Chapter 11 EDTA Titrations

11-1 Metal-Chelate Complexes (Chapter 6) Metal ion (M) + Ligand (L) = Complexes (ML) Lewis acid Lewis base Electron-pair Electron-pair coordination acceptor donor compound Adduct Monodentate: ( )– Multidentate: BOX 6-2 Notation For Formation Constants - Complex formation reaction is stepwise reaction • • • • • • K : formation constant (Kf, or stability constant) • • • • • • βn: overall(cumulative) formation constant

• Chelating ligand (or Chelates) ; bind to a metal ion through more than one donor atoms in a single ligand. (multidentate ligand)       Ex)  bidentate, tetradentate, pentadentate, hexadentate, … H2NNH2: Bidentate ligand EDTA: Hexadentate ligand Chelating ligand Macrocycles (Ionophore) Mn+ Mn+ Mn+

2 ethylenediamine molecules binds tighter than 4 methylamine molecules Chelate effect: ability of multidentate ligands to form stronger metal complexes compared to monodentate ligands. (Bidentate ligand) (11-1) (Monodentate ligand) (11-2) 2 ethylenediamine molecules binds tighter than 4 methylamine molecules ⇒ Larger K value for multidentate ligand (Chelate increase the stability of complex.)

The octadentate ligand in Figure 12-3 is being evaluated as an anticancer agent.5 The chelate is covalently attached to a monoclonal antibody, which is a protein produced by one specific type of cell in response to one specific foreign substance called an antigen.

11-2 EDTA Acid-Base Properties EDTA (Ethylenediaminetetraacetic acid) One of the most common chelating agents as a titrant. EDTA has 2N & 4O in its structure giving it 6 free electron pairs. High Kf values with metal ions, - polyprotic acid H6Y2+ - Neutral acid(H4Y) - Commonly used EDTA reagent : Na2H2Y∙2H2O (Na2EDTA∙2H2O) (⇒ Reagent grade, dried to the composition Na2H2Y∙2H2O at 80℃)

H6Y2+ H5Y+ H4Y H3Y- H2Y2- HY3- Y4- Low pH High pH Acid-Base Forms - EDTA exists in up to 7 different acid-base forms depending on the solution pH. - The most basic form (Y4-) is the one which primarily reacts with metal ions. Fractional composition diagram for EDTA

Fraction of EDTA in the form Y4- (=αY4-) ☞ Fraction (α) of the most basic form of EDTA(Y4-) is defined by the H+ concentration and acid-base equilibrium constants. where [EDTA] is the total concentration of all free EDTA species in solution (11-3) (11-4) αY4- is depended on the pH of the solution Ex) αY4- of 0.10 M EDTA at pH 6.00? Sol) at pH 6.00→[Y4-]=1.0×10-6M

EDTA Complexes The basic form of EDTA (Y4-) reacts with most metal ions to form a 1:1 complex. (Other forms of EDTA will also chelate with metal ions) (11-5) Note: This reaction only involves Y4-, but not the other forms of EDTA ⇒The equilibrium constant for the reaction of a metal with a ligand is called the formation constant (Kf) or the stability constant: Recall: the concentration of Y4- and the total concentration of EDTA ([EDTA]) are related as follows: where αY4-is dependent on pH (From table value)

The basic form of EDTA (Y4-) reacts with most metal ions to form a 1:1 complex. +n ion: Mn+ + Y4- MYn-4 Kf

Conditional formation constant (Kf : Table 11-2) (αY4- : Table 11-1) where [EDTA] is the total concentration of EDTA added to the solution not bound to metal ions (11-6) Kf’: Conditional formation constant (at given pH) ⇒ If pH is fixed by a buffer, then αY4- is a constant (Table 11-1) that can be combined with Kf (Table 11-2)  evaluate Kf‘ ⇒ Kf‘ is constant for a given pH

