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:


Table 10.1 Acid dissociation

constants for phosphoric acid

Ka pKa

First

dissociation7.1x10-3 2.15

Second


Third


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


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


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


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)


.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)


(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,


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


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

Template of pE/pH diagram

Chapter 10. Distribution of species in aquatic systems10.2 Two-variable diagrams: The sulfur system

Part 2. The Hydrosphere

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Transcript of Part 2. The Hydrosphere