CARBONATE GEOCHEMISTRY
Calcite (CaCO_{3}) is one of the most common minerals at or near the surface of Earth and thus is one of the main contributors to carbonate geochemistry. Less common carbonate minerals include dolomite (MgCa (CO_{3})_{2}), aragonite, a calcite polymorph (mineral of the same composition as calcite but having a different atomic structure), azurite and malachite (copper hydroxycarbonate minerals), siderite (FeCO_{3}) and rhodochrosite (MnCO_{3}) which can be important spatially and economically.
Although calcite does occur in igneous and metamorphic rocks, the mineral is present dominantly in the sedimentary environment which is the focus of this article. Calcite may be precipitated to form a relatively pure monomineralic rock (limestone), be present as a cement binding sediments into indurated rock, occurs simply as a trace mineral in rocks and composes many shells and fossils. Weathering of calcite occurs relatively easy and depends largely on the amount of carbonic acid present. Other carbonate minerals, with the exception of dolomite, generally are dissolved and precipitated in a manner geochemically similar to calcite.
Calcite Solubility Products
The solubility of CaCO_{3} depends on which polymorph is considered and the reference for the equilibrium constant. For example, at 25 _{} the ion concentration products (K_{sp}) for calcite and aragonite (the most common polymorphs of CaCO_{3}) are 10^{8.48} and 10^{8.34}, respectively (APHA , 1995). Krauskopf and Bird (1995) provide calcite and aragonite K_{sp}_{ }values of 10^{8.35} and 10^{8.22 ,} respectively. The K_{sp} values for calcite solubility from Krauskopf and Bird (1995) are 35% greater than those from APHA (1995). A similar relationship exists for aragonite with Krauskopf and Bird (1995) presenting K_{sp} values for aragonite that are 31% larger. Variation in solubility experiments can yield significant differences in the K_{sp}.
Temperature
Counter to the typical increase of mineral solubility with increasing temperature observed for most minerals, many carbonate minerals are more soluble in cold water. For example, the K_{sp} for calcite at 0 _{} and at 50 _{} is 10^{8.02} and 10^{8.63}, respectively (Garrels and Christ, 1965). These values represent about a fourfold difference in calcite solubility caused by temperature alone. A thorough discussion of the thermodynamic reactions of carbonate minerals solubilities is beyond the scope of this article. A simplified explanation for carbonate minerals being more soluble in cold water is that the dissolution reaction for carbonate minerals is exothermic, which results in higher temperatures favoring the solid phase over dissolved ions. A more detailed discussion for this unusual behavior can be found in Langmuir (1997).
In addition to an increase in solubility products with decreasing temperature, carbon dioxide is more soluble at lower temperatures, further favoring carbonate mineral dissolution in cooler environments. More carbonic acid is present in cold water at a given partial pressure of carbon dioxide (P_{}) and carbonic acid concentration is the controlling factor for the solubility of carbonate minerals under natural conditions. Carbon dioxide is obtained from the air or from decomposition of organic matter that releases carbon dioxide which reacts with water to form carbonic acid. These factors combine to form the calcite compensation depth (about 4,500 m) below which calcite dissolves.
When geothermal waters reach the surface of Earth and precipitate tufa, a calciumcarbonate rock, some reaction must overcome the temperature decrease or these waters would dissolve calcite rather than deposit tufa as the water cools. The required reaction is the loss of CO_{2} due to lower P_{} pressure at Earth’s surface and subsequent a decrease in the amount of carbonic acid, which controls the amount of dissolved calcite (see Calcite Solubility below).
Pressure
Increased partial pressure of CO_{2} near the surface of Earth increases the amount of CO_{2} that dissolves in water, therefore, increasing the solubility of carbonate minerals such as calcite. Pressure alone does not affect the solubility of calcite as much as the effect of temperature. Nonetheless, where pressure is large, for example, deep within the ocean, its effect alone can increase calcite solubility about two fold (Krauskopf and Bird, 1995).
Ionic Strength
The presence of other ions in solution shield _{} and _{} ions from interacting and precipitating. Faure (1998) describes this situation as “…the activity of the ions in electrolyte solutions is less than their concentration. It is plausible to expect that the interference by the other ions increases with their concentrations and charges.” Activity can be defined as the concentration of an ion at zero ionic strength. The affect of the concentration and charge of the ions is represented by the ionic strength (I) of the solution.
I = 0.5 Σ m_{i }z_{} eq. 1
where m_{i} is the molar concentration of an ion (i) and z is the charge of the ion.
