Transcript Complexation in Solution - environmentalgeochemistry

ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
COORDINATION CHEMISTRY
(Complexation in Solution)
Bruce Herbert
Geology & Geophysics
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Sampling the Aqueous Phase
Soil Water
http://ianrpubs.unl.edu/fieldcrops/g964.htm
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Sampling the Aqueous Phase
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://ianrpubs.unl.edu/fieldcrops/g964.htm
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Sampling the Aqueous Phase
Soil 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.
http://ianrpubs.unl.edu/fieldcrops/g964.htm
Complexation
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Sampling the Aqueous Phase
Soils
■ 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
Pu m p
S o lu t io n
in
ly s im e t e r
b arre l
P o ro u s
Cu p
Complexation
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Sampling the Aqueous Phase
Soils
■ 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.
www.usyd.edu.au/.../
sphysic/waterlab/field.htm
Complexation
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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
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Sampling the Aqueous Phase
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
C
D
A: Depth-integrated well.
B: Depth-specific well.
C: Nested piezometers for depthspecific sampling.
D: Depth-specific sampling using
inflated packers to isolate a
particular zone.
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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.
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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: CuCO30, 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.
Complexation
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Effect of free Cu2+ on
growth of algae in
seawater.
Figure 6-20 from Stumm & Morgan
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Common Metal Species
Cation
Acid Sys tems
Alkaline Sys tems
Na+
Na+
Na+, NaHCO3°, NaSO 4-
Mg2+
Mg2+, MgSO 4°, org
Mg2+, MgSO 4°, MgCO3°
Al3+
org, AlF2+, AlOH2+
Al(OH)4-, org
Si4+
Si(OH)4°
Si(OH)4°
K+
K+
K+, KSO 4-
Ca2+
Ca2+, CaSO 4°, org
Ca2+, CaSO 4°, CaHCO3+
Cr3+
CrOH2+
Cr(OH)4-
Cr6+
CrO4-
CrO4-
Mn2+
Mn2+, MnSO 4°, org
Mn2+, MnSO 4°, MnCO3°, MnHCO3+, MnB(OH) 4+
Fe2+
Fe2+, FeSO 4°, FeHPO 4+
FeCO3°, Fe2+, FeHCO3+, FeSO 4°
Fe3+
FeOH2+, Fe(OH)3°, org
Fe(OH)3°, org
Ni2+
Ni2+, NiSO 4°, NiHCO3+, org
NiCO3°, NiHCO3+, Ni2+, NiB(OH) 4+
Cu2+
org, Cu2+
CuCO3°, org, CuB(OH)4+, Cu[B(OH) 4]4°
Zn2+
Zn2+, ZnSO 4°, org
ZnHCO3+, ZnCO3°, org, Zn2+, ZnSO 4°, ZnB(OH) 4+
Mo5+
H2MoO4°, HMoO4-
HMoO4-, MoO42-
Cd2+
Cd2+, CdSO 4°, CdCl+
Cd2+, CdCl+, CdSO 4°, CdHCO3+
Pb2+
Pb2+, org, PbSO 4°, PbHCO3+
PbCO3°, PbHCO3+, org, Pb(CO3)22-, PbOH+
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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
Si(OH)4Ў
Central Ion
Si4+
Al(OH)2+
HCO3-
Al3+
H+ or CO32-
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MULTIDENTATE LIGANDS
HO
O
O
O
O
M
O
N
OH
N
OH
O
Oxalate (bidentate)
N 2H
O
M
HO
O
N 2H
Ethylendiamine (bidentate)
Ethylendiaminetetraacetic acid
or EDTA (hexadentate)
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Chelation
N H
2
H2N
N i
N H
2
H2N
Polynuclear complexes
S 2 -
S
S b
S
S b
S
Sb2S42-
O H O H
H g
2 +
H g H g
O H O H
Hg3(OH)42+
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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.
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FORMS OF OCCURRENCE OF METAL SPECIES
10 Å
100 Å
Free metal Inorganic ion
Organic
ion
pairs and
complexes,
complexes
chelates
1000 Å
Metals
bound to
high mol.
wt.
species
Me-lipids
Highly
dispersed
colloids
Metals
sorbed on
colloids
FeOOH
Mex(OH)y
Me- humic
acid
Fe(OH)3
MeCO3,
MeS,etc. on
clays
FeOOH or
Mn(IV) on
oxides
Cu2+
Cu2(OH)22+
Me-SR
Fe3+
PbCO30
Me-OOCR
Pb2+
CuCO30
Mn(IV)
oxides
Na+
AgSH0
Ag2S
Al3+
CdCl+
Zn2+
CoOH+
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Coordination Numbers
L
L
L
Me
CN = 2 (linear)
L
Me
L
L
CN = 4 (square planar)
L
L
L
L
M
Me
L
L
L
CN = 4 (tetrahedral)
e
L
L
L
CN = 6 (octahedral)
Coordination numbers 2, 4, 6, 8, 9 and 12 are most common
for cations.
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STABILITY CONSTANTS MEASURE THE STRENGTH OF COMPLEXATION
Stepwise constants
MLn-1 + L  MLn
Cumulative constants
M + nL  MLn
[ MLn ]
Kn 
[ MLn 1 ][ L]
[ MLn ]
n 
[ M ][ L]n
n = K1·K2·K3···Kn
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STABILITY CONSTANTS MEASURE THE STRENGTH OF COMPLEXATION
For a protonated ligand we have:
Stepwise complexation
MLn-1 + HL  MLn + H+
Cumulative complexation
M + nHL  MLn + nH+

