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Complexation - Geochemistry - Lecture Notes, Study notes of Geochemistry

In these Lecture Notes, the Lecturer has explained the fundamental concepts of Geochemistry. Some of which are : Complexation, Straight Forward, Equilibria, Dissolved Metal Ion, Dissolved Ligand, Dissolved Complex, Ion Pair, Coordination Compound, Strong Bonds, Stability Constant

Typology: Study notes

2012/2013

Uploaded on 07/25/2013

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Continental Waters
Lecture 17. Complexation and Solubility Equilibria
Complex formation (Viewgraph):
One of the most straight forward types of chemical equilibria is complex
formation which may be treated by the general expression:
mM + nL = MmLn
where: M = dissolved metal ion
L = dissolved ligand (may be inorganic or organic)
MmLn = dissolved complex
= ion pair (weak) or
= coordination compound (strong bonds, with well-defined
structure).
eqK=MmLn
a
M
m
aL
n
a=stabK
(at equilibrium) Stability Constant
Sometimes in the literature one sees the reaction expressed in reverse form, for
the dissociation of an existing complex species:
MmLn = mM + nL
Here, the relevant equilibrium constant is referred to the instability constant, or
the dissociation constant:
eq
K=M
m
aL
n
a
MmLn
a=diss
K
One also sees in the literature apparent equilibrium constants where
concentrations are used rather than activities. Apparent equilibrium constants are
only applicable under the specific conditions for which they are defined.
Kapp =MmLn
[ ]
M
[ ]
mL
[ ]
n=Keq
!
MmLn
!
Mm
!
Lm
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Continental Waters

Lecture 17. Complexation and Solubility Equilibria

Complex formation (Viewgraph) :

One of the most straight forward types of chemical equilibria is complex

formation which may be treated by the general expression:

mM + nL = MmLn

where: M = dissolved metal ion

L = dissolved ligand (may be inorganic or organic)

MmLn = dissolved complex

= ion pair (weak) or

= coordination compound (strong bonds, with well-defined

structure).

K eq

=

aMmLn

M

m

a L

n

a

=

Kstab

(at equilibrium) Stability Constant

Sometimes in the literature one sees the reaction expressed in reverse form, for

the dissociation of an existing complex species:

MmLn = mM + nL

Here, the relevant equilibrium constant is referred to the instability constant, or

the dissociation constant :

K eq

M

m

a

L

n

a

a MmLn

Kdiss

One also sees in the literature apparent equilibrium constants where

concentrations are used rather than activities. Apparent equilibrium constants are

only applicable under the specific conditions for which they are defined.

Kapp =

[ M^ m^ L^ n ]

[ M ]

m

[ L ]

n

= Keq

MmLn

M

m

-^!^ L

m

Complexation Reactions (viewgraph) - may involve a suite of ligands that each

react with the metal:

Simplifying the expressions so that m = 1 and n = 1

And further simplifying to use apparent equilibrium constants

[ ] = concentration:

M + L 1 = ML 1 K

1

ML

[ 1 ]

[^ M ] L

[ 1 ]

M + L 2 = ML 2 K

2

ML

[ 2 ]

[^ M ] L

[ 2 ]

etc.

M + Ln = MLn K n =

ML n

[ ]

[^ M ] L

n

[ ]

Mass balance for metal M:

[M]T = [M]F + [ML 1 ] + [ML 2 ] +... + [MLn]

[M]T = total concentration of metal M

[M]F = concentration of the free metal ion

Similarly for each ligand:

[L 1 ]T = [L 1 ]F + [ML 1 ]

[L 2 ]T = [L 2 ]F + [ML 2 ]

[Ln]T = [Ln]F + [MLn]

For each metal, there are:

2n + 1 equations, including mass balance and equilibrium expressions, and

2n + 1 unknowns (free [M], [MLi] 's, free [Li] 's)

so it is possible to compute the concentration of free metals and of each metal complex.

(Viewgraph) – NOT COVERED IN 2006

For: [Li]F ~= [Li]T

One can then express the concentration of each complex as:

ML [ (^) i ] = K i (^) F

[ M ]

T

L [ (^) i ]

Then the mass balance expression for [M]T can be written as"

[M]T = [M]F + K 1

F

[ M ]

T

L [ 1 ]

  • K 2 F

[ M ]

T

L [ 2 ] +... + Kn F

[ M ]

T

L [ (^) n ]

[M]T = [M]F (1 + K

1 T

L [ 1 ]

  • K 2 T

L [ 2 ]

+... + K

n T

L [ (^) n ]

rearranging:

[M]F = [M]T / (1 + K

1 T

L [ 1 ]

  • K 2 T

L [ 2 ]

+... + K

n T

L [ (^) n ]

One often sees in the literature:

α = [M]F/[M]T = 1/ (1 + K 1 T

L [ 1 ]

  • K 2 T

L [ 2 ]

+... + K

n T

L [ (^) n ]

But: CAUTION: some texts use an inverse format:

α = [M]T/[M]F

(Viewgraph) Solid-Solution (Precipitation-dissolution) reactions can be

written in the same form as complexation reactions:

mM + nL = MmLn

where: Keq =

aMmLn

M

m

a

L

n

a

at equilibrium

But, if MmLn is a pure solid, then by convention, its activity = 1.0.