Ionic strength can be use to calculate the activity coefficient (γ) which relates molar concentration to activity and γ is 1 or less.
m_{i} (γ) = a eq. 2
where a is the activity of the ion.
The γ can be calculated from the DebyeHückel equation (eq. 3) or other similar equations that make use of I and some constants that relate to the dielectric constant of water and temperature (A and B) and effective size (a) of ions. Values of the constants can be obtained from Faure (1998).
log γ = _{} eq. 3
Saturation Index
Waters tend to precipitate _{} when oversaturated with respect to _{} and tend to dissolve _{} if undersaturated with respect to _{}. The Saturation Index (SI) is perhaps the most widely used method to determine the amount of calcite that will be precipitated or dissolved. Many computer codes calculate RS (relative saturation) which is related to SI as shown below:
SI = log RS eq. 4
where RS = ratio of _{}_{ }activity product (_{}) to _{} solubility product (_{}).
SI values of 1 indicate saturation, negative values indicate undersaturation and positive values indicate oversaturation.
Measured Alkalinity
Alkalinity is the measure of the acid consuming ability (power) of a solution and is expressed as mg/L _{}. In nature the main ions that neutralize _{} ions are _{} and _{} (Drever, 2997). Although _{}, _{} and other negative ions can neutralize _{} ions, generally the concentrations of these ions is so small in the natural environment that _{}and _{} are the only significant acid neutralizing ions. In some situations, especially in anthropogenic influenced situations _{}^{ }can be important (e.g., the impact of cement on water chemistry); thus, _{} is included in the following calculations. Alkalinity is usually determined by titrating a 50 or 100 mL water sample with 0.02 N H_{2}SO_{4} to a pH of 8.3 for _{} and/or _{}. This 8.3 pH end point is often referred to as the phenolphthalein (or P) end point because this indicator changes colors at a pH of 8.3. Titration continues past 8.3 to a pH of about 4.5 as any _{}(originally present or formed from partial neutralization of _{}) is neutralized. The pH of 4.5 can vary from 4.34.9 depending on the presence and amounts _{} and certain anions (APHA, 1995). This final end point is referred to as total alkalinity. These pH titration end points are based on inflection points on the titration curve of pH versus milliliters of acid added to the water sample titration curve for neutralization of the bases. The amount of acid necessary to reach the phenolphthalein end point is equivalent to the amount of base (_{}) neutralized and is referred to as P alkalinity. The amount of _{} to “completely” or “totally” neutralize the _{} ions added is referred to as T alkalinity. Thus, T must be larger than or equal to P. There are five alkalinity conditions possible: (1) only _{}, (2) only _{}, (3) only _{}, (4) _{} plus _{} and (5) _{} plus _{}. Bicarbonate and _{} ions cannot coexist under typical natural conditions because these ions react to form _{} ions and _{}. Each of these five situations are discussed briefly below.
Bicarbonate alkalinityIf the initial pH of a sample is less than 8.3, there is only bicarbonate alkalinity and no P alkalinity. Or one can state that there is only T alkalinity (the amount of acid necessary to lower the pH below 4.5).
Carbonate alkalinityThere are two abrupt changes in pH during alkalinity titration, one at 8.3 and the other at 4.5. If only _{} ions are present, the amount of acid necessary to lower the pH below 8.3 is ½ the total acid (i.e., T) necessary to lower the pH below 4.5. The first abrupt pH change at 8.3 represents the conversion of carbonate to _{} (i.e., half of the carbonate has been neutralized), and the second abrupt pH change at 4.5 represents the neutralization of the _{} created from carbonate. If only _{} ions are present T = 2P.
Hydroxide alkalinityIf the initial pH is greater than 8.3 and the addition of acid rapidly lowers the pH below 4.5, there is only hydroxide alkalinity and thus T=P.
Bicarbonate plus carbonate alkalinity—Because P represents the conversion of _{} to _{} the same amount of acid (P) is required to neutralize the _{} ions formed from the _{} ions, i.e., 2P represents complete neutralization of _{} ions present. In addition, _{} originally present is included in T, which means that T>2P. Because _{} ions are present, there will be two abrupt changes in pH (at 8.3 and 4.5).
Carbonate plus hydroxide alkalinity—When both _{} and _{} ions are present, the amount of acid required to lower the pH below 8.3 is that necessary to convert _{} to _{} (P) plus that necessary to neutralize _{} ions. Neutralization of _{} ions formed from _{} requires P amount of acid. These conditions constrain the P and T relationship to T<2P.
Table 1 summarizes the equations necessary to determine the portion of alkalinity due to _{}, _{}ions and _{}. At a pH of 9 the _{}concentration is only 1.0 mg/L as CaCO_{3}, and can generally be neglected in alkalinity determinations for water with pH less than 9.0
Table 1. Alkalinity determined by titration.
