COORDINATION CHEMISTRY (Complexation in Solution)

ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY

http://environmentalgeochemistry.pbworks.com//

COORDINATION CHEMISTRY (Complexation in Solution)

Bruce HerbertGeology & Geophysics



Sampling the Aqueous Phase

Soil Water

http://ianrpubs.unl.edu/fieldcrops/g964.htm




Soil Water

Soil water is classified into three categories: (1) excess soil water or gravitational water, (2) available soil water, and (3) unavailable soil water.



http://environmentalgeochemistry.pbworks.com// Complexation

Sampling the Aqueous PhaseSoil Water Retention Curves

In unsaturated soils, water is under tension and it takes energy to remove it from the soil.

As the water content of a soil decreases from the saturation point, the tension used to hold water increases.

The relationship of soil water content and soil water tension is represented in the Figure.


Curves like Figure 6 are called water retention or soil water characteristic curves. They are different for each soil because of differences in soil textures and structures.




■ Soil solution is the water and gaseous phase held in interstial pores at various tensions (negative pressures)

■ Soil solution samplers have to use negative pressure (suction) to retrieve soil solution. Different tensions will retrieve different volumes and chemistry of samples

■ Typical instruments: the lysimeters■ Tension lysimeter■ Zero-tension lysimeter■ Vacuum extractor■ Pan and deep pressure vacuum lysimeters■ Porous ceramic samplers

Soils

Porous Cup

Solution inlysimeter barrel

Pump




■ Other methods■ Column displacement■ Centrifuge samples to extract solution■ Characterize saturated pastes. This is the only

method if the porous media is dry.■ Generally, all samplers are porous ceramic or teflon

bodies that can hold a tension.■ Preferably at the tension equal to the soil's field

moisture capacity.■ This creates a suction in the sample which

opposes capillary pressure.

Soils

www.usyd.edu.au/.../sphysic/waterlab/field.htm



Using Samplers■ Samplers need to be installed a year or so before use to

equilibrate system.■ Effects of spatial variability■ Small size of samplers may not incorporate large

heterogeneities■ Soils with macropores may require both tension and

zero-tension lysimeters to sample water in bulk soil and macropores

■ Application of vacuum: volatile components may be lost such as organics or CO2(g). This could change pH or redox■ pH changes of 0.28 to 0.44 pH units are common due to

CO2(g) degassing■ Ceramic cups can adsorb anions and possibly leach

cations. Clean ceramic cups with dilute acid with extensive washings with DI water

■ Teflon cups are less reactive than ceramic

www.usyd.edu.au/.../sphysic/waterlab/field.htm




Groundwater

■ Chemistry of water samples reflect the conditions in the groundwater over the entire screened interval. Samples can be taken from depth-integrated or depth-specific wells.■ Depth-integrated: Useful in identifying

regional patterns in GW chemistry, but misses variations over small depth scales. These variations are integrated into one sample.

■ Depth-specific: Useful in studying chemical processes in detail or producing 3D data sets.

A B DC

A: Depth-integrated well.B: Depth-specific well.C: Nested piezometers for depth-specific sampling.D: Depth-specific sampling using inflated packers to isolate a particular zone.



Groundwater Sampling

■ Sampling is concerned with contamination of the groundwater by drilling operations with drilling fluids, gravel pack or casing materials. It may take a long time for these disturbances to diminish.

■ Drilling mud can often change the cation exchange of the solid matrix, changing the cation distribution in GW.

■ Stagnant water in the well is usually flushed from the well before a sample is taken. Usually 3 or so well volumes are flushed from the well before a sample is taking. Too much flushing is wasteful and may result in drawing water from other formations.

■ When brought to the surface, GW is exposed to different physio-chemical conditions than in the subsurface. Major differences in O2 and CO2 can really affect GW chemistry.

■ O2 can redox of elements; CO2 affects alkalinity, carbonates, pH.



WHY IS CHEMICAL SPECIATION SO IMPORTANT?

■ The biological availability (bioavailability) of metals and their physiological and toxicological effects depend on the actual species present.■ Example: CuCO3

0, Cu(en)20, and Cu2+ all affect the growth of algae

differently■ Example: Methylmercury (CH3Hg+) is readily formed in biological

processes, kinetically inert, and readily passes through cell walls. It is far more toxic than inorganic forms.

■ Solubility and mobility depend on speciation.



Effect of free Cu2+ on growth of algae in

seawater.

Figure 6-20 from Stumm & Morgan



Common Metal SpeciesCation Acid Systems Alkaline Systems

Na+ Na+ Na+, NaHCO3°, NaSO4-

Mg2+ Mg2+, MgSO4°, org Mg2+, MgSO4°, MgCO3°

Al3+ org, AlF2+, AlOH2+ Al(OH)4-, org

Si4+ Si(OH)4° Si(OH)4°

K+ K+ K+, KSO4-

Ca2+ Ca2+, CaSO4°, org Ca2+, CaSO4°, CaHCO3+

Cr3+ CrOH2+ Cr(OH)4-

Cr6+ CrO4- CrO4-

Mn2+ Mn2+, MnSO4°, org Mn2+, MnSO4°, MnCO3°, MnHCO3+, MnB(OH)4+

Fe2+ Fe2+, FeSO4°, FeHPO4+ FeCO3°, Fe2+, FeHCO3+, FeSO4°

Fe3+ FeOH2+, Fe(OH)3°, org Fe(OH)3°, org

Ni2+ Ni2+, NiSO4°, NiHCO3+, org NiCO3°, NiHCO3+, Ni2+, NiB(OH)4+

Cu2+ org, Cu2+ CuCO3°, org, CuB(OH)4+, Cu[B(OH)4]4°

Zn2+ Zn2+, ZnSO4°, org ZnHCO3+, ZnCO3°, org, Zn2+, ZnSO4°, ZnB(OH)4+

Mo5+ H2MoO4°, HMoO4- HMoO4-, MoO42-

Cd2+ Cd2+, CdSO4°, CdCl+ Cd2+, CdCl+, CdSO4°, CdHCO3+

Pb2+ Pb2+, org, PbSO4°, PbHCO3+ PbCO3°, PbHCO3+, org, Pb(CO3)22-, PbOH+



DEFINITIONS

Coordination (complex formation) - any combination of cations with molecules or anions containing free pairs of electrons. Bonding may be electrostatic, covalent or a mix.

Central atom (nucleus) - the metal cation.Ligand - anion or molecule with which a cation forms complexes.Multidentate ligand - a ligand with more than one possible binding site.Chelation - complex formation with multidentate ligands.Multi- or poly-nuclear complexes - complexes with more than one central atom

or nucleus.

Aqueous Species Central IonSi(OH)4° Si4+

Al(OH)2+ Al3+

HCO3- H+ or CO32-



NH2

NH2

M

N

N

HO O

OH

O

OH

O

HO O

MULTIDENTATE LIGANDS

Oxalate (bidentate)

Ethylendiamine (bidentate) Ethylendiaminetetraacetic acidor EDTA (hexadentate)

O

O

O

O

M



ChelationNH2

NH2

Ni

H2N

H2N

Polynuclear complexes

Sb2S42-

OHHg

OHHg

OH

OHHg

2+

Hg3(OH)42+

Sb Sb

S

SS

S 2-



DEFINITIONS - II

Species - refers to the actual form in which a molecule or ion is present in solution.

Coordination number - total number of ligands surrounding a metal ion.Ligation number - number of a specific type of ligand surrounding a metal ion.Colloid - suspension of particles composed of several units, whereas in true

solution we have hydration of a single molecule, atom or ion.