[
ML
][
H
]
*
n
Kn 
[ MLn 1 ][ HL ]
 n
[
ML
][
H
]
*
n
n 
[ M ][ HL ]n
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.
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STABILITY CONSTANTS FOR POLYNUCLEAR COMPLEXES
mM + nL  MmLn
 nm
[ M m Ln ]

[ M ]m [ L]n
mM + nHL  MmLn + nH+
*
 nm
 n
[ M m Ln ][ H ]

[ M ]m [ HL ]n
If m = 1, the second subscript on nm is omitted and the expression
simplifies to the previous expressions for mononuclear complexes.
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Titration of H+ and Cu2+ with Ammonia and Tetramine (trien)
Figure 6-3 from Stumm & Morgan
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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- (ZnO22-)
May also get polynuclear species.
Kinetics of formation of mononuclear hydrolysis products is rather fast,
polynuclear formation may be slow.
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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+
Mg2+ + H2O  MgOH+ + H+
log *K1 = -8.0
log *K1 = -11.4


[
MOH
][
H
]
*
K1 
[ M 2 ]
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 MOH

[ MOH  ]



2
[ MOH ]  [ M ]
 MOH 

[ MOH  ]
[ MOH  ][ H  ]

[ MOH ] 
*
K1
1
[H  ]
1 *
K1
At infinite dilution, pH  7 so
CuOH+ = (1 + 10-7/10-8)-1 = 1/11 = 0.091
MgOH+ = (1 + 10-7/10-11.4)-1 = 1/25119 = 4x10-5
Only salts with p*K1 < (1/2)pKw or p*n < (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.
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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:
[Cu2 (OH )22 ]
[Cu2 (OH )22 ]
*


K22
 2
2
2 2
[CuOH ]
(CuT  [Cu ]  2[Cu2 (OH )2 ])
So [Cu2(OH)22+] is clearly dependent on total Cu concentration!
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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 = -3.05
Fe3+ + 2H2O  Fe(OH)2+ + 2H+
log *2 = -6.31
2Fe3+ + 2H2O  Fe2(OH)24+ + 2H+ log *22 = -2.91
FeT = [Fe3+] + [FeOH2+] + [Fe(OH)2+] + 2[Fe2(OH)24+]
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
K1
2
2[ Fe ]  22 


FeT  [ Fe ]1     2 
 2
[H ]
 [H ] [H ]

*
3
*
3 *
Optional
Now we define: 0 = [Fe3+]/FeT; 1= [FeOH2+]/FeT; 2= [Fe(OH)2+]/FeT; and 22=
2[Fe2(OH)24+]/FeT.

