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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 ]
[ M ]
T
L [ 2 ] +... + Kn F
[ M ]
T
L [ (^) n ]
[M]T = [M]F (1 + K
1 T
L [ 1 ]
L [ 2 ]
+... + K
n T
L [ (^) n ]
rearranging:
[M]F = [M]T / (1 + K
1 T
L [ 1 ]
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 ]
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.
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