Chapter 15

Solubility Equilibria

AP Chemistry

The Solubility Product Constant, Ksp

• Many important ionic compounds are only slightly soluble in water and equations are written to represent the equilibrium between the compound and the ions present in a saturated aqueous solution.

• The solubility product constant, Ksp, is the product of the concentrations of the ions involved in a solubility equilibrium, each raised to a power equal to the stoichiometric coefficient of that ion in the chemical equation for the equilibrium.

The Solubility Equilibrium Equation And Ksp

CaF2 (s) Ca2+ (aq) + 2 F- (aq)

Ksp = [Ca2+][F-]2 Ksp = 5.3x10-9

As2S3 (s) 2 As3+ (aq) + 3 S2- (aq)

Ksp = [As3+]2[S2-]3

• * Remember, solids are not in equilibrium expressions!

Some Values For Solubility Product Constants (Ksp) At 25 oC

Ksp And Molar Solubility

• The solubility product constant (Ksp) is related to the solubility of an ionic solute, but Ksp and

• Molar Solubility - the molarity of a solute in a saturated aqueous solution

• Ksp and Molar solubility are not the same thing.• Calculating solubility equilibria fall into two

categories:

– determining a value of Ksp from experimental data

– calculating equilibrium concentrations when Ksp is known.

Calculating Ksp From Molar Solubility

It is found that 1.2x10-3 mol of lead (II) iodide, PbI2, dissolves in 1.0 L of aqueous solution at 25 oC. What is the Ksp at this temperature?

• Ksp = [Pb2+][I-]2

• PbI2 Pb2+ + 2I-

• Ksp = [1.2 x 10-3] [2(1.2 x 10-3)]2

• 2 iodide ions form, so you must multiply molarity by 2!

• Ksp = 6.9 x 10-9

Calculating Molar Solubility From Ksp

Calculate the molar solubility of silver chromate, Ag2CrO4, in water from Ksp = 1.1x10-12 for Ag2CrO4.

Ag2CrO4(s) 2Ag+ + CrO42-

Ksp = [Ag+]2[CrO4-2]

At equilibrium 2x x

1.1 x 10-12 = (x)(2x)2

1.1 x 10-12 = 4x3

x = 6.5 x 10-5 M = [Ag2CrO4] = [CrO42-]

[Ag+] = 2(6.5 x 10-5)

The Common Ion Effect In Solubility Equilibria

• The common ion effect also affects solubility equilibria.

• Le Châtelier’s principle is followed for the shift in concentration of products and reactants upon addition of either more products or more reactants to a solution.

• The solubility of a slightly soluble ionic compound is lowered when a second solute that furnishes a common ion is added to the solution.

Solubility Equilibrium Calculation-The Common Ion Effect

What is the solubility of Ag2CrO4 in 0.10 M K2CrO4? Ksp = 1.1x10-12 for Ag2CrO4.

Comparison of solubility of Ag2CrO4

In pure water: 6.5 x 10-5 MIn 0.10 M K2CrO4: 1.7 x 10-6 MThe common ion effect!!Adding more CrO4

2- ions shifts the equilibrium back to the reactants, which is solid Ag2CrO4

Ag2CrO4 2Ag+ + CrO42-

Chapter SixteenPrentice-Hall ©2002 Slide 10 of 32

Common Ion Effect Example:What will the molar solubility of CaF2 (Ksp = 4.0 x 10-11)

in a 0.025M NaF solution

CaF2 Ca2+ + 2F- and Ksp = [Ca2+][F-]2

Before it dissolves

[Ca2+] = 0 [F-] = 0.025

After it dissolves

[Ca2+] = x [F-] = 0.025 + 2x

From NaF From CaF2

4.0 x 10-11 = x (0.025 – 2x)2Assume x is very small

due to small Ksp

4.0 x 10-11 = x(0.025)2x = 6.4 x 10-8 = molar

solubility

Determining Whether Precipitation Occurs

• Qsp is the ion product reaction quotient and is based on initial conditions of the reaction.

