Chapter 18:  Solubility Equilibrium

 

 

Section 18-1: Solubility Equilibrium Reactions and Ksp Expressions

Section 18-2: Molar Solubility and Ksp Calculations

Section 18-3: Predicting Precipitation Using Qsp

Section 18-4: Experiment - Determining Ksp Using pH

Chapter 18 Practice Exercises and Review Quizzes

 

 

 

 

 

Section 18-1:  Solubility Equilibrium Reactions and Ksp Expressions

Ionic compounds that are described as “insoluble” in water are actually soluble to a certain extent.  We can represent the dissolving of these slightly soluble ionic compounds in water using a solubility equilibrium reaction that shows the ionic solid on the left and the separated aqueous cations and anions on the right.  For example, the solubility equilibrium reaction for Ag₂CO₃ is written as follows:

 

Ag₂CO₃ (s) ⇌ 2 Ag⁺ (aq) + CO₃^2- (aq)

 

The equilibrium constant K_c for solubility equilibrium reactions is typically expressed as K_sp, known as the solubility product constant.  Since solubility equilibrium reactions are heterogeneous, the ionic solid is omitted from the K_sp expression.  Thus, the K_sp expression for Ag₂CO₃ is written as follows:

 

K_sp = [Ag⁺]²[CO₃^2-]

 

Sample Exercise 18A:

 

Write the solubility equilibrium reaction and the K_sp expression for magnesium phosphate.

 

Solution:

 

Mg₃(PO₄)₂ (s) ⇌ 3 Mg²⁺ (aq) + 2 PO₄^3- (aq)          K_sp = [Mg²⁺]³[PO₄^3-]²

 

 

Section 18-2:  Molar Solubility and Ksp Calculations

The extent to which an ionic compound dissolves in water can be expressed by indicating the molar solubility (s) in M.  If we know the value of K_sp for an ionic compound, we can calculate the molar solubility using a RICE chart.  The ionic solid is omitted from the left side of the RICE chart, and the relative molarities of the separated aqueous cations and anions formed on the right side of the RICE chart are found using the coefficients from the solubility equilibrium reaction as follows:

 

Sample Exercise 18B:

 

Calculate the molar solubility of magnesium phosphate (K_sp = 1.0 x 10^-25).

 

Solution:

 

K_sp = [Mg²⁺]³[PO₄^3-]²

1.0 x 10^-25 = (3s)³(2s)²

s = 3.9 x 10^-6 M

 

If we know the molar solubility of an ionic compound, we can calculate the value of K_sp using a RICE chart as follows:

 

Sample Exercise 18C:

 

The molar solubility of Ag₂CO₃ is 1.3 x 10^-4 M.  Calculate the value of K_sp for Ag₂CO₃.

 

Solution:

 

K_sp = [Ag⁺]²[CO₃^2-] = (2s)²(s) = 4s³ = 4(1.3 x 10^-4)³ = 8.8 x 10^-12

 

 

Section 18-3:  Predicting Precipitation Using Qsp

 

To predict if a solid precipitate will form when two ionic compound solutions are mixed, we will employ the following steps:

 

1. Using solubility rules, identify any combination of cation + anion that is unlikely to form an insoluble precipitate.  These will be spectator ions.

 

2. For any combination of cation + anion that may form an insoluble precipitate, write a solubility equilibrium reaction with the formula of the solid precipitate on the left and the separate aqueous cations and anions on the right.

 

3. Calculate the initial molarities of the cations and anions on the right by taking into account the dilution that occurs when the two solutions are mixed to increase the total volume.

 

4. Calculate the reaction quotient Q_sp using the calculated initial molarities of the cations and anions, and then compare Q_sp to K_sp (given in problem or on K_sp data table) as follows:

 

Q_sp > K_sp:  solubility equilibrium reaction goes to left = solid precipitate forms

Q_sp = K_sp:  solution is saturated, no precipitation occurs

Q_sp < K_sp:  solution is unsaturated, no precipitation occurs

 

 Sample Exercise 18D:

 

Predict if precipitation will occur when 33 mL of 0.0016 M Pb(NO₃)₂ is mixed with 11 mL of 0.0072 M KI.  (K_sp = 8.5 x 10^-9 for PbI₂)

 

Solution:

1. K⁺ and NO₃^- = spectator ions

 

2. PbI₂ (s) ⇌ Pb²⁺ (aq) + 2 I^- (aq)

 

3. total volume after mixing = 33 mL + 11 mL = 44 mL

 

[Pb²⁺]_i = 0.0016 M(33 mL/44 mL) = 0.0012 M

 

[I^-]_i = 0.0072 M(11 mL/44 mL) = 0.0018 M

 

4. Q_sp = (0.0012)(0.0018)² = 3.9 x 10^-9 < K_sp , no precipitate

 

 

Section 18-4:  Experiment – Determining Ksp Using pH

 

For the dissolving of a metal hydroxide in water, the molarity of hydroxide ions at equilibrium on the RICE chart can be determined by measuring the pH of a saturated solution.  The molarity of hydroxide ions can be used to determine the molar solubility of the metal hydroxide, which can then be used to calculate the value of K_sp as follows:

 

Sample Exercise 18E:

 

A metal hydroxide with the formula M(OH)₂ was mixed with water and stirred until a saturated solution was created.  The pH of the solution was found to be 9.53.  Calculate the value of K_sp for the metal hydroxide.

 

Solution:

 

pOH = 14.00 – 9.53 = 4.47

[OH^-] = 10^-4.47 = 3.4 x 10^-5 M = 2s

s = 1.7 x 10^-5 M

K_sp = [M²⁺][OH^-]² = (s)(2s)² = 4s³ = 4(1.7 x 10^-5)³ = 2.0 x 10^-14

 

 

 

Chapter 18 Practice Exercises and Review Quizzes:

 

 

 

 

 

 

 

 

 

 

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