Types of chemistry

Although any type of chemical reaction may be used for titrimetric analysis, the most often used fall under the categories of:

Bronsted acid - base: HA + B ↔ HB+ + A-

Complex formation: M(aq) + nL(aq) ↔ MLn(aq)

Oxidation – reduction: Ox + Red ↔ Red’ + Ox’

Precipitation: M(aq) + nL(aq) ↔ MLn(s)

Lewis acid-base chemistry is often involved in precipitation and complex formation chemistry.

• Lewis acids are electron pair acceptors.

• Coordination complexes: metal compounds formed by Lewis acid-base interactions.

• Complexes: Have a metal ion (can be zero oxidation state) bonded to a number of ligands. Complex ions can be charged. Example, [Ag(NH3)2]+.

• Ligands are Lewis bases.

• Square brackets enclose the metal ion and ligands.

Metal ComplexesMetal Complexes

Complexation reactionsComplexation reactions

• Chelate or chelon effect: More stable complexes are formed with chelating agents than the equivalent number of monodentate ligands. This is due to entropy (randomness) of the reaction – the more molecules, the lower the entropy and vice-versa. The interaction from all the different sites together is quite strong.

[Ni(H2O)6]2+(aq) + 6NH3 [Ni(NH3)6]2+(aq) + 6H2O(l) Kf = 4 108

[Ni(H2O)6]2+(aq) + 3en [Ni(en)3]2+(aq) + 6H2O(l) Kf = 2 1018

• Sequestering agents are chelating agents that are used to remove unwanted metal ions.

• In medicine sequestering agents are used to selectively remove toxic metal ions (e.g. Hg2+ and Pb2+) while leaving biologically important metals.

Ligands with More than One Donor AtomLigands with More than One Donor Atom

• One very important chelating agent is ethylenediaminetetraacetate (EDTA).

• EDTA occupies 6 coordination sites, for example [CoEDTA]- is an octahedral Co3+ complex.

• Both N atoms (blue) and O atoms (red) coordinate to the metal.

• EDTA is used in consumer products to complex the metal ions which catalyze decomposition reactions.

Widely used chelator: (1) Direct titration

(2) Indirect determination through a sequence of reactions

* It forms 1:1 complexes with most metals.• (Not with Group 1A metals – Na, K, Li)

* Forms stable water soluble complexes.

* High formation constants.

• A primary standard material – a highly purified compound that serves as a reference material.

EDTAEDTA

HNCH2CH2NH

CH2CO2H

CH2CO2H

HO2CH2C

HO2CH2C

H6Y2+

•Highlighted, acidic protons lost upon metal complexation.

pK1 = 0.0

pK2 = 1.5

pK3 = 2.0

pK4 = 2.66

pK5 = 6.6

pK6 = 10.24

Hydroxylprotons

Ammoniumprotons

432

23452

6

4

4

YHYYHYHYHYHYH

YY

EDTA

YY

4

4

Fraction of EDTA in the form Y Fraction of EDTA in the form Y 4-4-

[EDTA] : Total concentration of all “free” uncomplexed EDTA species in solution.

654321543214321

2

321

3

21

4

1

56654321

4

KKKKKKKKKKKHKKKKHKKKHKKHKHH

KKKKKKY

Note that only the fully ionised , -4 – charged anion binds to metal ions

Fractional Composition Diagram for EDTAFractional Composition Diagram for EDTA

At this range Y4- predominates, thus titrations are routinely done in buffered solutions near or above pH 10.

Formation Constant or Stability Constant:

Equilibrium constant for the reaction of metal with a ligand.

44 nn MYYM ]][[

][4

4

YM

MYK

n

n

f

EDTA

YY

4

4 EDTAYY

44 Therefore,

EDTAM

MYK

Y

n

n

f

4

4

and

Conditional Formation ConstantConditional Formation Constant

Fixing the pH by buffering: Then 4Y is constant.

Thus, conditional formation constant:

]][[

][ 4'

4

EDTAM

MYKK

n

n

fYf

Consider EDTA complex formation as if the uncomplexed EDTA is in one form.

At any fixed pH, find 4Y and evaluate Kf’

Effective titration: *Reaction must go to completion.

*Large Kf

*Analyte and titrant essentially completely reacted at the equivalence point and:n(Metal) = n(Titrant)

*pH and thus Kf’ dependent

*Metals with higher Kf values can be titrated at lower pH

Effect of pH on EDTA Titration of Ca Effect of pH on EDTA Titration of Ca 2+2+

Less distinctend point

EDTA Titration CurvesEDTA Titration Curves

Titration reaction: 4 nn MYEDTAM fYf KK 4'

For large Kf’: Reaction complete at each point in the titration.

Titration curve: Plot pM (= -log[M]) vs. volume EDTA

EDTA Titration CurveEDTA Titration CurveRegion 1

Excess Mn+ left after each additionof EDTA. Conc. of free metal equal to conc. of unreacted Mn+.

Region 2

Equivalence point:[Mn+] = [EDTA]Some free Mn+ generated by MYn-4 Mn+ + EDTA

Region 3Excess EDTA. Virtually all metalin MYn-4 form.

