## Carbonate Equilibria and log K Values

Carbonates are perhaps the most important dissolved components in natural waters. The basic equations for the open and closed carbonate systems are well understood and described in many textbooks. However, the nomenclature differs sometimes considerably, especially when thermodynamic data from different databases are involved.

In the following we consider four different thermodynamic datasets and show how they are interrelated. The datasets are:

 • Stumm & Morgan 1 (textbook) • database wateq4f 2 (used by Wateq4f, PhreeqC, and aqion) • database minteq 3 (used by MinteqA2, PhreeqC) • database llnl 4, EQ3/6 5 (used by PhreeqC and EQ3/6;6)

This list is by far not complete, but it contains the most representative and popular data compilations for hydrochemical modeling (i.e. for models based on the law-of-mass-action approach). They are in widespread use since 20 years and longer. The largest database is llnl or EQ3/6 (about 17000 lines); it comprises – in addition to the inorganic species and phases – a large amount of organic compounds, the Actinites, and REE. For most modeling tasks, however, wateq4f is a good choice; it is employed in plenty of hydrochemical and environmental studies.

The CO2-H2O System

The CO2-H2O system is completely characterized by four components:

 •   CO2 in the gas phase: CO2(g) •   composite carbonic acid: H2CO3*  (in short: CO2) •   bicarbonate (hydrogen carbonate): HCO3- •   carbonate: CO3-2

The interplay between these four components is determined by three distinct equilibrium constants (KH, K1, and K2):

 $CO_{2}(g)+H_2O \ \overset{K_H}{\Longleftrightarrow} \ H_2CO_3^* \ \overset{K_1}{\Longleftrightarrow} \ H^+ + HCO_3^- \ \overset{K_2}{\Longleftrightarrow} \ 2H^+ + CO_3^{-2}$

From the mathematical point of view, the system is governed by three equations (i.e., three reaction formulas with the corresponding equilibrium constants) as shown, for example, in Eq.(1a) to Eq.(1c) below. In practice, however, you will seldom find the equations in such simple form encoded in the thermodynamic databases. But, it is always possible to convert them into the “standard form” of dataset 1. This will now be shown in more detail.7

Dataset 1 – Stumm & Morgan

The three equilibrium reactions are defined by

 (1a) CO2(g) + H2O = H2CO3* log KH = -1.47 (1b) H2CO3* = H+ + HCO3- log K1 = -6.35 (1c) HCO3- = H+ + CO3-2 log K2 = -10.33

This should be our “standard dataset”. The other three datasets listed below will be converted to the standard dataset based on KH, K1, and K2.

Dataset 2 – Thermodynamic Database wateq4f

In this dataset the composite carbonic acid is abbreviated by CO2. The three equilibrium reactions are then defined by:

 (2a) CO2(g) = CO2 log KH = -1.468 (2b) CO2 + H2O = 2H+ + CO3-2 log K3 = -16.681 (2c) HCO3- = H+ + CO3-2 log K2 = -10.329

Please note the different form of the reaction formula in Eq.(2b). The relation between log K3 and the other two log K values is then given by:

 (2d) log K3  =  log K1 + log K2

[In wateq4f, the master species for carbon C(4) is CO3-2.]

Dataset 3 – Thermodynamic Database minteq

In minteq, the three equilibrium reactions are defined by:

 (3a) CO2(g) + H2O = 2H+ + CO3-2 log K4 = -18.16 (3b) H2CO3* = 2H+ + CO3-2 log K3 = -16.681 (3c) HCO3- = H+ + CO3-2 log K2 = -10.33

Please note the different form of the reaction formula in Eq.(3a). The relation between log K4 and log KH is given by:

 (3d) log K4  =  log KH + log K3  =  log KH + log K1 + log K2

The reaction formula (3b) is equivalent to Eq.(2b), except the different notation for the composite carbonic acid (here as H2CO3*).

[In minteq, the master species for carbon C(4) is also CO3-2.]

Dataset 4 – Thermodynamic Database llnl (EQ3/6)

In llnl.dat or EQ3/6 the composite carbonic acid is abbreviated by CO2(aq)+H2O. The three equilibrium reactions are then defined by:

 (4a) CO2(g) + H2O = H+ + HCO3- log K5 = -7.8136 (4b) CO2(aq) + H2O = H+ + HCO3- log K1 = -6.3447 (4c) HCO3- = H+ + CO3-2 log K2 = -10.3288

Please note the different form of the reaction formula in Eq.(4a). The relation between log K5 and log KH is given by:

 (4d) log K5 = log KH + log K1

The reaction formula (4b) is equivalent to (1b), except the different notation for the composite carbonic acid (here as CO2(aq) + H2O).

[In llnl or EQ3/6, the master species for carbon C(4) is HCO3-.]

Summary & Conclusions

It is no surprise, all data compilations are based on one and the same dataset of three equilibrium constants: KH, K1, and K2. (There are only very small deviations in their numerical values, which are practically unimportant.)

The reaction formulas differ from database to database, but they can always be converted to the “standard form”, i.e. to Eqs.(1a), (1b), and (1c). In this way, the corresponding log K values become linear combinations of log KH, log K1, and log K2 – as shown in Eqs.(2d), (3d), and (4d). [The only reaction formula that remains the same in all datasets is Eq.(1c).]

Confusion comes into play by the nomenclature of the composite carbonic acid, H2CO3*, as shown in the table below:

Dataset Composite Carbonic Acid Master Species for C(4)
Stumm & Morgan H2CO3*
wateq4f CO2 CO3-2
minteq H2CO3*   (but asterisk omitted) CO3-2
llnl, EQ3/6 CO2(aq) + H2O HCO3-

References & Remarks

1. W. Stumm and J.J. Morgan: Aquatic Chemistry, Chemical Equilibria and Rates in Natural Waters, 3rd ed. John Wiley & Sons, Inc., New York, 1996

2. J.W. Ball and D.K. Nordstrom: WATEQ4F – User’s manual with revised thermodynamic data base and test cases for calculating speciation of major, trace and redox elements in natural waters, U.S.G.S. Open-File Report 90-129, 185 p, 1991

3. J.D. Allison, D.S. Brown, K.J. Novo-Gradac: MINTEQA2/PRODEFA2, A Geochemical Assessment Model for Environmental Systems, Version 3.0, User’s Manual, EPA/600/3-91/021, March 1991

4. ‘thermo.com.V8.R6.230’ prepared by Jim Johnson at Lawrence Livermore National Laboratory, in Geochemist’s Workbench format. Converted to Phreeqc format by Greg Anderson with help from David Parkhurst (llnl.dat 4023 2010-02-09 21:02:42Z dlpark)

5. T.J. Wolery: EQ3/6, A Software Package for Geochemical Modeling of Aqueous Systems: Package Overview and Installation Guide (Version 7.0), Lawrence Livermore National Laboratory UCRL-MA-110662 PT I, Sep 1992

6. similar to CHESS database

7. The motivation for this article stems from the confusion a novice might feel when comparing different thermodynamic databases in respect to the “simple” carbonate system.