Using the Conditional Formation Constant Example Using the Conditional Formation Constant What is the concentration of free Ca2+ in a solution of 0.10 M CaY2- (Kf=1010.65) at pH 10.00 and at pH 6.00 ? Solution Ca2+ + EDTA CaY2- at pH 10.00 : Kf’=(1010.65)(0.30)=1.3×1010 at pH 6.00 : Kf’=(1010.65)(1.8×105)=8.0×105 Ca2+ + EDTA CaY2- Initial conc.(M) 0 0 0.10 Final conc.(M) x x 0.10-x ∴x=[Ca2+] = 2.7×10-6 M (at pH 10.00 ) = 3.5×10-4 M (at pH 6.00 ) ☞ M-EDTA complexes becomes less stable at lower pH (higher concentration of [Ca2+] at lower pH)

Complexometric Titrations are based on the reaction of a metal ion with a chemical agent(ligand) to form a metal-ligand complex. - Determination of metal ion concentration - Standard solution: chelating agent Ligand forms strong 1:1 complexes with most metal ion (The stoichiometry is 1:1 regardless of the charge on the ion) ☞Higher Kf  complete titration reaction (~99.9%) at the equivalence point

Minimum pH for Effective Titration of Metal Ions pH effect on EDTA titration Note that the metal–EDTA complex becomes less stable as pH decreases and Kf decreases. [Ca2+]=2.7×10-6 M at pH 10.0 [Ca2+]=3.5×10-4 M at pH 6.0 Minimum pH for Effective Titration of Metal Ions In order to get a “complete”(say, 99.9%) titration, EDTA requires a certain minimum pH for the titration of each metal ion. Ex) pH effect for the titration of Ca2+ ⇒ Below pH≈8, the end point is not sharp enough to allow accurate determination. (∵The K for CaY2- is just too small for “complete” reaction at low pH.)

11-3 EDTA Titration Curves The titration of a metal ion with EDTA is similar to the titration of a strong acid (Mn+) with a weak base (EDTA) Mn+ + EDTA MYn-4 (11-7) Titration curve (VEDTA vs. pM) The titration curve has three distinct regions: Region 1: Before the equivalence point : excess Mn+ left : calculation unreacted Mn+ (free Mn+) Region 2: At the equivalence point : exactly as much EDTA as metal : calculation free Mn+ from dissociation of MYn-4 ([EDTA]=[Mn+]) Region 3: After the equivalence point : excess EDTA left : calculation free Mn+ from dissociation of MYn-4

Titration reaction: Ca2+ + EDTA → CaY2- Titration Calculations Ex. Construct the titration curve for 50.0 ml of a 0.0400 M Ca2+ solution (buffered at pH 10.00) with 0.0800 M EDTA Titration reaction: Ca2+ + EDTA → CaY2- (From Table 11-2, 11-3) Kf(CaY2-)=1010.65 , αY4-=0.30 (at pH 10) ⇒ Kf’ is large, the reaction goes to completion with each addition of titrant. ☞ The equivalence volume (Ve) is, mmol Ca2+ mmol EDTA Titration curve: pCa2+ vs. VEDTA

Before the Equivalence Point Ex. 50.0 ml of a 0.0400 M Ca2+ (at pH 10.00) with 5.00 mL of 0.0800 M EDTA mmoles of Ca2+=original mmoles of Ca2+ – mmoles of EDTA added Volume is 55.00 mL (=50.00 mL + 5.00 mL) At the Equivalence Point Ex. 50.0 ml of a 0.0400 M Ca2+ (at pH 10.00) with 25.00 mL of 0.0800 M EDTA - Virtually all of the metal ion is now in the form CaY2- (∵Kf≫1) Just enough EDTA has been added to consume Ca2+ pCa determined by dissociation of CaY2- Ca2+ + EDTA CaY2- Initial conc.(M) 0 0 0.0276 Final conc.(M) x x 0.0276-x x=[Ca2+]=1.4×10-6 M ⇒ ∴pCa2+ = -log(1.4×10-6) = 5.85

