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Version 2012 Updated on 0510 Copyright © All rights reserved Dong-Sun Lee, Prof., Ph.D. Chemistry, Seoul Women’s University Chapter 15 Complexometric.

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Presentation on theme: "Version 2012 Updated on 0510 Copyright © All rights reserved Dong-Sun Lee, Prof., Ph.D. Chemistry, Seoul Women’s University Chapter 15 Complexometric."— Presentation transcript:

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2 Version 2012 Updated on 0510 Copyright © All rights reserved Dong-Sun Lee, Prof., Ph.D. Chemistry, Seoul Women’s University Chapter 15 Complexometric titrations & Precipitation titrations

3 Complexation reactions are important in many areas of science and everyday life, such as black-and-white photography. Shown to the left are photomicrographs of a capillary chromatogr- aphy column at ×1300 (top) and ×4900 (bottom) magnification. Black-and-white film consists of an emulsion of finely divided AgBr coated on a polymer strip. Exposure to light from SEM causes reduction of some of the Ag + ions to Ag atoms and corresponding oxidation of Br – to Br atoms. These atoms remain in the crystal lattice of AgBr as invisible defects, or so-called latent image. Developing reduces many more Ag + ions to Ag atoms in the granules of AgBr containing Ag atoms from the original latent image. This produces a visible negative image, in which dark regions of Ag atoms represent arears where light has exposed the film. The fixing step removes the unexposed AgBr by forming the highly stable silver thiosulfate complex. AgBr(s) + 2 S 2 O 3 2–  [Ag(S 2 O 3 ) 2 ] 3– (aq) + Br – (aq) Black metallic silver of the negative remains. After the negative has been fixed, a positive image is produced by projecting light through the negative onto photographic paper

4 Formation of complex  Many metal ions can accept unshared pairs of electrons from an anion or molecule to form coordinate covalent bonds. The molecule or ion species containing atom which donates the electrons is called a ligand or complexing agent. The ion which accepts the donated electrons is called the central ion or central atom. And the product resulting from a reaction between a metal ion and a ligand is referred to as a coordination compound or complex ion. Central atom Ligands(unidentate) [CoCl(NH 3 ) 5 ]Cl 2 Ionization sphere Coordination sphere Metal ions are Lewis acids, ligands are Lewis bases. Ag + + 2  C  N  – = [N  C—Ag—C  N] – Lewis acid Lewis base Complex ion electron-pair acceptor electron-pair donor

5 The coordination number is the maximum of atoms or groups that can combine, in the coordination sphere, with central atom. Ligands containing a single donor atom are called monodentate ; those which shares more than one pair of electrons are said to be bi-, tri-, poly-dentate. The complex can have either a positive or a negative charge, or it can be neutral. Ex. HgI 2 + 2I – = HgI 4 2– [Cu(H 2 O) 4 ] 2+ + 4 NH 3 = [Cu(NH 3 ) 4 ] 2+ + 4 H 2 O [Ag(CN) 2 ] – [Cu(CN) 3 ] 2 – [Fe(SCN)] 2+ cf. Analogous ions such SO 4 2–, CrO 4 2–, are not regarded as complex. We should remember that uncoordinated metal ions do not exist in polar solvents. A complex can contain more than one central metal ion. In such a case a ligand which is simultaneously attached to two or more metal ions binds the metal ions into single complex. A mononuclear complex contains a single metal ion ; a binuclear complex contains two central metal ions, and so forth.

6 Complexation Equilibria Consider complexation reactions occur in a stepwise fashion: a metal ion that forms complexes with the ligand L. The equivalent constants, β i, are called overall or cumulative formation constants. = K 1 = K 1 K 2 M + nL ML n β n = [ML n ] / [M][L] n = K 1 K 2 ··· K n

7 The mass balance for metal is Fraction of free metal ion = 1 / {1+ β 1 [L] + β 2 [L] 2 + ··· + β n [L] n }  M = fraction of the total metal concentration present at equilibrium as the free metal, C M = total metal concentration = [M] + [ML] + [ML 2 ] + ··· + [ML n ].