K1
2
2 Fe  

 0  1     2 
[H ]
 [H ] [H ]
*
02 2 FeT * 22
[ H  ]2
*
*
T 0
22
 2




1
*
*

K1
2 

 0 1     2   1  0
 [H ] [H ] 
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Optional
This last equation can be solved for 0 at given values of FeT and pH.
The remaining  values are obtained from the following equations:
 22 
 0 K1
 02 2 FeT *  22
[ H  ]2
*
1 
[H  ]
 0  22
*
2 
[ H  ]2
These equations can then be employed to calculate the speciation diagrams on
the next slide.
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Fe
100
FeT = 10-4 M
3+
80
Fe(OH) 2+
60
%Fe
40
FeOH
2+
20
0
FeT = 10-2 M
Fe3+
100
Fe2(OH) 24+
80
Fe(OH) 2+
60
%Fe
40
20
FeOH 2+
0
1
2
3
4
pH
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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 = 3.96
Fe(OH)3(s) + H2O  Fe(OH)4- + H+ log *Ks4 = -18.7
Fe3+
log [Fe3+] = log *Ks0 - 3pH
Fe(OH)4log [Fe(OH)4-] = log *Ks4 + pH
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FeOH+
Fe(OH)3(s) + 3H+  Fe3+ + 3H2O
log *Ks0 = 3.96
Fe3+ + H2O  FeOH2+ + H+
log *K1 = -3.05
Fe(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
Fe3+ + 2H2O  Fe(OH)2+ + 2H+
Fe(OH)3(s) + H+  Fe(OH)2+ + H2O
log *Ks0 = 3.96
log *2 = -6.31
log *Ks2 = -2.35
log [Fe(OH)2+] = log *Ks2 - pH
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Fe2(OH)24+
2Fe(OH)3(s) + 6H+  2Fe3+ + 6H2O 2log *Ks0 = 7.92
2Fe3+ + 2H2O  Fe2(OH)24+ + 2H+
log *22 = -2.91
2Fe(OH)3(s) + 4H+  Fe2(OH)24+ + 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.
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5
0
Fe(OH)3(s)
-5
log concentration
Fe(OH)4-10
Fe2(OH) 2
4+
3+
Fe
-15
0
2
4
6
Fe(OH)2
FeOH2+
8
10
+
12
14
pH
Complexation
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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
Complexation
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Metal Complexation
and 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
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Complexation & the HSAB Concept
Ionic potential
Ґ If IP < 30 n m-1, then metal cations tend to fo rm
solvation co mplexes with water
Ґ If 95 > IP > 30 n m-1, then metal cations can repel
protons f rom solvating water molecules to fo rm the
hydroxide co mplexes.
Ґ If IP > 95 n m-1, then repulsion is st rong enough to
form the oxy ion spec ies
Misono Softness
Ґ If Y < 25 n m, then meta l cat ions tend to fo rm
elect rostat ic bonds
Ґ If 0.25 < Y < 0.32 n m, then the meta l cat ions a re
borderline meta ls whose cova lency depends on
whethe r spec ific so lvent, ste reoche mical, and
elect ronic conf igurationa l facto rs a re p resent
Ґ If Y > 0.32 n m, then meta l cat ions tend to fo rm
cova lent bonds
Complexation
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Figure 6-4a from Stumm and
Morgan: Predominant pH
range for the occurrence of
various species for various
oxidation states
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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.
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Correlation
between
solubility
product of solid
oxide/hydroxide
and the first
hydrolysis
constant.
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Figure 6-6 from Stumm &
Morgan
Complexation
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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
Complexation
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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.
Complexation
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Classification of metals and ligands
in terms of PearsonХs
(1963)
ENVIRONMENTAL
GEOCHEMISTRY
ATHSAB
TEXAS A&M UNIVERSITY
principle.
Hard
Borderline
Soft
Acids
Acids
Acids
H+
+
+
+
+
+
Li > Na > K > Rb > Cs
2+
2+
2+
2+
Be > Mg > Ca > Sr >
2+
Ba
Al3+ > Ga3+
Sc3+ > Y3+; REE3+ (Lu3+ >
3+
4+
4+
La ); Ce ; Sn
4+
3+
4+
4+
Ti > Ti , Zr  Hf
Cr6+ > Cr3+; Mo6+ > Mo5+ >
Mo4+; W6+ > W4+; Nb5+, Ta5+;
Re7+ > Re6+ > Re4+; V6+ > V5+
4+
4+
3+
3+
5+
> V ; Mn ; Fe ; Co ; As ;
5+
Sb
4+
6+
4+
Th ; U > U
6+
PGE > PGE4+, etc. (Ru, Ir,
Os)
Bases
Fe2+, Mn2+, Co2+, Ni2+,
2+
2+
2+
2+
Cu , Zn , Pb , Sn ,
3+
3+
3+
As , Sb , Bi
Au+ > Ag+ > Cu+
2+
2+
Hg > Cd
2+
2+
Pt > Pd
2+
other PGE
Tl3+ > Tl+
Bases
Bases
F-; H2O, OH-, O2-; NH3; NO3-;
CO32- > HCO3-; SO42- > HSO4-;
PO43- > HPO42- > H2PO4-;
carboxylates (i.e., acetate,
oxalate, etc.);
22MoO4 ; WO4
Cl-
I- > Br-; CN-; CO;
S2- > HS- > H2S;
organic phosphines
(R3P); organic thiols
(RP);
2polysulfide (SnS ),
thiosulfate (S2O32-),
sulfite (SO32-);
22HSe , Se , HTe , Te ;
AsS2 ; SbS2
Complexation
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ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
ION PAIRS VS. COORDINATION COMPLEXES
ION 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
Complexation
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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, MgCO30, etc.)
log K  1.5 - 2.4 (I = 0)
For 3:3 pairs (e.g., LaPO40, AlPO40, etc.)
log K  2.8 - 4.0 (I = 0)
Stability constants for covalently bound coordination complexes cannot be estimated as
easily.
Complexation
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COMPLEX FORMATION AND SOLUBILITY
■ Total solubility of a system is given by:
[Me]T = [Me]free + [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, HgS22- or HgS2H-, Fe(OH)+, CuCO30 and Al(OH)4-.
Complexation
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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

