Part 2. The Hydrosphere
Chapter 10.
Distribution of Species
in Aquatic Systems
Single variable diagram: a plot of some measure of species conc. Vs. a particular variable like pH, redox status, or conc. of important complexing ligand. E.g.
Chapter 10. Distribution of species in aquatic systems 10.1 Single-variable diagrams: Phosphate species
p PO
p HPO
p PO
H PO H
a
C PO
C HPO
C PO H
PO HPO
PO H
PO H
PO H
PO H
O H PO
K H
PO HPO
PO H
PO H
] [
] [
] [
] [
] [
] [
] [
] [
] [
] ][
[
3 4
2 4
4 2
3 4 2
4 4
2 4
3
4 3
4 3
3 4
2 1
3 4 2
4 4
2 4
3
3 4
2 4
4 2
4 3
(10.1) (10.2)
(10.3)
(10.4)
(10.5)
(10.6)
Conc. of individual phosphate species:
Chapter 10. Distribution of species in aquatic systems 10.1 Single-variable diagrams: Phosphate species
Table 10.1 Acid dissociation constants for phosphoric acid
Ka pKa
First
dissociation 7.1x10-3 2.15 Second
dissociation 6.3x10-8 7.20 Third
dissociation 4.2x10-13 12.38
3 2 1 2 1 3
1 2 3 3 3
3 2 1 3
3 2 1 2 1 3
1 2 3 3 3
2 1 3
3 2 1 2 1 3
1 2 3 3 3
1 2 3
3 2 1 2 1 3
1 2 3 3 3
3 3
3 3 3 3 3 2 1 2 3 2 1 3
1 4
3
4 3
3 3
3 2 1 2
3 2 1 3
1 4
3
3 4 2
4 4
2 4
3
3 3
4 3 3 2 3 1
4
2 3
4 3 2 2 1
4
3 4 3 1 4
2
] [
] [
] [
] [
] [
] [
] [
] [
] [
] [
] [
] [
that find we ns, calculatio similar
Using
] [
] [
] [
] [
: ] [
by equation the
of side hand - right the of bottom and
top he multiply t then
We
) ] /[
] /[
] /[
1 ](
[
] [
10.3 eqn From
] ) [
] [
] 1 [
](
[
] [
] [
] [
] [
] [
] ] [
[
] [
] ] [
[
] [
] ] [
[
3 4
2 4
4 2
4 3
4 3
a a a a a a
a a a PO
a a a a a a
a a HPO
a a a a a a
a PO
H
a a a a a a
PO H
a a a a
a a
PO H
a a a a a a
p
a a a
a a
a
K K K K K O H K O
H O
H
K K K O H
K K K K K O H K O
H O
H
K K O H
K K K K K O H K O
H O
H
K O
H
K K K K K O H K O
H O
H
O H
O H O H K K K O
H K K O H K PO
H
PO H
O H
K K K O
H K K O H PO K
H
PO HPO
PO H PO H C
O H
PO H K K PO K
O H
PO H K HPO K
O H
PO H PO K
H
(10.7) (10.8) (10.9)
(10.10)
(10.11)
(10.12)
(10.13)
(10.14) (10.15)
Distribution of phosphate species in open water
In sea water, dissociation const. of phosphoric acid
Chapter 10. Distribution of species in aquatic systems
10.1 Single-variable diagrams: Phosphate species
Single variable diagram with logarithm scale: E.g. distribution of aq. cadmium chloro complexes as a function of chloride ion concentration.