ExampleExample

Consider the titration of 25.0 mL of 0.020 M MnSO4 with 0.010 M EDTA in a solution buffered at pH 8.00. Calculate pMn2+ at the following volumes of added EDTA and sketch the titration curve:

0 mL 50.0 mL20.0 mL 50.1 mL40.0 mL 55.0 mL49.0 mL 60.0 mL49.9 mL

Mn2+ + EDTA MnY2-

11133' 102.4)104.7)(106.5(4 xxxKK fYf

End point volume = 50.0 mL

Region 1

1. 0.0 mL EDTA:

0.020 M Mn2+:

p Mn2+ = -log[Mn2+] = -log(0.020) = 1.70

2. 20.0 mL EDTA:

0.45

0.25020.0

0.50

0.200.50][ 2Mn

FractionRemaining

OriginalMn2+ conc.

DilutionFactor

Initial Mn2+ volume

Total volume of solution

[Mn2+] = 0.00671 M pMn2+ = -log[Mn2+] = 2.18

Use same method to calculate pMn2+ for any EDTA volumebefore equivalence point (= 50.0 mL EDTA)

Region 2Region 2

At the Equivalence Point:

[Mn2+] = [EDTA] virtually all metal is in MnY2- form.

Assume negligible dissociation, then:

0.75

0.25)020.0(][ 2 MMnY

InitialMn2+ conc. Dilution

Factor

Initial Mn2+ volume

Total volume of solution

[MnY2-] = 6.67 x 10 –3 M

50.0 mL EDTA

Region 2Region 2 (continued)

At the Equivalence Point:

Mn2+ + EDTA MnY2-

Initial conc. - - 0.00667

Final conc. x x 0.00667 - x

11'2

2

102.4]][[

][xK

EDTAMn

MnYf

11'2

102.400667.0

xKx

xf

and

x = 3.98 x 10–8 M

pMn2+ = -log[Mn2+] = 7.40

Region 3Region 3

After the equivalence point: All Mn2+ in the MnY2- form& there is excess EDTA.

55.0 mL EDTA:

0.80

0.5)010.0(][EDTA

OriginalEDTA Conc. Dilution

Factor

Excess EDTAvolume

Total volumeof solution

[EDTA] = 6.25 x 10–4 M

0.80

0.25)020.0(][ 2 MMnY

InitialMn2+ conc.

DilutionFactor

Initial Mn2+ volume

Total volume of solution

[MnY2-] = 6.25 x 10–3 M

11'2

2

102.4]][[

][xK

EDTAMn

MnYf

11'

2102.4

00625.0][

000625.0xK

Mn f and

[Mn2+] = 2.31 x 10–14 M

pMn2+ = -log[Mn2+] = 13.62

Manganese Ion EDTA Titration

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Volume of 0.010 M EDTA Soln (mL)

pM

EDTA Titration Curves for Ca EDTA Titration Curves for Ca 2+2+ and Sr and Sr 2+2+

(Buffered at pH 10)(Buffered at pH 10)

*Ca*Ca2+2+ end point more distinct. end point more distinct.

*Lower pH, K*Lower pH, Kff’ decreases, &’ decreases, &

End point less distinct.End point less distinct.

*We cannot raise pH *We cannot raise pH arbitrarily:arbitrarily:

Metal hydroxides might precipitate.

Auxiliary Complexing AgentsAuxiliary Complexing Agents

*Ligand strongly binds to metal & prevents hydroxide precipitation at high pH.

*Auxiliary ligand binds less than EDTA binding to metal.

*NH3 normally used: NH3 fixes pH and complexes metal species

*Tartrate, citrate, or triethanolamine may be used.

Auxiliary Complexing AgentsAuxiliary Complexing Agents

Metal – Ligand EquilibriaMetal – Ligand Equilibria

M + L ⇌ ML ]][[

][1 LM

ML

M + 2L ⇌ ML2 22

2 ]][[

][

LM

ML

i = overall or cumulative formation constant

MM C

M ][*Fraction of uncomplexed metal ion, M:

CM is total concentration of all forms of metal

M = M, ML, and ML2.

CM = [M] + [ML] + [ML2]

Auxiliary Complexing AgentsAuxiliary Complexing Agents

Mass balance expression

]][[][ 1 LMML 222 ]][[][ LMML

221 ]][[]][[][ LMLMMCM

221 ][][1][ LLMCM

and

Therefore,

221 ][][1][

][

LLM

MM

2

21 ][][1

1

LLM

MM C

M ][

ExampleExample

Consider the titration of 50.0 mL of 0.00100 M Zn2+ with 0.00100 M EDTA at pH10 in the presence of 0.10 M NH3. (This is the concentration of NH3. There is Also NH4

+ in the solution.) Find pZn2+ after addition of 20.0, 50.0, and 60,0 mL of EDTA.

Note: We always assume that EDTA is a much strongercomplexing agent than NH3.

Kf for EDTA > Kf for NH3.

