Complexometric titrations

many metals form complex with a ligand:Cu++ + NH3 ⇔ Cu(NH3)++ Kf1

Cu(NH3)2+ + NH3 ⇔ Cu (NH3)22+ Kf2

Cu (NH3)22+ + NH3 ⇔ Cu (NH3)3

2+ Kf3

Cu (NH3)32+ + NH3 ⇔ Cu (NH3)4

2+ Kf4

Zn (NH3) complexes vs lg NH3

α

• theoretically could titrate Zn withammonia

• stepwise Kf very similar

• difficult to know stoichiometry

• to ensure all one form, need excess NH3

• titration never gives good equivalencepoint

• can’t use monodentate ligand to titratemetals

Titrations with EDTA• use multidentate ligands e.g. EDTA

• tetraprotic, always forms 1:1 complexes

• different stabilities depending on metal

• usually use more soluable sodium form

Na2H2Y (H4Y is insoluble)

Example EDTA- metal complexMn-EDTA

Co-EDTA

EDTA complexes• 1:1 complexes

• can form up to six bonds using lone pairs ineach oxygen of --COOH and each N

• lone pairs donated into empty metal orbitals

• 1:1 mole ratio simplifies calculations• Most metal chelates - very stable - many sites

for bonding

• charge on EDTA-metal depends on metal & pH

EDTA - weak acid, ionizes stepwise

Fraction of NaEDTA species ƒ(pH)

• specie that reacts with metal depends on pH

Fraction of EDTA species ƒ(pH)- the last two protons

α

pH

The formation constant• vary pH of EDTA solution

• different forms of EDTA present

• smaller stability constant complexes needhigher pH to give particular form ofcomplex

• Y4- present at pH>10

• H4Y has low solubility in water

• Na2H2Y 2H2O usually used (i.e. two acidgroups neutralized) dissociates to H2Y

2-

to give a solution of pH 4-5

• lg formation constants for various metals

numbers largeso chelates strong

• metal chelates very stable - many sites forbonding

• charge on EDTA-metal complex dependson metal and pH

M+ + H2Y2- ⇔ MHY2- + H+

M2+ + H2Y2- ⇔ MY2- + 2H+

M3+ + H2Y2- ⇔ MY- + 2H+

M4+ + H2Y2- ⇔ MY + 2H+

species present inmoderately acid solution

differentmetals

• In neutral to moderately basic solutionsMn+ + HY3- ⇔ MY(n-4)+ + H+

Mn+ (Y4-)(n-4)+

• EDTA chelates with almost all cationsexcept alkali metals

• chelates sufficiently stable for volumetricanalysis

• formation constants (next slide) refer to:Mn+ + Y4- ⇔ MY(n-4)+

KMY =MY (n− 4)+

[Mn +][Y 4− ]numbers largeso chelates strong

pH dependence of M-EDTA

• M-EDTA formation constant depends onpH because H+ competes with MYformationMn+ + HY3- ← MY(n-4)+ + H+

• add H+, eqn moves to LHS, and dependson Ka1

, Ka2, Ka3

, Ka4 and [EDTA] added

• [EDTA] known, but not concentrations ofindividual species

αY4- = fraction of EDTA as Y4- at a given pH

=

α can be calculated from K1, K2, K3, K4 and [H+](see Harris for the equations)

alpha

Y 4−

H4Y + H3Y− + H2Y

2− + HY3−

α =Y 4−

Ctot

where C tot is the total EDTA conc.

conditional formation constant

• αY4− modifies the formation constant forY4- to account for pH

• this gives the conditional formationconstant K'MY= α KMY

• KMY is stability constant for Y4-

α varies with pH

Effect of pH on K’ values for EDTA

Example titration curve calc.

• add EDTA (0.1M) to sample. Ca in 100 mLof solution of 0.1M Ca2+ at pH 10

• before titration pCa = -lg [Ca2+] =1.00

• before equiv point [Ca2+] ≈ unchelated Ca,as CaY dissociation is small

• i.e. [Ca] at start - [EDTA] reacted

• At equiv. point: pCa determined bydissociation of CaY at the given pH:

Example calc. cont.

• at equiv. all Ca2+ converted to CaY2-

• use KMY = [CaY2-]/[Ca2+] [Y4-] , which isthe formation constant for CaY2-

• KMY = [CaY2-]/[Ca2+] α C• C, the original concentration of EDTA

added, or the total conc. of all forms, isthe same as [Y4-] but modified by alpha toaccount for pH 10

• Hence: α KMY = [CaY2-]/[Ca2+] C

EDTA titration cont.

