Fundamental Chemistry of Precipitation and Mineral Scale Formation

Transcription

1 Fundmentl Chemistry of Precipittion nd Minerl Scle Formtion Aln W. Rudie, USDA Forest Service, Forest Products Lbortory, Mdison, WI Peter W. Hrt, MedWestvco Corportion, Corporte Reserch Center, Chillicothe, H Abstrct The minerl scle tht deposits in digesters nd blech plnts is formed by chemicl precipittion process. As such, it is ccurtely described or modeled using the solubility product equilibrium constnt. Although solubility product identifies the primry conditions tht need to be met for scle problem to exist, the cid bse equilibri of the scling nions often control where in the process scle will occur nd re the primry control method to minimize or prevent scle in blech plnt. As equilibrium processes, both the cid/bse equilibrium nd solubility product re influenced by temperture nd ionic strength. In this pper, the chemistry of precipittion nd cid/bse equilibri will be reviewed. The use of the Gibbs Free Energy expression tht connects equilibrium constnts to enthlpy entropy nd temperture will be discussed. The ffect of ionic strength on ion ctivity nd how it influences these processes will lso be presented. Terms nd generl principls There re some common terms used in queous inorgnic chemistry tht my need to be refreshed before strting. These terms re essentil for understnding the chemicl processes involved in scle formtion. Their use my hve been forgotten by those mong us who hve not worked with these concepts for severl yers. Anion is molecule contining negtive chrge. The typicl scle forming nions in the blech plnt re crbonte (C 3 ), oxlte (C ) nd sulfte (S ). Ction is molecule contining positive chrge. The trce metl nonprocess elements re ll ctions. The common ctions in blech plnt scles re clcium (C + ) nd brium (B + ). Monovlent nd divlent refer to the chrge of n ion. Monovlent nions nd ction contin single negtive or positive chrge, divlent nions nd ctions contin two negtive or two positive chrges. Typiclly slts of monovlent nions nd ctions re quite soluble, slts contining divlent nion or ction, nd two monovlent ions of the opposite chrge re lso typiclly very soluble. But slts where both the nion nd ction re divlent re typiclly springly soluble or insoluble. This trend cnnot be extended to trivlent ion (ions contining three chrges) becuse the chrge density is so high, they rrely exist in the 3+ or 3 stte in solution nd often form chrged molecules tht re soluble. Molrity (M), mollity (m) nd ctivity (): Molrity is the molr concentrtion of dissolved substnce reltive to 1 liter volume. Mollity is molr concentrtion reltive to 1 kg of totl mss. Activity is ion mobility nd is relted to both the concentrtion of the substnce nd the concentrtion of other dissolved ions. Ion ctivity is usully considered to be the product of concentrtion (either molrity or mollity) nd the pproprite ion ctivity coefficient (f). At infinite dilution nd 5 C, molrity, mollity nd ctivity of substnce re ll the sme. Introduction Some pulpmills hve lwys experienced minerl scle buildup, but with efforts to comply with environmentl requirements, these problems hve incresed. The recycle of wsher filtrtes implemented to reduce effluent volume in the lte 1970 s nd erly 1980 s incresed the concentrtions of both ctions nd nions nd with it the potentil for minerl scle deposits. Then the switch from chlorine initited blech sequences to the use of chlorine dioxide in the first stge decresed the bility of the blech plnt to remove clcium nd brium in the first stge. The result ws significnt increse in the frequency of clcium oxlte nd brium sulfte scle deposits in the first chlorine dioxide blech stge nd n increse in clcium crbonte deposits in the first extrction stge. In prticulrly severe cses, clcium oxlte lso forms in lter blech stges. 1,

