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) + CO32- (aq)

 

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

 

Ksp = [Ag+]2[CO32-]

 

Sample Exercise 18A:

 

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

 

Solution:

 

Mg3(PO4)2 (s) 3 Mg2+ (aq) + 2 PO43- (aq)          Ksp = [Mg2+]3[PO43-]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 Ksp 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 (Ksp = 1.0 x 10-25).

 

Solution:


R

   Mg3(PO4)2 (s)       3 Mg2+ (aq)      +        2 PO43- (aq)

I

 

0

0

C

+3s

+2s

E

3s

2s

 

Ksp = [Mg2+]3[PO43-]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 Ksp 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 Ksp for Ag2CO3.

 

Solution:


R

      Ag2CO3 (s)         2 Ag+ (aq)        +        CO32- (aq)

I

 

0

0

C

+2s

+s

E

2s

s

 

Ksp = [Ag+]2[CO32-] = (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 Qsp using the calculated initial molarities of the cations and anions, and then compare Qsp to Ksp (given in problem or on Ksp data table) as follows:

 

Qsp > Ksp:  solubility equilibrium reaction goes to left = solid precipitate forms

Qsp = Ksp:  solution is saturated, no precipitation occurs

Qsp < Ksp:  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.  (Ksp = 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. Qsp = (0.0012)(0.0018)2 = 3.9 x 10-9 < Ksp , 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 Ksp 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 Ksp for the metal hydroxide.

 

Solution:


R

     M(OH)2 (s)     ⇌       M2+ (aq)       +       2 OH- (aq)

I

 

0

0

C

+s

+2s

E

s

2s

 

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

Ksp = [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:

 

18-1) Calculate the molar solubility of barium fluoride (Ksp = 1.8 x 10-7).  Include the solubility equilibrium reaction and Ksp expression in your answer.

Click for Solution

18-1)

R

       BaF2 (s)               Ba2+ (aq)       +       2 F- (aq)

I

 

0

0

C

+s

+2s

E

s

2s

 

Ksp = [Ba2+][F-]2

1.8 x 10-7 = (s)(2s)2

s = 0.0036 M

 

 

18-2) The molar solubility of strontium phosphate is 1.3 x 10-6 M.  Calculate the value of Ksp for strontium phosphate.  Include the solubility equilibrium reaction and Ksp expression in your answer.

Click for Solution

18-2)

R

  Sr3(PO4)2 (s)     ⇌      3 Sr2+ (aq)      +       2 PO43- (aq)

I

 

0

0

C

+3s

+2s

E

3s

2s

 

Ksp = [Sr2+]3[PO43-]2 = (3s)3(2s)2 = 108s5 = 108(1.3 x 10-6)5 = 4.0 x 10-28 

 

 

18-3) Predict if precipitation will occur when 36 mL of 0.0039 M Na2CrO4 is mixed with 18 mL of 0.00033 M AgNO3.  (Ksp = 1.1 x 10-12 for Ag2CrO4)

Click for Solution

18-3)

Na+ and NO3- = spectator ions

 

Ag2CrO4 (s) 2 Ag+ (aq) + CrO42- (aq)

 

total volume after mixing = 36 mL + 18 mL = 54 mL

 

[Ag+]i = 0.00033 M(18 mL/54 mL) = 0.00011 M

 

[CrO42-]i = 0.0039 M(36 mL/54 mL) = 0.0026 M

 

Qsp = (0.00011)2(0.0026) = 3.1 x 10-11 > Ksp , precipitation occurs

 

 

18-4) 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 10.38.  Calculate the value of Ksp for the metal hydroxide.

Click for Solution

18-4)

R

       M(OH)2 (s)           M2+ (aq)       +       2 OH- (aq)

I

 

0

0

C

+s

+2s

E

s

2s

 

pOH = 14.00 – 10.38 = 3.62

[OH-] = 10-3.62 = 2.4 x 10-4 M = 2s

s = 1.2 x 10-4 M

Ksp = [M2+][OH-]2 = (s)(2s)2 = 4s3 = 4(1.2 x 10-4)3 = 6.9 x 10-12

 

 

 

Click for Review Quiz 1

Click for Review Quiz 1 Answers