Calcium Carbonate Precipitation Potential - …

1 John A. Wojtowicz Chapter CarbonatePrecipitation PotentialJohn A. WojtowiczChemconAlthough the Calcium Carbonate saturation indexis applicable to swimming pool water balance calcula-tions, it is only a qualitative indicator of calciumcarbonate Precipitation since it does not indicate theextent of Precipitation that can occur at positive valuesof SI. Utilizing the mathematics of aqueous carbonateand cyanurate equilibria allows calculation of thequantitative Calcium Carbonate Precipitation poten-tial (CCPP), , the equivalent Calcium carbonatesupersaturation. Precipitation of Calcium Carbonate isaccompanied by a drop in pH and a reduction inhardness of 1 mol and in total alkalinity of 2 equiva-lents for each mol of Calcium Carbonate Calcium Carbonate Precipitation Potential increaseswith saturation index and buffer intensity.

2 Bufferintensity in turn is a function of pH and total alkalin-ity. Because buffer intensity decreases with increasingpH, the CCPP also decreases as pH is contributes to total alkalinity, thus itinreases the CCPP for a given Carbonate alkalinity. Atconstant pH, Carbonate alkalinity, and Calcium hard-ness, the CCPP decreases with increasing TDS due toa decrease in SI. In Chapter of this series, labora-tory data on the Precipitation of Calcium carbonateunder different conditions will be presented and (K1) and concentration (cK1) equilibrium con-stants are:K1= [H+]gH+[HCO3 ]gHCO3 /([H2CO3*]gH2CO3*)cK1= [H+][HCO3 ]/[H2CO3*]= K1gH2CO3*/(gH+gHCO3 )where the bracketed terms are molar concentrationsand the g s represent activity coefficients. The tem-perature dependent equation (T in Kelvin) for K1 isgiven by (Plummer and Busenberg 1982):Log K1 = + + Log T 1684915/T2 Bicarbonate ion dissociates into hydrogen andcarbonate H+ + CO32 The activity (K2) and concentration (cK2) equilibriumconstants are given by the following expressions:K2= [H+]gH+[CO32 ]gCO23 /([HCO3 ]gHCO3 )cK2= [H+][CO32 ]/[HCO3 ]= K2(gHCO3 )/(gH+ gCO23 )The temperature dependent equation (T in kelvins)for K2 is given by (Plummer and Busenberg 1982):Log K2 = + + log T respective ionization fractions are calcu- Calcium Carbonate PrecipitationPotential TheoryCarbonate Equilibria Dissociation of car-bonic acid produces hydrogen and bicarbonate * H+ + HCO3 where H2CO3* @ [CO2] + [H2CO3].

3 The ac-Originally appeared in theJournal of the Swimming Pool and Spa IndustryVolume 2, Number 2, pages 23 29 Copyright 2001by JSPSIAll rights of reproduction in any form Chemistry and Treatment of Swimming Pool and Spa Waterlated as follows (where a0 + a1 + a2 = 1):a0 = (1 + cK1/[H+] + cK1cK2/[H+]2) 1a1 = ([H+]/cK1 + 1+ cK2/[H+]) 1a2 = ([H+]2/(cK1cK2) + [H+]/cK2 + 1) 1 The total concentration of Carbonate species (CT) isgiven by:CT = [H2CO3*] + [HCO3 ] + [CO32 ]The concentration of individual species is calculatedfrom CT and the ionization fractions.[H2CO3*] = CTa0 [HCO3 ] = CTa1 [CO32 ] = CTa2 Cyanurate Equilibria Below pH 9, the onlysignificant equilibrium in the cyanuric acid (CA) sys-tem is:H3Cy H+ + H2Cy KCA = [H+]gH+ [H2Cy ]gH2Cy /([H3Cy]gH3Cy)cKCA= [H+][H2Cy ]/[H3Cy]= KCAgH3Cy/(gH+gH2Cy )The temperature dependent equation (T in kelvins)for KCA is given by (Matte 1990):Log KCA = + ( 4)T2 The total concentration of species is:CT = [H3Cy] + [H2Cy ]The ionization fractions are (where a0 + a1 = 1 ):a0 = (KCA/[H+] + 1) 1a1 = ([H+]/KCA + 1) 1 The concentration of individual species is calculatedfrom CT and the ionization fractions.

4 [H3Cy] = CT a0 [H2Cy ] = CT a1 Calcium Carbonate Solubility The solubil-ity of Calcium Carbonate is controlled by the solubilityproduct, which is the equilibrium constant for thereaction representing the dissolution of a solid to formits constituent Ca2+ + CO32 Since the activity of solids ( , CaCO3) are equal toone, the activity solubility product (KS) is given by:KS = {Ca2+} {CO32 } = [Ca2+]gCa2+ [CO32 ]gCO23 The concentration solubility product (cKS) is given by:cKS = [Ca2+][CO32 ] = KS/(gCa2+ gCO23 )Where the braces and brackets in the above twoequations represent actual activities and concentra-tions, respectively, and gCa2+ and gCO23 are the activitycoefficients of Calcium and Carbonate ions which werecalculated using the Guntelberg approximation(Stumm and Morgan 1996).