2 Minerl scle formtion is chemicl precipittion process. Although the chemicl phenomenon of precipittion cn identify where nd when scle deposition is possible, it cnnot determine tht scle will definitely occur. The resons re mny, but to nme few: In loctions where precipittion is generl nd not directed towrds specific surfce, fiber represents the lrgest surfce re in the process nd precipittes tht deposit on fiber re generlly nd t lest temporrily hrmless. These precipittes tend to sty with the fiber nd crry trce elements further into the bleching process where they often do cuse problems. Precipittion is time nd concentrtion dependnt. 3 Under conditions tht brely exceed the sturtion concentrtions, it cn tke hours or longer for n obvious precipitte to form. The first precipittes tht form re very smll nnometer sized prticles. ver time, smll crystls tend to dissolve nd lrger crystls grow, but this cn tke long time before visible precipittes re observed. Some slts cn exceed the solubility by n order of mgnitude or more without precipitting. This supersturtion condition cn be mnipulted nd is one method of suppressing scle by dding chemicls tht interfere with crystl growth or interfere with crystl nucletion. 5 There my be orgnic frgments in blech plnt filtrtes tht behve in these wys to suppress precipittion. There re numerous orgnic frgments tht cn form complexes with trce metls. These complexes contin physicl bonds between the metl nd orgnic frgment nd form n equilibrium condition consisting of the complex, the free solvted trce metl nd the orgnic frgment. The equilibrium expression for this complex is clled formtion constnt nd these vlues re n indiction of the strength of the complex reltive to the independent molecules. For exmple, nerly ll crboxylic cids hve wek ttrction for clcium nd brium. Frgments with two cid groups form much more stble complexes, but complexes with one or two ppropritely plced lcohol groups cn lso form stronger complexes. For exmple, clcium nd mgnesium form very wek complexes with the cette nion. The formtion constnt for these two complexes is round 5. 6 The formtion constnt of these two metls with lctte [H C(H)CH(H)C ] is bout 5 times stronger t 5, nd the formtion constnt of these two ctions with the oxlte dinion ( CC ) is 0 to 100 times stronger yet t For cse where both the trce metl nd complexing orgnic molecule re both t 1mM strting concentrtion, the complex represents less thn 1% of the trce metl with formtion constnt of 5, but 50% of the trce metl for formtion constnt of xidized sugrs like gluconic cid re much like the sugr frgment lctic cid nd hve formtion constnts with clcium nd mgnesium round 5. 7 It is not possible with current industry cpbilities to ctlog ll the possible complexes nd determine their formtion constnts. Fortuntely in the blech plnt, orgnic frgments tht cn form strong complexes re usully t low concentrtions, nd frgments tht re common tend to form wek complexes. It ppers tht both cn lrgely be ignored in blech plnt environments. However, it needs to be recognized tht precipittion models tht ignore these effects represent worst cse nlysis. The chemist error. Chemistry is defined under unrelistic conditions. For exmple, wht is infinitely dilute supposed to men nd where cn you find this condition in pulp mill? The obvious nswer is tht whtever infinitely dilute mens, it does not pply nywhere in pulp mill or blech plnt. We need to understnd tht the pproximtions tht llow us to extend chemicl principls to the conditions in mill re just pproximtions nd becuse of this, the results re not bsolutes nd re subject to some interprettion. Precipittion 8 The scle tht forms in digesters nd blech plnts is bsiclly loclized chemicl precipittion process. As such it is usully described using the solubility product convention. For the generlized chemicl rection: ma + nb pc + qd the chemicl equilibrium is usully written s:

3 p q [ C] [D] m n [ A ] [B] = K Eqution 1 For solubility product, there is typiclly just one product nd following the equilibrium expression convention puts the concentrtion of the product in the numertor. But wht is the concentrtion of precipitte? By convention, the concentrtion or rther ctivity of the precipitte is defined s 1.0 nd the equilibrium expression is inverted. ma + nc A m C n The solubility product expression is m n [ A ] [C] = K sp Eqution. This is the equivlent of writing the initil chemicl eqution s dissolving the solid. For the common precipittes encountered in blech plnt, the chemicl eqution nd corresponding equilibrium equtions re s follows: 9 For clcium crbonte (lime, clcite or rgonite): 10 C + + C 3 CC 3 [C ][C ] = Eqution For clcium oxlte: C + + C CC [C ][ C ]= Eqution + 9 nd for brium sulfte (brite): B + + S BS [B ][S ]= Eqution All three solubility products re quite smll numbers. Assuming equl molr concentrtions of nion nd ction, ll will cuse precipittion t bout 10 molr concentrtion or bout or 5 prts per million. The typicl pulp mill blech plnt receives over ton of clcium dy in the unbleched pulp nd ll of this must be removed to void scle problems. Acid Bse Equilibri 11 A key issue in precipittion is tht the nions tht prticipte in the precipittion process re the divlent nions, not HC 3, HC or HS. This mens tht the conditions for scle formtion re strongly influenced by the process ph. 1 The generl chemicl eqution for n cid equilibrium is written s follows: HA Æ H + + A

