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Ch 13 - EDTA Titrations

EthyleneDiamineTetraacetic Acid

Formation Constants, Kf

[M][L]

[ML]K MLLM f

4

32

23

12

332 1.9x10

]][NH[Cu

])[Cu(NHK )Cu(NHNHCu

3

32

3

223

22233

23 3.6x10

])][NH)[Cu(NH

])[Cu(NHK )Cu(NHNH)Cu(NH

2

3223

233

32333

223 7.9x10

]][NH)[Cu(NH

])[Cu(NHK )Cu(NHNH)Cu(NH

2

3233

243

42433

233 1.5x10

]][NH)[Cu(NH

])[Cu(NHK )Cu(NHNH)Cu(NH

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EDTA Formation Constants

EDTA is a hexaprotic weak acid that complexes 1:1 with metal cations -

Notice that the first 4 protons are much more acidic than the last two, so the dominant form of EDTA in solution will be H2Y

2- ....

Mn+ + H2Y2- = MYn-4 + 2H+

By Le Chatelier's Principle, the complex will dissociate at low pH's, and it will be more stable at high pH's.

EDTA titrations are therefore pH dependent and analyte solutions must be buffered to the optimum pH.

low pH

high pH

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from "Fundamentals of Analytical Chemistry", Skoog and West, 4th ed.

Minimum pH for Titration

The pH-Dependent Metal-EDTA Equilibrium (Sec. 12-5 and Sec 13-5)

Fractional Composition Equations - the fraction (percentage) of each species of an acid or base existing at a given pH

HA = H+ + A- CT = [HA] + [A-]

A- = fraction of HA dissociated to A-

TC

][A

][A[HA]

][A

HA = fraction of HA still existing as HA

TC

[HA]

][A[HA]

[HA]

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[HA]

]][A[HK ,AHHA for a

[HA]

]][A[HK ,AHHA for a

the mass balance equation is -

rearranging and substituting into Ka -

T-

HA C ][A [HA] C

[HA]C ][A T

[HA]

[HA])-](C[HK T

a

][HA][H-]C[HK [HA] Ta

solve for [HA] -

][HA][H-]C[HK [HA] Ta Ta ]C[H][HA][HK [HA] so

][HK

][H

C

[HA]

aT

][HK

][Hα so

a

HA

to solve for A- substitute [HA] = CT - [A-] into Ka

][A-C

]][A[H

[HA]

]][A[HK

-T

a

]][A[H])K[A-(C so a-

T

]][A[H]K[A-KC a-

aT a

-aT ]K[A]][A[HKC and

)aaT K ]]([H[AKC

Ta

a

C

][A

K ][H

K so

][HK

Kαfinally so

a

a-A

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Fractional Composition Diagram for Monoprotic Acids

cross where pH = pKa

][HK

Kα

a

a-A

][HK

][Hα

a

HA

Fractional Composition Diagrams for Polyprotic Acids: General Forms

diprotic triprotic

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Fractional Composition Diagram H2CO3

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12 14

pH

alp

ha

Fractional Composition Diagram H3PO4

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12 14

pH

alp

ha

Ka1 = 4.46 x 10-7

Ka2 = 4.69 x 10-11

Ka1 = 7.11 x 10-3

Ka2 = 6.34 x 10-8

Ka3 = 4.50 x 10-13

Fractional Composition Diagrams for EDTA

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Conditional (Effective) Formation Constant, K'f

For EDTA titration curves, it's convenient to base calcuations on the Y4- form of EDTA and derive a new, pH-dependent formation constant K'f

]][Y[M

][MYK MYYM

4n

4n

f4n4n

CT = all forms of EDTA (Y4-, HY3- etc)

][YCα therefore and C

][Yα 4

TY4

T

4

Y4

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TY4n

4n

4n

4n

fC]α[M

][MY

]][Y[M

][MYK into ngsubstituti

Tn

4n

Y4f

TY4n

4n

f]C[M

][MYαK or

C]α[M

][MYKfinally and

Tn

4n

Y4f'f

]C[M

][MYαK K constant formation lconditiona the

All EDTA equilibrium calculations will use K'f at the pH of the titration. The value of Y4- at this pH is taken from Table 13-3.

Example, p. 300

The formation constant for FeY- is 1.3 x 1025

(Fe3+). Calculate the concentration of free Fe3+

in a solution of 0.10 M FeY- at pH = 4.00 and pH = 1.00.

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EDTA Titration Curves, Sec 13-6

A complex formation titration curve plots pM (analogous to pH) vs. volume of titrant (see next slide). To save time, we will only calculate the pM = -log[Mn+] at the equivalence point in order to select the correct indicator.

8

4n

4n

f2-42 10 x 6.2

]][Y[M

][MYK MgYYMg e.g.

Y4f'f αK K

p.302 - Calculate the titration curve for the reaction of 50.0 mL of 0.0500 M Mg2+, buffered to a pH of 10.0, with 0.0500 M EDTA. The equivalence pt. volume is 50.0 mL.

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At the equivalence pt. virtually all of the Mg is in the form MgY2-.

2-42 MgY Y Mg

Initial:

Change:

Equilibrium:

[MgY2-] at the eq. pt. =

The ICE table for the reaction is:

Kf CaY2- > Kf MgY2- so the endpoint is sharper for Ca2+

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The equiv. pt. becomes sharper as the pH of the titration approaches the optimal value for the analyte, e.g. for Ca2+…..

The equiv. pt. becomes sharper as the Kf of the EDTA-metal complexes becomes larger…..

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H2In- + H2O = HIn2- + H3O+ pKa2 = 8.1

red blue

HIn2- + H2O = In3- + H3O+ pKa3 = 12.4

blue orange

end point reaction with metal cation…..

MIn- + Y4- = MY2- + In3- Kf < Kf analyte

red blue

In the titration of Ca, Mg is added to the titrant in order to sharpen the end point.