Download - Part 2. The Hydrosphere
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 systems10.1 Single-variable diagrams: Phosphate species
pPO
pHPO
pPOH
POH
a
C
PO
C
HPO
C
POH
POHPOPOHPOH
POH
POH
OHPOHK
POHPOPOHPOH
][
][
][
][][][][
][
][
]][[
3
4
2
4
42
3
4
2
44243
43
43
3421
3
4
2
44243
34
24
42
43
(10.1)
(10.2)
(10.3)
(10.4)
(10.5)
(10.6)
Conc. of individual phosphate species:
Chapter 10. Distribution of species in aquatic systems10.1 Single-variable diagrams: Phosphate species
Table 10.1 Acid dissociation
constants for phosphoric acid
Ka pKa
First
dissociation7.1x10-3 2.15
Second
dissociation6.3x10-8 7.20
Third
dissociation4.2x10-13 12.38
3212131
2
3
3
3
3213
3212131
2
3
3
3
213
3212131
2
3
3
3
1
2
3
3212131
2
3
3
3
3
3
3
3
3
3321
2
3213143
43
3
3
321
2
3
21
3
143
3
4
2
44243
3
3
433213
4
2
3
43212
4
3
43142
][][][
][
][][][
][
][][][
][
thatfind wens,calculatiosimilar Using
][][][
][
:][by equation theof side hand-right theof bottom and tophemultiply t then We
)]/[]/[]/[1]([
][
10.3eqn From
)][][][
1]([
][][][][
][
][][
][
][][
][
][][
34
24
42
43
43
aaaaaa
aaa
PO
aaaaaa
aa
HPO
aaaaaa
a
POH
aaaaaa
POH
aaaaaa
POH
aaaaaa
p
aaa
aa
a
KKKKKOHKOHOH
KKKOH
KKKKKOHKOHOH
KKOH
KKKKKOHKOHOH
KOH
KKKKKOHKOHOH
OH
OH
OHKKKOHKKOHKPOH
POH
OH
KKK
OH
KK
OH
KPOH
POHPOPOHPOHC
OH
POHKKKPO
OH
POHKKHPO
OH
POHKPOH
(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 systems10.1 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 systems10.1 Single-variable diagrams: Cadmium complexes with chloride
2
4321f4
-2
4
2
2
321f3
-
3
2
2
21f22
2
1f1
2
21fn
f
3
2
44
2
43
2
3332
222
21
2
108.3 4
104.6 3
102.3 2
109.7
seen thatreadily isIt . as symbolized are constants
stability overall theand steps overall'' using described be alsomay reactions The
6.0]][[
][
0.2]][[
][
0.4]][[
][
109.7]][[
][
ffff
fff
ff
f
fnff
f
f
f
f
KKKKCdClClCd
KKKCdClClCd
KKCdClClCd
KCdClClCd
KKK
ClCdCl
CdClKCdClClCdCl
ClCdCl
CdClKCdClClCdCl
ClCdCl
CdClKCdClClCdCl
ClCd
CdClKCdClClCd
(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 systems10.1 Single-variable diagrams: Cadmium complexes with chloride
4
4
3
3
2
2
1
1
4
42
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
12
2
2
4
2
3
2
2
22
2
][][][][1
][][
][][][][1
][][
][][][][1
][][
][][][][1
][][
bygiven are species chloro cadmiumother of ionsconcentrat theSimilarly,
][][][][1][
:10.27eqn gRearrangin
][][][][1][
functions, for the sexpression thengSubstituti
][
][
][
][
][
][
][
][1
][
:][Cdby 10.25eqn dividingby begin We way.following in the
species cadmium five theofeach ofion concentrat for the sexpression derivecan We
ClClClCl
CClCdCl
ClClClCl
CClCdCl
ClClClCl
CClCdCl
ClClClCl
CClCdCl
ClClClCl
CCd
ClClClClCd
C
Cd
CdCl
Cd
CdCl
Cd
CdCl
Cd
CdCl
Cd
C
ffff
Cdf
ffff
Cdf
ffff
Cdf
ffff
Cdf
ffff
Cd
ffffCd
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
[Cd2+]=0.04, CdCl+=0.52, CdCl2=0.33, CdCl3-=0.10, CdCl42-=0.01
Chapter 10. Distribution of species in aquatic systems10.1 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 systems10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
nFE
K
a
aKapE
a
aK
a
aa
aK
aqFeeaqFe
eq
Fe
Feeqe
Fe
Feeq
e
eFe
Feeq
log RT -2.303G
Since
logloglog
have we10.36,eqn of sidesboth of logs takingand pE of definition theUsing
1
)()(
reaction half simple heConsider t
2
3
2
3
3
2
23
(10.34)
(10.35)
(10.36)
(10.37)
(10.38)
(10.39)
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
.calculated becan system talenvironmen particular
a of pE theequation, thisinto dsubstitute are Fe and Fe of ions)concentrat
by edapproximat(usually activities actual theand valuepE standard When the
pEpE
:conditions standard-nonFor
pEpE
and
log
:1 ,conditions standardUnder