Result of Titration 
Bicarbonate Alkalinity 
Carbonate Alkalinity 
Hydroxide Alkalinity 
P = 0 
T 
0 
0 
2P = T 
0 
T 
0 
P = T 
0 
0 
T 
P<0.5T or T<2P 
0 
2(TP) 
2PT 
P>0.5T or T>2P 
T2P 
2P 
0 
Calculation of Bicarbonate, Carbonate and Hydroxide Alkalinity
_{}
Bicarbonate, carbonate and hydroxide alkalinity can be calculated from total alkalinity (TA) if the pH is known. These concentrations are often calculated, especially for carbonate and hydroxide ion concentrations which are generally low and difficult to measure. The ion concentrations must be given in molar (M) concentrations, which are indicated by parentheses in this article. For most natural situations Equation 5, which takes into account charge differences, is adequate for determination of the various sources of alkalinity.
2TA = (_{}) + 2(_{}) + _{} eq. 5
TA is commonly expressed as mg/L _{} and must be converted to moles/L (M) in order to make the following calculations. The conversion of mg/L to M _{} is accomplished by use of Equation 6
(TA moles/L _{}) = _{} eq. 6
Rearranging the second disassociation constant for carbonic acid (eq. 7) in terms of
(_{}) yields Equation 8
_{} eq. 7
_{} eq. 8
Substitution of Equation 8 for (_{}) in Equation 5 and expressing (OH_{}) in terms of _{} based on Equation 9 yields Equation 10.
(_{}) = _{}= _{} eq. 9
2TA = (_{}) + 2(_{}) + _{} eq. 10
Rearranging Equation 10 to solve for _{} (eq. 12) is carried out by the following step (eq. 11).
2TA  _{} = (_{}) (1 + _{}) eq. 11
_{}= _{} eq. 12
Once (_{}) has been calculated (or determined by titration), this concentration can be substituted into Equation 8 and (_{}) can be calculated. To determine the hydroxide alkalinity, requires that only the pH be known (eq. 9).
To convert these molar alkalinity concentrations (eqs. 8, 9 and 12) to mg/L, the molar concentrations must be multiplied by the molecular weight of _{} (100,000 mg/mole) and in the case of (_{}) and (_{}) a factor of ½ is required because 1 mole of _{} is equivalent to 2 moles of _{} and 2 moles of _{}, whereas 1 mole of _{} is equivalent to 1 mole of (_{})
The equations necessary for calculation of bicarbonate, carbonate and hydroxide alkalinities as _{} mg/L are:
Bicarbonate alkalinity (_{} mg/L) = 50,000 (_{}) eq. 13
Carbonate alkalinity (_{} mg/L) = 100,000 (_{} eq. 14
Hydroxide alkalinity (_{} mg/L) = 50,000 (10_{}) eq. 15
Carbonate Species
The carbonate species (_{}), (_{}) and (_{}) concentrations can be calculated if the total dissolved inorganic carbonate (DIC) concentration and pH are known. (DIC) is often expressed as _{} because it is the dominant ion at typical pH values (Fig. 1). Figure 1 shows the concentrations for the carbonate species for an aqueous solution with a typical DIC concentration of _{} M with respect to the pH of the solution. The affect of temperature is also shown. The pertinent equilibrium reactions are the two disassociation constants for _{}(eq. 8 and 16).
_{} eq. 16
Because one mole of _{}neutralizes 2 moles of _{}, the molar concentration of _{} is multiplied by 2.
(DIC) = _{}+ _{}^{ }+ 2(_{}) eq. 17
By rearranging K_{1 }(eq.
16) to express _{}_{ } in terms of (_{}) and by rearranging
(DIC) = [_{}_{}(_{})] + _{} + 2[_{}_{}(
Factoring out (_{}) and rearranging Equation 16 to solve for (_{}) and expressing (_{}) as pH (negative exponent base log _{10} ) yields the following:
_{} = [_{}] eq. 19
Because K_{1},
[IMAGE 1]
Calcite Solubility
If only calcite were present in an aqueous solution with no carbon dioxide, one could determine the solubility of calcite by obtaining the square root of the solubility product for calcite (eq. 20). Reported K_{sp} values for calcite vary with the reference and range from K_{sp} = _{}to K_{sp} _{} at 25 _{} (APHA, 1995 and Krauskopf and Bird, 1995). The value of _{}will be used throughout this article.