FORMS OF OCCURRENCE OF METAL SPECIES

Free metalion

Inorganic ionpairs and

complexes

Organiccomplexes,

chelates

Metalsbound tohigh mol.

wt.species

Highlydispersedcolloids

Metalssorbed on

colloids

Cu2+ Cu2(OH)22+ Me-SR Me-lipids FeOOH Mex(OH)y

Fe3+ PbCO30 Me-OOCR Me- humic

acidFe(OH)3 MeCO3,

MeS,etc. onclays

Pb2+ CuCO30 Mn(IV)

oxidesFeOOH orMn(IV) on

oxidesNa+ AgSH0 Ag2S

Al3+ CdCl+

Zn2+ CoOH+

1000 Å100 Å10 Å



Coordination Numbers

Me

L

LL

L

MeL

L

L

LMe LL

MeL

L

L

LL

L

CN = 2 (linear)

CN = 4 (tetrahedral) CN = 6 (octahedral)

CN = 4 (square planar)

Coordination numbers 2, 4, 6, 8, 9 and 12 are most commonfor cations.



STABILITY CONSTANTS MEASURE THE STRENGTH OF COMPLEXATION

Stepwise constantsMLn-1 + L MLn

Cumulative constantsM + nL MLn

]][[][

1 LMLMLKn

nn

−

=

nn

n LMML

]][[][

=β

βn = K1·K2·K3···Kn



For a protonated ligand we have:Stepwise complexationMLn-1 + HL MLn + H+

Cumulative complexationM + nHL MLn + nH+

]][[]][[

1

*

HLMLHMLK

n

nn

−

+

=

n

nn

n HLMHML]][[]][[*

+

=β

The larger the value of the stability constant, the more stable the complex, and the greater the proportion of the complex formed relative to the simple ion.

STABILITY CONSTANTS MEASURE THE STRENGTH OF COMPLEXATION



STABILITY CONSTANTS FOR POLYNUCLEAR COMPLEXES

mM + nL MmLn

mM + nHL MmLn + nH+

nmnm

nm LMLM][][][

=β

nm

nnm

nm HLMHLM][][]][[*

+

=β

If m = 1, the second subscript on βnm is omitted and the expression simplifies to the previous expressions for mononuclear complexes.



Titration of H+ and Cu2+ with Ammonia and Tetramine (trien)




HYDROLYSIS

The waters surrounding a cation may function as acids. The acidity is expected to increase with decreasing ionic radius and increasing ionic charge. For example:

Zn(H2O)62+ Zn(H2O)5(OH)+ + H+

Hydrolysis products may range from cationic to anionic. For example:

Zn2+ ZnOH+ Zn(OH)20 (ZnO0)

Zn(OH)3- (HZnO2

-) Zn(OH)42- (ZnO2

2-)

May also get polynuclear species.Kinetics of formation of mononuclear hydrolysis products is rather fast,

polynuclear formation may be slow.



METAL HYDROLYSIS

■ The tendency for a metal ion to hydrolyze will increase with dilution and increasing pH (decreasing [H+])

■ The fraction of polynuclear products will decrease on dilution■ Compare

Cu2+ + H2O CuOH+ + H+ log *K1 = -8.0Mg2+ + H2O MgOH+ + H+ log *K1 = -11.4

][]][[

21*

+

++

=M

HMOHK



At infinite dilution, pH 7 so

CuOH+ = (1 + 10-7/10-8)-1 = 1/11 = 0.091MgOH+ = (1 + 10-7/10-11.4)-1 = 1/25119 = 4x10-5

Only salts with p*K1 < (1/2)pKw or p*βn < (n/2)pKw will undergo significant hydrolysis upon dilution. Progressive hydrolysis is the reason some salts precipitate upon dilution. This is why it is necessary to

add acid when diluting standards.

1*

2 ]][[][

][][][

][

KHMOHMOH

MOHMMOH

MOHMOH ++

+

+

++

+

+=

+=+

1*][1

1

KHMOH +

+=+



POLYNUCLEAR SPECIES DECREASE IN IMPORTANCE WITH DILUTION

Consider the dimerization of CuOH+:

2CuOH+ Cu2(OH)22+ log *K22 = 1.5

Assuming we have a system where:

CuT = [Cu2+] + [Cu(OH)+] + 2[Cu2(OH)22+]

we can write:

22*

2222

2

222

2

222

]))([2][(])([

][])([ K

OHCuCuCuOHCu

CuOHOHCu

T

=−−

= ++

+

+

+

So [Cu2(OH)22+] is clearly dependent on total Cu concentration!



