Equations used to develop the CO2-Ca-pH relationships
in calcareous soils are reviewed. The equation

PCO2(Ca) = (H)2 Kc,

is used to draw a three-dimensional surface and to derive
three partial differential equations to illustrate the relationships
between CO2 partial pressure, Ca activity and
pH. Kc is a combination of Henry's Law constant, the
first and second dissociation constants for carbonic acid
and the calcite solubility product. The three dimensional
CO2-Ca-pH surface illustrates how the three parameters
relate to each other under ideal conditions. The partial
differential equations are presented to illustrate how
changes in one parameter affect the other two. The
CO2-Ca-pH surface provides a graphical method for introducing
the idea of three component equilibria, while
the partial differential equations provide a mathematical
representation of these interactions for those with chemical
thermodynamics or strong mathematic or modeling
backgrounds. Deviations from this ideal model in
natural systems are discussed for those who wish to extend
the discussion to natural systems

Robbins, C.W.

Northwest Irrigation & Soils Research Laboratory Publications

The CaCO3-CO2-H2O system in soils

USDA - ARS - NWISRL

Reprinted from Journal of Agronomic EducationVol. 14, No. 1 (Spring 1985), p. 3-7The CaCO3-CO2-H20 system in soils'C. W. Robbins'ABSTRACTEquations used to develop the CO2 -Ca-pH relation-ships in calcareous soils are reviewed. The equationPco, (Ca) --- (H) 2 Ke ,is used to draw a three-dimensional surface and to derivethree partial differential equations to illustrate the rela-tionships between CO 2 partial pressure, Ca activity andpH. lc is a combination of Henry's Law constant, thefirst and second dissociation constants for carbonic acidand the calcite solubility product. The three dimensionalCO2-Ca-pH surface illustrates how the three parametersrelate to each other under ideal conditions. The partialdifferential equations are presented to illustrate howchanges in one parameter affect the other two. TheCO,-Ca-pH surface provides a graphical method for in-troducing the idea of three component equilibria, whilethe partial differential equations provide a mathematicalrepresentation of these interactions for those with chem-ical thermodynamics or strong mathematic or modelingbackgrounds. Deviations from this Ideal model innatural systems are discussed for those who wish to ex-tend the discussion to natural systems.Additional index words: Calcite, Aragonite, Vaterite,Carbonate minerals, Calcareous soils, Lime.SOH, solutions and natural waters in contact withcalcium carbonate minerals are buffered with re-spect to carbon dioxide (CO2), pH, carbonate (C0? 4),bicarbonate (HCO;), calcium (Cal, and several com-plex ion pair activities. Equilibrium in natural calciumcarbonate systems is also affected by other ions in solu-tion that produce common ion effects, or activity coef-ficient changes due to total ion concentrations. Pre-cipitation and dissolution rates and equilibria can alsobe affected by contamination of mineral surface sites byinorganic ions or organic solutes. Calcium carbonatesystems have been described by a number of differentapproaches, but most models imposed arftificial con-straints or simplifications on the system. The con-straints make the system easier to describe, but limit themodels' ability in describing natural systems. Thesesimplifications are discussed in detail. by Nakayama(1970).Computer models (Robbins et al., 1980; and Tanjiand Doifeen, 1966) and graphical calculation methods(Suarez, 1982) have been developed for estimating cal-cium carbonate equilibrium. It is not always easy tolook at these calcium carbonate models and gain an in-tuitive feel for what is actually happening when solutioncomponents are varied. The objective here is to describea calcareous soil system in a way that is easier tovisualize CO 2 , water, and calcium carbonate equilibri-um without oversimplification. The system is open withrespect to Ca 2+ , H 4 , HCOi, CO;-, CO,, and any otherions, ion pairs, or dissolved gases that may be found in anatural system. This approach allows for CO, additionfrom biological activity or removal by escape into theatmosphere or as a leachate solute. Cations and anionsare allowed to enter or leave the system as solutes, dis-solution and precipitation products or reactants, orcation exchange products or reactants. In the initial de-velopment, chemical equilibrium is assumed and thenlater, departure from equilibrium will be discussed.As CO, gas dissolves in water, less than 0.3% of theCO200 is hydrated to H 2 CO 3 at 25°C (Ponnamperuma,1967). Since it is difficult to distinguish between CO20,0and H 2 CO 3 , the composite acid H 2 CO: is defined as theanalytical sum of CO2(aq) and H 2 CO 3 . The pure acid,H,CO, is much stronger (pKH,co, = 3.8) than the com-posite, H 2 COP (pIC Elico7 = 6.3) (Stumm and Morgan,1970). The difficulty in identifying the species involvedin the above reaction makes it more practical to use the"apparent" solubility expressionH2O + CO2(8) 7-= H 2C0 1:with the equilibrium for the combined reactions ex-pressed as(11 2CM K HPco, [11where Pco, is the CO, partial pressure and K H is Henry'sLaw constant. The carbonic acid thus formed quicklydissociates to form HCO; and H4 ions, and at high pHthe second dissociation produces CO3 4 and a second H4ion.' Contribution from ARS, USDA, Snake River Conservation Re-search Center, Kimberly, ID 83341.'Soil scientist.34	 JOURNAL OF AGRONOMIC EDUCATION, Vol. 14, Spring 1985The first and second dissociation reactions are repre- 	 eq. [7] can be written assented as(H+)/ PCM (Ca')and	 orHOD; r—"' H* +	 Pep, (Ca2+) (fr)'&	 [10]+ HCO; 19]with the equilibrium dissociation constants Kdi and Kd2calculated as(H 4)(HCO;)(H 2C0t)and(H +)(00 2 -) —(HCO;)where the species in parentheses represent activities.By rewriting Eq. [3] in terms of (HC0i) and substitut-ing into Eq. [2], the equation0412(03n — Kai .1Cd2(H,con [4]is obtained. Now if eq. [4] is written in terms of(H,CO*) and substituted into eq. [1] and the results re-written in terms of Pco, the following expression is ob-tained.(1.11 2(C0f-)PCO, KH Kdt Kd2This gives an expression for Pco,, (IP), and (COT)equilibrium in an aqueous system. This system can thenbe brought into equilibrium with calcium carbonate byfirst considering the dissolution reactionCaCO3(, )	 +with the solubility product, Kip , calculated as	(Ca2+)(C0f-) =	 [6]By rewriting eq. [6] in terms of (COT), and substitutingit into eq. [5] the equation(H4)2 Ksp PCOJ KH	 Kd2(Ca21is obtained. If the equilibrium constants are combinedsuch thatK, — 	 ,KH Ad] Nd2	Ksp	[ 8 ]Using the values of 4.45 x 10-9, 3.38 x 10-1, 4.45 x10' and 4.67 x 10-" for Kw, KH, Ko l and Kd2 respec-tively (Adams, 1971), IC, has the value 6.34 x 10 9 .Equation [10] can be written in several other formsafter taking the log of each term, such aslogPco, + log(Ce+) = 2 log(H +) + 9.80	 [11]or by rearranging	2pH = 9.80 — logFico, — log(Ce)	 [12]or	pH = 4.90 + 1/2p13cth + 1/2p(Ca2+)	 [13]When eq. [13] is plotted as a three-dimensional surface(Fig. 1) the variables pH, pPc0„ or p(Ca l+) can beshown as a function of the other two.An example for using Fig. 1 could be; if Pop, is 2%( — log 0.02 = 1.7) and the pH is 7.5, the p(Ca) would befound by going up the constant pPc0, line 1.7 (a) untilthe pH 7.5 line is intercepted (b) and then by followingthe constant p(Ca 2+) line to the left margin, then p(Ca) isread as 3.5 which is equal to the (Cal of 2.5 x 10'moles/L. If the Pop, is increased to 5% ( — log 0.05 =1.3) (c), the pH must drop to 7.30 if the (Ca l+) is to re-main constant or the (Ca 2+) will increae to 1.26 x 10-4moles/L (p(Ca) = 3.9) if the pH remains constant. Thethird alternative is a combination of the pH decreasingwhile