_{} = (_{}) (_{}) = K_{sp} = _{} eq. 20
Hydrolysis
Although one can calculate the solubility of (_{}) as _{}M or 6.8 X _{}from Equation 20, the _{} ion will undergo hydrolysis (eq. 21).
_{} + _{} = (_{}) + (_{}) + (_{}) eq. 21
K = (_{}) (_{}) (_{}) = _{} eq. 22
Inspection of Equation 21, indicates that all three product ions are equal. The cube root of _{}, yields a concentration of _{} M for all three ions; thus, the pH of the solution is 10. At this high pH there is appreciable disassociation of _{} to _{} and _{} (which is quickly neutralized). Then these _{} ions undergo hydrolysis producing equal amounts of (_{}) and (_{}) (eq. 23).
(_{}) + _{} = (_{}) + (_{}) eq. 23
Furthermore, water with a pH of 10 has a _{}ratio of ½ (from eq. 7). The total carbonate in this situation is the sum of (_{}) and (_{}) (H_{2}CO_{3} is negligible at this high pH—see Fig. 1) and total carbonate is equal to (_{}) (eq. 24).
Σ(_{}) = (_{}) + (_{}) = (_{}) eq. 24
Because _{}= 0.5, Equation 7 can be modified to:
(_{}) = (_{}) + 0.5 (_{}) = 1.5 (_{}) eq.25
Instead of (_{}) having the same concentration as (_{}) and (_{}), (_{}) will be equal to 1.5 (_{}) and 1.5 (_{}) since (_{}) = (_{}) (eq. 23).
Equation 22 is then modified to:
K = (_{}) 1.5 (_{}) 1.5 (_{}) _{} ^{ }eq. 26
Since (_{}) = 1.5(_{}) = 1.5(_{}) the _{} concentration can be estimated by the cube root of 2.25 x _{}or 1.3 x _{}M (equivalent to 5.2 mg/L). This value is about twice that obtained in Equation 20 and represents the lowest equilibrium concentration of (_{}) for pure water not in contact with _{}. Using this method results in a pH change from 10.00 to 9.94. Re calculation using this method and based on the new pH of 9.94 yields a 2% change in (_{}) and a new pH of 9.93. Another iteration of these calculations yields a (_{}) difference of 1% and the pH remains 9.93.
Carbonic Acid
The main factor controlling carbonate solubility in nature is the amount (partial pressure) of _{} that forms H_{2}CO_{3} (eq. 25). The partial pressure for _{} in the atmosphere is 0.0003 or 0.03% of the atmospheric pressure at the surface of Earth (i.e., 1 bar or atmosphere). Partial pressure is equal to moles per liter (Faure, 1998); thus, there is 10^{5.0} M _{} present in water in contact with the atmosphere (eq. 26 and 27).
CO_{2} + H_{2}O = H_{2}CO_{3} eq. 27
K = _{} = _{} = 10^{1.5} eq. 28
_{} = _{} eq. 29
In most natural environments the appropriate equation for calcite solubility is Equation 30 i.e., _{}is present.
_{} + H_{2}CO_{3} = _{} + 2_{} eq. 30
Equation 29 (Krauskopf and Bird, 1995) takes into account presence of _{} at Earth’s surface which forms carbonic acid (eq. 27) that readily dissolves _{}.
K = _{}= 10^{4.4} eq. 31
(_{}) = 2(_{}) from inspection of Equation 30; therefore,
K = 10^{4.4} = _{} = _{} eq. 32
The _{}concentration calculated from Equation 32 is 4.7 x _{}M (equivalent to 18.8 mg/L). This is the solubility of calcite at surface conditions, i.e., 25 _{} and 1 atmosphere pressure, which provides a “minimum” concentration with atmospheric carbonic acid. More _{} can be dissolved in cold water and the _{} partial in soil can be rather high leading to increased calcite solubility. Decaying vegetation in soil can have _{} partial pressure in excess of 0.1 atmospheres (Krauskopf and Bird, 1995) which can significantly raise _{} concentrations of infiltrating meteoric water. The solubility of calcite in water in contact with 0.1 atmosphere of _{} can be calculated as in Equations 28 and 32, producing a calcite solubility of 3.2 x 10^{3} M (equivalent to 128 mg/L _{}). This value is not an absolute maximum but does give an approximate upper limit for _{} concentrations from limestone near the surface of Earth. Other acids, e.g., sulfuric from the oxidation of sulfide minerals such as pyrite (FeS_{2}), can also have a significant affect on calcite solubility locally.
