Ely Mine Trip

Be here by 8 am! – we should be back by 5pm Sunday at the latest

Need: camping gear, warm clothes, clothes that can get messy!

Field Notebook and pen, rock hammer if you have it, camera if you want one

pH0 2 4 6 8 10 12 14

log

ai

-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!

THE CO2-H2O SYSTEM - I

Carbonic acid is a weak acid of great importance in natural waters. The first step in its formation is the dissolution of CO2(g) in water according to:

CO2(g) CO2(aq)

At equilibrium we have:

Once in solution, CO2(aq) reacts with water to form carbonic acid:

CO2(aq) + H2O(l) H2CO30

2

2

2

CO

COCO p

aK

THE CO2-H2O SYSTEM - II

In practice, CO2(aq) and H2CO30 are combined and this

combination is denoted as H2CO3*. It’s formation is dictated by the reaction:

CO2(g) + H2O(l) H2CO3*

For which the equilibrium constant at 25°C is:

Most of the dissolved CO2 is actually present as CO2(aq); only a small amount is actually present as true carbonic acid H2CO3

0.

46.1* 102

32

2

CO

COHCO p

aK

THE CO2-H2O SYSTEM - III

Carbonic acid (H2CO3*) is a weak acid that dissociates according to:

H2CO3* HCO3- + H+

For which the dissociation constant at 25°C and 1 bar is:

Bicarbonate then dissociates according to:

HCO3- CO3

2- + H+

35.6

*1 10

32

3

COH

HHCO

a

aaK

33.102 10

3

23

HCO

HCO

a

aaK

THE RELATIONSHIP BETWEEN H2CO3* AND HCO3

-

We can rearrange the expression for K1 to obtain:

This equation shows that, when pH = pK1, the activities of carbonic acid and bicarbonate are equal.

We can also rearrange the expression for K2 to obtain:

This equation shows that, when pH = pK2, the activities of bicarbonate and carbonate ion are equal.

*

1

32

3

COH

HCO

Ha

a

a

K

3

232

HCO

CO

Ha

a

a

K

BJERRUM PLOT - CARBONATE• closed systems with a specified total carbonate

concentration. They plot the log of the concentrations of various species in the system as a function of pH.

• The species in the CO2-H2O system: H2CO3*, HCO3-,

CO32-, H+, and OH-.

• At each pK value, conjugate acid-base pairs have equal concentrations.

• At pH < pK1, H2CO3* is predominant, and accounts for nearly 100% of total carbonate.

• At pK1 < pH < pK2, HCO3- is predominant, and accounts for

nearly 100% of total carbonate.

• At pH > pK2, CO32- is predominant.

pH0 2 4 6 8 10 12 14

log

ai

-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

COH

HCO a

MKM *1 32

3

H

COCO

HCO 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

COCO

HCO a

pKKM 22

3

1

3

23

2

HCO

HCO

M

aMK

H

HCO

CO a

MKM 3

23

2

2

12 2223

H

COCO

CO 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

2

211 2222

22

H

COCO

H

COCOCOCOT a

KpKK

a

KpKKpC

2

2111loglog22

HH

COCOT a

KK

a

KKpC

pH2 3 4 5 6 7 8 9 10 11 12

log

conc

entr

atio

n (m

olar

)

-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

entr

atio

n (m

olar

)

-8

-6

-4

-2

0

CT

H+

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 H2PO42-=H+ + HPO4

-…

Mineral Solubility

• CaCO3 -> Ca2+ + CO32-

• Log K=8.48