# Chapter 15: Solubility Equilibrium

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Chapter 15: Solubility Equilibrium
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15.6 Solubility Equilibria
Solubility of various compounds plays important roles. Sugar and table salt’s ability to dissolve in water help us to flavor food. Calcium sulfate is less soluble in hot water than cold water, which allows us to coat tubes in boilers. The low solubility of barium sulfate allows a safe way to X-ray the gastrointestinal tract.

Aqueous Equilibria Assume that when an ionic solid dissolves, that it dissociates completely. CaF2(s) → Ca2+ (aq) + 2F- (aq) There is a possibility for the ions to collide and re-form the solid phase. Ca2+ (aq) + 2F- (aq)→ CaF2(s) Finally, equilibrium is reached, and no more solid will dissolve (saturated). CaF2(s) ↔ Ca2+ (aq) + 2F- (aq)

Solubility Product Constant
Remember that solids are left out of equilibrium expressions Ksp=[Ca2+][F-]2 Ksp is the solubility product constant (sometimes referred to as just the “solubility product”). *Notice that the amount of solid present nor the size of particles effect the equilibrium.

Solubility vs. Solubility Product
Solubility is an equilibrium position. Solubility product is an equilibrium constant and has ONE value for a particular solid at a particular temperature.

Calculating Ksp from Solubility
Calculate Ksp for bismuth sulfide (Bi2S3), which has a solubility of 1.0 x mol/L at 25°C. Ksp= [Bi3+]2[S2-]3 =(2.0 x 10-15)2 (3.0 x 10-15)3 = 1.1 x 10-73 HW odd on page 743 Bi2S3(s) ↔ 2Bi3+(aq) + 3S2- (aq) I Not needed C -1.0 x = -x +2x +3x E 2.0 x 10-15 3.0 x 10-15

Calculating Solubility from Ksp
The Ksp value from Cu(IO3)2 is 1.4 x 10-7 at 25°C. Calculate its solubility. Ksp=[Cu2+][IO3-]2=[x][2x]2=(x)(4x2)=4x3 1.4 x 10-7=4x3 X=3.3 x 10-3 mol/L= Cu(IO3)2 solubility HW on page 743 Cu(IO3)2 (s) ↔ Cu2+(aq) + 2 IO3- (aq) I Not needed C -x +x +2x E

Relative Solubilities
Use Ksp values to predict relative solubilities of a group of salts. Salts producing the same number of ions Ex. AgI (s), CuI (s), CaSO4 (s) Solubility is directly proportional to Ksp because each compound produces 2 ions. Largest Ksp= most soluble Smallest Ksp= least soluble Salts producing differing numbers of ions. Ex. CuS (s), Ag2S (s), Bi2S3 (s) Solubility NOT directly proportional to Ksp and you have to calculate the solubilities.

Practice Problems HW 15.83,15.87 on page 743

Common Ion Effect Consider, the solubility of solid Ag2CrO4 (Ksp=9.0x10-12) in a M aqueous solution of AgNO3. What is the common ion? What is the [Ag+]0? What is the [CrO4-2]0? What is the Ksp expression?

X=9.0 x 10-10 M= solubility of Ag2CrO4 (s)
2 Ag+ (aq) + CrO4 2- (aq) I Not needed 0.100 M C -x +2x +x E x Ksp = [Ag+]2[CrO4]2- 9.0 x = ( x)2 (x) *Since Ksp is small, x is considered negligible compared to M; therefore x ≈ 0.100 9.0 x = (0.100)2 (x) X=9.0 x M= solubility of Ag2CrO4 (s) [Ag+]=0.100 M and [CrO4-]=9.0 x M

Solubility of Ag2CrO4 in pure water = 1.3 x 10-4 M
Solubility of Ag2CrO4 in M AgNO3=9.0x10-10 M *Note that solubility of a solid is lowered due to the common ion effect. Example on page 743 HW and on page 743.

pH and Solubility If the anion (X-) is an effective base (or HX is a weak acid), the salt MX will increase solubility in an acidic solution. Effective bases include OH-, S2-, CO3-, C2O42-, and CrO42-. Salts with these anions are more soluble in acidic solutions that pure water. HW (in reference to 15.81) on page 743

Precipitation Precipitation: the formation of a solid from solution
Ion Product (Q)=defined the same as Ksp except initial concentrations are used Ex. Ca(NO3)2 (aq) is mixed with NaF (aq). What is the ion product for CaF2? Q=[Ca2+]0[F-]02

To predict if precipitation will occur:
If Q>Ksp, precipitation occurs until concentrations are reduced to satisfy Ksp. If Q<Ksp, no precipitation occurs.