5 The temperature depen-dent equation for KS for the calcite form of calciumcarbonate is given by (Plummer and Busenberg 1982):Log KS = + + Log TWhere T is the temperature in solubility (s) of Calcium Carbonate in CO2 free distilled water can be calculated from aqueousequilibria. The mass balance is:s = [Ca2+] = CT = cKS/[CO32 ] = cKS/CTa2 = (cKS/a2).5 The charge balance is:2[Ca2+] + [H+] = [OH ] + [HCO3 ] + 2[CO32 ]Substituting the first equation into the second andrearranging gives the following equation; where Kw =[OH ][H+] and Kw = + (cKS/a2).5(2 a1 2a2) + [H+] Kw/[H+] = 0 John A. Wojtowicz Chapter equation can be solved for [H+] by iteration. At25 C the solubility is g/L and the pH is 1 shows calculated values of Calcium carbonatesolubility as a function of temperature and total dis-solved (mg/L) Temperature TDS F 1000 mg/L 5000 1 Calculated Solubility ofCalcium CarbonateThe solubility of Calcium Carbonate increaseswith decreasing pH due to the reactions:CO32 + H+ HCO3 H+ + HCO3 H2CO3*Although the solubility of Calcium Carbonate increasesas pH decreases, the solubility product remains un-changed.

6 The lower the pH the lower the carbonateconcentration. Therefore, in order to maintain satu-rated conditions, the Calcium concentration must Carbonate Supersaturation Su-persaturated solutions of Calcium Carbonate can beformed from saturated or undersaturated solutionswhen the Calcium hardness, pH or alkalinity areincreased. The degree of Calcium Carbonate saturation(S) is given by the ratio of the actual ion activityproduct (IAP) and the thermodynamic solubility prod-uct constant at infinite dilution (KS):S=IAP/KS = {Ca2+}{CO32 }/KS=[Ca2+]gCa2+ [CO32 ]gCO23 /KSS=[Ca2+][CO32 ]/cKSS values of <1, 1, and >1 represent undersaturation,saturation, and oversaturation, of Calcium Carbonate Ex-cess Calcium Carbonate is precipitated as follows:Ca2+ + CO32 CaCO3 Bicarbonate ions dissociate to replenish the H+ + CO32 The result of the above reactions is:Ca2+ + HCO3 CaCO3 + H+The hydrogen ions liberated in the above reaction canreact with alkalinity, , bicarbonate and cyanurateions:xH+ + xHCO3 xH2CO3*(1 x)H+ + (1 x)H2Cy (1 x)H3 CyThe overall reaction is.

7 Ca2+ + (1+x)HCO3 + (1 x)H2Cy CaCO3 + xH2CO3*+ (1 x)H3 CyThe relative extents of neutralization of bicarbonateand cyanurate depend on pH ( , the first ionizationfractions of carbonic and cyanuric acid) and the re-spective levels of bicarbonate and cyanurate alkalin-ity. Below pH 9, the reaction of hydrogen ions withhydroxyl ions is negligible. The Precipitation of cal-cium Carbonate results not only in a decrease incalcium hardness and alkalinity, but also in pH. Onemol of hardness and two equivalents of alkalinity areconsumed for each mol of Calcium Carbonate of Calcium CarbonatePrecipitation PotentialCalculation Model Total alkalinity (AlkT,equivalents) is represented by:AlkT = [HCO3 ] + 2[CO32 ] + [H2Cy ] + [OH ] [H+]Below pH 9 the concentrations of hydrogen and hy-droxyl ions can be neglected.

8 Substitution of appropri-ate terms for bicarbonate, Carbonate , and cyanurate,gives the following equation, where i represents initialvalues of the various terms:AlkT,i = CT,i (a1,i + 2a2,i) + CT a1,i 54 The Chemistry and Treatment of Swimming Pool and Spa WaterAfter equilibration, , after Precipitation of calciumcarbonate is completed ( , the saturation index isequal to 0), the following relationship holds:AlkT,i 2x = (CT,i x)(a1,f + 2a2,f) + CT a1,f where: x is the concentration of Calcium and carbonateions precipitated as CaCO3. Solving for x we have(where the subscripts i and f refer to initial and finalconditions):x = [CT,i (a1,f + 2a2,f) + CT a1,f AlkT,i]/(a1,f + 2a2,f 2)Substituting x into the equation for the degree ofcalcium Carbonate saturation, Sf = [Ca2+][CO32 ]/cKS,gives:Sf = [Ca2+ x][CO32 x]/cKSThis is one form of a working equation for calculationof CCPP.

9 Another form is obtained by substitutingcK2[HCO3 ]/[H+] for the Carbonate concentration andconverting concentration equilibrium constants toactivity equilibrium constants by introducing activitycoefficients:S = [Ca2+]gCa2+K2[HCO3 ]gHCO3 /([H+]gH+ KS)Taking logs of both sides, and noting that pH = [H+]gH+,we have the saturation index equation with concen-trations in =pH + Log [HCO3 ] + Log [Ca2+] + Log (K2/KS)+ Log gHCO3 + Log gCa2+This is further modified as follows:SI =pH + Log [(CT x)a1] + Log ([Ca2+]i x)+ Log (K2/KS) + Log gHCO3 + Log gCa2+A computer program was written to perform thecalculations using this working equation. The proce-dure involved inputting the initial pH, hardness, totalalkalinity, and cyanuric acid and calculating the ini-tial ionization fractions.

10 The pH was then incrementedand the new ionization fractions were calculated fol-lowed by calculation of the value of x which wasinserted into the working equation. A test was madeto determine if SIf was equal to 0, , the IAP wasequal to KS or the ratio IAP/KS = 1. The iterationprocess (utilizing a Newton Rhafson convergence al-gorithm) was continued until this testwas satisfied to within the toleranceset. The model assumes no loss ofcarbon dioxide during the precipita-tion process, thus the acidity (Acy)remains constant:Acy =2[H2CO3*] + [HCO3 ] + [H3Cy]+ [H+] [OH ]Values of CCPP at 80 F for variousconditions calculated using the abovecomputer program are shown in Tables1 6. For consistency, the TDS in mostinstances was set at 5000 ppm, al-though it is understood that this isFigure 1 CCPP as a Function ofpH for Unstabilized andStabilized Water(SI = , C.)