4 Note, the eqution is the reverse of the typicl chemicl equilibrium eqution the product in chemicl process involving n cid is considered to be H +. The resulting equilibrium expression is shown in eqution 6. [H + ][A ] = K Eqution [HA] It is common to express H + s H 3 +, recognizing tht the proton is hevily solvted in wter nd relly does not exist independent of the surrounding wter. This convention hs not been dopted here for simplicity, but it is recognized tht the solvted nottion is more ccurte representtion of the stte of this ion. The choice s to how to represent this ction does not impct the equilibri or clcultion to be discussed in this pper. For ll three cses contributing to scle, there re two cid dissocitions to consider, but only the second of the two is importnt to the precipittion process. For crbonic cid: 6 H C 3 Æ H + + HC 3 nd HC 3 Æ H + + C 3. The corresponding equilibrium equtions re presented below nd grph of the ph dependence of the crbontes is provided in Figure 1. [C 3 [HC 3 ] [HC 3 ][H [ H C ] ][H + ] + ] 3 = = Eqution 7 nd b 13 The crbonte ion domintes t ph bove 10 but is still mesurble t ph levels down to7. Bicrbonte domintes between ph 6 nd ph 10, nd crbonic cid domintes t ph below 6. Since mny ppermchines operte with clcium crbonte filler t neutrl ph, we know tht lime scle is somewht stble down to ph of 7. The chemicl equtions for oxlic cid re s follows: H C Æ H + + HC HC Æ H + + C [ C ][H ] + =. 1 [ HC ] + ][H ] [ HC [ H C ] = Eqution 8 nd b The oxlte ion exists t ny ph bove bout nd is the dominnt form of oxlte t ph bove. The cidbse specition of oxlic cid is shown in Figure. Sulfuric cid is strong cid nd for prcticl purposes, when diluted with wter, the first proton is lwys dissocited. So only the second cid dissocition constnt usully needs to be considered.

5 HS Æ H + + S [S [HS ] ][H + ] = Eqution 9 The ph dependence of sulfuric cid nd the sulftes is shown in Figure 3. The sulfte ion domintes t ny ph bove nd still exists t ph ner 0. When evluting the likelihood of precipittion, both the cid/bse behvior of the nion nd the solubility product need to be considered. nly when the bsic form, the divlent nion nd the ction combined exceed the solubility product is precipittion likely. Figure shows clcultion for precipittion of clcium crbonte. Precipittion strts t ph of 8, bout the sme ph the grph shows mesurble mount of crbonte. For this grph, crbonte ws t 1 M nd clcium t.01mm. The clcium crbonte precipittion ws determined using the ESP equilibrium softwre from LI Systems, Inc. (Morris Plins, NJ) nd the scle for the precipitte hs been djusted to mke it fit on the grph. A similr grph of clcium oxlte precipittion is provided in Figure 5. In this grph, the oxlte ph dt is the sme s in Figure nd t 1 M concentrtion. The clcium oxlte precipittion ws clculted for solution tht hd 1 mm strting concentrtion of both clcium nd oxlte. The two grphs disply the sme issue precipittion does not usully occur t ph conditions where the divlent ion is t low concentrtion. For clcium crbonte, this ph is 7 8, nd for clcium oxlte it is bout.5. For sulfte, this would be ph round 0.5. This feture mkes ph control the most powerful tool for eliminting minerl scle in blech plnts. Although solubility product nd the cid/bse chemistry of the precipitting nions hve the biggest influence on when nd where process will develop minerl scle, there re other process vribles tht influence scling processes. Temperture is probbly the next in significnce. Most slts become more soluble s the temperture increses nd this is true for brium sulfte nd clcium oxlte. But the solubility of clcium crbonte decreses with temperture (Figure 6). This is the reson tht clcium crbonte scle is common in digester heters nd other process het exchngers. This effect my lso contribute to clcium oxlte nd brium sulfte scle on wsher wires. As the filtrte penetrtes the mt, it enters the prtil vcuum of the drop leg cusing it to cool few degrees. f course, the prtil vcuum lso evportes some of the wter, cusing the concentrtions to increse s well. Ion Activity The solubility product nd cid bse equilibri presented so fr re ccurte only for very dilute conditions. To move from the lbortory to rel situtions, it is necessry to understnd how other dissolved ions ffect the equilibrium. As slts build up in solution, the nions nd ctions begin to orgnize to reduce repulsion of like chrges. With incresing ionic strength, the wek orgniztion of solution chrges begins to strengthen nd impede ion mobility. For clcium ction to come into contct with crbonte. nion it my need to escpe wekly ttrctive cge of chloride nd hydroxide nions nd the surrounding wekly repulsive cge of sodium, potssium nd mgnesium ctions The influence of ionic strength is known s ion ctivity. Activity Coefficients for NCl, CCl, N C 3 nd CdS re shown in Figure 7. At typicl blech plnt concentrtions, slt of monovlent nion with monovlent ction hs n ctivity coefficient round 0.8. Tht mens the effective concentrtion in equilibrium clcultions is just 80% of the ctul concentrtion. For slt of divlent nion with divlent ction, the men ctivity coefficient under blech plnt conditions is bout In prcticl terms, this mens the rel solubility of clcium crbonte, clcium oxlte or brium sulfte is bout ten times the solubility s determined by the solubility product without considering ion ctivity. To pply the men ctivity coefficient (f (CC3) ) to the solubility product, the product of the concentrtions is multiplied by the ctivity of the slt rised to the power of the sum of the stoichiometries. Including the ion ctivity, the solubility product for clcium crbonte chnges from eqution 3 to eqution 10 below..