Therefore, it is more convenient to define equilibrium with respect to the reverse

reaction:

MmLn = mM + nL

where: Ksp = M

m

a

L

n

a Ksp = 1/Keq = solubility product

K sp

M

m

a

L

n

a^ --^ product of activities^ at equilibrium

equivalent to the dissociation constant for complexes

Ion Activity Product (IAP) = M

m

a

L

n

a

IAP is a specific form of “Q” ( see previous lecture)

For any system, whether or not at equilibrium

Saturation Index = IAP/Ksp

SI is an intensity parameter , designed to test the possible formation of a solid

phase.

SI is a specific form of Q/Keq (see previous lecture)

Just as an atmosphere supersaturated in H 2 O requires condensation nuclei

to form water precipitation, likewise a solution supersaturated with respect to the

precipitation of a solid phase requires nuclei to initiate precipitation of the solid.

Heterogeneous nucleation : Nuclei may form on other surfaces, including

minerals, biota, etc.

Crystal growth may be impeded by sorption of interfering ions onto the

crystal surface (referred to sometimes as poisoning ). Therefore, the kinetics of

solid formation is dependent on the chemical conditions of the system, and may

be slow. Similarly, the kinetics of dissolution may be slow in undersaturated

conditions, as well.

(Figure 2) Buffle Table 3.

We have seen the general form of two types of reactions: complexation and

precipitation. Without making the point explicitly, we have also seen that there

exists a parameter to provide an intensity scale for each type of reaction.

For complexation reactions the intensity parameter =α, the ratio of free to

total metal. However, it is more intuitive to think in terms of 1/α, because this

expressed the extent to which any metal exists in solution as complexes.

For precipitation reactions the intensity parameter = SI (saturation index).

For acid - base and redox reactions, we have pH and pE.

(Figure 3) "Hard" vs. "Soft" Metal-ligand classification scheme.

Metals and ligands can both be characterized as "hard" or "soft". Hard metals

tend to react preferentially with hard ligands, while soft metals prefer to react

with soft ligands.

(Text viewgraph) "Hard" ions tend to form electrostatic bonds. Soft ions are

more prone to forming covalent bonds. "Softness" refers to the ability of the

electron cloud to be distorted to form a covalent bond.

(Figure 4) "Essential" vs. "Toxic" Metal classification scheme.

Another classification of metals: essential vs. toxic. Ligands are classified as

simple (inorganic) and organic. Note that organic ligands can be either hard or

soft.

(Text viewgraph) Alkali and alkaline earth cations usually occur as simple

hydrated ions, and rarely as weak complexes with oxygen-donor ligands.

Transition metals form strong complexes with oxygen containing ligands, such as

carbonate and phosphate.

Transition metals (Group II in Figure 3) often occur bound in enzymes where

their multiple oxidation states can be used to transfer electrons.

(Text viewgraph) Soft metal ions (Group III in Figure 3) tend to be toxic. For

example, when a Group III metal replaces a Group II metal in an enzyme, the

enzyme is likely to be disabled and cease to function, with lethal consequences if

the extent of enzyme-metal replacement is extensive.

(Figure 5) Metal speciation in natural waters (rough generalities). Table

shows principal species of certain elements in typical freshwaters, as well as the

fraction of each element existing as a free hydrated ion. Note that the alkali and

alkaline earth ions are predominantly free, whereas only a miniscule fraction of

other elements exist as a free ion. The fraction of some elements that exist as

free ions would decrease even further if organic complexes were included.

Copper, for example, forms particularly strong complexes with organic matter.

Complexation reactions and solubility reactions are often intimately linked, and

often compete with one another for free cations and ligands, in natural waters.

As Jim may have pointed out in an earlier lecture, weathering of aluminosilicate

minerals (which represents a complex example of a precipitation/dissolution

reaction) are often accelerated by complexation reactions. For example,

complexation of Al 3+ by oxalate ions reduces the concentation of free dissolved

Al 3+

. In terms used in a previous lecture, reducing the concentration of free Al 3+

lowers the value of "Q", (the quotient of the activities of the products divided by

the activities of the reactants), thereby driving the reaction to the right,

accelerating the dissoluton of aluminosilicate minerals.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure