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Part 2. The Hydrosphere

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(1)

Part 2. The Hydrosphere

Chapter 10.

Distribution of Species

in Aquatic Systems

(2)

 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)

(3)

 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)

(4)

 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

(5)

 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)

(6)

 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)

(7)

 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

(8)

 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)

(9)

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)

(10)

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

(11)

 Consider a half-reaction

 Therefore

pE

0

from 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

(12)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: Methods of calculating pE

0

(13)

 Suppose the initial conc. of [Cr

3+

]=26 mg L

-1

, then dissolved oxygen in downstream oxidize to Cr

2

O

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

(14)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: Chromium in tannery wastes

(15)

 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

(16)

 Consider aq. sulfur system where the species of interest are: SO

42-

(aq), HSO

4-

(aq), S(s), HS

-

(aq), and H

2

S (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

(17)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: pE/pH diagrams

(18)

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

(19)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(20)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(21)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(22)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(23)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(24)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(25)

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

(26)

 Template of pE/pH diagram

Chapter 10. Distribution of species in aquatic systems

10.2 Two-variable diagrams: The sulfur system

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