6 + [C ][C 3 ]f (CC3 = K Eqution ) sp 10 This form uses the men molr ctivity coefficient for the slt. The men molr ctivity coefficient is squred for 1 to 1 slt nd cubed for to 1 slt. It is possible to clculte the ctivity coefficient for the individul nions in which cse, the concentrtion of ech ion is multiplied by the ctivity coefficient rised to the power of the stoichiometric vlue of tht ion. The individul ion ctivity coefficients re derived from the ctivity coefficient determined for the slt ccording to the eqution: m n f x = m+n m y n f x f y Eqution 11 There re suitble tbles in severl stndrd chemicl references tht provide mesured ctivity coefficients suitble for determining if existing nlyzed conditions exceed the solubility limit for scle formtion. For modeling purposes, it is useful to estimte the ctivity coefficient using one of severl model equtions. The extended DebyeHückel eqution is typiclly the strting point for estimting ctivity coefficients. I log( )= Az 1 + b I f Eqution 1 The vlue A vries slightly with temperture, but is round , b lso vries with temperture nd is round 0.391, nd is the hydrted rdius of the nion or ction. For clcium nd mngnese this vlue is bout 6, nd for brium nd crbonte this vlue is 5. Becuse of the log scle, the exct vlues do not hve lrge effect on f, nd it is common to use 0.5 for A nd either 1.0 or 1.5 for b. I is ionic strength, defined s: I = (C i z i + A j z j )/ Eqution 13 Where C i represents the ctions in solution, A j the nions nd z their respective chrges. The sums re over ll nions nd ctions in solution. The bsic form of the DebyeHückel eqution is n symptotic decline from vlue of 1 t zero ionic strength, to low vlue t high ionic strength. Relity is fr different. At high ionic strength, the sme wek electrosttic order tht limited mobility t low ionic strength begins to impose piring of chrges tht increses the effective ctivity. Most ions (or slts) rech minimum ctivity coefficient somewhere between n ionic strength of 0.5 to 5 M, but there re lso mny cses where the minimum is outside this rnge. In generl, this minimum is quite vrible nd ppers to be unpredictble bsed on first principles. The form of the extended DebyeHückel eqution hs no minimum it cnnot predict n increse in ctivity t higher ionic strengths. The solutions hve been mny, vried, nd not ltogether stisfctory. There hve been numerous suggestions for dding or subtrcting term in ionic strength such s the Dvies, 1 Guggenheim, nd bdot equtions: I log( f )= Az I 1 + b I b Eqution 1 For the Dvies eqution, the recommended vlue of b * is either 0. or 0.3 depending on the reference. For the bdot eqution, b * is n ionspecific vlue. The effect of the dded prmeter is to multiply the ctivity coefficient estimted by the extended DebyeHückel eqution by vlue of 10 b*i. For b * = 0. nd n ionic strength of 0.5 M this increses the DebyeHückel estimte by 1.5. I is ionic strength nd is formlly defined s An exmple of the fit of both the extended DebyeHuckel nd the Dvies equtions to the mesured ctivity coefficient for the divlent slt copper sulfte is shown in Figure 8. A divlent slt ws selected purposefully for this nlysis since ll the scle forming slts in the blech plnt re divlent ctions with divlent nions. In generl, the solubility of this type slt is low nd there is reltively little dt

7 vilble in the literture for the specific scleforming slts. This prticulr slt hs not reched minimum vlue t ionic strengths below molr, but the Dvies eqution estimtes minimum vlue t n ionic strength of 0.6 molr (0.15 M CuS concentrtion). Similr results re obtined with the sulfte slts of cdmium, zinc, nickel, mgnesium nd beryllium. At ionic strengths up to bout 0.5 molr, there is very little difference in the predicted vlue of the ctivity coefficients by ny of these lterntives. At ionic strengths greter thn 0.5 molr, the Dvies eqution mtches experimentl vlues for some ions better, but with the slts, does not provide good fit. For most blech plnt modeling, the extended Debye Hückel eqution provides sufficiently ccurte ctivity coefficients nd this is the method generlly used in our blech plnt equilibrium modeling. However, this is not the sitution in the pulp mill nd recovery res of the mill where concentrtions re much higher. For these res, the Pitzer equtions provide resonble ccurcy nd re more suitble for equilibrium modeling. 15 The Impct of Temperture: As shown in Figure 6, solution equilibriums re often influenced by temperture. Chemicl equilibriums re relted to Free Energy by the expression: ΔG = RTln(K) = ΔH TΔS Eqution 15 Where G, H, nd S re respectively the free energy of rection, the enthlpy of rection nd the entropy of the rection. R is the gs constnt nd T is temperture in K. Grphing ln(k) vs 1/T, provides stright line reltionship where the intercept is ΔS/R nd slope is ΔH/(R). This provides mechnism to estimte cid dissocition constnts nd solubility products for tempertures tht hve not been directly mesured or re slightly beyond the rnge of convenient lbortory experiments. A ph Control Exmple As n exmple of the use of these equilibrium concepts, consider the use of sulfuric cid nd sodium sesquisulfte for djusting ph. Sodium sesquisulfte hs the formul N 3 HS 8 nd is bislt of sodium bisulfte nd sodium sulfte tht cn be obtined s the spent cid from some chlorine dioxide genertors. The cid equilibrium ws presented erlier s eqution 9. Sulfuric cid is strong cid nd the first of the two protons is lwys dissocited under norml lbortory conditions. The second dissocition is still strong cid, but hs been estimted with pk round. The rection is: H S H + + HS H + + S Determining the mount of cid needed to rech trget ph using sulfuric cid, requires the following mss blnce equtions: H + = (S ) + HS Eqution 16 S T = S + HS Eqution 17 Where S T is the totl mount of sulfuric cid dded. Note tht for simplicity, the squre brckets indicting molr concentrtion hve been dropped. These two equtions re solved to give the S nd HS in terms of hydrogen nd S T. Reorgnizing eqution 17 gives: S = S T HS. Eqution 18 Replcing the S in eqution 16 with eqution 18 gives: H + = (S T HS ) + HS = S T HS