Chapter 10. Distribution of species in aquatic systems
10.1 Single-variable diagrams: Cadmium complexes with chloride
2 4
3 2
1 f4
- 2 4 2
2 3
2 1
f3 -
3 2
2 2
1 f2
2 2
1 f1
2
2 1
fn f
3 2 4 4
2 4 3
2 3 3
3 2
2 2
2
1 2 2
10 8 . 3
4
10 4 . 6
3
10 2 . 3
2
10 9 . 7
seen that readily
is It . as symbolized are
constants
stability overall
the and steps overall'
' using described
be also may reactions
The
6 . ] 0 ][
[
] [
0 . ] 2 ][
[
] [
0 . ] 4 ][
[
] [
10 9 . ] 7 ][
[
] [
f f
f f
f f
f
f f
f
fn f
f f
f f f
K K
K K
CdCl Cl
Cd
K K
K CdCl
Cl Cd
K K
CdCl Cl
Cd
K CdCl
Cl Cd
K K
K
Cl CdCl
K CdCl CdCl
Cl CdCl
Cl CdCl K CdCl
CdCl Cl
CdCl
Cl CdCl
K CdCl CdCl
Cl CdCl
Cl Cd
K CdCl CdCl
Cl Cd
(10.16)
(10.17)
(10.18)
(10.19)
(10.20) (10.21) (10.22) (10.23) (10.24)
Total conc. of cadmium in an aq. solution containing chloride
Chapter 10. Distribution of species in aquatic systems
10.1 Single-variable diagrams: Cadmium complexes with chloride
4 4
3 3
2 2
1 1
4 4
2 3
4 4
3 3
2 2
1 1
3 3
3
4 4
3 3
2 2
1 1
2 2
2
4 4
3 3
2 2
1 1
1 1
4 4
3 3
2 2
1 1 2
4 4
3 3
2 2
1 2 1
2 2 4 2
3 2
2 2
2
2
] [ ]
[ ]
[ ]
[ 1
] ] [
[
] [ ]
[ ]
[ ]
[ 1
] ] [
[
] [ ]
[ ]
[ ]
[ 1
] ] [
[
] [ ]
[ ]
[ ]
[ 1
] ] [
[
by given are species chloro
cadmium other
of ions concentrat the
Similarly,
] [ ]
[ ]
[ ]
[ ] 1
[
: 10.27 eqn g Rearrangin
] [ ]
[ ]
[ ]
[ ] 1
[
functions, for the
s expression the
ng Substituti
] [
] [
] [
] [
] [
] [
] [
] 1 [
] [
: ] [Cd by 10.25 eqn dividing by
begin We
way.
following in the
species cadmium
five the of each of ion concentrat for the
s expression derive
can We
Cl Cl
Cl Cl
C CdCl Cl
Cl Cl
Cl Cl
C CdCl Cl
Cl Cl
Cl Cl
C CdCl Cl
Cl Cl
Cl Cl
C CdCl Cl
Cl Cl
Cl Cl
Cd C
Cl Cl
Cl Cd Cl
C
Cd CdCl Cd
CdCl Cd
CdCl Cd
CdCl Cd
C
f f
f f
Cd f
f f
f f
Cd f
f f
f f
Cd f
f f
f f
Cd f
f f
f f
Cd
f f
f f
Cd Cd
(10.26)
(10.27)
(10.28)
(10.29)
(10.30)
(10.31)
(10.32)
E.g. line b, surface water salinity=10 %
0, [Cl
-1]=0.16 mol L
-1 [Cd
2+]=0.04, CdCl
+=0.52, CdCl
2=0.33, CdCl
3-=0.10, CdCl
42-=0.01
Chapter 10. Distribution of species in aquatic systems
10.1 Single-variable diagrams: Cadmium complexes with chloride
Concept of pE: pE =
A large negative value of pE indicates a large value for the e- activity in solution, implying
A large positive value of pE: low activity of e- in solution, implying
pE values in water = -12~25
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
nFE
K a K a
a pE
a a K a
a a
K a
aq Fe e
aq Fe
eq Fe Fe e eq
Fe eq Fe e
e Fe
Fe eq
log RT -2.303 G
Since
log log
log
have we 10.36, eqn
of sides both of logs taking and
pE of definition the
Using
1
) ( )
(
reaction half
simple he
Consider t
2 3 2
3 3
2
2
3 (10.34)
(10.35) (10.36)
(10.37)
(10.38) (10.39)
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
. calculated be
can system tal
environmen particular
a of pE the equation, this
into d substitute are
Fe and Fe of ions) concentrat
by ed approximat (usually
activities actual
the and value pE
standard When the
pE pE
: conditions standard
- non For
pE pE
and
log
: 1 ,
conditions standard
Under
0591 log . 0
and
0591 . log 0
so 1, n case, In this
0591 . 0 303
. log 2
have we ), 485Cmol 96
F and mol K 8.314J (R
298K at
reaction), half
in the
ed transferr electrons
of number the
i.e.