After the Equivalence Point Ex. 50.0 ml of a 0.0400 M Ca2+ (at pH 10.00) with 26.00 mL of 0.0800 M EDTA ☞ Virtually all of the metal ion is now in the form CaY2- and there is excess, unreacted EDTA.  A small amount of free Ca2+ exists in equilibrium with CaY2- and EDTA. - Calculate excess, unreacted moles of EDTA: mmols of total EDTA – mmoles of Ca2+ =(26.00mL)(0.080) – (50.0mL)(0.040) = 0.08mmol - Calculate excess, unreacted [EDTA]: - Calculate [CaY2-]: Ca2+ + EDTA CaY2- Initial conc.(M) 0 0.00105 0.0263 Final conc.(M) x 0.00105+x 0.0263-x

The Titration Curve : Ca2+ and Sr2+ show a distinct break at the equivalence point, where the slope is greatest. Kf’ & pH effects on titration - The equivalence point is sharper for Ca2+ than Sr2+. This is due to Ca2+ having a larger Kf’. - If the pH is lowered, the Kf’ decrease (because αY4- decrease), and the end point becomes less distinct. ⇒ The completeness of these reactions is dependent on αY4- and correspondingly pH. ⇒ The pH cannot be raised arbitrarily high, because metal hydroxide precipitate. The pH is an important factor in setting the completeness and selectivity of an EDTA titration.

11-5 Auxiliary Complexing Agents Metal Hydroxide (M(OH)x) : In general, as pH increases a titration of a metal ion with EDTA will have a higher Kf. ⇒ Larger change at the equivalence point as pH increases. ⇒ Exception: If Mn+ reacts with OH- to form an insoluble metal hydroxide Auxiliary Complexing Agents: a ligand can be added that complexes with Mn+ strong enough to prevent hydroxide formation. - Binds metal weaker than EDTA(⇒Auxiliary complexing agents are displaced by EDTA during the titration). - Ammonia, tartrate, citrate or triethanolamine, ….. Ex) Zn2+ in ammonia buffer (pH 10.00) to prevent Zn(OH)2(s) - At pH=10.00 ([OH-]=104 M), Ksp(Zn(OH)2)=3.0×1016=[Zn2+](104)2 ⇒[Zn2+]=3.0×108 M →[Zn2+] should be less than 3.0×108 M to prevent Zn(OH)2(s) ☞ Fix the pH 10.00 for Zn2+ solution, i) by OH-: [Zn2+]>3.0×108 M→Zn(OH)2 precipitation→titration (X) ii) By ammonia buffer: soluble Zn-NH3 complex ion→titration (O) ⇒ Ammonia complexes the metal ion to keep it in solution at pH 10.

Metal-Ligand Equilibria - Consider a metal ion that form two complexes with the auxiliary complexing ligand L: (11-13) (11-14) βn: overall(cumulative) formation constant Fraction of free metal ion(αM): the fraction of metal ion in the uncomplxed state (11-15) [M]: conc. of metal ion in the uncomplxed state Mtot: total conc. of all forms M (=M, ML, ML2) (11-16) ⇒ depends on the equilibrium constants or cumulative formation constants

Ex) Example Ammonia Complexes of Zinc Calculate αZn2+ in ammonia buffer (NH3=0.10M) solution. ⇒ All Zinc species: Zn2+, Zn(NH3)2+, Zn(NH3)22+, Zn(NH3)32+, Zn(NH3)42+ Solution From Appendix I [Zn(NH3)2+] Zn2+ + NH3 → Zn(NH3)2+ β1= =102.18 [Zn2+][NH3] [Zn(NH3)22+] Zn2+ + 2NH3 → Zn(NH3)22+ β2= =104.43 [Zn2+][NH3]2 [Zn(NH3)22+] Zn2+ + 3NH3 → Zn(NH3)32+ β2= =106.74 [Zn2+][NH3]2 [Zn(NH3)22+] Zn2+ + 4NH3 → Zn(NH3)42+ β2= =108.70 [Zn2+][NH3]2 Zntot = [Zn2+]+[Zn(NH3)2+]+[Zn(NH3)22+]+[Zn(NH3)32+]+[Zn(NH3)42+] = [Zn2+]/ (1+β1[NH3]+ β2[NH3]2 +β3[NH3]3 +β4[NH3]4) (11-17) L(=[NH3])=0.10M (⇒ Very little zinc is in the form Zn2+ in the presence of 0.10 M NH3)

