pH0 2 4 6 8 10 12 14

log

a i

-8

-7

-6

-5

-4

-3

-2

6.35 10.33H2CO3* HCO3- CO3

2-

H+

OH-

Common pHrange in nature

Bjerrum plot showing the activities of inorganic carbon species as a function of pH for a value of total inorganic carbon of 10-3 mol L-1.

In most natural waters, bicarbonate is the dominant carbonate species!

SPECIATION IN OPEN CO2-H2O SYSTEMS - I

• In an open system, the system is in contact with its surroundings and components such as CO2 can migrate in and out of the system. Therefore, the total carbonate concentration will not be constant.

• Let us consider a natural water open to the atmosphere, for which pCO2

= 10-3.5 atm. We can calculate the concentration of H2CO3* directly from KCO2

:

Note that M H2CO3* is independent of pH!

2

32

2

*

CO

COHCO p

MK

2232 * COCOCOH KpM

2232logloglog * COCOCOH KpM

SPECIATION IN OPEN CO2-H2O SYSTEMS - II

• The concentration of HCO3- as a function of pH is next

calculated from K1:

but we have already calculated M H2CO3*:

so2232 * COCOCOH KpM

*1

32

3

COH

HHCO

M

aMK

H

COHHCO a

MKM *1 32

3

H

COCOHCO a

pKKM 22

3

1

pHpKKM COCOHCO

2231loglog

SPECIATION IN OPEN CO2-H2O SYSTEMS - III

• The concentration of CO32- as a function of pH is next

calculated from K2:

but we have already calculated M HCO3- so:

and

H

COCOHCO a

pKKM 22

3

1

3

23

2HCO

HCO

M

aMK

H

HCOCO a

MKM 3

23

2

212 22

23

H

COCOCO a

pKKKM

pHpKKKM COCOCO2loglog

2223

12

SPECIATION IN OPEN CO2-H2O SYSTEMS - IV

• The total concentration of carbonate CT is obtained by summing:

23332 * COHCOCOHT MMMC

2211 2222

22

H

COCO

H

COCOCOCOT a

KpKKa

KpKKpC

2

2111loglog22

HHCOCOT a

KKaKKpC

pH2 3 4 5 6 7 8 9 10 11 12

log

conc

entra

tion

(mol

ar)

-8

-6

-4

-2

0

CTH+

OH-

H2CO3*

HCO3-

CO32-

pK1 pK2

Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2

= 10-3.5 atm.

pH

2 3 4 5 6 7 8 9 10 11 12

log

conc

entra

tion

(mol

ar)

-8

-6

-4

-2

0

CTH+

OH-

H2CO3*

HCO3-

CO32-

pK1 pK2

Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2

= 10-2.0 atm.

Methods of solving equations that are ‘linked’

• Sequential (stepwise) or simultaneous methods• Sequential – assume rxns reach equilibrium in

sequence:• 0.1 moles H3PO4 in water:

– H3PO4 = H+ + H2PO42- pK=2.1

– [H3PO4]=0.1-x , [H+]=[HPO42-]=x

– Apply mass action: K=10-2.1=[H+][HPO42-] / [H3PO4]

– Substitute x x2 / (0.1 – x) = 0.0079 x2+0.0079x-0.00079 = 0, solve via quadratic equation

– x=0.024 pH would be 1.61• Next solve for H2PO4

2-=H+ + HPO4-…

Calcite Solubility• CaCO3 -> Ca2+ + CO3

2- log K=8.48• We consider minerals to dissolve so that 1 Ca2+

dissolves with 1 CO32-

• If dissolving into dilute water (effectively no Ca2+ or CO3

2- present): x2=10-8.48, x= aCa2+ = aCO32-

• If controlled by atmospheric CO2, substitute CO32-

for expression

• What happens in real natural waters??

pHpKKKM COCOCO2loglog

2223

12

Charge Balance• Principle of electroneutrality For any solution, the

total charge of positively charged ions will equal the total charge of negatively charged ions.– Net charge for any solution must = 0

• Charge Balance Error (CBE)

– Tells you how far off the analyses are (greater than 5% is not good, greater than 10% is terrible…)

• Models adjust concentration of an anion or cation to make the charges balance before each iteration!