• mmoles of CaY2- formed = mmoles Ca atstart except for dissociation

• [CaY2-] = 10.0 mmoles/200 mL = 0.05 M

Started with0.1M x 100 mL

Started with100 mL, added100 mL EDTA atequiv. point

EDTA titration example, cont.

• CaY2- ⇔ Ca2+ + Y4-

• 0.05M - x x + x

• can neglect x comparted to 0.05M

• 0.05/x2 = 1.8 x 1010

• this is KMY (5 x 1010) x alpha (0.35)

• from which x = 1.7 x 10-6 M = [Ca2+]

• pCa = - lg 1.7 x 10-6 = 5.7

EDTA titrn, beyond equiv. pt.

• pCa is again determined by dissociationof chelate but volume has changedbecause of the addition of EDTA anddissociation of CaY2- will be smallerbecause of excess EDTA.

Titration curves EDTA vs Ca

• 100 mL 0.1M Ca

• 0.1 M Na-EDTA• pH 7 and pH 10

Shape of titration curves• The more stable the chelate (big KMY), equm

moves to RHS and the larger the end pointbreak

• Ca2+ + Y4- ⇔ CaY2-

• More stable chelate - lower pH at whichtitration can be performed (smaller loss due todissociation of complex)

Minimum pH to titrate metals

• points are pH atwhich K' is 106 foreach metal

• judged as minimumK' needed for sharpendpoint

• at high pH allmetals will titrate

• at most acidic onlyfirst group titrate

pH <4

pH 4-7

pH > 7

Groups of metals in different pH regions

Titration curves

• pH changes the equilibrium constant of the MYcomplex

• less stable complexes can only be titrated inbasic solution

• more stable complexes can be titrated in moreacid solution, without significant dissociation

• metals that don’t form a stable complex at lowpH will not interfere wit determination ofstable complexes

Titration of Ca with EdTA

• 25 ml Ca++, 5 mL pH 10 buffer, 2 mL MgY2-

complex, HIn indicator• CaY2- stronger complex than MgY2-, (KfCa > KfMg)• Ca2+ + MgY2- ⇔ CaY2- + Mg2+

• Mg2+ + HIn2- ⇔ MgIn + H+

blue red

• this frees the Mg++ which complexes the indicator

• have used up a small amount of Ca++ which is equal toMg++ comlexed with indicator

Titration of Ca with EDTA (cont.)

• Ca2+ + MgY2- ⇔ CaY2- + Mg2+

• Mg2+ + HIn2- ⇔ MgIn + H+

blue red

• During most of titration:• Ca2+ + Y4- ⇔ CaY2-

titrant

Ca2+ + MgY2- ⇔ CaY2- + Mg2+

Mg2+ + HIn2- ⇔ MgIn + H+

Ca2+ + Y4- ⇔ CaY2-

During most of the titration:

titrant

Just before the endpoint:

MgIn + Y4- ⇔ MgY2- + HIn2-

At end point, actually titrating Mg

Y2- is equivalent

to Y4-

Blank measurement

• Necessary because of the possiblepresence of Ca, Mg in the reagents not inthe sample or the Mg added as MgY2-

Masking Agents

• auxillary ligand that forms stablecomplex with potential interference• at pH=10, CN- masks

M= Co2+, Ni2+, Cu2+, Zn2+, Cd2+, Hg2+

M(CN)xy+

• masking agent complex has greaterstability constant than EDTA complex

Masking Agents

masking agent pH ions masked ions titrated

cyanide 10 Cu, Co, Ni, Zn, Cd, Hg, Pt, Pd

alkaline earths, rare earths, Pb, Mn

triethanolamine 10 Sn, Al, Fe Zn, Cd, Pb, Mn, rare earths

aluminum flouride 10 Al, alkaline earths,rare earths

Zn, Cd, Mn

6 Al, Ti Cu

ascorbic acid 2 Cu, Fe, Hg Bi, Th

Displacement of metal ions

• determine Fe3+:Fe3+ + MgY2- ⇔ FeY- + Mg2+

• liberated Mg2+ can be titrated with standardEDTA where:

• Mg2+ ≡ Fe3+

Titration of Hydrogen ion

• Mn+ + EDTA ⇔ M-EDTA + H+

excess

• liberated H+ can be titrated with NaOHwhere:

• H+ ≡ Mn+

Direct titration

• metal ion, adjust pH, masking agent,indicator in solution

• titrate with EDTA to endpoint

Back titration

• known excess of EDTA is added toanalyte

• excess EDTA titrated with std. soln. of asecond metal ion

• back titration necessary if analyteprecipitates in absence of EDTA

– reacts too slowly with EDTA

– blocks the indicator

Indirect titration

• anions that precipitate certain metals canbe analyzed with EDTA

• sulfate analyzed by precipitation withexcess Ba+2