SOLUBILITY CONSTANT -1CALCULATING

SOLUBILITY CONSTANTDr. Sapna Gupta

SOLUBILITY

• Ionic salts can be soluble or insoluble in water.

• Solubility constants are just like Kc – except its called Ksp.

• One can use the Ksp values to determine the concentrations of ions.

• Ksp is also used to calculate the concentration of salts required for precipitation of a salt.

• Writing equations for solubility:

MXn(s) Mn+(aq) + nX−(aq)

• For the above reaction,

Ksp = [Mn+][X−]n

• The coefficients for the ions are used as powers for the ions.

• Solids and liquids are not included in the expressions.

Dr. Sapna Gupta/Solubility - Ksp 2

EXAMPLE: WRITING

Write the solubility−product expression for the following salts:

a. Hg2Cl2

b. HgCl2

Solution:

Hg2Cl2(s) Hg22+(aq) + 2Cl−(aq)

Ksp = [Hg22+][Cl−]2

(Note: Hg22+ is a polyatomic ion)

HgCl2(s) Hg2+(aq) + 2Cl−(aq)

Ksp = [Hg2+][Cl−]2

Dr. Sapna Gupta/Solubility - Ksp 3

Ksp

SOME TERMS

• Molar solubility (s)– number of moles of solute in 1 L of a saturated solution (mol/L)

• Solubility - number of grams of solute in 1 L of a saturated solution (g/L)

• Ksp can be used to determine molar solubility (and solubility)

• Handle as an equilibrium problem

• Use an equilibrium table

• Molar solubility can be used to determine the value of the Ksp.

Dr. Sapna Gupta/Solubility - Ksp 4

EXAMPLE: CALCULATING SOLUBILITY -1

Calculate the solubility of SnS in g/L at 25°C. Ksp = 1.0 x 10-26)

Solution:

SnS(s) Sn2+ + S2-(aq)

Initial 0 0

Change +s +s

Eq conc s s

Dr. Sapna Gupta/Solubility - Ksp 5

2622

sp 10 x 1.0]][S[Sn K

2sss ))((10 x 1.0 26

Ms 10 x 1.0 13

L

g10 x 1.5

mol

150.77gx

L

mol 10 x 1.0solubility

1113

EXAMPLE: CALCULATING SOLUBILITY - 2

Calomel, whose chemical name is mercury(I) chloride, Hg2Cl2, was once used in medicine (as a laxative and diuretic). It has a Ksp of 1.3 10

18. What is the solubility of Hg2Cl2 in grams per liter?

Solution: Hg2Cl2(s) Hg22+(aq) + 2Cl−(aq)

Initial 0 0

Change +x +2x

Eq conc x 2x

Ksp = [Hg22+][Cl−]2

Ksp = x(2x)2

Ksp = x(4x2)

Ksp = 4x3

1.3 × 10−18 = 4x3

x3 = 3.25 × 10−19

x = 6.88 × 10−7 M

Dr. Sapna Gupta/Solubility - Ksp 6

The molar solubility is 6.9 × 10−7 M, but we also need the solubility in g/L:

mg/L 0.32

g/L 10 3.2 mol 1

g 472.086

L

mol 10 6.88 4-7

EXAMPLE: CALCULATING - 1

Exactly 0.133 mg of AgBr will dissolve in 1.00 L of water. What is the value of Ksp for AgBr?

Solution:

Solubility equilibrium: AgBr(s) Ag+(aq) + Br−(aq)

Solubility−product constant expression: Ksp = [Ag+][Br−]

The solubility is given as 0.133 mg/1.00 L, but Ksp uses molarity:

[Ag+] = [Cl−] = x = 7.083 × 10−7 M

Ksp = (7.083 × 10−7)2

Ksp = 5.02 × 10−13

Dr. Sapna Gupta/Solubility - Ksp 7

370.133 10 g 1 mol 7.083 10

1.00 L 187.77 gM

Ksp

EXAMPLE: CALCULATING - 2

An experimenter finds that the solubility of barium fluoride is 1.1 g in 1.00 L of water at 25°C. What is the value of Ksp for barium fluoride, BaF2, at this temperature?

Solution: BaF2(s) Ba2+(aq) + 2F−(aq)

Initial 0 0

Change +x +2x

Eq conc x 2x

Ksp = [Ba2+][F−]2

The solubility is given as 1.1 g/1.00 L, but Ksp uses molarity:

[Ba2+] = x = 6.27 × 10−3 M and [F−] = 2x = 2(6.27 × 10−3) = 1.25 × 10−2 M

Ksp = (6.27 × 10−3)(1.25 × 10−2)2

Ksp = 9.8 × 10−7

Dr. Sapna Gupta/Solubility - Ksp 8

M 10 6.27g 175.32

mol 1

L 1.00

g 1.1 x 3

Ksp

EXAMPLE: CALCULATING KSP - 3

The solubility of lead(II) chromate (PbCrO4) is 4.5 x 105 g/L. Calculate the

solubility product (Ksp) of lead(II) chromate.

Solution:

Dr. Sapna Gupta/Solubility - Ksp 9

Pb2+

(aq)

+ CrO42-

(aq)PbCrO4(s)

Ms 75

10 x 1.4g 323.2

mol x

L

g10 x 4.5

]][CrO[Pb2

4

22

sp

sK

1477

sp 10 x 2.0]10 x ][1.410 x [1.4 MMK

FOR SOME SALTS

Dr. Sapna Gupta/Solubility - Ksp 10

Ksp

CONCEPT CHECK

Lead compounds have been used as paint pigments, but because the lead(II) ion is toxic, the use of lead paints in homes is now prohibited. Which of the following lead(II) compounds would yield the greatest number of lead(II) ions when added to the same quantity of water (assuming that some undissolved solid always remains): PbCrO4, PbSO4, or PbS?

Solution:

We can begin by identifying the value of Ksp for each compound:

PbCrO4 1.8 × 10−14

PbSO4 1.7 × 10−8

PbS 2.5 × 10−27

Each salt produces two ions, so each has the same expression for the solubility−product constant: Ksp= x

2.

The solubility will be largest for PbSO4.

Dr. Sapna Gupta/Solubility - Ksp 11

KEY CONCEPTS

• Calculate molar solubility

• Calculate Ksp

• Predict relative solubilities

Dr. Sapna Gupta/Solubility - Ksp 12