the (Ca 2+) increases as the Pro, increases. Equa-tion [13] and Fig. 1 provide a graphical method for in-troducing the relationships between the three interactivecomponents of the CO,-Ca-pH system to students whohave not been exposed to these kinds of systems.in the (F1 4), (Ca 2+), Pco, relationship that exists whenCaCO, minerals are in aqueous or moist natural sys-tems, each of the three variables can be taken, one at atime and considered as dependent on the other two andtreated as a dependent variable in a differential func-tion. If (H 4) is considered the dependent variable, thedifferential change in H ion activity can be expressed as	so-n2  )dp	 [14]co,( 6014,)2,) d(Ca21 k OPco, (Ca")d(H+, — v(Ca-+),Pc0,When (Ca) is considered the dependent variable the dif-ferential change in Ca ion activity can be expressed as[2][3][5]- Constant PH- Constant Ca Activity- Constant CO2Partial PressureEQUATIONS FOR CARBON SYSTEM IN SOILS	 5PPG%Fig. 1. The pPc0,-pH-pea activity surface for gas-liquid-solid phasesystem in equilibrium with calcite.d(Ca 2+) — eCpa021)(gco, + (56((Clia;?)cpiCf14)2 [15]and likewise the differential Pco, change when CO2partial pressure is the dependent variable can be ex-pressed as161dFco(  'Wm d(H12 V(Cal)d(r-1(C) e+) [, — k .5(1-1 4)1 (ce)These differential functions can be expressed this waybecause the total differential of the dependent variableis the sum of the differential changes caused by chang-ing the independent variables separately. Consequently,a change caused by one independent variable does notinfluence the change caused by another independentvariable (Granville et al., 1957).Equations [14], [15], and [16] can be used in teachingstudents with strong chemical thermodynamics or dif-ferential calculus backgrounds and students modelingcalcareous systems. These equations illustrate i) that anytwo components can be varied independently of eachother as long as the third component is allowed to vary,or ii) that one component can be varied with the effectbeing distributed over the other two. Adding calciumchloride to a soil would raise the pH and increase the(Ca"), thus causing the Pco, to increase, this being anexample of the first case. Respiring plant rootsproducing CO, in the soil increases Pco , and thusincreasing the pH which in turn increases CaCO, solu-bility. This is an example of the second case. If either ofthe above reactions take place in a sodic, calcareoussoil, calcium will exchange with sodium, thus decreasing(Ca') and again changing the balance between the threecomponents.This (Cal, (FP), Pco, equilibrium model requiresthat C&* and H4 are expressed as activities and that thesystem contains a solid phase CaCO, mineral in theaqueous phase, and CO2 in the gas phase. Other miner-als may be present in the solid phase, other ions or ionpairs may be present in the liquid phase, and there maybe other gases in the gaseous phase. This model does notpreclude cation exchange.The Kn, value for the CaCO 3 mineral calcite is 4.45 x10-9 . The product of Ca" activity times the CO;- activityis the calcium carbonate ion activity product (IA?).When the IAP is greater than the 1( 9, for calcite thatpoint will be above the surface in Fig. 1, and the solu-tion will be supersaturated with respect to calcite. If theIAP is less than the Ksp, the point will be below the sur-face in Fig. 1, and the solution will be undersaturatedwith respect to calcite. When K, p = IAP, the solution isin equilibrium with solid phase calcite, and the pointwill be on the surface shown. However, none of thethree conditions just mentioned are by themselves proofof the presence or absence of calcite or any other CaCO,mineral.Subsurface drainage waters and soil extracts fromarid and semiarid region calcareous soils are seldom inequilibrium with calcite as indicated by their CaCO,IAP. The mean IA? from 28 wells below irrigatedArizona fields was 11.3 