system? Explain.

Exercises 5

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?

Exercises 7

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, and ZnS?

Exercises 9

Write the ionic equation for the dissolution and the K $_{s p}$ expression for each of the following slightly soluble ionic compounds:

(a) LaF₃

(b) CaCO₃

(d) Pb(OH)₂

Exercises 11

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

(d) La₂(MoO₄)₃, 0.00179 g/100 mL

Exercises 13

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

(d) Hg₂I₂

Exercises 15

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

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

Exercises 17

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. State whether or not it is 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 0.313 M KF

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

Exercises 21

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.

Exercises 23

Public Health Service standards for drinking water set a maximum of 250 mg/L (2.60 $\times$ 10–3 M) of $SO_{4}^{2-}$ 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 $SO_{4}^{2-}$ in such water?

Exercises 25

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 $SO_{4}^{2-} ?$

Exercises 27

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

(d) Sr(OH)₂·8H₂O

(e) the mineral brucite, Mg(OH)₂

Exercises 29

The following concentrations are found in mixtures of ions in equilibrium with slightly soluble solids. From the concentrations given, calculate K $_{s p}$ 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, $[IO_{3}^{-}]$ = 2.6 10–13

Exercises 31

Which of the following compounds precipitates from a solution that has the concentrations indicated? (See Appendix J for K $_{s p}$ values.)

(a) CaCO₃: [Ca²⁺] = 0.003 M, $[CO_{3}^{2-}]$ = 0.003 M

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

Exercises 33

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

Exercises 35

Calculate the concentration of $PO_{4}^{3-}$ when Ag₃PO₄ starts to precipitate from a solution that is 0.0125 M in Ag⁺.

Exercises 37

Calculate the concentration of Ag⁺ required to begin precipitation of Ag₂CO₃ in a solution that is 2.50 $\times$ 10–6 M in $CO_{3}^{2-} .$

Exercises 39

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

Exercises 41

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 $_{s p}$ = 1.36 $\times$ 10–7).

(b) If the NiCO₃ were a contaminant in a sample of CoCO₃ (K $_{s p}$ = 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.

Exercises 43

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?

Exercises 45

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 $_{s p}$ values given in Appendix J.)

(a) $Hg_{2}^{2+}$ and Cu²⁺

(b) $SO_{4}^{2-}$ and Cl–

Exercises 47

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?

Exercises 49

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?

Exercises 51

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:

$Mg^{2+} (a q) + Ca(OH)_{2} (a q) ⟶ Mg(OH)_{2} (s) + Ca^{2+} (a q)$

Exercises 53

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 $_{s p}$ .

(b) Find the concentration of iodate ions in a saturated solution of Cu(IO₃)₂ (K $_{s p}$ = 7.4 $\times$ 10–8).

Exercises 55

How many grams of Pb(OH)₂ will dissolve in 500 mL of a 0.050-M PbCl₂ solution (K $_{s p}$ = 1.2 $\times$ 10–15)?

Exercises 57

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

Exercises 59

The carbonate ion concentration is gradually increased in a solution containing equal concentrations of the divalent cations of magnesium, calcium, strontium, barium, and manganese. Which of the following carbonates will precipitate first? Which will precipitate last? Explain.

(a) $MgCO_{3} •3 H_{2} O K_{sp} = 1 \times 1 0^{- 5}$

Key terms · 4

common ion effect: effect on equilibrium when a substance with an ion in common with the dissolved species is added to the solution; causes a decrease in the solubility of an ionic species, or a decrease in the ionization of a weak acid or base
molar solubility: solubility of a compound expressed in units of moles per liter (mol/L)
selective precipitation: process in which ions are separated using differences in their solubility with a given precipitating reagent
solubility product constant (K_sp): equilibrium constant for the dissolution of an ionic compound

Learn 15.1 on the whiteboard

The tutor teaches the whole section, drawing it out step by step and answering your questions as you go.

Read 15.1 in the textbook · This section on openstax.org