8 Conditional formation constant  Complexation with protonating ligands Fe 3+ ions form complexes with oxalate (C 2 O 4 2– : Ox 2– ) with formulas (FeOx) +, (FeOx 2 ) – and (FeOx 3 ) 3 –. Oxalic acid can protonate to form HOx – and H 2 Ox. C T = [H 2 Ox] + [HOx – ] + [Ox 2– ]  0 = [H 2 Ox] / C T = [H + ] 2 / {[H + ] + K a1 [H + ] + K a1 K a2 }  1 = [HOx – ] / C T = K a1 [H + ] 2 / {[H + ] + K a1 [H + ] + K a1 K a2 }  2 = [Ox 2– ] / C T = K a1 K a2 / {[H + ] + K a1 [H + ] + K a1 K a2 } [Ox 2– ] = C T  2 Conditional formation constant ; effective formation constant K f1 = [FeOx + ] / [Fe 3+ ] [Ox 2– ] = [FeOx + ] / [Fe 3+ ] C T  2 K f1 ’ = [FeOx + ] / [Fe 3+ ] C T =1 / K f1  2 At any given pH, we can find  2 and K f1 ’. K f ’ is the effective formation constant at the fixed pH of the solution.

9 The Chelate Effect A central metal ion bonds to a multidentate ligand in more than one location to form a ring structure. Such compounds are called chelates. Generally, ring formation results in increased stability of the complex. This generalization is called the chelate effect. The stability of the multidendate complex is mainly an entropy effect. ① The chelate effect is the ability of multidentate ligands to form more stable metal complexes than those formed by similar monodentate ligands. ② The chelate effect can be understood from thermodynamics. The two tendencies that drive a chemical reaction are decreasing enthalpy and increasing entropy

10 2+ Ethylenediamine Cd(H 2 O) 6 2+ with two molecules of ethylenediamine ΔH = -55.6KJ/mol ΔS = -2J/(mol K) A reaction is favorable if ΔG < 0. ΔG = ΔH -TΔS

11 2+ Methylamine Cd(H 2 O) 6 2+ with four molecules of methylamine ΔH = -58 KJ/mol ΔS = -71 J/(mol K)

12 Common monodentate ligands Neutral Anionic H 2 O F –, Cl –, Br –, I – NH 3 SCN –, CN – RNH 2 (aliphatic amines) OH –, RCOO –, S 2–

13 Common polydentate ligands Type Name Structure Bidentate Ethylenediamine(en) H 2 NCH 2 CH 2 NH 2 Tetradentate Triethylenetetraamine (Trien) H 2 NCH 2 CH 2 NHCH 2 CH 2 NHCH 2 CH 2 NH 2 Nitrilotriacetic acid (NTA) HOOCCH 2 NCH 2 COOH ATP CH 2 COOH Hexadentate Ethylenediaminetetraacetic acid (EDTA) HOOCCH 2 NCH 2 CH 2 NCH 2 COOH HOOCCH 2 CH 2 COOH Cyclohexanediaminetetraacetic acid (CDTA) Octadentate Diethylenetriaminepentaacetic acid (DTPA)

14 Structures of analytically useful chelating agents. NTA tends to form 2:1 (ligand:metal) complexes with metal ions, whereas the others form 1:1 complexes.

15 Zn 2+ + 2 N O–O– N N Zn O O Neutral chelate

16 Fe Olefin complex Ferrocene Dicylcopentadienyl iron Molecular complex Charge transfer Hydrogen bonded COOC 4 H 9 NH 2 OH NO 2 O2NO2N COOH OH Butesin picrate

17 I. Type of bonding or interaction Charge transfer Hydrogen bonding Hydrophobic interaction Stacking interaction II. Type or structure of interaction Small molecule-small molecule complex Small molecule-macromolecule complex Drug-protein binding Enzyme-substrate complex Drug- receptor complex Antigen-antibody complex III. Type of structure of complex Self associated aggregate Micelle Inclusion complex Clathrate Classification of molecular complexes

18 The cyclodextrine molecule. Topology of the  -cyclodextrin ring. No hydroxyl group is present within the toroid cavity which, accordingly, has a hydrophobic character. As a consequence, the ability of the BCD to form inclusion complexes in aqueous solution derives from its cavity, the interior of which is less polar than water. B. Manunza *, S. Deiana, M. Pintore, and C. Gessa http://www1.elsevier.com/homepage/saa/eccc3/paper60/welcome.html

19 Macrocycles : Cyclic organic compounds Molecular model of 18-crown-6. This crown ether can form strong complexes with alkali metal ions. The formation constant of the Na +, K + and Rb + co- mplexes are in the 10 5 to 10 6 range.