x 10- 9 , and the mean IAP from35 well water samples from The Grand Valley ofColorado was 10.7 x 10- 9 (Suarez, 1977). When threecalcareous soils were mixed'at 1:5 soil:water ratios, andequilibrated for 29 and 41 days at 25°C, two solutionshad IAP values greater and one less than that of calcite(Marion and Babcock, 1977). Many other examples ofnon-equilibrium with calcite in carbonate systems canbe found in the literature.These discrepancies between the calcite IC11, and thecalculated IAP can be due to any of a combination offactors such as (i) carbonate minerals other than calcitecontrolling the IAP, (ii) calcite solubility differences dueto ion substitution in the crystal lattice, (iii) variations incalcite specific surface area, (iv) crystal surface contami-nation, or (v) lack of precipitation-dissolution equilibri-urn,MINERALS OTHER THAN CALCITEhoner and Pratt (1969) found that when CaCO, wasprecipitated in the presence of MgC1 2 , calcite andaragonite were formed, but when CaCO, was precipi-tated in the presence of SOi- salts, vaterite, anhydrousCaCO 3 , and calcite were formed. Argonite, vaterite,and anhydrous CaCO,, which are all polymorphicforms, are more soluble than calcite (Marion andBabcock, 1977). If during soil solution concentration(due to evapotranspiration), CaCO, precipitates in the6	 JOURNAL OF AGRONOMIC EDUCATION, Vol. 14, Spring 1985presence of other ions, it is very likely that mineralsother than calcite could form. When these more solublespecies precipitate, the LAP would be greater than thecalcite Kw .ION SUBSTITUTION IN THECRYSTAL LATTICEHassett and Jurinak (1971) found that in low Ca-1-1CO 3 water, MillviIle soil which contains 45% calcare-ous material that was predominantly dolomite, releasedmore moles/L of calcareous [(Ca5Mg2,„)(CO 3 ) 2 1 ma-terials into solution than did the Portneuf soil whichcontains about equal amounts of calcite and dolomite.Marion and Babcock (1977) present data that suggestthat calcite solubility increases with a 2 to 10% Mg sub-stitution in the crystal lattice. Levy et aI. (1982) showedthat as the ratio of solution Mg to Ca increases from 0.4to 26.1 the log IAP increased from -8.52 to -7.15 andthe Mg to Ca ratio in the solid phase increased from0.01 to 1.75 when precipitated with CO;- in the presenceof bentonite.SURFACE AREA DIFFERENCESA calcite sample with a 13.5 rn'ig surface area wasfound to be more soluble than compared to one with a0.8 Wig surface area sample, when equilibrated with anunder-saturated solution. When equilibrated at a higherCa' and HCO3- concentration the differences in thetwo materials were not significantly different (Hassettand Jurinak, 1971).CRYSTAL SURFACE CONTAMINATIONOlsen and Watanabe (1959) found that clay, resin, ornoncalcareous soil added to calcite suspensions did notaffect calcite solubility, but when CaCO 3 was precipi-tated in suspensions of these same materials, the result-ing precipitates were more soluble than calcite. Organiccompounds present in natural systems during precipita-tion can also increase CaCO, solution IAP by coating orblocking crystal surfaces (Suess, 1970).LACK OF EQUILIBRIUMIn addition to the above conditions which can causeCaCO 3 precipitates to be more soluble than calcite,other calcium containing minerals may be in contactwith the soil solution. Reaction rate differences betweencalcite and metastable forms such as aragonite, vateriteor monohydrate CaCO 3 affect the soil systemequilibrium. In soil solutions where the solution concen-tration is continually changing due to wetting and dry-ing cycles, steady state equilibrium with calcite willseldom exist.Weathering of non-calcareous minerals that containCa such as gypsum (CaSO4 .2H20) or anorthite(CaA1 2 Si 208 ) in the presence of CO2 producing soil or-ganisms will produce a continual Ca' and LICO; ionsupply. If these ions are not removed by leaching, theremay be an accumulation of