2
[
H
][
S
]
14
K2  10 
[ HS  ]

2
[
H
][
S
]

[ HS ] 
1014
[ H  ][ S 2 ]
2
0.1 

[
S
]
14
10
Complexation
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G
1013[ S 2 ] E 2
2
0.1 

[
S
]

11
[
S
]
14
10
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[S2-] = 9.1x10-3 M
[Ag+]2 = 10-49.7/10-2.04 = 10-47.66
[Ag+] = 10-23.85 = 1.41x10-24 M
Obviously, 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+ ionselective electrode would read [Ag+] = 10-23.85 nevertheless.
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AT TEXAS
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Estimate the concentration of all species in aENVIRONMENTAL
solution of SGTEOCHEMISTRY
= 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[Ag2S3H22-]
Ks0 = [Ag+]2[S2-], but [S2-] = 2ST so
Ks0 = [Ag+]2 2ST

[ Ag ] 
Ag+ + HS-  AgHS0
AgHS0 + HS-  Ag(HS)2Ag2S(s) + 2HS-  Ag2S3H22-
Ks0
ST2
log K1 = 13.3
log K2 = 3.87
log Ks3 = -4.82
Complexation
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0
[ AgHS ]
K1 


[ Ag ][ HS ]
ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
[ AgHS 0 ]
K1 
[ Ag  ]1ST
[ AgHS ]  K11ST [ Ag ]
[ HS ]  1ST


0
[ AgHS ]  K11ST
0
[ Ag ( HS )2 ]
K2 
[ AgHS 0 ][ HS  ]
Ks0
ST2
[ Ag ( HS )2 ]  K2 [ AgHS 0 ][ HS  ]
[ Ag ( HS ) ]  K2 K S 

2
2 2
1 T 1
Ks0
ST2
Complexation
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[ Ag2 S3 H 22 ]
Ks3 
 2
[ HS ]
[ Ag2 S3 H 22 ]  K s 3ST212
[ Ag ]T 
Ks0
2 2
2 2

1  K1ST1  K2 K1ST1  2 K s 3ST1
ST2
Complexation
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-6
-8
-10
-12
Ag(HS) 2
AgHS 0
-
Ag 2S3H2
-14
2-
-16
pH = pK 1(H2S)
-18
log concentration
-20
Ag +
-22
-24
0
2
4
6
8
10
12
14
pH
Complexation
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-7
3
2
4
-8
Ag 2S3H2
5
2-
1
pH = pK 1(H2S)
AgHS 0
log concentration
-9
Ag(HS) 2-
-10
0
2
4
6
8
10
12
14
pH
Complexation
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ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
Region 1: AgHS0 and H2S0 are predominant
Ag2S(s) + H2S0  2AgHS0
log [AgHS0] = 1/2log [H2S0] + 1/2log K
  log[ Ag ]T

 pH

  0
 H2S
Region 2: Ag(HS)2- and H2S0 are predominant
Ag2S(s) + 3H2S0  2Ag(HS)2- + 2H+
log [Ag(HS)2-] = 3/2log [H2S0] + 1/2log K + pH
  log[ Ag ]T

 pH

  1
 H 2S
Complexation
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Region 3: Ag(HS)2- and HS- are predominant
Ag2S(s) + 3HS- + H+  2Ag(HS)2log [Ag(HS)2-] = 3/2log [HS-] + 1/2log K - 1/2pH
  log[ Ag ]T

 pH

  1 / 2
 HS 
Region 4: Ag2S3H22- and HS- are predominant
Ag2S(s) + 2HS-  Ag2S3H22log [Ag2S3H22-] = 2log [HS-] + log K
  log[ Ag ]T

