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Section 8

Section 8. Complex-Formation Titrations. Complex-Formation Titrations General Principles. Most metal ions form coordination compounds with electron-pair donors (ligands) M n+ + qL m-  ML q n-mq K f = [ML q n-mq ]/[ M n+ ][L m- ] q

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Section 8

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  1. Section 8 Complex-Formation Titrations

  2. Complex-Formation TitrationsGeneral Principles • Most metal ions form coordination compounds with electron-pair donors (ligands) • Mn+ + qLm- MLqn-mq Kf = [MLqn-mq]/[Mn+][Lm-]q • The number of covalent bonds formed is called the “coordination number” (e.g. 2,4,6) • e.g., Cu2+ has coordination number of 4 • Cu2+ + 4 NH3 Cu(NH3)42+ • Cu2+ + 4 Cl- Cu(Cl)42-

  3. Typical Inorganic Complex-Formation Titrations Complex-Formation TitrationsGeneral Principles

  4. Complex-Formation TitrationsGeneral Principles • The most useful complex-formation reactions for titrimetry involve chelate formation • A chelate is formed when a metal ion coordinates with two of more donor groups of a single ligand (forming a 5- or 6- membered heterocyclic ring)

  5. Complex-Formation TitrationsGeneral Principles • Chelate Formation Titrations • Ligands are classified regarding the number of donor groups available: • e.g., NH3 = “unidentate” (one donor group) • Glycine = “bidentate” (two donor groups) • (also, there are tridentate, tetradentate, pentadentate, and hexadentate chelating agents) • Multidentate ligands (especially with 4 and 6 donors) are preferred for titrimetry. • react more completely with metal ion • usually react in a single step • provide sharper end-points

  6. Complex-Formation TitrationsGeneral Principles • Aminopolycarboxylic acid ligands • The most useful reagents for complexometric titrations are aminopolycarboxylic acids • (tertiary amines with carboxylic acid groups) • e.g., ethylenediaminetetraacetic acid (EDTA) • EDTA is a hexadentate ligand • EDTA forms stable chelates with most metal ions

  7. Complex-Formation TitrationsSolution Chemistry of EDTA(H4Y) • EDTA has four acid dissociation steps • pKa1= 1.99, pKa2= 2.67, pKa3= 6,16, pKa4= 10.26 • 5 forms of EDTA, (H4Y, H3Y-, H2Y2-, HY3-, Y4-) • EDTA combines with all metal ions in 1:1 ratio • Ag+ + Y4- AgY3- • Fe2+ + Y4- FeY2- • Al3+ + Y4-  AlY- • KMY = [MYn-4]/[Mn+][Y4-]

  8. Complex-Formation TitrationsFormation Constants for EDTA Complexes

  9. Complex-Formation TitrationsEquilibrium Calculations with EDTA • For Mn+ + Y4-  MYn-4KMY = [MYn-4]/[Mn+][[Y4-] • Need to know [Y4-], which is pH-dependent • pH dependence of Y4-: • Define: a4 = [Y4-]/CT • CT = [Y4-] + [HY3-] + [H2Y2-] + [H3Y-] + [H4Y] • Conditional Formation Constant, KMY’ • [MYn-4]/[Mn+][[a4CT] = KMY • KMY’ = a4 KMY = [MYn-4]/[Mn+][[CT]

  10. Complex-Formation TitrationsEquilibrium Calculations with EDTA • Computing free metal ion concentrations: • Use conditional formation constants, KMY’ • a4values depend on pH • Thus, KMY’ are valid for specified pH only • a4 values have been tabulated vs pH • a4 = (K1K2K3K4) / ([H+]4 + K1[H+]3 + K1K2[H+]2 + K1K2K3[H+] + K1K2K3K4)

  11. Y4- complexes with metal ions, and so the complexation equilibria are very pH dependent. Only the strongest complexes form in acid solution, e.g., HgY2-; CaY2- forms in alkaline solution. ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Fig. 9.1. Fraction of EDTA species as a function of pH.

