Equilibrium thermodynamics and speciation calculations of an open and closed H2O-CO2 system.

1. H2O + CO2
Open vs. Closed System
aqion.de

2. Prelude1
Pure CO2 System2
Pure CO2 System + Acid/Base3

3. Prelude
(Concepts & Notation)
Part 1

4. CO2(g)
closed system open system
H2CO3
*
HCO3
-
CO3
-2
OH-
H+
H2CO3
*
HCO3
-
CO3
-2
OH-
H+

5. H2CO3
*
HCO3
-
CO3
-2
OH-
H+
CO2(g)
Open
System
6Species
H2CO3
*
Composite
Carbonic Acid
= + = CO2CO2(aq) H2CO3
dissolved CO2
True
Carbonic Acid
KH
abbreviation
(used in PhreeqC)

6. Open
System
Composite
Carbonic Acid
{H2CO3
*} = KH ∙ PCO2
Henry’s Law
CO2 Partial
Pressure
KH = 10-1.47 Matm-1 (at 25°C)
H2CO3
*
HCO3
-
CO3
-2
OH-
H+
CO2(g)
6Species
KH

7. Three Uncharged Species (Notation !)
{CO2} = {H2CO3
*} = KH ∙ 10-pCO2
Henry’s Law
CO2 partial pressure
CO2(g) CO2 in gas phase
CO2(aq) dissolved CO2 (part of H2CO3
*)
CO2 composite carbonic acid (H2CO3
*)
log {CO2} = log KH – pCO2
PCO2 = 10-pCO2
curly braces {...} denote activities (i.e. effective concentrations)

8. Pure Water in Contact with Atmosphere
Henry’s Law
composite
carbonic acid: (at 25°C)
log {CO2} = log KH – pCO2
{CO2} = {H2CO3
*} = 0.013 mM
CO2 Partial pressure
PCO2 = 10-pCO2 = 0.00039 atm
log {CO2} = – 1.47 – 3.408 = – 4.878
[ N.B. In this dilute system: activities = molar concentrations ]

9. The Pure CO2 System
(Equilibrium Speciation)
Part 2

10. Equilibrium
Thermodynamics
CO2(g)
H2CO3
*
KH
K1
H2O
K2
Kw Kw
H+ HCO3
- H+ CO3
-2
CO2(g)  H2CO3
* log KH = -1.47
H2CO3
*  H+ + HCO3
- log K1 = -6.35
HCO3
-  H+ + CO3
-2 log K2 = -10.33
H2O  H+ + OH- log Kw = -14.0
equilibrium constants (at 25°C)
Law of
Mass Action
4 equations

11. Equilibrium
Thermodynamics
KH = {H2CO3
*} / PCO2 = 10-1.47
K1 = {H+} {HCO3
-} / {H2CO3
*} = 10-6.35
K2 = {H+} {CO3
-2} / {HCO3
-} = 10-10.33
Kw = {H+} {OH-} = 10-14.0
CT = [CO3
-2] + [HCO3
-] + [CO2] (Mass Balance)
0 = [H+] – [HCO3
-] – 2 [CO3
-2] – [OH-] (Charge Balance)
Law of
Mass Action
closedsystem
opensystem
CO2(g)
H2CO3
*
KH
K1
H2O
K2
Kw Kw
H+ HCO3
- H+ CO3
-2
6 unknowns  6 equations

12. KH = {H2CO3
*} / PCO2 = 10-1.47
K1 = {H+} {HCO3
-} / {H2CO3
*} = 10-6.35
K2 = {H+} {CO3
-2} / {HCO3
-} = 10-10.33
Kw = {H+} {OH-} = 10-14.0
CT = [CO3
-2] + [HCO3
-] + [CO2] Mass Balance
0 = [H+] – [HCO3
-] – 2 [CO3
-2] – [OH-] Charge Balance
Law of
Mass Action
Equilibrium
Thermodynamics
ion activities {i}
molar concentrations [i]

13. Open
CO2 System
Closed
CO2 System
Given
(Input)
pCO2 DIC
Calculate
(Output)
 pH
 carb. speciation
 DIC
 pH
 carb. speciation
 pCO2
DIC = [CO2] + [HCO3
-] + [CO3
-2] pCO2 = – log KH – log {CO2}
In an open system you set pCO2; in a closed system you set DIC.
You cannot set both values independently.

14. Equilibrium Speciation
Example Calculations
(with PhreeqC)

15. Equilibrium Speciation at 25 °C
H2O + 1 mM DIC
open system closed system
input pCO2 = 3.408 DIC = 1 mM
pH 5.61 4.68
CO2 mM 0.0133 0.979
HCO3
- mM 0.0024 0.021
CO3
-2 mM 4.7·10-8 4.8·10-8
DIC mM 0.0157 1.000
pCO2 3.408 1.54
CO2 abbreviates the composite carbonic acid: H2CO3
* = CO2(aq) + H2CO3
= CO2 + HCO3
- + CO3
-2
H2O in contact with atmosphere
(PCO2 = 0.00039 atm = 10-pCO2)
= H2CO3
*
= – 1.47 – log CO2 (in M)

16. A closed system with 0.0157 mM DIC mimics
an open CO2 system in contact with atmosphere.
An open CO2 system with pCO2 = 1.54
mimics an closed system with 1 mM DIC.
typical for groundwater
(enhanced CO2 emerges
from degradation of organic matter)
In an open system you set pCO2; in a closed system you set DIC.
You cannot set both values independently.
However, you can outmaneuver this concept:

17. But this is only half the story, and the less important half.
The concept of open/closed systems becomes especially
relevant when the solution is attacked by acids or bases:
In a open system the CO2 (or pCO2 value) remains
constant, while in a closed system DIC remains constant
(and CO2 changes).

