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Transcript
Lecture 21
Water-Related Complexes
• Ferric iron, will form a Fe(H2O)63+ aquo-complex. The
positive charge of the central ion tends to repel
hydrogens in the water molecules, so that water
molecules in these aquo-complexes are more
readily hydrolyzed than otherwise. Thus these aquocomplexes can act as weak acids. For example:
Fe(H2O)63+ ⇄ Fe(H2O)5(OH)2+ + H+
⇄ Fe(H2O)4(OH)2+ + 2H+
⇄ Fe(H2O)3(OH)3 + 3H+
⇄ Fe(H2O)2(OH)4- + 4H+
• Thus equilibrium between these depends strongly
upon pH.
Hydroxo- and Oxo-Complexes
•
•
•
•
•
•
•
Loss of hydrogens from the solvation shell
results in hydroxo-complexes.
The repulsion between the central metal
ion and protons in water molecules of the
solvation shell will increase with decreasing
diameter of the central ion and with
increasing charge of the central ion.
Not surprisingly, the complexes also
depend on the abundance of H+ and OH–
ions, i.e., pH.
For highly charged species, the repulsion of
the central ion is sufficiently strong that all
hydrogens are repelled and it is surrounded
only by oxygens.
Such complexes, for example, and , are
known as oxo-complexes.
Oxo-complexes are generally more soluble
than hydroxo-complexes, so 6+ ions of a
metal can be more soluble than lesser
charged species (e.g., U).
Intermediate types in which the central ion
is surrounded, or coordinated, by both
oxygens and hydroxyls are also possible, for
example MnO3(OH) and CrO3(OH)–, and
are known as hydroxo-oxo complexes.
Summary of Water
Complexes
• For most natural waters,
metals in valence
states I and II will be
present as “free ions”,
that is, aquocomplexes, valence III
metals will be present
as aquo- and hydroxocomplexes (depending
on pH), and those with
higher charge will be
present as oxocomplexes.
Polynuclear Complexes
•
•
•
•
Polynuclear hydroxo- and oxo-complexes,
containing two or more metal ions, are also
possible.
The extent to which such polymeric species form
increases with increasing metal ion concentration.
Most highly-charged metal ions (3+ through 5+) are
highly insoluble in aqueous solution. This is due in
part to the readiness with which they form hydroxocomplexes, which can in turn be related to the
dissociation of surrounding water molecules as a
result of their high charge.
When such ions are present at high concentration,
formation of polymeric species such as those
above quickly follows formation of the hydroxocomplex. At sufficient concentration, formation of
these polymeric species leads to the formation of
colloids and ultimately to precipitation. In this
sense, these polymeric species can be viewed as
intermediate products of precipitation reactions.
2+
Mn — OH — Mn2+
Cu Hydroxides
•
•
Interestingly enough, however, the tendency
of metal ions to hydrolyze decreases with
concentration. The reason for this is the effect
of the dissociation reaction on pH. For
example, increasing the concentration of
dissolved copper decreases the pH, which in
turn tends to drive the hydrolysis reaction to
the left. To understand this, consider the
following reaction:
Cu2+ + H2O ⇄ CuOH+ + H+
for which the apparent equilibrium constant is
Kapp = 10–8. We can express the fraction of
copper present as CuOH+, αCuOH+ as:
[CuOH + ]
K app
a=
=
CuT
[H + ] + K app
•
For a fixed amount of dissolved Cu, we can
also write a proton balance equation:
[H +] = [CuOH+]+ [OH –]
•
and a mass balance equation. Combining
these with the equilibrium constant expression,
we can calculate both α and pH as a function
of CuT
Other
Complexes
• When non-metals are
present in solution, as they
would inevitably be in
natural waters, then other
complexes are possible.
• We can divide the elements
into four classes:
o
o
o
o
Ligand Formers: Non-metals, which
form anions or anion groups.
“A-type” or “hard” metals They can
be viewed as hard, charged spheres.
They preferentially complex with
fluorine and ligands having oxygen
as the donor atoms (e.g., OH–,CO32,SO42-).
B-type, or “soft”, metals. Their
electron sheaths are readily
deformed by the electrical fields of
other. They preferentially form
complexes with bases having S, I, Br,
Cl, or N (such as ammonia; not
nitrate) as the donor atom. Bonding
is primarily covalent and is
comparatively strong. Thus Pb forms
strong complexes with Cl– and S2–.
First transition series metals. Their
electron sheaths are not spherically
symmetric, but they are not so
readily polarizable as the B-type
metals. On the whole, however, their
complex-forming behavior is similar
to that of the B-type metals.
Irving-Williams Series
•
•
the Irving-Williams series is the
sequence of complex stability
among first transition metals:
Mn2+<Fe2+<Co2+<Ni2+ <Cu2+>Zn2+.
In the figure, all the sulfate
complexes have approximately
the same stability, a reflection of
the predominantly electrostatic
bonding between sulfate and
metal. Pronounced differences
are observed for organic ligands.
The figure demonstrates an
interesting feature of organic
ligands: although the absolute
value of stability complexes
varies from ligand to ligand, the
relative affinity of ligands having
the same donor atom for these
metals is always similar.