HYDROLYSIS OF IRON(III)

Example 1: Compute the equilibrium composition of a homogeneous solution to which 10-4 (10-2) M of iron(III) has been added and the pH adjusted in the range 1 to 4.5 with acid or base.

The following equilibrium constants are available at I = 3 M (NaClO4) and 25°C:

Fe3+ + H2O FeOH2+ + H+ log *K1 = -3.05Fe3+ + 2H2O Fe(OH)2

+ + 2H+ log *β2 = -6.312Fe3+ + 2H2O Fe2(OH)2

4+ + 2H+ log *β22 = -2.91FeT = [Fe3+] + [FeOH2+] + [Fe(OH)2

+] + 2[Fe2(OH)24+]



Now we define: 0 = [Fe3+]/FeT; 1= [FeOH2+]/FeT; 2= [Fe(OH)2+]/FeT; and 22=

2[Fe2(OH)24+]/FeT.

⎟⎟⎠⎞

⎜⎜⎝⎛

+++= +

+

+++

222

*3

22

*1

*3

][][2

][][1][

HFe

HHKFeFeT

ββ

1

222

*0

22

*1

*

0 ][2

][][1

−

+++ ⎟⎟⎠⎞

⎜⎜⎝⎛

+++=H

FeHH

K T ββ

01][][

1][

22

2*

1*

0222

*20 =−⎟⎟⎠

⎞⎜⎜⎝⎛

+++ +++ HHK

HFeT ββ

Optional



These equations can then be employed to calculate the speciation diagrams on the next slide.

222

*20

22 ][2

+=HFeT β

][1

*0

1 +=HK

222

*0

2 ][ +=Hβ

This last equation can be solved for 0 at given values of FeT and pH. The remaining values are obtained from the following equations:

Optional



FeT = 10-4 M

%Fe

0

20

40

60

80

100

FeT = 10-2 M

pH1 2 3 4

%Fe

0

20

40

60

80

100

Fe3+

FeOH2+

Fe(OH)2+

Fe2(OH)24+

Fe3+

FeOH2+

Fe(OH)2+



Example 2: Compute the composition of a Fe(III) solution in equilibrium with amorphous ferric hydroxide given the additional equilibrium constants:

Fe(OH)3(s) + 3H+ Fe3+ + 3H2O log *Ks0 = 3.96Fe(OH)3(s) + H2O Fe(OH)4

- + H+ log *Ks4 = -18.7

Fe3+

log [Fe3+] = log *Ks0 - 3pH

Fe(OH)4-

log [Fe(OH)4-] = log *Ks4 + pH



FeOH+

Fe(OH)3(s) + 3H+ Fe3+ + 3H2O log *Ks0 = 3.96Fe3+ + H2O FeOH2+ + H+ log *K1 = -3.05Fe(OH)3(s) + 2H+ FeOH2+ + 2H2O log *Ks1 = 0.91

log [FeOH2+] = log *Ks1 - 2pH

Fe(OH)2+

Fe(OH)3(s) + 3H+ Fe3+ + 3H2O log *Ks0 = 3.96Fe3+ + 2H2O Fe(OH)2

+ + 2H+ log *β2 = -6.31Fe(OH)3(s) + H+ Fe(OH)2

+ + H2O log *Ks2 = -2.35

log [Fe(OH)2+] = log *Ks2 - pH



Fe2(OH)24+

2Fe(OH)3(s) + 6H+ 2Fe3+ + 6H2O 2log *Ks0 = 7.922Fe3+ + 2H2O Fe2(OH)2

4+ + 2H+ log *β22 = -2.912Fe(OH)3(s) + 4H+ Fe2(OH)2

4+ + 4H2O log *Ks22 = 5.01

log [Fe2(OH)24+] = log *Ks22 - 4pH

These equations can be used to obtain the concentration of each of the Fe(III) species as a function of pH. They can all be summed to give the total solubility.


http://environmentalgeochemistry.pbworks.com// ComplexationpH

0 2 4 6 8 10 12 14

log concentration

-15

-10

-5

0

5

Fe(OH)3(s)

Fe(OH)4-

Fe(OH)2+

FeOH2+

Fe2(OH)24+

Fe3+



Complexation & the HSAB Concept

■ Metal ions can be titrated by ligands in the same way that acids and bases can be titrated.