20 The characteristic chemistry of crown ethers involves complexation of the ether oxygens with various ionic species. This is termed "host-guest" chemistry, with the ether as host and the ionic species as guest. Crown ethers may be used as phase-transfer catalysts and as agents to promote solubility of inorganic salts in organic solutions. Crown Ether Complexation Martin Jones http://www.molecules.org/experiments/jones/jones.html Crown Ethers are cyclic polyethers discovered by Pederson in 1967. Structures of three typical ethers are given below. The common names of these ethers include a number as a prefix to designate the total number of atoms in the ring and a number as a suffix to designate the number of oxygen atoms in the ring. Thus, 15-crown-5 is comprised of 15 atoms in the ring, 5 of which are O and 10 of which are C. Pederson shared the Nobel Prize in Chemistry in 1987 with Cram and Lehn for work in this area.

21 A Chelating Ligand Captures Its Prey Structure of nonactin, with ligand atoms in color Nonactin molecule envelops a K + ion.

22 Ionophore carries K + across a cell membrane

23 Titration curves for complexometric titrations. Titaration of 60.0 ml of a solution that is 0.020M in M with A)A 0.020M solution of the tetradentate ligand D to give MD as the product; B)A 0.040M solution of the bidentate ligand B to give MB 2 ; C)A 0.080M solution of the unidentate ligand A to give MA 4. The overall formation constant for each product is 10 20. Titrations with Inorganic Complexing Agents

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25 Organic Complexing Agents

26 EDTA  HOOCCH 2 NCH 2 CH 2 N CH 2 COOH HOOCCH 2 H H CH 2 COOH Ethylenediaminetetraacetic acid (EDTA) ++ Hexatropic system : H 6 Y 2+ EDTA disodium salt Na 2 H 2 Y  2H 2 O pK 1 = 0.0 pK 2 = 1.5 Carbonyl protons pK 3 = 2.0 pK 4 = 2.66 pK 5 = 6.16 Ammonium protons pK 6 = 10.24

27 Structure of a metal/EDTA complex. Note that EDTA behaves here as a hexadentate ligand in that six donor atoms are involved in bonding the divalent metal cation.

28 Effect of pH on the equilibrium of EDTA H 6 Y 2+  H 5 Y +  H 4 Y  H 3 Y –  H 2 Y 2 –  HY 3 –  Y 4 –

29 Composition of EDTA solutions as a function of pH.

30 EDTA Complexes The equilibrium constant for the reaction of a metal with a ligand is called the formation constant, K f, or the stability constant Formation constant : Note that K f for EDTA is defined in terms of the species Y 4- reacting with the metal ion. The equilibrium constant could have been defined for any of the other six forms of EDTA in the solution.

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32 Titration of Ca 2+ with EDTA as a function of pH.

33 Influence of pH on the titration of 0.0100M Ca 2+ with 0.0100M EDTA.

34 Titration curves for 50.0 ml 0f 0.0100 M solutions of various cations at pH 6.0.

35 Minimum pH needed for satisfactory titration of various cations with EDTA.

36 Conditional formation constant of EDTA complex  MY n –4 = M n+ + Y 4 – K = 1 / K f = [M n+ ][Y 4 – ] / [MY n –4 ] = [M n+ ]  Y 4– [EDTA ] / [MY n –4 ] Conditional formation constant ; effective formation constant K f ’ = 1 / K f  Y 4– = [M n+ ][EDTA ] / [MY n –4 ] MY n –4 = M n+ + EDTA K f ’ = 1 / K f  Y 4– At any given pH, we can find  Y 4– and K f ’. K f ’ is the effective formation constant at the fixed pH of the solution. Key points 

37 Ex. Calculate free [Fe 3+ ] in 0.10M Fe(EDTA) – at pH 8.00. K f Fe(EDTA) – = 1.3×10 25  Y 4– =5.6 ×10 –3 K’ = 1 / K f  Y 4– = 1 / (1.3×10 25 )(5.6 ×10 –3 ) = 1.4 ×10 –23 Fe(EDTA) – = Fe 3+ + EDTA initial 0.10 0 0 final 0.10–x x x x 2 / (0.10 –x) = K’ = 1.4 ×10 –23 [Fe 3+ ] = x = 1.2 ×10 –12 M