• Qsp can then be compared to Ksp.

• To predict if a precipitation occurs:

- Precipitation should occur if Qsp > Ksp.

- Precipitation cannot occur if Qsp < Ksp.

- A solution is just saturated if Qsp = Ksp.

Sometimes the concentrations of the ions are not high enough to produce a precipitate!

Determining Whether Precipitation Occurs – An Example

The concentration of calcium ion in blood plasma is 0.0025 M. If the concentration of oxalate ion is 1.0x10-7 M, do you expect calcium oxalate to precipitate? Ksp = 2.3x10-9.

Three steps:

(1) Determine the initial concentrations of ions.

(2) Evaluate the reaction quotient Qip.

(3) Compare Qsp with Ksp.

Chapter SixteenPrentice-Hall ©2002 Slide 13 of 32

The concentration of calcium ion in blood plasma is 0.0025 M. If the concentration of oxalate ion is 1.0x10-7 M, do you expect calcium oxalate, CaC2O4, to precipitate? Ksp = 2.3x10-9.

Determining Whether Precipitation Occurs

Qsp = [Ca2+][C2O42-] = (0.0025)(1.0 x 10-7)

Qsp = 2.5 x 10-10

• Qsp < Ksp therefore, no precipitate will form!!!

Determining Whether Precipitation Occurs

In applying the precipitation criteria, the effect of dilution when solutions are mixed must be considered.

Example: A 250.0 mL sample of 0.0012 M Pb(NO3)2 (aq) is mixed with 150.0 mL of 0.0640 M NaI (aq). Should precipitation of PbI2 (s), Ksp = 7.1x10-9, occur?

Calculate new concentrations in total volume of 400mls = 0.4L

[Pb2+] = (0.250L)(0.0012M)/(0.400L) = 7.5 x 10-4 M

[I-] = (0.150L)(0.0640M)/(0.400L) = 0.024 M

Qsp = [Pb2+][I-]2 = (7.5 x 10-4)(0.024)2 = 4.32 x 10-7

Qsp > Ksp therefore a precipitate will form!

Selective Precipitation

a) The first precipitate to form when AgNO3(aq) is added to an aqueous solution containing Cl- and I- is yellow AgI(s).

b) Essentially all the I- has precipitated before the precipitation of white AgCl(s) begins.

AgCl (s) Ag+ (aq) + Cl- (aq) Ksp = 1.8x10-10

• AgI (s) Ag+ (aq) + I- (aq) Ksp = 8.5x10-17

Selective Precipitation An Example

Example: An aqueous solution that is 2.00 M in AgNO3 is slowly added from a buret to an aqueous solution that is 0.0100 M in Cl- and also 0.0100 M in I-

AgCl (s) Ag+ (aq) + Cl- (aq) Ksp = 1.8x10-10

AgI (s) Ag+ (aq) + I- (aq) Ksp = 8.5x10-17

a. Which ion. Cl- or I-, is the first to precipitate from solution?

(this depends on the Molar solubility not Ksp, but since both compounds give equal ions, then you can use Ksp)

a. Is separation of the two ions by selective precipitation feasible?

• AgI will precipitate first, lower Ksp

Chapter SixteenPrentice-Hall ©2002 Slide 17 of 32

Comparing Solubilities• Which salt will be the most soluble in water.

1. CuS Ksp = 8.5 x 10-45

2. Ag2S Ksp = 1.6 x 10-49

3. Bi2S3 Ksp = 1.1 x 10-73

Ksp = x2

Ksp = (2x)2x = 4x3

Ksp = (2x)2(3x)3 = 108x5

Molar solubility

x = 9.2 x 10-23

x = 3.4 x 10-17

x = 1.0 x 10-15

• Most Soluble = highest molar solubility!!!! Do not use Ksp!!