8 Reorgnizing this gives: HS = S T H + Eqution 19 Eqution 17 cn lso be reorgnized to solve for HS : HS = S T S Eqution 0 Substituting eqution 0 for HS in eqution 16 gives: H + = (S ) + S T S = S + S T Reorgnizing this gives: S = H + S T Eqution 1 Rewriting eqution 9 with the ion ctivity coefficients dded to the eqution gives: [S ]f[h + ]f 1 = K Eqution [HS ]f 1 Where f 1 is the ctivity coefficient for the monovlent bisulfte nions nd proton (ction) nd f is the ctivity coefficient for the divlent sulfte. Writing the eqution this wy recognizes tht the ctivity coefficients for the monovlent proton nd bisulfte nion re nerly the sme, nd for prcticl purposes, equl within the ccurcy of the formuls for estimting ctivity coefficients. They cncel. Substituting Eqution 1 for the [S ] nd Eqution 19 for [HS ] in Eqution gives: [H + S T ]f [H + ] = K [S H ] + T Reorgnizing into qudrtic nd reinserting the squre brckets gives the following: ([H + ] [ ])[H + ]= S T K f S T ([ ] [H + ]) K S T S T [H + ] [ ][H + ] K [ ]+ [H + ]= 0 Eqution 3 [H ] + + [H ] + K f f f [ ] K S S T T = 0 f [ ] This eqution cn then be solved using the qudrtic formul, providing the vlue of [H + ] for ny given totl chrge of sulfuric cid, nd then using equtions 19 nd 1, cn determine the solution concentrtions of HS nd S. Similrly, for sodium sesquisulfte, the chemicl rection is N 3 HS 8 3N + + S + HS 3N + + (1+x)S + xh + + (1x)HS This leds to the mss blnce equtions

9 H + = Se HS Eqution Se = S + HS Eqution 5 Where Se is used to indicte totl sesquisulfte. Solving for S nd HS s before gives: HS = Se H + Eqution 6 And S = Se HS = Se (Se H + ) = Se + H + Eqution 7 nd substituting into eqution gives: [Se + H + ]f [Se H + [ ] H + ] = K Agin, reorgnizing this into qudrtic eqution. Se [H + K K ]+ [H ] + = Se [H f ] + f Eqution 8 K K [H + ] + Se + [H + ] Se = 0 f f Agin, the eqution cn be solved with the qudrtic formul nd the concentrtion of the other ions determined using in this cse, Equtions 6 nd 7. These equtions were solved in Excel using the qudrtic formul. The mss blnce equtions were used to determine the sulfte, bisulfte nd proton concentrtions for ech chrge concentrtion of either sulfuric cid or sodium sesquisulfte, nd the ion ctivity estimted using the extended DebyeHückel formul (Eqution 1) using s the vlue for A nd 1.5 s the vlue for b. Ionic strength ws clculted from the clculted concentrtions of the three ions nd fctored into the qudrtic s n itertive feedbck loop. Since ph is proton ctivity, the solution to the qudrtic equtions needed to be multiplied by the ctivity coefficient for monovlent ion to give finl ph. Rther thn plot the resulting ph ginst cid chrge, we show ph ginst resultnt sulfte concentrtion in Figure 9. At high ph, nd bove, sodium sesquisulfte dds bout times the sulfte ions to solution s sulfuric cid. At ph.5, the sesquisulfte is forming buffer nd levels off. The mount of sesquisulfte required is diverging from the mount of sulfuric cid nd now produces over six times the sulfte produced when using sulfuric cid.. Using sulfuric cid, the sulfte ion concentrtion continues to increse t slower rte, nd phs levels below re possible. The key issues this grph rises re tht use of sesquisulfte to control the ph ner.5 substntilly increses the concentrtion of sulfte in the blech plnt nd with it the potentil for encountering brium sulfte scle. The second key issue is tht it is not possible to decrese the sulfte ion concentrtion nd potentil for brium sulfte scle using sulfuric cid. This severely restricts the bility to use ph control to eliminte brium sulfte scle problem. Summry: The chemicl process tht forms minerl scles in pulp mills nd blech plnts is precipittion nd the conditions tht led to scle formtion re redily understood in terms of the solubility product for the precipitte nd the cidbse behvior of the scling nion. Both the solubility product nd cid equilibrium constnts re temperture dependnt nd these chnges my need to be considered when evluting the likelihood of scle formtion. In ddition, the high dissolved ion concentrtion tht exists in pulp mill blech plnts reduces the ion ctivities. These lst two fctors (temperture nd ion ctivity) cn

