Calculation of equilibrium constants from kinetic rates of the H2O-CO2 system.

1. H2O + CO2
Carbonate Kinetics
aqion.de

2. True and
Composite Carbonic Acid
Part 1

3. Three components are
involved in the carbonic acid
formation:
CO2(aq)
H2CO3
HCO3
-
true carbonic acid
dissolved CO2
hydrogen carbonate

4. Two of them are bundled
into one entity:
CO2(aq)H2CO3
true carbonic acid dissolved CO2
the composite carbonic acid H2CO3* =
+
It‘s just the composite carbonic acid (and not the
true carbonic acid) that is commonly known as
the carbonic acid.

5. True and Composite Carbonic Acid
true carbonic acid: H2CO3
composite carbonic acid: H2CO3* = CO2(aq) + H2CO3
There are two types of carbonic acid:
Each of these two acids is characterized by
its own equilibrium constant :
Carbonic acid Reaction formula
Equilibrium
constant
true H2CO3  H+ + HCO3
- Ktrue
composite
(apparent)
H2CO3
*  H+ + HCO3
- K1
Note:Thisisnot
areactionequation.

6. True and Composite Carbonic Acid
true carbonic acid: H2CO3
composite carbonic acid: H2CO3* = CO2(aq) + H2CO3
There are two types of carbonic acid:
Each of these two acids is characterized by
its own equilibrium constant :
Carbonic acid Reaction formula
Equilibrium
constant
true H2CO3  H+ + HCO3
- Ktrue = 2.0·10-4 M
composite
(apparent)
H2CO3
*  H+ + HCO3
- K1 = 4.4·10-7 M
500 times
stronger !

7. }COH{}OH)aq(CO{
}HCO}{H{
K
3222
3
1



}COH{
}HCO}{H{
K
32
3
true


Law of Mass Action
Reaction Kinetics
log Ktrue = -3.7
log K1 = -6.35
?Equilibrium Constant
?

8. The underlying
Reaction Kinetics
Part 2

9. Three components are
involved in the carbonic acid
formation:
CO2(aq)
H2CO3
HCO3
-
true carbonic acid
dissolved CO2
hydrogen carbonate
ReactionKinetics

10. Reaction
Kinetics
CO2(aq) + H2O
true carbonic acid
HCO3
- + H+
H2CO3
1
2 3
k21 k13
k31
composite carbonic acid
k23
k32
k12
slow
1 = HCO3
- + H+
2 = H2CO3
3 = CO2(aq) + H2O2k1k3)kk(
dt
3d
3k1k2)kk(
dt
2d
3k2k1)kk(
dt
1d
23133231
32122321
31211312



1
2
3
1 2 3
2 1 3
3 1 2
1
2
3

11. Reaction
Kinetics
CO2(aq) + H2O
true carbonic acid
HCO3
- + H+
H2CO3
1
2 3
k21 k13
k31
composite carbonic acid
k23
k32
k12
slow
1 = HCO3
- + H+
2 = H2CO3
3 = CO2(aq) + H2O2k1k3)kk(
dt
3d
3k1k2)kk(
dt
2d
3k2k1)kk(
dt
1d
23133231
32122321
31211312



1
2
3
1 2 3
2 1 3
3 1 2
1
2
3

12. k13 , k31 (slow) << k12 , k21 (fast)
4-5 orders of magnitude
smaller
From Experiment:

13. k13 , k31 (slow) << k12 , k21 (fast)
2k1k3)kk(
dt
3d
3k1k2)kk(
dt
2d
3k2k1)kk(
dt
1d
23133231
32122321
31211312



1
2
3
1 2 3
2 1 3
3 1 2
X
X
CO2(aq) + H2O
true carbonic acid
HCO3
- + H+
H2CO3
1
2 3
k21 k13
k31
composite carbonic acid
k23
k32
k12
slow
X
2k1k
dt
1d
2112 
1
1 2

14. Fast Reaction  Equilibrium
02k1k
dt
1d
2112 
1
1 2
true
32
3
12
21
K
}COH{
}HCO}{H{
2
1
k
k


1
2
Law of Mass Action
2K1 true1 2

15. 2)kKk(3)kk(
dt
3d
2k1k3)kk(
dt
3d
23true133231
23133231


3
3 1 2
3
3 2
2K1 true1 2
ab kk
... simplify

16. 0
32
22
b
a
K
}COH{
}OH)aq(CO{
2
3
k
k



3
2
Law of Mass Action
Equilibrium
02k1k
dt
1d
ab 
3
3 2

17. CO2(aq) + H2O
H2CO3
ka kb
HCO3
- + H+
k12
k21
CO2(aq) + H2O
H2CO3 HCO3
- + H+
K0
Ktrue
Kinetic Rates
Equilibrium Constants

18. Composite Equilibrium Constant K1
The two species CO2(aq) and H2CO3 are treated
together as if they were one substance
(denoted by H2CO3*) with
}COH{}OH)aq(CO{
}HCO}{H{
K
3222
3
1



}COH{
}HCO}{H{
K *
32
3
1



19. 1}COH/{}OH)aq(CO{
K
}COH{}OH)aq(CO{
}COH}{H{K
}COH{}OH)aq(CO{
}HCO}{H{
K
3222
true
3222
32true
3222
3
1








1K
K
K
0
true
1


CO2(aq) + H2O
H2CO3
HCO3
- + H+
K1K0
Ktrue
H2CO3
*

20. Equilibrium Constants
k12 = 5·1010 M-1 s-1 [1]
k21 = 1·107 s-1 [1]
ka = kH2CO3 ≈ 18 s-1 [2]
kb = kCO2 ≈ 0.04 s-1 [2]
[1] Pocker & Blomkquist 1977
[2] Stumm & Morgan 1996: kH2CO3 = 10 ... 20 s-1, kCO2 = 0.025 ... 0.04 s-1
K0 = ka /kb = 450  log K0 = 2.65
Ktrue = k21 /k12 = 2.0·10-4 M  log Ktrue = -3.7
K1 = Ktrue /(K0 + 1) = 4.4·10-7 M  log K1 = -6.35
Kinetic
Rates

21. Résumé
H2CO3
* = H+ + HCO3
- log K1 = -6.35
Carbonate kinetics metamorphosed
into equilibrium thermodynamics:
... enters hydrochemistry models
and programs (PhreeqC, etc.)

22. Ref
aqion.de
www.aqion.de/site/175