 pH

  0
 HS 
Complexation
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Region 5: Ag2S3H22- and S2- are predominant
Ag2S(s) + 2S2- + 2H+  Ag2S3H22log [Ag2S3H22-] = 2log [S2-] + log K - 2pH
  log[ Ag ]T

 pH

  2
 S 2
Complexation
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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.
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WHAT IS THE CAUSE OF THE CHELATE EFFECT?
Gro = Hro - TSr0
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+ + 4NH30  Cu(NH3)42+ + 4H2O
Cu(H2O)42+ + N4  Cu(N4)2+ + 4H2O
The second reaction results in a greater increase in Sr0.
Complexation
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Figure 6-11 from Stumm and Morgan. EEffect
of dilution
on degree
of UNIVERSITY
NVIRONMENTAL
GEOCHEMISTRY
AT TEXAS A&M
complexation.
Complexation
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6-12a
from
Stumm
&
ENVIRONMENTAL GFigure
EOCHEMISTRY
AT TEXAS
A&M
UNIVERSITY
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.
Complexation
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Figure 6-12b from Stumm & Morgan. Chelation of Zn(II).
ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
Complexation
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ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
METAL-ION BUFFERS
Analogous to pH buffers. Consider:
Me + L  MeL
K [ MeL ]
[ Me ] 
[ L]
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!
Complexation
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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.
[CaY 2 ]
10.6

K

10
CaY
2
4
[Ca ][Y ]
[CaHY  ]
3.5

K

10
CaHY
2
3
[Ca ][ HY ]
(i ) CaT  [Ca 2 ]  [CaY 2 ]  [CaHY  ]
 [Ca 2 ]1  KCaY [Y 4 ]  KCaHY K 41[ H  ][Y 4 ]
1
 [Ca 2 ]Ca
Ca
[Ca 2 ]

CaT
Complexation
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2 ENVIRONMENTAL
3
4
2 A&M UNIVERSITY


(ii ) YT  [ H 4Y ]  [ H 3Y ]  [ H 2Y ]  [ HY ]  [Y ]  [CaY ]  [CaHY ]
0
 [Y 4 ](4* )1  [Ca2 ][Y 4 ]KCaY  [Ca2 ][ H  ][Y 4 ]K41KCaHY
 
*
4
 [H ] [H ]
[H ]
[H ] 

 1 



K4
K 4 K3 K 4 K3 K 2 K 4 K3 K 2 K1 
4 i

[H Y ]
4
[Y ]
4

i 0

 2
 3
 4
1
i
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 [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-] =
Complexation
8.21x10-4 M; [H4Y0] = 2.26x10-8 M.
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MIXED COMPLEXES
Examples: Zn(OH)2Cl22-, Hg(OH)(HS)0, PdCl3Br2-, etc.
Generalized complexation reaction:
M + mA + nB  MAmBn
log  MAm Bn
m
n

log  MAm  n 
log  MBm  n  log S
mn
mn
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.
Complexation
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In simple cases we can use the following
formula:
( m  n )!
S
! npredominate
!
In general, mixed complexes usuallym
only
under a very
restricted set of conditions.
Complexation
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Figure
6-15
from
ENVIRONMENTAL GEOCHEMISTRY
AT TEXAS
A&M
UNIVERSITY
Stumm and Morgan.
Predominance of
Hg(II) species as a
function of pCl and pH.
In seawater, HgCl42predominates.
Complexation
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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-  FeYlog KFeY = 25.1
Ca2+ + Y4-  CaY2- log KCaY = 10.7
These data suggest that Fe3+ should be complexed by EDTA.
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But, let us combine the two above expressions to get:
CaY2- + Fe3+  FeY- + Ca2+
log Kexchange = 14.4
2
2
[Ca ]
[CaY ]
 14.4
3

[ Fe ]
[ FeY ]
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.
Complexation
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Figure 6.17a from Stumm & Morgan.
Competitive
effect
of Ca2+ on
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complexation of Fe(III) with EDTA. Fe(OH)3(s) precipitates at pH >
8.6.
Complexation
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ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
Morgan. Competitive effect of Ca2+ on
Figure 6.17b from Stumm &
complexation of Fe(III) with EDTA.
Complexation
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ENVIRONMENTAL GEOCHEMISTRY AT TEXAS A&M UNIVERSITY
Morgan. Competitive effect of Ca2+ on
Figure 6.17c from Stumm &
complexation of Fe(III) with citrate.
Complexation
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