EDTA Titration with an Auxiliary Complexing Agents In the presence of auxiliary complexing agents, use a new conditional formation constant that incorporates the fraction of free metal at a fixed pH. : at a fixed pH (consider αY4-) : at a fixed conc. of auxiliary complexing agent (consider αM) (11-18) K”f : Effective(or conditional) formation constant (☞ at a fixed pH and fixed conc. of auxiliary complexing agents)

Example EDTA Titration in the Presence of Ammonia Consider the titration of 50.0 mL of 1.00×103M Zn2+ with 1.00×103M EDTA at pH 10.00 in the presence of 0.10 M NH3. Find pZn2+ after addition of 20.0, 50.0, and 60.0 mL of EDTA. Solution - Y4 = 0.30 (pH=10, from Table 11-1) - Zn2+ = 1.8×105 (from Eq. 11-17) ⇒ Conditional formation constant (K”f) = αZn2+αY4-Kf = (1.8×105)(0.3)(1.00×1016.5) = 1.7×1011 (a) Before the equivalence point (20.0 mL of EDTA) - Zinc not bound to EDTA(CZn2+) is bound to ammonia: calculation CZn2+ mmoles of Zn2+ = original mmoles of Zn2+ - mmoles of EDTA added Volume is 70.00 mL (=50.00 mL + 20.00 mL) - The concentration of free Zn2+ ([Zn2+]) = (1.8×105)(4.3×10-4) = 7.7×10-9 M ∴ pZn2+ = -log[Zn2+] = 8.11 Check reality!: Zn(OH)2 precipitation at pH 10 in the presence of 0.10 M NH3.? (Ksp of Zn(OH)2) =10-15.52 ) Q=[Zn2+][OH-]2 = (10-8.11)(10-4.00)2 = 10-16.11 <10-15.52 ⇒ Do not precipitate Zn(OH)2(s).

(b) At the equivalence point (50.0 mL of EDTA) Zn2+ + Y4- = ZnY2 Kf” = (Zn2+)(Y4-)(Kf) = 1.7×1011 - Virtually all of the zinc ion is now in the form ZnY2- (∵Kf (ZnY2-) ≫ Kf Zn(NH3)x2+) Just enough EDTA has been added to consume Zn2+ pZn determined by dissociation of ZnY2- CZn2+ + EDTA = ZnY2- Initial conc.(M) 0 0 5.00×10-4 Final conc.(M) x x 5.00×10-4 – x ⇒ x = CZn2+ = 5.4×10-8 M - The concentration of free Zn2+ ([Zn2+]) ⇒[Zn2+] = Zn2+CZn2+ = (1.8×105)(5.4×10-8) = 9.7×10-13 M ∴pZn = -log[Zn2+] = 12.01

Titration curves and effect of auxiliary complexing agents (c) After the equivalence point (60.0 mL of EDTA) - Virtually all of the zinc ion is now in the form MgY2- and there is excess, unreacted EDTA  A small amount of free Zn2+ exists in equilibrium with ZnY2- and EDTA. - Calculate excess, unreacted [EDTA]: - Calculate [ZnY2-]: Zn2+ + EDTA = ZnY2- Initial conc.(M) 0 9.1×10-5 4.5×10-4 Final conc.(M) x 9.1×10-5+x 4.5×10-4-x (Not Kf”) Titration curves and effect of auxiliary complexing agents