38 EDTA titration curve M n+ + EDTA = MY n –4 K = [MY n –4 ] / [M n+ ][EDTA] = K f  Y 4– Ex. 0.0500M Mg 2+ 50.0ml (pH=10.00) vs 0.0500M EDTA Titration reaction : Mg 2+ + EDTA = MgY 2 – K = [MgY 2– ] / [Mg 2+ ][EDTA] = K f  Y 4– = (0.36)(6.2×10 8 ) = 2.2 ×10 8 Equivalence point : 0.0500M×50ml = 0.0500M×V e V e = 50.0ml

39 Three regions in an EDTA titration illustrated for reaction of 50.0mL of 0.050 0M M n+ with 0.050 0M EDTA, assuming K f ’ = 1.15  10 16.

40 In this region, there is excess M n+ left in solution after the EDTA has been consumed. There is exactly as much EDTA as metal in the solution. [M n+ ] = [EDTA] There is excess EDTA, and vitually all the metal ion is in the form My n-4 Three regions in an EDTA titration illustrated for reaction of 50.0mL of 0.050 0M M n+ with 0.050 0M EDTA, assuming K f ’ = 1.15  10 16.

41 A. Before the V Eq Theoretical titration curve: 0.0500M Mg 2+ (pH 10.00) 50.0ml vs 0.0500M EDTA Mg 2+ = {(V i –V a )/V i }F{V i /(V i +V a )} B. At equivalence point [MgY 2– ] = F{V i /(V i +V a )} [MgY 2– ] / [Mg 2+ ][EDTA] = K f  Y 4– = (0.36)(6.2×10 8 ) = 2.2 ×10 8 [Mg 2+ ] = [MgY 2– ] / 2.2 ×10 8 [EDTA] C. After equivalence point [EDTA] = F {(V i –V a ) / (V i +V a )} [MgY 2– ] = F{V i /(V i +V a )}

42 Region 1 : Before the Equivalence Point Fraction remaining ( = 4/5) Original concentration of Ca 2+ Dilution factor Initial volume of Ca 2+ Total volume of solution Titration Calculations Reaction of 50.0mL of 0.04 M Ca 2+ (buffered to pH 10.00) with 0.08 M

43 Region 2 : At the Equivalence Point Initial concentration of Ca 2+ Dilution factor Total volume of solution Initial volume of Ca 2+ Initial concentration (M) ㅡㅡ 0.026 7 Final concentration (M) xx 0.026 7- x

44 Region 3 : After the Equivalence Point Original concentration of Ca 2+ Original concentration of EDTA Volume of excess EDTA Total volume of solution Dilution factor Original volume of Ca 2+ Total volume of solution Dilution factor

45 Theoretical titration curves for the reaction of 50.0mL of 0.040 0M metal ion with 0.080 0 M EDTA at pH 10.00

46 EDTA Titration with an Auxiliary Complexing Agent K f ’’ is the effective formation constant at a fixed pH and fixed concentration of auxiliary complexing agent. Now consider a titration of Zn 2+ by EDTA in the presence of NH 3. The EDTA is in the form Y 4- The Zinc not bound to EDTA is in the form Zn 2+ 

47 Effect of complexing buffer : auxiliary complexing agent  At pH 10.00 Zn 2+ + 2 OH – = Zn(OH) 2  (ppt) Ksp = 3.0×10 –16 Auxiliary complexing agent : ammonia (0.10~0.02M), tartrate, citrate, triethanolamine Zn 2+ + 4 NH 3 = Zn(NH 3 ) 4 2+ K=  4 = 5.0 ×10 4 Zn(NH 3 ) 4 2+ = Zn 2+ + 4 NH 3 K= 1/  4 Zn 2+ + Y 4 – = ZnY 2– K f Zn(NH 3 ) 4 2+ + Y 4 – = ZnY 2– + 4 NH 3 K= K f /  4 = large

48 Titration curves for the reaction of 50.0mL of 1.00  10 -3 M Zn 2+ with 1.00  10 -3 M EDTA at pH 10.00 in the presence of two different concentrations of NH 3. Influence of ammonia concentration on the end point for the titration of 50.0ml of 0.00500M Zn 2+.