■ According to the Lewis definition, metal ions are acids because they accept electrons; ligands are bases because they donate electrons.

■ We can use the concepts of hard/soft acid and bases to predict propensity and stability of different complexation reactions.■ Like complexes like



Metal Complexationand Toxicity

Representative data illustrating the relationship between metal effects and metal ion characteristics. Responses range widely from enzyme inhibition (lactic dehydrogenase, LDH) (22) to toxicity of cultured turbot cells (23) to acute lethality of a crustacean (amphipod) (27) to chronic toxicity of mice (1) and Daphnia magna (8).

http://ehpnet1.niehs.nih.gov/docs/1998/Suppl-6/1419-1425newman/abstract.html



Complexation & the HSAB Concept

• If IP < 30 nm-1, then metal cations tend to formsolvation complexes with water

• If 95 > IP > 30 nm-1, then metal cations can repelprotons from solvating water molecules to form thehydroxide complexes.

• If IP > 95 nm-1, then repulsion is strong enough toform the oxyion species

• If Y < 25 nm, then metal cations tend to formelectrostatic bonds

• If 0.25 < Y < 0.32 nm, then the metal cations areborderline metals whose covalency depends onwhether specific solvent, stereochemical, andelectronic configurational factors are present

• If Y > 0.32 nm, then metal cations tend to formcovalent bonds

Ionic potential

Misono Softness



Figure 6-4a from Stumm and Morgan: Predominant pH range for the occurrence of various species for various oxidation states



Figure 6-4b from Stumm & Morgan: The linear dependence of the first hydrolysis constant on the ratio of the charge to the M-O distance (z/d) for four groups of cations at 25°C.



Correlation between solubility product of solid oxide/hydroxide and the first hydrolysis constant.




PEARSON HARD-SOFT ACID-BASE (HSAB) THEORY

■ Hard ions (class A)■ small■ highly charged■ d0 electron configuration■ electron clouds not easily deformed■ prefer to form ionic bonds

■ Soft ions (class B)■ large■ low charge■ d10 electron configuration■ electron clouds easily deformed■ prefer to form covalent bonds



Pearson’s Principle - In a competitive situation, hard acids tend to form complexes with hard bases, and soft acids tend to form complexes with soft bases.

In other words - metals that tend to bond covalently preferentially form complexes with ligands that tend to bond covalently, and similarly, metals that tend to bond electrostatically preferentially form complexes with ligands that tend to bond electrostatically.



Classification of metals and ligands in terms of Pearson’s (1963) HSABprinciple.Hard Borderline SoftAcids

H+

Li+ > Na+ > K+ > Rb+ > Cs+

Be2+ > Mg2+ > Ca2+ > Sr2+ >Ba2+

Al3+ > Ga3+

Sc3+ > Y3+; REE3+ (Lu3+ >La3+); Ce4+; Sn4+

Ti4+ > Ti3+, Zr4+ ≈ Hf4+

Cr6+ > Cr3+; Mo6+ > Mo5+ >Mo4+; W6+ > W4+; Nβ5+, T5+;Re 7+ > Re6+ > Re4+; V6+ > V5+

> V4+; Mn4+; Fe3+; Co3+; As5+;Sβ 5+

Th4+; U6+ > U4+

PGE6+ > PGE4+, etc. (Ru, Ir,Os)

Acids

Fe2+, Mn2+, Co2+, Ni2+,Cu2+, Zn2+, Pβ2+, Sn2+,As3+, Sβ3+, Bi3+

Acids

Au+ > Ag+ > Cu+

Hg2+ > Cd2+

Pt2+ > Pd2+

other PGE2+

Tl3+ > Tl+

Bses

F-; H2O, OH-, O2-; NH3; NO3

-;CO3

2- > HCO3-; SO4

2- > HSO4-;