11-6 Metal Ion Indicators Determination of EDTA Titration End Point - Four Methods: 1. Metal ion indicator (This chapter) 2. Mercury electrode 3. pH electrode 4. Ion-selective electrode Potential Measurements (Potential(V)=logM=pM, Ch. 14~16) ■ Metal Ion Indicator (In): a compound that changes color when it binds to a metal ion In + M MIn (blue) (red) : Similar to pH indicator, which changes color with pH (or as the compound binds H+) ⇒ For an EDTA titration, the indicator must bind the metal ion less strongly than EDTA : Similar in concept to Auxiliary Complexing Agents : Needs to release metal ion to EDTA Ex) In EDTA titration: Mg-In + EDTA Mg-EDTA + In (11-19) (red) (colorless) (colorless) (blue) Before eq. point At eq. point ⇒ End Point indicated by a color change from red to blue

: Most are pH indicators and can only be used over a given pH range : Most are pH indicators and can only be used over a given pH range. ⇒ Most indicators can be used only in certain pH ranges. Ex) Calmagite with metal ion (at pH 10):

- If a metal(M) does not freely dissociate from an indicator(In), the metal is said to block by the indicator (∵Kf(M-In)>Kf(M-EDTA) or slow reaction). Ex) For Eriochrome black T(EBT): 1) Direct titration of Cu2+, Ni2+, Co2+, Cr3+, Fe2+, Al3+ ⇒ impossible (∵blocking of EBT by stable M-In complex) 2) Back titration of Cu2+ ⇒ possible i) Add excess standard EDTA to Cu2+  Cu-EDTA+free EDTA ii) Add In; In cannot take Cu from already formed Cu-EDTA  Cu-EDTA+free EDTA+In iii) Titration of excess EDTA with standard Mg2+; Mg2+ can only take free EDTA (∵Kf (Mg2+-EDTA)<Kf (Cu2+-EDTA)  Cu-EDTA + Mg-EDTA + Mg-In ☞ Color change of back titration at end point? :Blue(In) to Red(Mg-In) (∵Kf (Mg2+-In)<Kf (Mg2+-EDTA)

Guide to EDTA titrations of some common metals; pH ranges, auxiliary complex agents, indicators Ex) Pb-EDTA titration; - Possible pH range for EDTA titration: pH 3 to 12 - Auxiliary complex agents are need to pH 9-12

11-7 EDTA Titration Techniques Almost all elements can be determined by EDTA titration. Some Common Techniques used in these titrations include: - Direct Titrations - Back Titrations - Displacement Titrations - Indirect Titrations - Masking Agents + pH control with buffer solution Direct Titrations • Analyte (metal ion) is buffered to appropriate pH and is titrated directly with standard EDTA. • Kf large • Metal ion indicator does not block the metal. • An auxiliary complexing agent may be required to prevent precipitation of metal hydroxide. Back Titrations • Approach necessary if analyte: - precipitates in the absence of EDTA (Ex. Al3+ at pH 7→ Al(OH)3(s)) - Reacts slowly with EDTA - Blocks the indicator • Second metal ion must not displace analyte from EDTA Step 1) A known excess of standard EDTA is added to analyte. ⇒Free EDTA left over after all metal ion is bound with EDTA Step 2) The remaining excess of EDTA is then titrated with a standard solution of a second metal ion.