49 End point detection methods 1) Metal ion indicator   Compound whose color changes when it binds to a metal ion. Ex. Eriochrome black T Mg 2+ + In  MgIn MgIn + EDTA  MgEDTA + In (Red) (Colorless) (Colorless) (Blue) 2) Mercury electrode 3) Glass(pH) electrode 4) Ion selective electrode

50 Metal Ion Indicators   Metal ion indicators are compounds whose color changes when they bind to a metal ion. Useful indicators must bind metal less strongly than EDTA does. A typical titration is illustrated by the reaction of Mg 2+ with EDTA, using Eriochrome black T as the indicator. MgIn + EDTA  MgEDTA + In (red) (colorless) (colorless) (blue) Structure and molecular model of Eriochrome Black T(left) and Calmagite (right).

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52 Application 1) Calcium determination in food using EDTA titration AOAC Method 968.31 2) Water hardness (Ca, Mg) 3) Ca or Al content of drugs such as calcium pantothenate or alumina. Typical kit for testing for water hardness in household water.

53 EDTA titration curves for 50.0 ml 0f 0.00500 M Ca 2+ (K’ CaY = 1.75 ×10 10 ) and Mg 2+ (K’ MgY = 1.72 × 10 8 ) at pH 10.00.

54 EDTA titration technique 1) Direct titration : standard EDTA  analyte (appropriate pH) auxiliary complexing agent 2) Back titration : Analyte Excess EDTA standard Zn 2+ or Mg 2+ 3) Displacement titration : Analyte Mg(EDTA) 2– Mg 2+ standard EDTA

55 EDTA Titration Techniques Direct Titration In a direct titration, analyte is titrated with standard EDTA. Conditional formation constant for the metal-EDTA complex is large The color of the free indicator is distinctly different from that of the metal-indicator complex. Back Titration In a back titration, a known excess of EDTA is added to the analyte. The excess EDTA is then titrated with a standard solution of a second metal ion. Necessary if the analyte precipitates in the absence of EDTA, if it reacts too slowly with EDTA under titration conditions, or if it blocks the indicator. The metal ion used in the back titration must not displace the analyte metal ion from its EDTA complex

56 Displacement Titration For metal ions that do not have a satisfactory indicator, a displacement titration maybe feasible. Indirect Titration Anions that precipitate with certain metal ions can be analyzed with EDTA by indirect titration. Alternatively, an anion can be precipitated with excess metal ion. The precipitate is filtered and washed, and the excess metal ion in the filtrate is titrated with EDTA. Anions such as CO 3 2-, CrO 4 2-, S 2-, and SO 4 2- can be determined by indirect titration with EDTA. Masking A masking agent is a reagent that protects some component of the analyte from reaction with EDTA. Demasking release metal ion from a masking agent.

57 Precipitation titration Precipitation titrations are based on precipitation of the analyte with a precipitant Precipitation : Precipitation is the conversion of a dissolved substance into insoluble form by chemical or physical means. Ex. Ba 2+ + SO 4 2–  BaSO 4 (white)  Detection of end point: 1) Turbidimetry : stabilizer(glycerol-alcohol mixture) 2) Indicator : rhodizonate + Ba 2+  Red ppt  T V(titrant, ml) End point Turbidimetry : The intensity of light scattered by particles of precipitate is measured

58 Box Turbidimetry and nephelometry Detector PoPo P Light sourceMonochromator Sample cuvet Lambert Beer’s law Transmittance : T = P / P o Absorbance : A = – log T = – log (P / P o ) = k b[C] Nephelometry : the light scattered at 90 o to the incident beam by the turbid solution is measured b [C] Light sourceMonochromatorSample cuvet Detector

59 Sigmoidal titration curveLinear segment titration curve. Spectrophotometric titration curve of transferrin with ferric nitriloacetate.

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61 Titration curve for the titration of 50.00 ml of 0.1000M AgNO 3 with 0.1000M KSCN.