18. CO2 System + Acid/Base
(Titration Calculations)
Part 3

19. For a given value of DIC, say 1 mM, the pH is fixed to 4.68.
There is no chance to alter pH
unless the pure CO2 system is attacked
by HCl (to decrease pH) or NaOH (to increase pH).
H2O +
1 mM DIC
HCl
pH  1
H2O +
1 mM DIC
NaOH
pH  14

20. pH Dependence
Titration Calculations
(with PhreeqC)

21. NaOH
HCl
Closed CO2-System + HCl or NaOH
Note: Na forms
aqueous complexes
H2O + 1 mM DIC

22. Closed CO2-System + HCl or NaOH
H2O + 1 mM DIC (pure system)
pH HCl NaOH DIC CO2 HCO3- CO3-2 NaHCO3 NaCO3- I Alk
mM mM mM mM mM mM mM mM mM mM
1 122.38 1 1 5.9E-06 5.9E-15 122.38 -122.38
2 10.99 1 1 4.8E-05 2.9E-13 10.99 -10.99
3 1.035 1 0.999 4.6E-04 2.4E-11 1.035 -1.035
4 0.097 1 0.996 4.5E-03 2.2E-09 0.101 -0.10
4.5 0.018 1 0.986 0.014 2.1E-08 0.032 -0.02
4.68 0 0 1 0.979 0.021 7.8E-08 0.021 0
5 0.033 1 0.957 0.043 2.1E-07 7.8E-07 1.2E-11 0.033 0.03
6 0.311 1 0.688 0.312 1.6E-05 5.3E-05 8.3E-08 0.31 0.31
7 0.822 1 0.172 0.821 4.3E-04 3.6E-04 5.7E-06 0.82 0.82
8 0.985 1 0.021 0.973 5.1E-03 5.0E-04 8.1E-05 0.99 0.99
9 1.059 1 2.10E-03 0.947 0.050 5.2E-04 8.4E-04 1.06 1.06
10 1.46 1 1.40E-04 0.644 0.347 4.8E-04 7.8E-03 1.46 1.46
11 2.93 1 3.00E-06 0.144 0.821 2.1E-04 0.034 2.93 2.93
12 13.2 1 2.60E-08 0.013 0.855 7.6E-04 0.132 13.2 13.2
13 137.2 1 8.70E-11 5.1E-04 0.530 2.3E-05 0.469 137.2 137.2
14 1745 1 7.40E-14 7.4E-06 0.139 2.3E-06 0.861 1745 1745
ionic strength

23. There are several types
of graphical display
(linear or log scale,
XY plots, stacked-area charts, etc.)

24. linear scale
logarithmic
scale
ClosedCO2-System(1mMDIC)

25. Closed CO2-System: Speciation = f(pH)
In this (symmetric)
form it enters a lot of
textbooks.
add together
both curves

26. linear scale
logarithmic
scale
ClosedCO2-System(1mMDIC)

27. XY chart
stacked-
area chart
ClosedCO2-System(1mMDIC)

28. 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1 2 3 4 5 6 7 8 9 10 11 12 13 14
mM
pH
HCO3-
CO3-2
CO2
NaHCO3
NaCO3-
Closed CO2-System: Mass Balance
DIC = CO2 + HCO3
- + CO3
-2 + NaHCO3 + NaCO3
- = 1 mM
stacked-areachart

29. Equivalence Points[H+] = [HCO3
-]
Species Distribution
CT = 10-4 M
CT = 10-3 M

30. ... and now the Open System
(which is quite different)

31. pH
NaOH
HCl
Open CO2-System + HCl or NaOH
pure H2O-CO2 system

32. Open CO2-System + HCl or NaOH
pure CO2-H2O system
pH HCl NaOH DIC CO2 HCO3- CO3-2 I Alk
mM mM mM mM mM mM mM mM
1 122.38 0.0129 0.0129 7.6E-08 7.6E-17 122.4 -122.38
2 10.99 0.0133 0.0133 6.5E-07 4.2E-15 10.99 -10.99
3 1.035 0.0133 0.0133 6.1E-06 3.2E-13 1.035 -1.035
4 0.101 0.0134 0.0133 6.0E-05 2.9E-11 0.101 -0.10
5 0.009 0.0139 0.0133 0.001 2.9E-09 0.010 -0.01
5.3 0.0037 0.0145 0.0133 0.001 1.2E-08 0.005 -0.001
5.61 0 0 0.0157 0.0133 0.002 4.7E-08 0.002 0
5.7 0.001 0.0162 0.0133 0.003 6.8E-08 0.003 0.001
6 0.004 0.0183 0.0133 0.005 2.0E-07 0.005 0.005
6.5 0.009 0.0228 0.0133 0.010 7.3E-07 0.010 0.01
7 0.013 0.0266 0.0133 0.013 0 0.013 0.01
8 0.017 0.0301 0.0133 0.017 0 0.017 0.02
9 0.027 0.0400 0.0133 0.027 0 0.027 0.03
9.5 0.050 0.0631 0.0133 0.050 0 0.050 0.05
10 0.122 0.1353 0.0133 0.122 0 0.123 0.12
ionic strength
There is no DIC conservation !
DIC grows exponentially for pH > 5.6

33. linear scale
logarithmic
scale
OpenCO2-System(pCO2=3.408)

34. CO2 System Conserved quantity
Open CO2 (or pCO2)
Closed DIC
Titration Calculations:

35. www.aqion.de/site/161 (EN)
www.aqion.de/site/156 (DE)
Ref