Determining Precipitation Conditions
A solution is prepared by adding mL of 4.00 x 10-3 M Ce(NO3)3 to mL of 2.00 x 10-2 M KIO3. Will Ce(IO3)3 (Ksp=1.9 x 10-10) precipitate from this solution? Calculate initial conditions. Solve for Q. Q=[Ce3+]0[IO3-]03=(2.86x10-3)(5.71x10-3)3= 5.32 x 10-10 Compare Q to Ksp. Q>Ksp, so Ce(IO3)3 will precipitate. Example on page 743 (Ksp values on page 718)

Precipitation and Equilibrium Concentrations
A solution is prepared by mixing mL of 1.00x10-2 M Mg(NO3)2 and mL of 1.00x10-1 M NaF. Calculate the concentrations of Mg2+ and F- at equilibrium with solid MgF2 (Ksp=6.4x10-9).

Find Initial Concentrations
2. Find Q 3. Compare Q vs. Ksp Q>Ksp, so solid MgF2 will form. * The next steps are used to determine equilibrium concentrations.

Run the reaction to completion. (BRA)
Calculate the concentration of excess reactant. [F-]excess=22.0 mmol / mL = 5.50 x 10-2 M Mg2+ + 2 F → MgF2(s) Before rxn (150.0 mL) (1.00x10-2M) =1.50 mmol (250.0 mL) (1.00x10-1M) =25.0 mmol Reaction -x -2 x +x After rxn =0 *limiting reactant 25.0-2(1.50)=22.0 mmol *excess 1.50 mmol

Determine concentrations at equilibrium (ICE).
Ksp= 6.4x10-9=[Mg2+][F-]2 =(x)(5.50x10-2+2x)2 ≈ (x)(5.50x10-2)2 X=2.1 x 10-6 M = [Mg2+] [F-]=5.50x10-2 M HW15.99 on page 743 MgF2 (s) ↔ Mg2+ (aq) + 2F- (aq) I Not needed 0 M 5.50 x 10-2 M C -x +x +2x E + x 5.50 x x

Selective Precipitation
Using anions that form precipitates with only one or a few metal ions in a mixture in order to separate the metal ions. Most insoluble sulfide salts can be precipitated in an acidic solutions. Soluble sulfide salts can be precipitated by making the solution slightly basic.

-For PbI2: Ksp=1.4x10-8=[Pb2+][I-]2 1.4x10-8=(2.0x10-3) [I-]2
A solution contains 1.0x10-4 M Cu+ and 2.0x10-3 M Pb2+. If a source of I- is added gradually to this solution, will PbI2 (Ksp=1.4x10-8) or CuI (Ksp=5.3x10-12) precipitate first? Specify the [I-] necessary to begin precipitation of each salt. -For PbI2: Ksp=1.4x10-8=[Pb2+][I-]2 1.4x10-8=(2.0x10-3) [I-]2 [I-]=2.6 x 10-3 M is necessary to begin precipitation -For CuI: Ksp=5.3x10-12=[Cu+][I-] 5.3x10-12=(1.0x10-4)[I-] [I-]=5.3x10-8 M is necessary to begin precipitation *CuI will precipitate first since [I-] required is less. HW on page 744

Qualitative Analysis

Groups: Insoluble Chlorides (Ag+, Pb2+, Hg22+)
Sulfides insoluble in acid solution (Hg2+, Cd2+, Bi3+, Cu2+, Sn4+) Sulfides insoluble in basic solution (Co2+, Zn2+, Mn2+, Ni2+, Fe2+, Cr3+, Al3+) Insoluble Carbonates (Group 2A) Alkali Metal and ammonium ions (flame test)

Complex Ion Equilibria
Complex Ion: a charged species with a metal ion surrounded by ligands (Ag(NH3)+) The ligand donates its lone electron pair to an empty orbital of the metal ion to form a covalent bond Ligand: a Lewis base (H2O, NH3, Cl-, CN-) Coordination number: the number of ligands attached to the metal ion

Formation constants or stability constants:
Metal ions add ligands one at a time in steps characterized by their own equilibrium constants Ag+ + NH3↔ Ag(NH3)+ K1=2.1x103 Ag(NH3)+ + NH3↔ Ag(NH3)2+ K2=8.2x103 All species (Ag+, NH3, Ag(NH3)+, Ag(NH3)2+) exist at equilibrium. HW on page 744

Usually, [ligand] is much larger than [metal ion] and approximations are used to simplify problems.
Assume both reactions go to completion Ag+ + NH3↔ Ag(NH3)+ K1=2.1x103 Ag(NH3)+ + NH3↔ Ag(NH3)2+ K2=8.2x103 Ag+ + 2 NH3 → Ag(NH3)2+ K=K1 x K2 From here, use BRA to find concentrations and the equilibrium constant. Assume the ligand amount consumed is neglible Examples a, 105, 109 on page 744 HW b, 107on page 744

Strategies for Dissolving Water-Insoluble Ionic Solids
If the anion of the solid is a good base, solubility is increased with the addition of an acid If the anion is NOT a good base, solids can be dissolved in a solution containing a ligand to form stable complex ions with its cation.

Aqueous Ammonia is Added to Silver Chloride (white)
Aqueous Ammonia is Added to Silver Chloride (white). Silver Chloride, Insoluble in Water, Dissolves to Form Ag(NH3)2+ (aq) and Cl-(aq)

Ex on page 745 HW and on page 745

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