Solubility and Simultaneous Equilibrium

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Solubility and Simultaneous Equilibrium
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Summary

• Solubility product constant, KSP
• Solubility and common-ion effect
• Precipitation calculations
• Complex-ion equilibria

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Solubility Equilibria for Salts

• Solubility of salts differ from each other
• Solubility product, Ksp, is used to express the
  degree of dissociation of a salt
• AgCl(s) ? Ag(aq) Cl-(aq)
• Ksp AgCl-
• Less soluble salts precipitate before more
  soluble ones

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Calculating KSP from Solubility

• Solubility of a salt is the amount of solute
  dissolved in a saturated solution.
• Example
• Calculate the KSP of PbF2 if 2.08x10-3 mol is
  dissolved in 1 L water at 25 0C.
• Solution
• PbF2 ? Pb2 2F-
• s 2s
• KSP (s)(2s)2 4s3 4(2.08x10-3)3 3.6x10-8

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Calculating Solubility from KSP

• What is the molar solubility of Ag2CO3?
• (KSP 8.1x10-12)
• Solution
• Ag2CO3(s) ? 2Ag CO32-
• 2s s
• (2s)2(s) 8.1x10-12
• s 1.3x10-4

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Common Ion Effect and Solubility

• Common ion shifts the equilibrium in the
  direction to reduce the solubility of a salt.
• Example
• What is the molar solubility of PbI2 in a 0.1 M
  NaI solution.
• Solution
• PbI2 ? Pb2 2I-
• s 0.12s
• s(0.12s)2 7.9x10-9
• s 7.9x10-7

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Common Ion Effect and Solubility

• Solubility of PbI2 in water
• s (7.9x10-9)1/2
• s 8.9x10-4
• Solubility of PbI2 in 0.1 M NaI solution
• s 7.9x10-7
• Solubility of PbI2 decreases a factor of thousand
  in the presence of 0.1 M I- ion.

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Formation of Precipitate in a Solution
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Example (precipitation formation)

• Will a precipitate of PbBr2 form if 50 mL of
  0.010 M PbNO3 is mixed with 50 mL of 0.010 M KBr?
  (KSP(PbBr2)2.1x10-6)
• Solution
• Pb2 2Br- ? PbBr2
• (0.005) (0.005)2
• Q(ion product) 1.3x10-7
• QltKSP no precipitate forms

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Example (precipitate formation)

• What precipitate is expected if 50 mL 0.10 M
  PbNO3 and 20 mL of 0.04 M NaCl are mixed?
• Solution
• Ions present in solution Pb 2, Na, NO3- ,
  Cl-. PbCl2 can form a precipitate. PbNO3 and NaCl
  are strong electrolytes. KSP(PbCl2) 1.7x10-5
• QltK no precipitate forms

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Example (separation)

• A K2CrO4 solution is gradually added to 100 mL of
  a solution that contains both Ba2 and Sr2, 0.10
  M each,
• Which ion precipitates first?
• What will be the Ba2 concentration when SrCrO4
  just begins to precipitate?
• What percentage of the strontium ion has
  precipitated when SrCrO4 just begins to
  precipitate?
• KSP(BaCrO4) 1.2x10-10
• KSP(SrCrO4) 3.5x10-5

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Solution

• Less soluble BaCrO4 precipitates first
• SO42- (1.2x10-10)½1.1x10-5 (SrCrO4 dont
  ppt)
• When SrCrO4 just begins to precipitate
• SO42- (3.5x10-5)/0.10 3.5x10-4
• The Barium concentration at this sulfate
  concentration
• Ba2 (1.2x10-10)/(3.5x10-4) 3.4x10-7
• Ba2 (3.4x10-7/0.10)x100 0.00034

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Complex Ions and Solubility

• Solubility of some salts may be increased by
  complex formation
• AgCl(s) ? Ag(aq) Cl-(aq)
• Ksp AgCl-
• Silver-Ammonia complex increases solubility of
  AgCl(s)
• Ag(aq) 2NH3(aq) ? Ag(NH3)2(aq)

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Solubility of Ag-Ammonia complex

• AgCl(s) ? Ag(aq) Cl-(aq)
  Ksp
• Ag(aq) 2NH3(aq) ? Ag(NH3)2(aq) Kf
• AgCl(s) 2NH3(aq) ? Ag(NH3)2(aq) Cl-(aq)
• Kc KSP . Kf

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Example

• Calculate the molar solubility of AgCl in 1.0 M
  NH3.
• KSP(AgCl)1.8x10-10
• Kf(Ag-NH3)1.7x107
• Solution
• AgCl(s) 2NH3(aq) ? Ag(NH3)2(aq) Cl-(aq)
• KC Kf.KSP 3.1x10-3
• x0.05 mol/L

1.0-2x
x
x