Cave Formation
Carbonic acidrich water forms limestone caves, which are the most common type of caves. When the water table is high, carbonic acidrich water dissolves the limestone (calcite). Later when the water table drops, a “void” filled with air is formed and a large void is called a cave. Smaller amounts of water rich in _{}and _{} may continue to flow through the void. When these waters enter the void, _{} partial pressure decreases and _{} is released. This degassing of _{} drives the reactions in equations 27 and 30 to the left, leading to the precipitation of calcite and formation of stalagmites, stalactites and other cave features. Although evaporation may play a small role in the deposition of calcite, it is the loss of _{} that is the most important factor.
Hardness
Water hardness is a measure of how difficult it is for soap to lather, i.e., most of the divalent ions must be precipitated with soap before soap can produce suds. The most abundant divalent ions in nature are _{} and _{}, although _{} and other divalent ions can be important in some waters. The major source of _{} and _{} is carbonate minerals; therefore, hardness is expressed as mg/L _{}. The range in hardness values with descriptive terms is shown in Table 2.
Table 2. Hardness ranges. Units are in mg/L of calcium carbonate. After Hem (1985). 

060 
Soft 
51 – 120 
Moderately Hard 
121180 
Hard 
>180 
Very Hard 


In the past, hardness was determined by a titration analysis of divalent ions (Hem, 1985). Today hardness is calculated by converting _{} and _{} molar concentrations to mg/L _{} by multiplying the mg/L concentrations of the two ions by the inverse of the equivalent weights of the ions and summing the two concentrations (eq. 31).
Hardness as mg/L _{} = 2.497(_{}mg/L) + 4.118 (_{}mg/L) eq. 33
Some scientists consider hardness more of a water quality (use) factor that relates to scaling in hot water heaters and in industrial setting, rather than an important geochemical factor. However, comparison of hardness and alkalinity (both expressed as mg/L _{}) can yield helpful water chemistry information. If hardness exceeds alkalinity, the excess is termed “noncarbonate” hardness, meaning that there are noncarbonate mineral sources of _{}and _{} ions. The remainder of the hardness is considered to be “carbonate” hardness and derived from carbonate minerals. In this discussion it is assumed that there is “no” hydroxide alkalinity. If alkalinity exceeds hardness, there must be carbonate mineral sources that do not contain _{} and/or _{} e.g., NaHCO_{3 }or cation exchange has occurred with clay minerals (e.g., _{} replacing _{})
Dolomite
Dolomite has a very small K_{sp} with values ranging from _{} to _{} (Krausdopf and Bird, 1995). The K_{sp} is too small to produce large thicknesses of dolomite and furthermore there is no true dolomite being precipitated today. Some “protodolomite” is precipitated in restricted environments, e.g., evaporite lagoons. Dolomite should not exist and yet there are thick sequences of dolostone throughout the world and throughout the geologic recordhence, the “dolomite problem.”
Dolostone characteristically has poor preservation of fossils, is coarse grained and commonly has cavities/pore spaces, which all indicate a replacement of limestone as the origin of the rock. In addition, it is known that saline water, high pH, low _{}/_{} ratio and elevated temperatures all favor dolostone formation. Based on these factors, various marine and deep water reflux models have been proposed, as well as mixing models for fresh water and sea water but no “perfect” model has been developed for the formation of dolomite. The dolomite atomic structure is highly ordered which may affect the amount of time necessary to develop the structure. At any rate the formation and dissolution of dolomite is complex and not well understood in comparison with other carbonate minerals. Dolomite undergoes incongruent dissolution with _{} dissolving before _{}(Krauskopf and Bird, 1995).
References
Eaton, Andrew D., Lenore S. Clesceri and Arnold E. Greenberg (eds),1995, Standard Methods for the Examination of Water and Wastewater, American Public Health Association, Washington D.C., p. 225238 and 417—418.
Drever, James I., 1997, The
Geochemistry of Natural WatersSurface and Groundwater Environmentes
(3^{rd} ed), PrenticeHall,
Fauer, Gunter, 1998, Principles and Applications of Geochemistry (2^{nd}
ed.), PrenticeHall Inc.,
Garrels , Robert M. and Charles L. Christ, 1965, Solutions,
Minerals and Equilibria, Harper & Row,
Hem, John D., 1985, Study and Interpretation of the Chemical
Characteristics of Natural Water (3^{rd} ed),
U.S. Geological Survey Water Supply Paper 2254, U.S. Geological Survey,
Krauskopf, Kondrad B. and Dennis K. Bird, 1995,
Introduction to Geochemistry (3^{rd} ed.), McGrawHill, Inc.,
Langmuir, Donald, 1997, Aqueous
Environmental Geochemistry, PrenticeHall, Inc., upper