these ions in solution when-ever any process slows precipitation relative to the rateof weathering.Under conditions where more soluble CaCO,minerals dissolve first and only calcite is left, the systemmay go from a supersaturated calcite condition to onethat is in equilibrium with calcite as the soil solution isdiluted (Levy, 1981a, 1981b). As the soil solution be-comes more concentrated by evapotranspiration, moresoluble CaCO3 species may again form as a result of anyof the mentioned conditions.Realizing that the equilibrium model assumes that ac-tivities are used for Ca and that natural systems areseldom at equilibrium, Fig. I allows for a quick way ofchoosing a set of conditions in a calcareous soil. Thenby changing one or two of the three variables, thechanges in the remaining variable can be predicted. Onemust recognize that in soils the cation exchange capacitywill buffer a change in Ca 2+ activity to some degree byexchange with other cations (Cruz-Romero andColeman, 1974). The principles discussed here can alsobe extended to lake and stream interactions with bottomand suspended sediments.REFERENCES1. Adams, Fred. 1971. tonic concentrations and activities in soilsolutions. Soil Sci. Soc. Am. Proc. 35:420-426.2. Cruz-Romero, G., and N. T. Coleman. 1974. Reactions amongcalcium carbonate, carbon dioxide, and sodium adsorbents. SoilSci. Soc. Am. Proc. 38:738-742.3, Doner, H. E., and P. F. Pratt. 1969. Solubility of calcium car-bonate precipitated in aqueous solutions of magnesium and sul-fate salts. Soil Sci. Soc. Am. Proc. 33:690-693.4, Granville, W. A., P. F. Smith, and W. R. Langley. 1957. Ele-ments of calculus. Ginn and Co., Boston, MA, p. 445.5. Hassett, J. J., and J. J. Jurinak. 1971. Effect of Mg ion on thesolubility of soil carbonates. Soil Sci. Soc. Am. Proc. 35:403-406.6. Levy, Rachel. 1981a. Effect of Dissolution of aluminosilicatesand carbonates on ionic activity products of calcium carbonatein soil extracts. Soil Sci. Soc. Am. J. 45:250-255.7. ----. 198 lb. Ionic activity product of calcium carbonate precipi-tated from soil solutions of different degrees of supersaturation.Soil Sci. Soc. Am. J. 45:1070-1073.8. ----, D. Whittig, and K. K. Tanji. 1982. Ionic activity productsand crystal forms of calcium and magnesium carbonates precipi-tated from calcium-magnesium bentonites. Soil Sci. Soc. Am. J.46:497-502.9. Marion, G. M., and K. L, Babcock. 1977. The solubilities of car-bonates and phosphates in calcareous soil suspensions. Sail Sci.Soc. Am. J. 41:724-728.10. Nakayama, F. S. 1970. Hydrolysis of CaCO3, Na:CO, andNaHCO, and their combinations in the presence and absence ofexternal CO: source. Soil Sci. 109:391-398.11. Olsen, S. R., and F. S. Watanabe. 1959. Solubility of calciumcarbonate in calcareous soils. Soil Sci. 88:123-129.12. Pannamperuma, F. N. 1967. A theoretical study of aqueous car-bonate equilibria. Soil Sci. 103:90-100.13. Robbins, C. W., R. J. Wagenet, and J. J. Jurinak. 1980. A com-bined salt transport-chemical equilibrium model for calcareousand gypsiferous soils. Soil Sci. Soc. Am. J. 44:1191-1194.714. Stumm, W., and J. J. Morgan. 1970. Aquatic chemistry. JohnWiley and Sons, Inc., New York.15. Suarez, D. L. 1977. Ion activity products of calcium carbonatein waters below the root zone. Soil Sci. Soc. Am. J. 41:310-315.16. ----. 1982. Graphical calculation of ion concentrations in cal-cium carbonate and/or gypsum soil solutions. .1. Environ. Quaff.11:302-308.17. Suess. E. 1970. Interaction of organic compounds with calciumcarbonate. I. Association phenomenon and geochemical imp-dons. Geochim. Cosmochim. Acta 34:157-164.18. Tanji, K. K., and L. D. Doneen. 1966. A computer technique forprediction of CaCO, precipitation in HCO, salt solutions. SoilSci. Soc. Am. Proc. 30:53-56.

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The CaCO3-CO2-H2O system in soils

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