Overview Activity Chem Equilibrium Acids Carbonate System Mineral Phases

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 thdyn data from different databases are involved.

In the following we consider four different thdyn 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 hydrochem modeling (i.e. for models based on the law-of-mass-action approach). They are in widespread use since 25 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 actinides, and REE. For most modeling tasks, however, wateq4f is a good choice; it is employed in plenty of hydrochem 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 (K_H, 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 math point of view, the system is governed by three equations (i.e., three reaction formulas with the corresponding equilibrium constants) as shown below in 1a to 1c, for example). In practice, however, you will seldom find the equations in such simple form encoded in the thdyn databases. However, it is always possible to convert them to the “standard form” of dataset 1. This will now be explained 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 K_H, 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 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 3a. The relation between log K₄ and log K_H is given by:

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

The reaction formula (3b) is equivalent to 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 4a. The relation between log K₅ and log K_H 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

All data compilations are based on one and the same dataset of three equilibrium constants: K_H, 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 1a, (1b), and (1c). In this way, the corresponding log K values become linear combinations of log K_H, log K₁, and log K₂ — as shown in 2d, (3d), and (4d). [The only reaction formula that remains the same in all datasets is 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