10 increse the solubility of slt by bout one order of mgnitude. Even with this level of error, simple solubility product clcultion is still good strting point for understnding minerl scle problems. Given the norml process vrition in pulp mill or blech plnt, n order of mgnitude sfety fctor is desirble to insure scle free opertion. Thus even simple solubility product provides good first trget for use in mill to minimize deposition of minerl scle. In the second pper of this series, other fctors tht influence the solubility of trce ctions in blech plnts will be discussed nd more detiled precipittion scenrio evluted using mill dt. References 1. Dexter, R.J., nd Wng, X.H., The formtion nd control of blech plnt scle s result of wter minimiztion Proceedings, 1998 TAPPI Pulping Conference, pp Anker, L.S., Zidovec, D.F., nd Korol, R.T., Effect of clcium loding on blech line scling potentil, proceedings, 001 TAPPI Pulping Conference. 3. Skoog, D.A., nd West, D.M., Fundmentls of nlyticl chemistry, Holt, Rinehrt nd Winston, Inc., New York, 1969, pp Ibid, p Guo, J., nd Severtson, S.J., Influence of orgnic dditiives on clcium crbonte precipittion during krft pulping, Tppi J., 1: 1(00). Guo, J., Severtson, S.J., Appliction of clssicl nucletion theory to chrcterize the influences of crboxylte contining dditives on CC 3 nucletion t high temperture, ph nd ionic strength, Industril nd Engineering Chemistry Reserch, (1): (003). 6. Lnge s Hndbook of Chemistry, 1 th Edition, J.A. Den ed., McGrwHill, Inc, 199, pp Swyer, D.T., Metlgluconte complexes, Chemicl Reviews, 6: 63363(196). 8. Skoog, D.A., nd West, D.M., Fundmentls of nlyticl chemistry, Holt, Rinehrt nd Winston, Inc., New York, 1969, pp Ibid, p Lime is the common minerl term used for clcium crbonte. There re two nturlly occurring forms, clcite nd rgonite with clcite the crystlline form most frequently found in nture, mill nd lbortory settings. 11. Skoog, D.A., nd West, D.M., Fundmentls of nlyticl chemistry, Holt, Rinehrt nd Winston, Inc., New York, 1969, pp Ibid, pp Ibid, p Dvies, C.W., Ionic Assocition, Butterworths, London, 196, pp Pitzer, K.S., Thermodynmics of electrolytes. I Theoreticl Bsis nd Generl Equtions, J. Physicl Chemistry, 77(): 6877(1973). Pitzer, K.S., nd Kim, J.J., Thermodynmics of Electrolytes. IV. Activity nd smotic Coefficients for mixed electrolytes, J. Americn Chemicl Society, 96(18): (197).

11 Fundmentl Chemistry of Precipittion nd Minerl Scle Formtion Session 1 of tutoril on minerl scle Aln W. Rudie USDA, Forest Service, Forest Products Lbortory Peter W. Hrt Medwestvco Corp., Corporte Reserch Center, Chillicothe, H Wht will we lern Scle is chemicl precipittion process Precipittion depends on Chemic l concentrtions nd solubility product Acid/bse equilibrium of the precipitting nion Ion ctiviti es s ffected by ionic strength Temperture Solubility product, cid/bse equilibrium nd ionic strength re interdependent equilbri. We will go through n cid/bse equilibrium clcultion for sulfuric cid nd sodium sesquisul fte. Chnges reltive to the preprint Use of free energy to determine K Sulfuric cid vs sodium sesquisulfte The clcult on method ssumes known (or trget) ph nd determines the mount of sulfuric cid or sodium sesquisulfte needed. This method results in direct lgebric solution rther thn qudrtic solution tht results when determining ph by dding known mount of these cids. sp i 1