62 Titration curve : a graph showing how the concentration, pX of one the reactatnts varies as titrant is added pX = – logA X = – log[X] f X The shape of a precipitation titration curve Ex. 0.05000M Ag + 0.1000M I – 25.00 ml Titration reaction : Ag + + I –  AgI  K = (1 / Ksp) = 1.2×10 16 Ksp = [Ag + ][I – ] = 8.3 ×10 –17 Equivalence point : 0.05000M×V e ml = 0.10000M × 25.00ml V e = 50.00 ml Ksp = [Ag + ][I – ] = x 2 = 8.3 ×10 –17 [Ag + ] = [I – ] = x = 9.1×10 –9 pAg + = 8.04

63 Before the equivalence point : V < Ve [Ag + ] = Ksp / [I – ] = 8.3 ×10 –17 / [I – ] [I – ] = (fraction remaining) (original concentration) (dilution factor) =[(V e –V) / V e ] [M] [V i / (V i +V)] if V= 10.00ml, [I – ] = [(50.00–10.00)/50.00](0.1000M)[25.00/(25.00+10.00)] = 0.05714 M [Ag + ] = Ksp / [I – ] = 8.3 ×10 –17 / 0.05714 = 1.45 ×10 –15  pAg + = 14.84 After the equivalence point : V > V e [Ag + ] = (original concentration) (dilution factor) = [M] [(V–V e ) / (V i +V)] if V= 52.00ml, [Ag + ] = 0.05000M ×(52.00 –50.00)/(25.00+52.00) = 1.30×10 –3  pAg + = 2.89

64 Factors influencing the sharpness of end points 1) Reagent concentration [T], [A]   e T  2) Completeness of reaction Solubility   e.p. change jump  I – Ksp=8.3 ×10 –17 Br – Ksp=5.0 ×10 –13 Cl – Ksp=1.8 ×10 –10 IO 3 – Ksp=3.0×10 –8 BrO 3 – Ksp=5.7×10 –5

65 Titration of a mixture by potentiometric detection Two precipitable ions (ex. Cl –, I – ) Titrant (ex. Ag + ) Ex. 0.0502M KI + 0.0500M KCl 0.0845 M AgNO 3 Ksp AgI << Ksp AgCl 8.3×10 –17 1.8 ×10 –10 Coprecipitation [Ag + ][Cl – ] / [Ag + ][I – ] = [Cl – ] / [I – ] = 8.3×10 –10 /1.8×10 –17 = 1/ 4.6 ×10 –7

66 Titration curves for 50.0 ml of a solution 0.0800 M in Cl  and 0.0500 M in I  or Br .

67 End point detection in argentometric titration  Detection techniques in precipitation titrations :  Indicator  Potentiometry  Light scattering / turbidimetry of nephelometry Titration Mohr Volhard Fajans Titration Ag + + Cl –  AgCl  Ag + + Cl –  AgCl  Ag + + Cl –  AgCl  reaction white Back titration : Ag + + SCN –  AgSCN  white End point 2Ag + + CrO 4 2–  Ag 2 CrO 4  SCN – + Fe 3+  FeSCN 2+ Electric double layer reaction red soluble red with adsorption Ind. pH 7~10.5 K f = 1.05×10 3 Dichlorofluorescein Use Cl –, Br –, CN – Cl –, Br –, I – Cl –, Br –, I –, SCN – No use I –, SCN –

68 AgCl = Ag + + Cl – [Ag + ][Cl – ] = Ksp = 1.82×10 –10 [Ag + ] = 1.35 ×10 –5 M Ag 2 CrO 4 = 2Ag + + CrO 4 2– [Ag + ] 2 [CrO 4 2– ] = Ksp = 1.2 ×10 –12 [CrO 4 2– ] = Ksp / [Ag + ] 2 = 1.2 ×10 –12 / (1.35 ×10 –5 ) 2 = 6.6×10 –3 M Fe 3+ + SCN –  FeSCN 2+ (red) K f = [FeSCN 2+ ] / [Fe 3+ ] [SCN – ] = 1.05 ×10 3

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70 Table 13-3, p.362

71 Summary Complex, complexometric titration, Chelate, chelating agent Chelate effect : entropy effect Coordination number, monodentate, multidentate Formation constant : stability constant EDTA Conditional formation constant Auxiliary complexing agent Metal ion indicator Masking, demasking Turbidimetry, nephelometry, Light scattering Lamber-Beer’s law Titration curve, potentiometry Argentometry, Mohr, Volhard, Fajans titration Adsorption indicator


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