PO43- > HPO4

2- > H2PO4-;

crβoxyltes (i.e., cette,oxlte, etc.);MoO4

2-; WO42-

Bses

Cl-

Bses

I- > Br-; CN-; CO;S2- > HS- > H2S;orgnic phosphines(R 3P); orgnic thiols(RP);polysulfide (SnS

2-),thiosulfte (S2O3

2-),sulfite (SO3

2-);HSe -, Se2-, HTe-, Te2-;AsS2

-; SβS2-



ION PAIRS VS. COORDINATION COMPLEXESION PAIRS

■ formed solely by electrostatic attraction

■ ions often separated by coordinated waters

■ short-lived association■ no definite geometry■ also called outer-sphere

complexes

COORDINATION COMPLEXES large covalent component to

bonding ligand and metal joined directly longer-lived species definite geometry also called inner-sphere

complexes



STABILITY CONSTANTS OF ION PAIRS CAN BE ESTIMATED FROM ELECTROSTATIC MODELS

For 1:1 pairs (e.g., NaCl0, LiF0, etc.)log K 0 - 1 (I = 0)

For 2:2 pairs (e.g., CaSO40, MgCO3

0, etc.)log K 1.5 - 2.4 (I = 0)

For 3:3 pairs (e.g., LaPO40, AlPO4

0, etc.)log K 2.8 - 4.0 (I = 0)

Stability constants for covalently bound coordination complexes cannot be estimated as easily.



COMPLEX FORMATION AND SOLUBILITY

■ Total solubility of a system is given by:[Me]T = [Me]free + S[MemHkLn(OH)i]

■ Solubilities of relatively “insoluble” phases such as: Ag2S (pKs0 = 50); HgS (pKs0 = 52); FeOOH (pKs0 = 38); CuO (pKs0 = 20); Al2O3 (pKs0 = 34) are probably not determined by simple ions and solubility products alone, but by complexes such as: AgHS0, HgS2

2- or HgS2H-, Fe(OH)+, CuCO30 and Al(OH)4

-.



Calculate the concentration of Ag+ in a solution in equilibrium with Ag2S with pH = 13 and ST = 0.1 M (20°C, 1 atm., I = 0.1 M NaClO4).

Ks0 = 10-49.7 = [Ag+]2[S2-]At pH = 13, [H2S0] << [HS-] because pK1 = 6.68 and pK2 = 14.0 so

ST = [HS-] + [S2-] = 0.1 M

][]][[10

214

2 −

−+− ==

HSSHK

14

2

10]][[][ −

−+− =

SHHS

][10

]][[1.0 214

2−

−

−+

+= SSH



[S2-] = 9.1x10-3 M[Ag+]2 = 10-49.7/10-2.04 = 10-47.66

[Ag+] = 10-23.85 = 1.41x10-24 MObviously, in the absence of complexation, the solubility of Ag2S is exceedingly low

under these conditions.The concentration obtained corresponds to ~1 Ag ion per liter. What happens if we take

100 mL of such a solution? Do we then have 1/10 of an Ag ion? No, the physical interpretation of concentration does not make sense here. However, an Ag+ ion-selective electrode would read [Ag+] = 10-23.85 nevertheless.

][11][10

][101.0 2214

213−−

−

−−

=+= SSS



Estimate the concentration of all species in a solution of ST = 0.02 M and saturated with respect to Ag2S as a function of pH (in other words, calculate a solubility diagram).

