Solution of complex equilibria requres a systematic approach

1
Complex Equilibria - Solubility

• Solution of complex equilibria requres a
  systematic approach
• Example Find the solubility of PbCO3 in water.
• The initial setup is the same as the previous
  problem
• 1. Write balanced chemical equations
• PbCO3 Pb2 CO32-
• CO32- H2O HCO3- OH-
• HCO3- H2O H2CO3(aq) OH-
• H2O H OH-
• 2. We want the solubility of PbCO3 s Pb2
• 3. Write equilibrium constant expressions and
  find the values of Ks
• 4. Write a mass balance equation(s)
• Pb2 CO32- HCO3- H2CO3
• The pH is not fixed, so there is no mass balance
  equation involving H
• 5. Write a charge balance equation
• 2Pb2 H 2CO32- HCO3- OH-
• 6. 6 unknowns Pb2, CO32-, HCO3-, H2CO3,
  H, OH-, 6 equations

2
Complex Equilibria - Solubility

• Solution of complex equilibria requres a
  systematic approach
• Example Find the solubility of PbCO3 in water
• 7. Make chemically reasonable approximations to
  simplify the algebra
• Rearrange the charge balance equation
• 2Pb2 - 2CO32- - HCO3- OH- - H
  solution is basic
• Examine the mass balance equation
• Pb2 CO32- HCO3- H2CO3 expect
  H2CO3 ltlt CO32- HCO3-
• 2 unknowns have been eliminated for now
• Multiply resulting mass balance equation by 2 and
  compare to charge balance equation
• 2Pb2 2CO32- 2HCO3-
• 2Pb2 2CO32- HCO3- OH-
• 0 0 HCO3- - OH-
  subtract
• HCO3- OH-

3
Complex Equilibria - Solubility

• Solution of complex equilibria requres a
  systematic approach
• Example Find the solubility of PbCO3 in water
• 8. Solve the algebra
• From Kb1
• From the simplified mass balance equation
• Pb2 CO32- HCO3-
• Solve using the method of successive
  approximations or Mathcad
• Pb2 3.6 x 10-5

4

• Complex Equilibria - Solubility
• Solution of complex equilibria requires a
  systematic approach
• Example Find the solubility of PbCO3 in water
• 9. Check assumptions
• The assumptions were
• H2CO3 ltlt CO32- HCO3- 2.2 x 10-8 ltlt
  0.44 x 10-5 3.2 x 10-5 ?
• H ltlt OH-
  3.1 x 10-10 ltlt 3.2 x 10-5 ?
• At pH8.00, Pb2 19 x 10-5 at pH9.5,
  Pb23.6 x 10-5
• increasing the pH to 9.5 from 8.0 decreases the
  solubility by a factor of about 5
• If CO32- did not hydrolyze
• Pb2 CO32- and
• The hydrolysis of CO32- enhances the
  solubility of PbCO3 by a factor of 3!

5
Complex Equilibria - Solubility

• Solution of complex equilibria requres a
  systematic approach
• Example Examine the calculation of the
  solubility of AgS in pure water
• Example 9-9, p. 175 FAC7