Example A Back Titration Back titration of 25.00 mL of Ni2+ in dilute HCl with standard Zn2+ at pH 5.5 using xylenol orange indicator. ⇒ [Ni2+] = ? (∵ Nickel reacts too slowly with EDTA) Adding excess 25.00 mL Na2EDTA (0.05283M); [Ni-EDTA + free EDTA] Neutralized with NaOH  then, pH adjusted to 5.5 with acetate buffer; [Ni-EDTA + free EDTA] Indicator (xylenol orange, In) added: [Ni-EDTA + free EDTA + In] Titration of free EDTA with Zn2+(0.02299 M, 17.61 mL) at end point ; [Ni-EDTA + Zn-EDTA + Zn-In ] Solution mmol of EDTA added = (25.00 mL)(0.05283 M) = 1.3208 mmol mmol of free(unreacted) EDTA = (17.61 mL)(0.02299 M) = 0.4909 mmol ⇒ mmol of Ni2+ = mmol of EDTA added - mmol of free EDTA = 1.3208 - 0.4909 = 0.9151 mmol ∴ [Ni2+] = 0.9151 mmol/42.61 mL = 0.03664 M Ex) Back titration of Al3+: EDTA prevent precipitation of Al(OH)3 at pH 7 (formed stable Al3+–EDTA complex at pH 7)

Displacement Titration ☞ Used for some analytes that don’t have satisfactory metal ion indicators. Step1) Analyte (Mn+) is treated with excess Mg(EDTA)2-, causes release of Mg2+. (∵Kf(MgY2-)<Kf(MY2-) ⇒ MY2- + MgY2- + Mg2+) Step2) Amount of Mg2+ released is then determined by titration with a standard EDTA solution (∵Kf(MgY2-)<Kf(MY2-)  Concentration of released Mg2+ equals [Mn+] Step1: Mn+ + MgY2- ⇌ MYn-4 + Mg2+                                ↳ Step2: titrate with standard EDTA (11-20) Analyte excess Ex) Hg2+ titration Hg2+ + MgEDTA2- ⇌ HgEDTA2- + Mg2+ Then, Mg2+ is titrated with standard EDTA Ex) Ag+ titration 2Ag+ + Ni(CN)42- ⇌ 2Ag(CN)22- + Ni2+ Then, Ni2+ is titrated with standard EDTA

Indirect Titration ☞ Used to determine anions that precipitate with metal ion. Ex) CO32-, CrO42-, S2-, SO42- Step1) Anion is precipitated from solution by addition of excess metal ion - Ex) SO42- + excess Ba2+  BaSO4(s) (pH 1) - Precipitate(BaSO4(s)) is filtered & washed Step2) Precipitate(BaSO4) is then reacted with excess EDTA to bring the metal ion back into solution (boiled at pH 10)  BaEDTA2- + EDTA Step3) The excess EDTA is titrated with Mg2+ standard solution. Alternatively, Step1) Anion is precipitated from solution by addition of excess standard metal ion Step2) Excess standard metal ion in the filtrate is titrated with EDTA. BOX 11-3 Water Hardness • Hardness: the total concentration of alkaline earth ion(mainly Ca2+ and Mg2+) - unit: mg/L as CaCO3 :[Ca2+]+[Mg2+]=1mM→CaCO3=1mM→100mg CaCO3→hardness=100mg/L - Soft water: 0 to 60 mg/L as CaCO3, Hard water: ~270 mg/L as CaCO3 - Determination of hardness by EDTA titration [Ca2+]+[Mg2+]: pH=10 (ammonia buffer) [Ca2+]: pH=13 (without ammonia)(at pH 13, Mg(OH)2(s))

Masking • Masking Agents : A reagent added to prevent reaction of some metal ion with EDTA (⇒remove interferences of specific metal ion) Al3+ + 6F- → AlF63- ⇒Al3+ is not available to bind EDTA because of the complex with F- Requires: Ex) CN- masking: Cd2+ , Cu2+ , Ag2+ , Bi2+, ….. (CAUTION: CN- formed toxic HCN gas below pH 11) F- masking: Al3+, Fe3+, Ti+, Be2+ (CAUTION: HF formed by F- in acidic solution) Triethanolamine masking: Al3+, Fe3+, Mn2+ 2,3-Dimercaptopropanol masking: Bi3+, Cd2+, Cu2+, Hg2+, Pb2+ • Demasking: refers to the release of a metal ion from a masking agent Ex) Cyanide demasking with formaldehyde Masking, demasking, pH control ⇒ selective titration of individual metal ion from complex mixtures of metal ions