1 = 1.51 x 102, 2 = 2.69 x 104, 3 = 5.50 x 106, and 4 = 5.01 x 108

[L] = [NH3] = 0.10 M

SolutionSolution

Zn2+ - NH3 complexes:

Zn(NH3)2+, Zn(NH3)22+, Zn(NH3)3

2+, and Zn(NH3)42+

44

33

221 ][][][][1

12

LLLLZn

5108.12 x

Zn

Very little free Zn2+ in the presence of 0.10 M NH3. Most Zn2+ complexed by NH3

At pH 10, 36.04 Y

fYZnfZnf KKK 422'''

= (1.8 x10-5) (0.36) (1016.50) = 2.05 x 1011

0.70

0.5000100.0

0.50

0.200.502Zn

C

1. Addition of 20.0 mL EDTA sol’n:

= 4.3 x 10-4 M

MxxxCZnZnM

9452 107.7)103.4)(108.1(][ 2

pZn2+ = -log[Zn2+] = 8.11

2. Equivalence point: Addition of 50.0 mL EDTA:

0.100

0.50)00100.0(][ 2 MZnY = 5.00 x 10-4 M

11''2

4

1005.21000.5

xKx

xxf

X = 2ZnC =4.9 x 10-8 M

MxxxCZnZnM

13852 109.8)109.4)(108.1(][ 2

pZn2+ = -log[Zn2+] = 12.05

3. After the equivalence point: 60.0 mL EDTA

0.110

0.10)00100.0(][EDTA

0.110

0.50)00100.0(][ 2 MZnY

= 9.1 x 10-5 M

= 4.5 x 10-4 M

1650.16'2

2

101.1)10)(36.0(]][[

][4 xKK

EDTAZn

ZnYfYf

[Zn2+] = 4.3 x 10–16 M pMn2+= 15.36

Note: Past equivalence point problem independent on presence of NH3. Both [EDTA] and [ZnY2-] known.

EDTA Titrations at Different Concentrations of EDTA Titrations at Different Concentrations of Auxiliary Complexing Reagent (NHAuxiliary Complexing Reagent (NH33).).

Small pZn near equivalence point.

Significant pZn Near equiv. Point.(More distinct end point)

Metal Ion IndicatorsMetal Ion Indicators

At the end point:3. MgIn + EDTA MgEDTA + In(red) (colourless) (colourless) (Blue)

Before Titration:• Mg2+ + In MgIn (colourless) (blue) (red)

During Titration: Before the end point• Mg2+ + EDTA MgEDTA (free Mg2+ ions) (Solution red due to MgIn complex)

Compounds changing colour when binding to metal ion.Kf for Metal-In < Kf for Metal-EDTA.

EDTA Titration TechniquesEDTA Titration Techniques

1. Direct Titration

*Buffer analyte to pH where Kf’ for MYn-2 is large,*and M-In colour distinct from free In colour.

*Auxiliary complexing agent may be used.

2. Back Titration2. Back Titration

*Known excess std EDTA added.

*Excess EDTA then titrated with a std sol’n of a second metal ion.

*Note: Std metal ion for back titration must not displace analyte from MYn-2 complex.

2. Back Titration2. Back Titration: When to apply it: When to apply it

*Analyte precipitates in the absence of EDTA.

*Analyte reacts too slowly with EDTA.

*Analyte blocks indicator

3. Displacement Titration

*Analyte treated with excess Mg(EDTA)2-

Mn+ + MgYn-2 MYn-4 + Mg2+

* Kf’ for MYn-2 > Kf’ for MgYn-2

*Metal ions with no satisfactory indicator.

4. Indirect Titration

*Anions analysed: CO32-, CrO4

2-, S2-, and SO42-.

Precipitate SO42- with excess Ba2+ at pH 1.

*BaSO4(s) washed & boiled with excess EDTA at pH 10.

BaSO4(s) + EDTA(aq) BaY2-(aq) + SO42-(aq)

Excess EDTA back titrated:EDTA(aq) + Mg2+MgY2-(aq)

Alternatively: *Precipitate SO42- with excess

Ba2+ at pH 1.

*Filter & wash precipitate.

*Treat excess metal ion in filtrate with EDTA.

5. Masking

*Masking Agent: Protects some component of analytefrom reacting with EDTA.

*F- masks Hg2+, Fe3+, Ti4+, and Be2+.

*CN- masks Cd2+, Zn2+, Hg2+, Co2+, Cu+, Ag+, Ni2+, Pd2+, Pt2+, Hg2+, Fe2+, and Fe3+,

but not Mg2+, Ca2+, Mn2+, Pb2+.

*Triethanolamine: Al3+, Fe3+, and Mn2+.

*2,3-dimercapto-1-propanol: Bi3+, Cd2+, Cu2+, Hg2+, and Pb2+.

*Demasking: Releasing masking agent from analyte.

mHCOmHCNM mnm 2

mH2C

CN

OH

Mn+

Metal-CyanideComplex

Formaldehyde

*Oxidation with H2O2 releases Cu2+ from Cu+-Thiourea complex.

*Thus, analyte selectivity:1. pH control2. Masking3. Demasking