[Ag]T = [Ag+] + [AgHS0] + [Ag(HS)2-] + 2[Ag2S3H2

2-]Ks0 = [Ag+]2[S2-], but [S2-] = 2ST so

Ks0 = [Ag+]2 2ST

2

0][Ts

SKAg =+

Ag+ + HS- AgHS0 log K1 = 13.3AgHS0 + HS- Ag(HS)2

- log K2 = 3.87Ag2S(s) + 2HS- Ag2S3H2

2- log Ks3 = -4.82



]][[][ 0

1 −+=HSAg

AgHSK

TSAgAgHSK

1

0

1 ][][

+=

TSHS 1][ =−

][][ 110 += AgSKAgHS T

2

011

0][

T

sT S

KSKAgHS =

]][[])([

02

2 −

−

=HSAgHS

HSAgK ]][[])([ 022

−− = HSAgHSKHSAg

2

021

2122 ])([

T

sT S

KSKKHSAg =−



2

2232

3 ][][

−

−

=HS

HSAgKs

21

23

2232 ][ Ts SKHSAg =−

( ) 21

23

21

21211

2

0 21][ αααα TsTTT

sT SKSKKSK

SKAg +++=



0 2 4 6 8 10 12 14

log concentration

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

Ag+

AgHS0

Ag(HS)2-

Ag2S3H22-

pH = pK1(H2S)



0 2 4 6 8 10 12 14

log concentration

-10

-9

-8

-7

AgHS0

Ag(HS)2-

Ag2S3H22-

pH = pK1(H2S)

1

2

3

4

5



Region 1: AgHS0 and H2S0 are predominantAg2S(s) + H2S0 2AgHS0

log [AgHS0] = 1/2log [H2S0] + 1/2log K

0]log[

2

=⎟⎟⎠⎞

⎜⎜⎝⎛

∂∂

SH

T

pHAg

Region 2: Ag(HS)2- and H2S0 are predominantAg2S(s) + 3H2S0 2Ag(HS)2

- + 2H+

log [Ag(HS)2-] = 3/2log [H2S0] + 1/2log K + pH

1]log[

2

=⎟⎟⎠⎞

⎜⎜⎝⎛

∂∂

SH

T

pHAg



Region 3: Ag(HS)2- and HS- are predominant

Ag2S(s) + 3HS- + H+ 2Ag(HS)2-

log [Ag(HS)2-] = 3/2log [HS-] + 1/2log K - 1/2pH

2/1]log[−=⎟⎟⎠

⎞⎜⎜⎝⎛

∂∂

−HS

T

pHAg

Region 4: Ag2S3H22- and HS- are predominant

Ag2S(s) + 2HS- Ag2S3H22-

log [Ag2S3H22-] = 2log [HS-] + log K

0]log[=⎟⎟⎠

⎞⎜⎜⎝⎛

∂∂

−HS

T

pHAg



Region 5: Ag2S3H22- and S2- are predominant

Ag2S(s) + 2S2- + 2H+ Ag2S3H22-

log [Ag2S3H22-] = 2log [S2-] + log K - 2pH

2]log[2

−=⎟⎟⎠⎞

⎜⎜⎝⎛

∂∂

−S

T

pHAg



THE CHELATE EFFECT

■ Multidentate ligands are much stronger complex formers than monodentate ligands.

■ Chelates remain stable even at very dilute concentrations, whereas monodentate complexes tend to dissociate.



WHAT IS THE CAUSE OF THE CHELATE EFFECT?

Gro = Hr

o - TSr0

For many ligands, Hro is about the same in multi- and mono-dentate complexes,

but there is a larger entropy increase upon chelation!

Cu(H2O)42+ + 4NH3

0 Cu(NH3)42+ + 4H2O

Cu(H2O)42+ + N4 Cu(N4)2+ + 4H2O

The second reaction results in a greater increase in Sr0.



Figure 6-11 from Stumm and Morgan. Effect of dilution on degree of complexation.



Figure 6-12a from Stumm & Morgan. Complexing of Fe(III). The degree of complexation is expressed as pFe for various ligands at a concentration of 10-2 M. The complexing effect is highly pH-dependent because of the competing effects of H+ and OH- at low and high pH, respectively.



Figure 6-12b from Stumm & Morgan. Chelation of Zn(II).



METAL-ION BUFFERS

Analogous to pH buffers. Consider:Me + L MeL

][][][

LMeLKMe =

If we add MeL and L in approximately equal quantities, [Me] will be maintained approximately constant unless a large amount of additional metal or ligand is added.

If [MeL] = [L], then pMe = pK!