log0591.0
and
0591.0log
so 1,n case, In this
0591.0303.2log
have we),485Cmol 96F and molK 8.314J(R298K at reaction), half in the
ed transferrelectrons ofnumber thei.e. - meaning micalelectroche usual thehas(n
23
1-1-1-
2
3
23
2
3
Fe
Fe
FeFe
Fe
Fe
eq
eq
a
a
aa
a
aEpE
EK
nE
RT
nFEK (10.40)
(10.41)
(10.42)
(10.43)
(10.44)
(10.45)
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams (Pourbaix diagram)
(10.48)
thenis 10.45eqn of form general The
m.equilibriuat just thosenot ,conditionsany under obtain that ions)concentrat ion,approximat
an as (or, activities usesbut constant, mequilibriuan of form theakesquotient treaction The
(10.47) ][
][
)(
)(
as defined is (Q)
quotientreaction thecouple,redox a of forms reduced and oxidized theare B andA where
(10.46)
reaction afor case, general In the
a
b
a
A
b
B
A
B
a
aQ
bBneaA
Consider a half-reaction
Therefore
0pE from eq (10.44)
Second method, using eqs. (10.40) and (10.44)
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: Methods of calculating pE0
)34.10( 771.0 )()( 023 VEaqFeeaqFe
(10.51c) 6)(3)(3
(10.51b) )()(
(10.51a) )(3)()(
of sum theisreaction The
(10.51) 6)()(3)(
:foundeasily is valueE tabulatednofor which reaction half heConsider t
reaction. half overallan produce tocombined bemay reactions several cases, someIn
known. isconstant mequilibriu
eappropriat thebut where available,not is valueEan when applicable isrelation This
(10.50) log
(10.49) 0591.0
log
10.44 and 10.40 eqnsin relations theof use makes pE gcalculatinfor method secondA
23
23
3
3
2
2
33
OHaqOHaqOH
aqFeeaqFe
aqOHaqFeOHFe
OHaqFeeaqOHOHFe
n
KpE
npEnE
K
eq
eq
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: Methods of calculating pE0
Suppose the initial conc. of [Cr3+]=26 mg L-1, then dissolved oxygen
in downstream oxidize to Cr2O72-, pH=6.5 (aH3O+=10-6.5)
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: Chromium in tannery wastes
1.14
)10(209.0
1log
4
18.20
)(/
1log
1
:10.48eqn Using
23.1
(10.55) 64)(4)(
is system) aerated well
a called(often r with watemequilibriuin O catmospherifor reaction relevant The
45.6
4
232
2
32
OHO aPPnpEpE
pE
VE
OHeaqOHgO
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: Chromium in tannery wastes
In the diagram, areas define the regions where particular species are
dominant
P0 =101325 Pa =1 atm: this is the min. pressure required for gas evolution
from the aq. solution. I.e. when Pgas > P0,
E.g. gas evolution from acidic solution
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams
(10.59) 6)(2)(4
and
(10.58) )(2)(
are cases two theseof Examples
insoluble. is that one form toreacting species soluble a is thereor where involved,
are species solubleonly wheresituation for the required iscondition of peAnother ty
(10.57) 2)(2)(2
2
2
32
24
223
OHaqMneaqOHMnO
aqSneaqSn
OHgHeaqOH
Consider aq. sulfur system where the species of interest are: SO42- (aq),
HSO4- (aq), S(s), HS- (aq), and H2S (aq)
To consider first water itself,
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams
ions). hydronium and hydroxylfor except activitiesthan
rather ionsconcentrat use will wens,calculatio subsequentin and here again that (note
(10.61)
as written isreaction for this 10.48Equation
0.14
828.0
reaction For this
(10.60) )(2)(22 22
pE
VE
aqOHgHeOH
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: pE/pH diagrams
pH
apE
PaP
aPpEpE
OH
OHO
80.20
)/1log(80.20
325,101P
pressure.
catmospheri equal gas theof pressure that therequirescondition boundary theagain, Once
(10.64) ))(/1log(4
1
3
2
32
O
4
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system
Template of pE/pH diagram
Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system