aacc

aacc

zmzmzmzm

CBE

Using Keq to define equilibrium concentrations

G0R = -RT ln Keq

• Keq sets the amount of ions present relative to one another for any equilibrium condition

i

ni

n

eq reactants

productsQK

][

][AT Equilibrium

i

ni

n

eq reactants

productsK

][

][

Speciation• Any element exists in a solution, solid, or gas

as 1 to n ions, molecules, or solids

• Example: Ca2+ can exist in solution as: Ca++ CaCl+ CaNO3

+ Ca(H3SiO4)2 CaF+ CaOH+ Ca(O-phth) CaH2SiO4 CaPO4

- CaB(OH)4

+ CaH3SiO4+ CaSO4

CaCH3COO+ CaHCO3+ CaHPO4

0 CaCO3

0

• Plus more species gases and minerals!!

How do we know about all those species??

• Based on complexation how any ion interacts with another ion to form a molecule, or complex (many of these are still in solution)

• Yet we do not measure how much CaNO3

+, CaF+, or CaPO4- there is in a

particular water sample• We measure Ca2+ But is that Ca2+ really

how the Ca exists in a water??

Aqueous Complexes

• Why do we care??1. Complexation of an ion also occuring in a

mineral increases solubility2. Some elements occur as complexes more

commonly than as free ions3. Adsorption of elements greatly determined

by the complex it resides in4. Toxicity/ bioavailability of elements depends

on the complexation

Defining Complexes

• Use equilibrium expressions:G0

R = -RT ln Keq

• cC + lHL CL + lH+

• Where B is just like Keq!

)reactants()( 000i

iii

iiR GnproductsGnG

lc

nc

i HLCHCL

][][][][

Mass Action & Mass Balance

• mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- +

CaHCO3+ + CaCO3

0 + CaF+ + CaSO40 +

CaHSO4+ + CaOH+ +…

• Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equation

lc

nc

i HLCHCL

][][][][

nxLmCamCa 22

Mineral dissolution/precipitation

• To determine whether or not a water is saturated with an aluminosilicate such as K-feldspar, we could write a dissolution reaction such as:

• KAlSi3O8 + 4H+ + 4H2O K+ + Al3+ + 3H4SiO40

• We could then determine the equilibrium constant:

• from Gibbs free energies of formation. The IAP could then be determined from a water analysis, and the saturation index calculated.

4

344

3

H

SiOHAlK

aaaa

K

INCONGRUENT DISSOLUTION

• Aluminosilicate minerals usually dissolve incongruently, e.g.,

2KAlSi3O8 + 2H+ + 9H2O

Al2Si2O5(OH)4 + 2K+ + 4H4SiO40

• As a result of these factors, relations among solutions and aluminosilicate minerals are often depicted graphically on a type of mineral stability diagram called an activity diagram.

ACTIVITY DIAGRAMS: THE K2O-Al2O3-SiO2-H2O SYSTEM

We will now calculate an activity diagram for the following phases: gibbsite {Al(OH)3}, kaolinite {Al2Si2O5(OH)4}, pyrophyllite {Al2Si4O10(OH)2}, muscovite {KAl3Si3O10(OH)2}, and K-feldspar {KAlSi3O8}.

The axes will be a K+/a H+ vs. a H4SiO40.

The diagram is divided up into fields where only one of the above phases is stable, separated by straight line boundaries.

log aH4SiO4

0

-6 -5 -4 -3 -2 -1

log

(aK

+ /aH

+ )

0

1

2

3

4

5

6

7

KaoliniteGibbsite

Muscovite

K-feldspar

Pyrophyllite

Qua

rtz

Am

orph

ous

silic

a

Activity diagram showing the stability relationships among some minerals in the system K2O-Al2O3-SiO2-H2O at 25°C. The dashed lines represent saturation with respect to quartz and amorphous silica.

2 3 4 5 6 7 8 9 10 11 12-10

-8

-6

-4

-2

0

2

pH

log

a A

l+++

Al+++

Al(OH)2+

Al(OH)4-

AlOH++

Gibbsite

25oC

Greg Mon Nov 01 2004

Dia

gram

Al+

++,

T =

25

C,

P

= 1

.013

bar

s, a

[H

2O

] =

1

Seeing this, what are the reactions these lines represent?