Example: Calculate [Ca2+] of a solution with the composition - EDTA = YT = 1.95x10-2 M, CaT = 9.82x10-3 M, pH = 5.13 and I = 0.1 M (20°C).

For EDTA, pK1 = 2.0; pK2 = 2.67; pK3 = 6.16; and pK4 = 10.26.

6.1042

2

10]][[][

==−+

−

CYKYC

CY 5.332 10]][[

][==−+

−

CHYKHYC

CHY

( )12

414

42

22

][

]][[][1][

][][][)(

−+

−+−−+

−−+

=

++=

++=

Ca

CaHYCaY

T

Ca

YHKKYKCa

CaHYCaYCaCai

α

TCa Ca

Ca ][ 2+

=



CaHYCaY

T

KKYHCaKYCaY

CaHYCaYYHYYHYHYHYii14

42421*4

4

243223

04

]][][[]][[)]([

][][][][][][][)(−−++−+−−

−−−−−−

++=

++++++=

1

1234

4

234

3

34

2

44

0

4

4*4

][][][][1][

][−++++

=

−

−

⎟⎟⎠⎞

⎜⎜⎝⎛

++++==∑ KKKK

HKKK

HKK

HKH

YH

Y

i

ii

Equations (i) and (ii) must be solved by trial and error. We know pH so we can calculate 4* directly. We can then assume that S[HiY4-i] YT - CaT. This permits us to calculate [Y4-] and then solve (i) for [Ca2+]. This approach leads to: [CaY2-] = 9.66x10-3 M; [CaHY-] = 1.09x10-4 M; [Ca2+] = 4.12x10-5 M; [Y4-] = 6.05x10-9 M; [H3Y-] = 3.07x10-5 M; [H2Y2-] = 8.8x10-3 M; [HY3-] = 8.21x10-4 M; [H4Y0] = 2.26x10-8 M.



MIXED COMPLEXES

Examples: Zn(OH)2Cl22-, Hg(OH)(HS)0, PdCl3Br2-, etc.Generalized complexation reaction:

M + mA + nB MAmBn

Snm

nnm

mnmnmnm MBMABMA loglogloglog +

++

+=

++βββ

Log S is a statistical factor. For example, the probability of forming MAB relative to MA2 and MB2 is S = 2 because there are two distinct ways of forming MAB, i.e., A-M-B and B-M-A. The probability of forming MA2B relative to MA3 and MB3 is S = 3.



In general, mixed complexes usually only predominate under a very restricted set of conditions.

!!)!(

nmnmS +

=

In simple cases we can use the following formula:



Figure 6-15 from Stumm and Morgan. Predominance of Hg(II) species as a function of pCl and pH. In seawater, HgCl42- predominates.



COMPETITION FOR LIGANDS

■ The ratio of inorganic to organic substances in most natural waters are usually very high.

■ Does a large excess of, say, Ca2+ or Mg2+, decrease the potential of organic ligands to complex trace metals?

■ Example: Fe3+, Ca2+ and EDTA

Fe3+ + Y4- FeY- log KFeY = 25.1Ca2+ + Y4- CaY2- log KCaY = 10.7

These data suggest that Fe3+ should be complexed by EDTA.



But, let us combine the two above expressions to get:CaY2- + Fe3+ FeY- + Ca2+ log Kexchange = 14.4

][][4.14

][][ 2

3

2

−

−

+

+

=FeYCY

FeC

Thus, the relative importance of the two EDTA complexes depends also on the ratio of calcium to iron in solution.

For an exact solution to this problem, we also need to consider the species FeYOH and FeY(OH)2.



Figure 6.17a from Stumm & Morgan. Competitive effect of Ca2+ on complexation of Fe(III) with EDTA. Fe(OH)3(s) precipitates at pH > 8.6.



Figure 6.17b from Stumm & Morgan. Competitive effect of Ca2+ on complexation of Fe(III) with EDTA.



Figure 6.17c from Stumm & Morgan. Competitive effect of Ca2+ on complexation of Fe(III) with citrate.

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COORDINATION CHEMISTRY (Complexation in Solution)

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