Complexation Computations
•
•
Where only one metal is
involved, the
complexation calculations
are straightforward, as in
Example 6.7. Natural
waters, however, contain
many ions. The most
abundant of these are
Na+, K+, Mg2+, Ca2+, Cl–,
SO42-, HCO3–, CO32-, and
there are many possible
complexes between them
as well as with H+ and OH–.
To calculate the
speciation state of such
solutions, an iterative
approach is required, such
as Example 6.08.
Most major ions are not
complexed in most
situations.
free ion
OH–
HCO3-
CO32-
SO42-
1x10-06
9.12x10-04 1.12x10-06 1.65x10-04
1x10-08
—
2.06x10-05 9.12x10-04 1.58x10-10
Na+
3.03x10-04
—
1.57x10-07 2.35x10-08 5.64x10-07
K+
5.69x10-05
—
Mg2+
1.40x10-04 5.03x10-08
1.84x10-06 1.45x10-06 5.14x10-06
Ca2+
2.80x10-04 3.92x10-09
4.64x10-06 1.83x10-06 9.16×10-06
free
ion
H+
—
—
Percent Free Ion in Stream Water
Na+
99.76%
Cl–
100%
K+
99.85%
SO42-
91.7%
Mg2+
94.29%
HCO3–
99.3%
Ca2+
94.71%
CO32-
25.3%
8.40x10-08
Dissolution and
Precipitation
Carbonate Solubility
•
•
Carbonate is the most
common kind of chemical
sediment and carbonate
components (Ca, Mg, CO3) are
often the dominant species in
natural waters.
Using equilibrium constants, we
can calculate calcite solubility
as a function of PCO2:
1/3
ìï
K1K sp-cal K CO2 üï
[Ca 2+ ] = í PCO2
ý
2
K
g
2+ g
2
ï
Ca
HCO3 þ
îï
•
•
•
Thus calcite solubility increases
with 1/3 power of PCO2.
One consequence is that
calcite shells tend to dissolve in
deep ocean water.
A second is that calcite will
dissolve out of soils when
microbial activity is present.
Carbonate Solubility
1/3
ìï
K1K sp-cal K CO2 üï
2+
[Ca ] = í PCO2
ý
2
K 2g Ca2+g HCO
ïî
3 ï
þ
• Another interesting
feature is because
of this non-linearity,
mixing of two
saturated waters
can produce an
undersaturated
water.
Carbonate Solubility
• Open system solutions,
those in equilibrium
with CO2 gas in the
atmosphere or soil (in
red), can dissolve
more calcite than
closed systems waters
(in black).
• In a sense, this is
because dissolving
CO2 in water lowers
pH, resulting in greater
dissolution.
Mg Solubility
•
Several Mg-bearing minerals can
precipitate from solution:
o
o
o
•
ΣCO2 = 10-2.5 M
brucite, Mg(OH)2
dolomite CaMg(CO3)2
magnesite MgCO3
We can use equilibrium constant
expressions, such as:
2
-11.6
K bru = aMg2+ aOH
- = 10
to construct a predominance diagram showing
which phase will precipitate under a given set of
conditions.
•
We construct these in the same
way we constructed pe-pH
diagrams, namely manipulate
the log equilibrium constant
expressions to get [Mg2+] on one
side of the equation and pH on loga
= - pK bru + 2 pKW - 2 pH = 16.4 - 2 pH
Mg2+
the other.
o
We simplify things by calculating equilibrium
with only 1 carbonate species at a time and
ignoring the others.
Mg Solubility
•
ΣCO2 = 10-2.5 M
For magnesite:
K mag = aMg2+ aCO2- =10-7.5
3
•
•
•
We can think of three limiting cases:
where carbonic acid, bicarbonate
ion, and carbonate ion
predominate.
In the latter case, [CO32- ] ≈ ΣCO2.
When bicarbonate ion
predominates, [HCO3- ] ≈ ΣCO2, and
the carbonate ion concentration is:
log [CO32–] = pK2 + log [HCO3–] +pH = 12.88+pH
•
What about when H2CO3
dominates?
logaMg+ = 26.68 - 2 pH
logaMg+ = 5.33- pH
logaMg+ = -log aCO2- - pK mag
3
Mg solubility as a function of
CO2 & pH
[Mg2+] = 10-4 M
Mg solubility as a function of
CO2 & Ca/Mg
Mg2+ = 10-4 M
Constructing stability
diagrams
ΣCO2 = 5x 10-2 M
• This diagram shows the stability
of ferrous iron minerals as a
function of pH and sulfide for
fixed total Fe and CO2.
• Procedure: manipulate
equilibrium constant
expressions to obtain and
expression for ΣS in terms of pH.
For example:
[Fe2+] = 10-6 M
(Pyrrhotite)
(Siderite)
o FeCO3 + H+ ⇋ Fe2+ + HCO3–
o FeCO3 + 2H2O ⇋ HCO3- H+ + Fe(OH)2
o FeS + 2H2O ⇋ Fe(OH)2 + H+ + HS-
• Trick: simplify by ignoring
pH = log K FeCO - log[HCO3- ]- log[Fe2+ ] = 7.5
②
species present at low conc.
(e.g., CO32- at low pH).
③ pH = log[HCO3 ]+13.0
3
- pH
➄ log SS = pH - pK FeS + pK Fe(OH )2 + log(K S +10 )