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Lecture 17 - Open Systems (Solid/Liquid Equilibrium)

Lecture 17 - Open Systems (Solid/Liquid Equilibrium). Exam #3 (Dec 5 @ 1:30pm) Precipitation & Dissolution Solubility product (Ks0) Estimating solubility From Ks0 - ignoring complex formation Effects of complexation pC-pH diagram (estimate max/min solubility).

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Lecture 17 - Open Systems (Solid/Liquid Equilibrium)

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  1. Lecture 17 - Open Systems (Solid/Liquid Equilibrium) • Exam #3 (Dec 5 @ 1:30pm) • Precipitation & Dissolution • Solubility product (Ks0) • Estimating solubility • From Ks0 - ignoring complex formation • Effects of complexation • pC-pH diagram (estimate max/min solubility)

  2. Example - Ferric iron solubility Fe(OH)3 = Fe3+ + 3OH- log Kso = -38.8

  3. Ferric Iron Solubility

  4. Metal Solubility

  5. Metal Solubility - Effect of Complexes • Metal cations exist in solution as species other than the aquo ion • These complexes impact metal solubility substantially and must be accounted for Example - Ferric Iron

  6. Fe(III) Hydrolysis* (A) Fe3+ + OH- = FeOH2+ logK1 = 11.81 (B) Fe3+ + 2OH- = Fe(OH)2+ logb2 = 23.4 (C) Fe3+ + 4OH- = Fe(OH)4- logb4 = 34.4 OR (A*) Fe3+ + H2O = FeOH2+ + H+ logK1* = -2.19 (B*) Fe3+ + 2H2O = Fe(OH)2+ + 2H+ logb2* = -4.60 (C*) Fe3+ + 4H2O = Fe(OH)4- + 4H+ logb4* = -21.6

  7. System for Fe(III) solubility & hydroxo complexes • System: Open • Components: Fe3+ & H2O • Species: Fe3+, FeOH2+, Fe(OH)2+, Fe(OH)3(s), Fe(OH)4-, H2O, OH-, H+ • Equilibria: H2O = H+ + OH- Kw = [H+][OH-] = 10-14 (plus 4 reactions for Fe-hydoxo & Fe-solubility) • Mass Balance: Don't need! • Charge Balance: Don't need!

  8. Combine solubility and complex formation equilibria • Fe3+/Fe(OH)3(s) Fe(OH)3 + 3H+ = Fe3+ + 3H2O log Ks = 3.20 • FeOH2+/Fe(OH)3(s) Fe(OH)3 + 2H+ = FeOH2++ 2H2O logKs1 = 1.01 • Fe(OH)2+/Fe(OH)3(s) Fe(OH)3 + H+ = Fe(OH)2++ H2O logKs2 = -1.40 • Fe(OH)4-/Fe(OH)3(s) Fe(OH)3 + H2O = Fe(OH)4- + H+ logKs4 = -18.40

  9. Fe(III) - solubility Fe(OH)3(s) FeOH2+ Fe(OH)4- Fe3+ Fe(OH)2+

  10. Ferric Iron Solubility & Predominance

  11. So What? • Complexes increase mineral solubility • Diagram gives pH of min or max solubility • What are these for ferric iron? • Many other ligands form solids (e.g., CO32-) • For systems dominated by a particular solid we can estimate total metal concentration and dominant species.

  12. Carbonate System - Mixed Open System • System: Open • Components: Ca2+, CO2(g) & H2O • Species: H2CO3, HCO3-,CO32-, CO2(g), H2O, OH-, H+, CaCO3, Ca2+ • Equilibria: H2O = H+ + OH- Kw = [H+][OH-] = 10-14 H2CO3 = H+ + HCO3- KA1 = [H+][HCO3-]/[H2CO3] = 10-6.35 HCO3- = H+ + CO32- KA2 = [H+][CO32-]/[HCO3-] = 10-10.33 CO2(g) = CO2(l) KH = [CO2(l)]/PCO2 = 10-1.5 (mol/L-atm) CaCO3 = Ca2+ + CO32- Kso = 10-8.48 • Mass Balance: CT = [H2CO3] + [HCO3-] +[CO32-] CaT = [Ca2+] • Charge Balance: 2[CO32-] + [HCO3-] + [OH-] = [H+] + 2[Ca+] • Proton Balance: Invalid because CO2 is proton active!!

  13. What do we know? • Our carbonate species in open systems • Total Ca based on solid/liquid

  14. Final Equation • Substitute in charge balance equation • Assume water pH near neutral, thus [H+], [OH-] & [CO32-] are negligible. • Solve for [H+] to get pH 8.24

  15. Importance of mineral dissolution/precipitation • Natural Waters • Dictate major cation concentrations (e.g., Ca2+, Mg2+) • Dictate carbonate system (particularly in g.w.) • Treatment systems • Hardness removal • Iron removal by aeration • Phosphate removal • Polluted waters • Acid mine drainage results from pyrite dissolution

  16. Importance of mineral dissolution/precipitation • Typically non-equilibrium processes (due to slow kinetics), but we can use equilibrium approaches because • Often one solid phase controls solution composition • The optimum pH for mineral precipitation dictated by equilibrium solubility constant

  17. Solubility • Described like all other reactions AaBb(s) = aA + bB Ks • Ks termed solubility product • For uncomplexed ligand we get Ks CaCO3(s) = Ca2+ + CO32- Kso • For complexed ligand we use Ks CaCO3(s) + H+ = Ca2+ + HCO3- Ks

  18. Aluminum Hydroxide

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