Effect of pH on Solubility

• The solubility of an ionic solute may be greatly affected by pH if an acid-base reaction also occurs as the solute dissolves.

• In other words, some salts will not dissolve well in pure water, but will dissolve in an acid or a base.

• If the anion (A-) of the salt/precipitate is that of a weak acid, the salt/precipitate will dissolve more when in a strong acid (H+ ions will form HA with A-)

• However, if the anion of the precipitate is that of a strong acid, adding a strong acid will have no effect on the precipitate dissolving more.

Chapter SixteenPrentice-Hall ©2002 Slide 19 of 32

• How would the addition of HCl affect the solubility of PbCl2?– Cl- is the conjugate base of a strong acid, thus it is a weak

base.

– It will not react with H+ ions, so there is no effect.

• How would the addition of HCl affect the solubility of FeS?– S2- is a strong base (conjugate base of weak acid)

– Thus, it will react with H+ ions to form H2S,

– This will shift the equilibrium to make more FeS dissolve!

Effect of pH on Solubility

Chapter SixteenPrentice-Hall ©2002 Slide 20 of 32

Summary

• The solubility product constant, Ksp, represents equilibrium between a slightly soluble ionic compound and its ions in a saturated aqueous solution.

• The common ion effect is responsible for the reduction in solubility of a slightly soluble ionic compound.

• The solubilities of some slightly soluble compounds depends strongly on pH.

Qualitative Inorganic Analysis

• Acid-base chemistry, precipitation reactions, oxidation-reduction, and complex-ion formation all come into sharp focus in an area of analytical chemistry called classical qualitative inorganic analysis.

• “Qualitative” signifies that the interest is in determining what is present, not how much is present.

• Although classical qualitative analysis is not as widely used today as instrumental methods, it is still a good vehicle for applying all the basic concepts of equilibria in aqueous solutions.

Cations of Group 1• If aqueous HCl is added to an unknown solution of

cations, and a precipitate forms, then the unknown contains one or more of these cations: Pb2+, Hg2

2+, or Ag+.

• These are the only ions to form insoluble chlorides.• If there is no precipitate, then these ions must be

absent from the mixture.• If there is a precipitate, it is filtered off and saved for

further analysis.• The supernatant liquid is also saved for further

analysis.

Cation Group 1 (continued)Analyzing For Pb2+

• Of the three possible ions in solution, PbCl2 is the most soluble in water.

• The precipitate is washed with hot water and the washings then treated with aqueous K2CrO4.

• If Pb2+ is present, chromate ion combines with lead ion to form a precipitate of yellow lead chromate, which is less soluble than PbCl2.

• If Pb2+ is absent, then the washings just become tinged yellow but no precipitate is in evidence.

Cation Group 1 (continued)Analyzing For Ag+

• Next, the undissolved precipitate is treated with aqueous ammonia.

• If AgCl is present, it will dissolve in this solution.• If there is any remaining precipitate, it is separated

from the supernatant liquid and saved for further analysis.

• The supernatant liquid (which contains the Ag+, if present) is then treated with aqueous nitric acid.

• If a precipitate reforms, then Ag+ was present in the solution, if no precipitate forms, then Ag+ was not present in the solution.

Cation Group 1 (continued)Analyzing For Hg2

2+

• When precipitate was treated with aqueous ammonia in the previous step, any Hg2

2+ underwent an oxidation-reduction reaction to form a dark gray mixture of elemental mercury and HgNH2Cl that precipitates from the solution.

• If this dark gray precipitate was observed, then mercury was present in the original unknown sample.

• If this dark gray precipitate was not observed, then mercury must have been absent from the original unknown sample.

Group 1 Cation Precipitates

left: cation goup 1 ppt: PbCl2, PbCl2, AgCl (all white)

middle: product from test for Hg2

2+: mix of Hg (black) and HgNH2Cl (white)

right: product from test for Pb2+: PbCrO4 (yellow) when K2CrO4(aq) is reacted with saturated PbCl2