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 lawofmassaction 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 CO_{2}H_{2}O System
The CO_{2}H_{2}O system is completely characterized by four components:
• CO_{2} in the gas phase:  CO_{2}(g) 
• composite carbonic acid:  H_{2}CO_{3}^{*} (in short: CO_{2}) 
• bicarbonate (hydrogen carbonate):  HCO_{3}^{} 
• carbonate:  CO_{3}^{2} 
The interplay between these four components is determined by three distinct equilibrium constants (K_{H}, K_{1}, and K_{2}):
\(CO_{2}(g)+H_2O \ \overset{K_H}{\Longleftrightarrow} \ H_2CO_3^* \ \overset{K_1}{\Longleftrightarrow} \ H^+ + HCO_3^ \ \overset{K_2}{\Longleftrightarrow} \ 2H^+ + CO_3^{2}\) 
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)  CO_{2}(g) + H_{2}O = H_{2}CO_{3}^{*}  log K_{H} = 1.47 
(1b)  H_{2}CO_{3}^{*} = H^{+} + HCO_{3}^{}  log K_{1} = 6.35 
(1c)  HCO_{3}^{} = H^{+} + CO_{3}^{2}  log K_{2} = 10.33 
This should be our “standard dataset”. The other three datasets listed below will be converted to the standard dataset based on K_{H}, K_{1}, and K_{2}.
Dataset 2 – Thermodynamic Database wateq4f
In this dataset the composite carbonic acid is abbreviated by CO_{2}. The three equilibrium reactions are then defined by:
(2a)  CO_{2}(g) = CO_{2}  log K_{H} = 1.468 
(2b)  CO_{2} + H_{2}O = 2H^{+} + CO_{3}^{2}  log K_{3} = 16.681 
(2c)  HCO_{3}^{} = H^{+} + CO_{3}^{2}  log K_{2} = 10.329 
Please note the different form of the reaction formula in Eq.(2b). The relation between log K_{3} and the other two log K values is then given by:
(2d)  log K_{3} = log K_{1} + log K_{2} 
[In wateq4f, the master species for carbon C(4) is CO_{3}^{2}.]
Dataset 3 – Thermodynamic Database minteq
In minteq, the three equilibrium reactions are defined by:
(3a)  CO_{2}(g) + H_{2}O = 2H^{+} + CO_{3}^{2}  log K_{4} = 18.16 
(3b)  H_{2}CO_{3}^{*} = 2H^{+} + CO_{3}^{2}  log K_{3} = 16.681 
(3c)  HCO_{3}^{} = H^{+} + CO_{3}^{2}  log K_{2} = 10.33 
Please note the different form of the reaction formula in Eq.(3a). The relation between log K_{4} and log K_{H} is given by:
(3d)  log K_{4} = log K_{H} + log K_{3} = log K_{H} + log K_{1} + log K_{2} 
The reaction formula (3b) is equivalent to Eq.(2b), except the different notation for the composite carbonic acid (here as H_{2}CO_{3}^{*}).
[In minteq, the master species for carbon C(4) is also CO_{3}^{2}.]
Dataset 4 – Thermodynamic Database llnl (EQ3/6)
In llnl.dat or EQ3/6 the composite carbonic acid is abbreviated by CO_{2}(aq)+H_{2}O. The three equilibrium reactions are then defined by:
(4a)  CO_{2}(g) + H_{2}O = H^{+} + HCO_{3}^{}  log K_{5} = 7.8136 
(4b)  CO_{2}(aq) + H_{2}O = H^{+} + HCO_{3}^{}  log K_{1} = 6.3447 
(4c)  HCO_{3}^{} = H^{+} + CO_{3}^{2}  log K_{2} = 10.3288 
Please note the different form of the reaction formula in Eq.(4a). The relation between log K_{5} and log K_{H} is given by:
(4d)  log K_{5} = log K_{H} + log K_{1} 
The reaction formula (4b) is equivalent to (1b), except the different notation for the composite carbonic acid (here as CO_{2}(aq) + H_{2}O).
[In llnl or EQ3/6, the master species for carbon C(4) is HCO_{3}^{}.]
Summary & Conclusions
It is no surprise, all data compilations are based on one and the same dataset of three equilibrium constants: K_{H}, K_{1}, and K_{2}. (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 K_{H}, log K_{1}, and log K_{2} – 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, H_{2}CO_{3}^{*}, as shown in the table below:
Dataset  Composite Carbonic Acid  Master Species for C(4)  

Stumm & Morgan  H_{2}CO_{3}^{*}  
wateq4f  CO_{2}  CO_{3}^{2}  
minteq  H_{2}CO_{3}^{*} (but asterisk omitted)  CO_{3}^{2}  
llnl, EQ3/6  CO_{2}(aq) + H_{2}O  HCO_{3}^{} 
References & Remarks

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

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. OpenFile Report 90129, 185 p, 1991 ↩

J.D. Allison, D.S. Brown, K.J. NovoGradac: MINTEQA2/PRODEFA2, A Geochemical Assessment Model for Environmental Systems, Version 3.0, User’s Manual, EPA/600/391/021, March 1991 ↩

‘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 20100209 21:02:42Z dlpark) ↩

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 UCRLMA110662 PT I, Sep 1992 ↩

similar to CHESS database ↩

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. ↩