1. Chapter 11 EDTA Titrations

2. 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 Notation For Formation Constants
- Complex formation reaction is stepwise reaction
• • •
• • •
K : formation constant (Kf, or stability constant)
• • •
• • •
βn: overall(cumulative) formation constant

3. • 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+

4. 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.)

5. 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.

6. 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℃)

7. 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

8. 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

9. 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)

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

11. 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

12. 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= ) at pH and at pH 6.00 ?
Solution
Ca2+ + EDTA CaY2-
at pH : Kf’=( )(0.30)=1.3×1010
at pH 6.00 : Kf’=( )(1.8×105)=8.0×105
Ca2+ + EDTA CaY2-
Initial conc.(M)
Final conc.(M)
x x x
∴x=[Ca2+] = 2.7×10-6 M (at pH )
= 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)

13. 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

14. 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 [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.)

15. 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

16. Titration reaction: Ca2+ + EDTA → CaY2-
Titration Calculations
Ex. Construct the titration curve for 50.0 ml of a M Ca2+ solution (buffered at pH 10.00) with M EDTA
Titration reaction: Ca2+ + EDTA → CaY2-
(From Table 11-2, 11-3)
Kf(CaY2-)= , 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

17. Before the Equivalence Point
Ex ml of a M Ca2+ (at pH 10.00) with 5.00 mL of M EDTA
mmoles of Ca2+=original mmoles of Ca2+ – mmoles of EDTA added
Volume is mL (=50.00 mL mL)
At the Equivalence Point
Ex ml of a M Ca2+ (at pH 10.00) with mL of 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-
Ca EDTA CaY2-
Initial conc.(M)
Final conc.(M)
x x x
x=[Ca2+]=1.4×10-6 M ⇒ ∴pCa2+ = -log(1.4×10-6) = 5.85

18. After the Equivalence Point
Ex ml of a M Ca2+ (at pH 10.00) with mL of 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 Ca =(26.00mL)(0.080) – (50.0mL)(0.040) = 0.08mmol
- Calculate excess, unreacted [EDTA]:
- Calculate [CaY2-]:
Ca2+ + EDTA CaY2-
Initial conc.(M)
Final conc.(M)
x x x

19. 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.

20. 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 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.

21. 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

22. 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)

23. 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)

24. 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 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 )
⇒ 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 mL (=50.00 mL 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) = )
Q=[Zn2+][OH-]2 = ( )( )2 = < ⇒ Do not precipitate Zn(OH)2(s).

25. (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 ZnY (∵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)
×10-4
Final conc.(M)
x x ×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

26. 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)
× ×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

27. 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

28. : 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):

29. - 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)

30. 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

31. 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.

32. Example
A Back Titration
Back titration of 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 mL Na2EDTA ( M); [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+( M, mL) at end point ; [Ni-EDTA + Zn-EDTA + Zn-In ]
Solution
mmol of EDTA added = (25.00 mL)( M) = mmol
mmol of free(unreacted) EDTA = (17.61 mL)( M) = mmol
⇒ mmol of Ni2+ = mmol of EDTA added - mmol of free EDTA
= = mmol
∴ [Ni2+] = mmol/42.61 mL = M
Ex) Back titration of Al3+: EDTA prevent precipitation of Al(OH)3 at pH 7
(formed stable Al3+–EDTA complex at pH 7)

33. 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
Hg 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

34. 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))

35. 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+, Be (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