12 Mjor Sources Fundmentls of nlyticl chemistry ( nd edition) by D. Skoog nd D. West, Quntittive chemicl nlysis (th edition) by D. Hrris, Lng s hndbook of chemistry (1th edition), J. Den, editor, 199. The mteril in this session cn be found in ny good nlyticl chemistry textbook of trditionl methods (s opposed to instrumentl methods). Terms (we just hve to live with them) Ction: n tom or molecule contining positive chrge: H +, N +, Mg +, K +, C +, Mn + nd B + re ll ctions. Anion: n tom or molecule contining negtive chrge: Cl, H, HC 3, C 3, HC, C, HS nd S re ll nions. Monovlent: n tom or molecul e contining just one chrge. Divlent: n tom or molecule contining two chrges Concentrtions Molr: (M) The concentrtion of substnce given in moles per liter of volume. Moll: (m) The concentrtion of substnce given in moles per kilogrm totl. Ion Frction: x = z M /(Σ z i M i ). Ionic frction is used to express concentrtion in ion exchngers where z M is the chrge contribution of prticulr counterion, nd Σz i M i is the totl fixed ion content of the ion exchnger.

13 Activity Activity : in either molr or moll bsis, the ctivity is the pprent concentrtion in terms of equilibrium behvior. The term ctivity embrces the decrese in solution vilbility of ions when in the presence of other ions. i = f i [M i ] i is the ctivity, f i is the ctivity coefficient tht converts molr or moll concentrtion to ctivity. Generlized Chemicl Equilibrium ma + nb oc + pd o [ C ] [ D ] m [ A ] [ B ] p n = K The equilibrium The equilibrium represents the minimum free energy for the system nd therefore is the stte the system will nturlly trend towrds. The rte t which process chieves equilibrium is not ddressed in the theory nd cnnot be predicted. We del with nonequilibrium sttes ll the time: Chlorine dioxide, nd dimond. In scle, supersturtion is nonequilibrium stte. 3

14 Equilibrium expressions Solubility Product: A m B n ma + nb The ctivity of the precipitte is ssigned the vlue 1 Acid dissocition: AH m mh + Am Techniclly, ll concentrtions re ctivities m n [ A ] [ B ] m m [ H ] [ A ] [ H A ] m = K = K sp Exmple of solubility product Precipittion of clcium oxlte Wht typiclly is the need? Do the concentrtions of clcium nd oxlte exceed the solubility? At wht ph will they no longer cuse precipittion? Pertinent solubility product [C + ][C 9 ] =.3 x 10 Pertinent cid dissocition [H + ][C ]/[HC ] = 6.1 x 105 The cse dt: ph.5 ( mg/ kg )/1000(mg/ g) = g/ kg ~ g/l. g/ L/AMU = Molr or moll concentrtion. Element mu mg/ kg Molr z M H + N Mg C Mn x X 10 B X X xlte

15 Solubility Product Solution: Solve cid bse equilibrium for divlent oxlte concentrtion. Determine the concentrtion product to see if it is less thn the solubility product. This method involves the solution of just one equilibrium. Solution Acid mss blnce: [HC ] = x [C ] where x is totl oxlte ion. Substitute in the cid dissocition: [C + ][H ] = K (x[c ]) [C ]([H + ] + K ) = K x [C ] = K x/([h+ ] + K ) K + ph is known, H = 10 nd xlte is obtined nlyticlly. Solution The clculted divlent oxlte is multiplied by the nlyticlly determined clcium concentrtion to give the ion product. If this is greter thn the solubility product, precipittion or scle is likely. [C + ] = Kx/([H ] + K) = (6.1 x 10 5)(0.0001)/{( )+6.1 X 105 ) =.69 X X 106 X [C + ] =.69 X 106 X 0.00 =5.9 X 10 9 >.3 X 109 so the condition could cuse scle formtion. 5

16 ther issues Temperture At typicl blech plnt tempertures, the solubility product is higher, but the cid dissocition fvors more dissocition. Activity At typicl blech plnt concentrtions, the ctivity of divlent ion is pproximtely hlf of it s solution concentrtion, monovlent ion bout 85% of solution concentrtion. Complex formtion Ion Activity pposites ttrct: The presence of other ions in solution forces dditionl order on dissolved nions nd ctions. This order mkes it hrder for them to move freely nd typiclly reduces the probbility of rection. At high ionic strength, this effect cn reverse nd ion mobility increses. Activity is the effective concentrtion fter djusting for ionic strength Ion Activity: low ionic strength 1 Activity Coefficient NCl CCl NC3 CdS Ionic Strength (M) 6

