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The Solubility Product Constant, Ksp Many ionic compounds are only slightly soluble in water: ex. Ag salts, sulfides Equations are written to represent the equilibrium between the compound and the ions present in a saturated aqueous solution AgCl(s) Ag+(aq) + Cl–(aq) Ksp = [Ag+][Cl–]
Ksp’s (25 °C)
Ksp and Molar Solubility
Ksp = [Ag+][Cl–]; solubility given by [Ag+] From stoichiometry, the ion ratio is 1:1, so [Ag+] = [Cl–], both of which are unknown (x) Ag+ Cl– Ag+ Cl– + Ksp = x2 and [Ag+] = (Ksp)1/2 The solubility product constant is related to the solubility of an ionic solute
The Common Ion Effect
The solubility of a slightly soluble ionic compound is lowered when a second solute that furnishes a common ion is added to the solution Ag2SO4(s) 2 Ag+(aq) + SO4–2(aq) Solubility of Ag2SO4 if MgSO4 is added to solution Le Châtelier’s principle is followed for the shift in concentration of products and reactants upon addition of either products or reactants to a solution
Common Ion Effect Illustrated
Does Precipitation Occur? Qip is the ion product reaction quotient and is based on initial conditions of the reaction Precipitation should occur if Qip > Ksp
Precipitation cannot occur if Qip < Ksp
A solution is just saturated if Qip = Ksp
Example
If 1.00 mg of Na2CrO4 is added to 225 mL of 0.00015 M AgNO3, will a precipitate form?
Ag2CrO4(s) 2 Ag+(aq) + CrO42–(aq) Ksp = 1.1 x 10–12
A Conceptual Example
Pictured here is the result of adding a few drops of concentrated KI(aq) to a dilute solution of Pb(NO3)2. What is the solid that first appears? Explain why it then disappears.
Example
If 0.100 L of 0.0015 M MgCl2 and 0.200 L of 0.025 M NaF are mixed, should a precipitate of MgF2 form?
MgF2(s) Mg2+(aq) + 2 F–(aq) Ksp = 3.7 x 10–8
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–.
Which ion, Cl– or I–, is the first to precipitate from solution?
When the second ion begins to precipitate, what is the remaining concentration of the first ion?
Is separation of the two ions by selective precipitation feasible? AgCl(s) Ag+(aq) + Cl–(aq) Ksp = 1.8 x 10–10 AgI(s) Ag+(aq) + I–(aq) Ksp = 8.5 x 10–17
Selective Precipitation
AgNO3 added to a mixture containing Cl– and I–
Effect of pH on Solubility
If, however, the anion of the precipitate is that of a strong acid, lowering the pH will have no effect on the precipitate. Added H+ reacts with, and removes, F–; LeChâtelier’s principle says more F– forms. H+ does not consume Cl– ; acid does not affect the equilibrium. CaF2(s) Ca2+(aq) + 2 F–(aq) AgCl(s) Ag+(aq) + Cl–(aq) If the anion of a precipitate is that of a weak acid, the precipitate will dissolve somewhat when the pH is lowered:
Mg(OH)2(s) Mg2+(aq) + 2 OH–(aq) Ksp = 1.8 x 10–11 A Conceptual Example
Without doing detailed calculations, determine in which of the following solutions Mg(OH)2(s) is most soluble:
(a) 1.00 M NH3
(b) 1.00 M NH3 /1.00 M NH4+
(c) 1.00 M NH4Cl. Example
What is the molar solubility of Mg(OH)2(s) in a buffer solution having [OH–] = 1.0 x 10–5 M, that is, pH = 9.00?
Equilibria Involving Complex Ions
Silver chloride becomes more soluble, not less soluble, in high concentrations of chloride ion.
Complex Ion Formation
Ag+(aq) + 2 Cl–(aq) [AgCl2]–(aq) [AgCl2]–
Kf = –––––––––– = 1.2 x 108
[Ag+][Cl–]2 A complex ion consists of a central metal atom or ion, with other groups called ligands bonded to it.
The metal ion acts as a Lewis acid (accepts electron pairs).
Ligands act as Lewis bases (donate electron pairs).
The equilibrium involving a complex ion, the metal ion, and the ligands may be described through a formation constant, Kf:
Complex Ion Formation
Concentrated NH3 added to a solution of pale-blue Cu2+ … … forms deep-blue Cu(NH3)42+.
Complex Ion Formation and Solubilities
AgCl is insoluble in water. But if the concentration of NH3 is made high enough … … the AgCl forms the soluble [Ag(NH3)2]+ ion.
Ag+(aq) + 2 NH3(aq) [Ag(NH3)2]+(aq) Kf = 1.6 x 107 Example
If 1.00 g KBr is added to 1.00 L of the solution described in Example 16.13, should any AgBr(s) precipitate from the solution?
AgBr(s) Ag+(aq) + Br–(aq) Ksp = 5.0 x 10–13 Example
Calculate the concentration of free silver ion, [Ag+], in an aqueous solution prepared as 0.10 M AgNO3 and 3.0 M NH3.
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