  12. Kf’ = conditional formation constant = Kfa4. It is used at a fixed pH for equilibrium calculations (but varies with pH since a4 does). ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Fig. 9.2. Effect of pH on Kf’ values for EDTA chelates.

  13. Complex-Formation TitrationsEquilibrium Calculations with EDTA • Example: Add excess EDTA to Ni2+ solution at pH 3.0. • 50.0 mL 0.0500M EDTA added to 50.0 mL 0.030M Ni2+ • Assume very little Ni2+ is uncomplexed: • C(NiY2-) = [NiY2-] = 50.0 mL x 0.030M/100.0mL = 0.015M • C(EDTA) = ((50.0 x 0.050) – (50.0 x 0.030))/100.0 = 0.010 M • KMY’ = a4KMY = [NiY2-]/[Ni2+][0.010] =0.015/[Ni2+][0.010] • KMY = 4.2 x 1018; a4 = 2.5 x 10-11 @ pH = 3.0 • [Ni2+] = 1.4 x 10-8M

  14. Complex-Formation TitrationsMetal-EDTA Titration Curves • Titration curve is: pM vs EDTA volume • Conditional Formation Constant, KMY’ for specific pH • e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0 • at pH 10.0, K(CaY2-)’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010 • (a) pCa values before the equivalence point (10.0mL) • Ca2+ + Y4- CaY2- • assume: [CaY2-] = added EDTA – dissociated chelate • [Ca2+] = unreacted Ca2+ + dissociated chelate • Dissociated chelate = CT << [Ca2+], [CaY2-] • [Ca2+] =((50.0 x 0.020) –(10.0 x 0.050))/(60.0) = 0.0083M • pCa = 2.08 at 10.0mL EDTA

  15. Complex-Formation TitrationsMetal-EDTA Titration Curves • Titration curve is: pM vs EDTA volume • Conditional Formation Constant, KMY’ for specific pH • e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0 • at pH 10.0, K(CaY2-)’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010 • (b) pCa value at the equivalence point (20.0mL) • assume: [CaY2-] = added EDTA – dissociated chelate • [Ca2+] = dissociated chelate = CT<< [CaY2-] • [CaY2-] = ((20.0mL x 0.050M)/(70.0mL))-CT  0.0142M • K(CaY2-)’ = [CaY2-] / [Ca2+] [CT] = (0.0142)/[Ca2+]2 • [Ca2+] = ((0.0142)/(1.75 x 1010))1/2 = 9.0 x 10-7M; • pCa = 6.05 at 20.0mL EDTA • Note: assumption (CT << [CaY2-]) is OK

  16. Complex-Formation TitrationsMetal-EDTA Titration Curves • Titration curve is: pM vs EDTA volume • Conditional Formation Constant, KMY’ for specific pH • e.g., 50.0mL 0.020M Ca2+ with 0.050M EDTA, pH 10.0 • at pH 10.0, K(CaY2-)’ = (a4)(KCaY) = (0.35)(5.0 x 1010) = 1.75 x 1010 • (c) pCa value after the equivalence point (25.0mL) • assume: [CaY2-] = stoichiometric amount – [Ca2+] • CT = [excess EDTA] + [Ca2+]  [excess EDTA] • CT = ((25.0 x 0.050)-(50.0 x 0.020))/(75.0) = 0.0033M • [CaY2-] = ((50.0mL x 0.020M)/(75.0mL))-[Ca2+]  0.0133M • K(CaY2-)’ = [CaY2-] / [Ca2+] [CT]; [Ca2+] = (0.0133)/(0.0033)(K(CaY2-)’) • [Ca2+] = 2.30 x 10-10 • pCa = 9.64 at 25.0mL EDTA • Note: assumption ([Ca2+]<<CT << [CaY2-]) is OK

  17. As the pH increases, the equilibrium shifts to the right. ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Fig. 9.3. Titration curves for 100 mL 0.1 M Ca2+ versus 0.1 M Na2EDTA at pH 7 and 10.

  18. The points represent the pH at which the conditional formation constant, Kf', for each metal is 106, needed for a sharp end point. ©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley) Fig. 9.4. Minimum pH for effective titrations of various metal ions with EDTA.

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