17 Low ionic strength Activity for CCl nd N C 3 re nerly the sme. Activity t low ionic strength is reltively simple nd esily estimted. The ctivities shown re the men ctivities for the slts. Monovlent ions hve higher ctivities thn divlent ions. f = (f m f n b ) ( 1/n+m,b ) where m nd n re the stoichiometric coefficients of the slt. DebyeHückel Eqution log ( f ) Az = 1 + b I I A nd b re temperture dependnt constnts, is hydrted rdius, z is the chrge of the ion nd I is ionic strength DebyeHückel Approximtion A hs the vlue t room temperture b hs the vlue of t RT is ion dependnt, rnging typiclly from bout Å to 7Å. A good pproximtion of ctivity cn be obtined from: log ( f ) 0.5 = I I 7

18 t Fit of DebyeHückel t low ionic strength Activity Coefficien NCl CCl NC3 CdS DH 1 DH 11 DH Ionic Strength, M Ionic strength: ~ M Techniclly, ionic strength is one hlf the sum of the ctions, ech times their chrge squred, plus the sum of the nions times their chrges squred. Anions re typiclly H, S, C 3, Cl, nd C. These re typiclly hrder to nlyze for thn the ctions. I usully use the ionic strength contribution of the ctions s ionic strength nd ssume the mixture of monovlent nd divlent nions is similr to the ctions. Activity Coefficients: xlte cse f = 10 f 1 = ( ) = = 0.60 Ignoring the effect of hydrted rdius, we cn estimte the ctivity of the monovlent nd divlent ions nd use them in the cid dissocition nd solubility product determintions. 8

19 Temperture: K sp Cn determine Ksp from ΔG ΔH for CC H is 1.11 kj/mole ΔS for CC H is 9.15 J/deg/ mole At 5 C, ΔG = ΔHTΔ S = 1.11{ kj/mole} (73+5){ deg }(9.15{ J/deg/mole}/ 1000{ J/kJ}) = 9.17 kj/mole. Ln(K) = ΔG/RT = 9.17{ kj/mo le}/ {kj/deg/mole}/98{deg} K 9 sp =. X 10 At 65 C, K = 6.6 X 109 sp Temperture: K Lng s Hndbook 1 Ed, pp th.7 (5 ),.95 (30 ),.39 (0 ),.09 (50 ). Log(K ) = 98.59/T where T is in degrees Kelvin Extrpolting to 65 : pk.93, K 3. X 105 Equilibrium expressions Solubility Product: CC C + + C Acid dissocition: HC H + + C Note tht ph gives proton ctivity not concentrtion. Note tht the f 1 cncels but need to correct H+ from ph for ctivity. + [ C ] f [ C ] f = K sp + [ H ] 1 f [ C ] f = K [ HC ] f 1 9

20 Solution: ctivity nd Temperture [C ] = (K /f )x/{[h + ] + (K /f )} = (3. x 10 5/0.60 )( )/{( /0.88) + (3. X 10 5/0.60)} =.1 X 106 (.1 X 106 )f + X [C ]f 6 =.1 X 10 X 0.00 X 0.60 =1.7 X 10 9 < 6.6 X 109 At this level of nlysis, the condition is no longer considered likely to cuse scle. Sulfuric cid vs Spent cid Determine how much sulfuric cid or sodium sesquisulfte is required to djust 1 liter of wter to ph.5. Pertinent cid dissocition: HS Æ H + + S K = 0.01 By strting with ph trget nd determining the cid required, the clcultion is simplified. Sulfuric cid Chemicl eqution: H S Æ H + + HS H + + S H S Æ (+b)h + +b S + (b)hs (+b)h + = 10.5 = [S ]/[HS ] = K /[H + ] = 0.01/ = 3.8 b/(b) = 3.8 b = b.8b = 3.8 b =

21 Sulfuric Acid b = b = = = = b = H S = moles HS = b = molr S = molr Sodium sesquisulfte Chemicl Eqution: N 3(S )(HS ) Æ 3 N + + S + HS Æ 3 N + + (+b) S + (b) HS + b H + bh + = [S ]/[HS ] = 3.8 = (+b)/( b) b = + b.8 =.8 b = 1.7b b = = S = , HS = The comprison S t ph.5 using sulfuric cid for ph control is Molr S t ph.5 using spent cid for ph control is Molr To control to this ph, spent cid dds 6 times more sulfte thn sulfuric cid. 11

22 Entire ph rnge 5 Sufuric l cid Sesquisufte l 3 ph Sulfte m/l Wrp up This session hs reviewed the fundmentl chemicl equilibri involved in determining solubility product. This session hs crried out exmple equilibrium clcultions for cid bse equilibri of oxlic cid nd sulfuric cid. This session hs crried out solubility product clcultion for solution concentrtions of clcium nd oxlic cid. Preview of session II The next session of this tutoril will introduce the effect of wood fiber ion exchnge on trce metl concentrtions nd will demonstrte the solubility product clcultion for cse with wood fiber present. 1

23 In: Proceedings of the 005 TAPPI engineering, pulping & environmentl conference. 005 August 831; Phildelphi, PA. Norcross GA: TAPPI Press: 10 p. CD RM: ISBN