- meaning mical
electroche usual
the has (n
2 3
1 - 1
- 1 -
2 3 2 3
2 3
Fe Fe Fe Fe
Fe Fe eq
eq
a a a a
a E a
pE K E
nE RT
K nFE (10.40)
(10.41)
(10.42)
(10.43)
(10.44)
(10.45)
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
(10.48)
then is
10.45 eqn
of form general
The
m.
equilibriu at
just those not
, conditions any
under obtain
that ions)
concentrat ion,
approximat
an as (or, activities
uses but constant,
m equilibriu an
of form the
akes quotient t
reaction The
(10.47)
] [
] [ )
( ) (
as defined is
(Q)
quotient reaction
the couple, redox
a of forms reduced
and oxidized
the are B and A where
(10.46)
reaction a
for case, general
In the
a b a
A b B
A B a
Q a
bB ne
aA
Consider a half-reaction
Therefore
pE
0from eq (10.44)
Second method, using eqs. (10.40) and (10.44)
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: Methods of calculating pE
0) 34 . 10 (
771 . 0
)
( )
( 2 0
3 aq e Fe aq E V
Fe
(10.51c)
6
) ( 3 ) ( 3
(10.51b)
) ( )
(
(10.51a)
) ( 3 ) ( )
(
of sum the is reaction The
(10.51)
6
) ( )
( 3
) (
: found easily is
value E
tabulated no
for which reaction
half he Consider t
reaction.
half overall an
produce to
combined be
may reactions several
cases, some
In
known.
is constant m
equilibriu
e appropriat the
but where available,
not is value E
an when applicable
is relation This
(10.50)
log
(10.49)
0591
. log 0
10.44 and 10.40 eqns
in relations the
of use makes pE
g calculatin for
method second
A
2 3
2 3
3 3
2 2
3 3
O H aq
OH aq
O H
aq Fe e
aq Fe
aq OH aq
Fe OH
Fe
O H aq
Fe e
aq O H OH
Fe
n pE K
nE npE K
eq eq
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: Methods of calculating pE
0 Suppose the initial conc. of [Cr
3+]=26 mg L
-1, then dissolved oxygen in downstream oxidize to Cr
2O
72-, pH=6.5 (a
H3O+=10
-6.5)
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: Chromium in tannery wastes
1 . 14
) 10 ( 209 . 0 log 1 4 8 1 . 20
) (
/ log 1
1
: 10.48 eqn
Using
23 . 1
(10.55)
6 4
) ( 4
) (
is system)
aerated well
a called (often
r with wate m
equilibriu in
O c atmospheri for
reaction relevant
The
4 5 . 6
4 2 3
2
2
2 3
O
O P aH
P pE n
pE
pE
V E
O H e
aq O
H g
O
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: Chromium in tannery wastes
In the diagram, areas define the regions where particular species are dominant
P
0=101325 Pa =1 atm: this is the min. pressure required for gas evolution from the aq. solution. I.e. when P
gas> P
0,
E.g. gas evolution from acidic solution
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams
(10.59)
6
) ( 2
) ( 4
and
(10.58)
) ( 2
) (
are cases two
these of
Examples
insoluble.
is that one
form to
reacting species
soluble a
is there or where
involved,
are species soluble
only where
situation for the
required is
condition of
pe Another ty
(10.57)
2 ) ( 2
) ( 2
2 2
3 2
2 4
2 2
3
O H aq
Mn e
aq O
H MnO
aq Sn
e aq
Sn
O H g
H e
aq O
H
Consider aq. sulfur system where the species of interest are: SO
42-(aq), HSO
4-(aq), S(s), HS
-(aq), and H
2S (aq)
To consider first water itself,
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams
ions).
hydronium
and hydroxyl for
except activities
than
rather ions
concentrat use
will we ns, calculatio subsequent
in and here again that
(note
(10.61)
as written is
reaction for this
10.48 Equation
0 . 14
828 . 0
reaction For this
(10.60)
) ( 2
) ( 2
2
2 2
pE
V E
aq OH
g H e
O H
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams
Chapter 10. Distribution of species in aquatic systems
10.2 Two-variable diagrams: pE/pH diagrams
pH a pE
Pa P
a P
pE pE
O H
O O H
80 . 20
) /
1 log(
80 . 20
325 , 101 P
pressure.
c atmospheri equal
gas the of pressure that the
requires condition
boundary the
again, Once
(10.64)
)
) (
/ 1 4log(
1
3 2
2 3
O
4