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A pH-dependent model for the chemical speciation of copper, zinc, cadmium, and lead in seawater

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A pH-dependent model for the chemical speciation of copper, zinc, cadmium, and lead in seawater
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  A pH-DEPENDENT MODEL FOR THE CHEMICAL SPECIATION OF COPPER, ZINC, CADMIUM, AND LEAD IN SEAWATER Alberta Zirino and Sachio Yamamoto Marine Environment Division, Naval Undersea Center, San Diego, California 92132 ABSTRACT A pH-dependent model for the speciation of divalent Cu, Zn, Cd, and Pb ions in seawater was constructed with available and estimated thermodynamic stability constants and indi- vidual ion activity coefficients. This model was used to calculate the degree of interaction bctwccn each of the metal ions and the anions Cl-, Sod’-, HCOX-, CO,‘-, and OH- as a function of pH. Interactions between a cation and an anion were assumed to result only in the formation of complexes with coordination numbers of 1 to 4; polynuclcar and mixed- ligand complexes wcrc not included in the model. The calculations showed the following: All four metals are complexed to a considerable extent in seawater; with the exception of Cd, the distributions of chemical species of the metals vary greatly with changes in pH; Cu interacts primarily with OH- and COs2-, Zn with OH-, Pb with COa2- and Cl-, and Cd with Cl-; complexes with high coordination numbers (i.e. 3 and 4) are not formed to any appreciable extent in seawater. INTRODUCTION Although trace elements contribute neg- ligibly to the total salt content of seawater, they do play an important role in the oceans. Certain tract metals, such as zinc and copper, are essential for the growth of marine organisms, although others such as lead and cadmium may be toxic to life in the sea. The uptake of trace metals and the paths by which they travel from source to sediment depend on their chemical state in the marine environment (Fukai and Huynh-Ngoc 1968 ) . Predictions regarding the extent of complexation of certain tract metals in scawatcr were made by Sillcn (1961), who indicated the most likely forms of the dissolved species at pH 8.1. The scope of his paper, however, did not permit extcnsivc calculations for any given trace metal and his predictions were largely qualitative. Garrels and Thompson (19f32) dcvcl- opcd a chemical model for seawater from available thermodynamic data and from it calculated the degree of complexation be- twccn the major cations (Na+, K+, Mg2+, and Ca2+) and the anions SQd2-, HC03-, and COs2-. Explicit in their calculations were the assumptions that the interactions bctwcen the ions under consideration re- sulted only in the formation of ion pairs and that chloride complexes were negligi- ble. Goldberg (1965) suggested that the model of Garrcls and Thompson could bc applied to the trace clcments in seawater and, as an example, calculated the dcgrcc of interaction between Cd2-b and the anions Cl-, SOh2-, and OH-. In our work, the approach devclopcd by Garrels and Thompson (1962) has been ex- panded to include higher order complexes and applied to the divalent ions of Cu, Zn, Cd, and Pb. These metals were chosen bccausc of their importance in the bio- sphere and because some experimental in- formation regarding their speciation was available. The primary purposes of this paper are to estimate the cxtcnt of com- plexation of these cations with the anions OH-, Cl-, SOa2-, HCOs-, and COs2- and to detcrminc the effect of pH changes nor- mally encountered in seawater on the dis- tribution of the chemical species of each metal. TILE MODEL For each metal considcrcd, available and estimated individual ion activity coef- ficients and stability constants were used LIMNOLOGY AND OCEANOGRAPHY 661 SEPTEMBER 1972, V. 17(5)  662 ALBERT0 ZIRLNO AND SACIIIO YAMAMOTO TABLE 1. Expressions for the total metal concentration and for the concentration of each species ex- pressed as a percentage of the total metal 1. Total metal concentration: n (Ml = (Ml + 2 i P(il,(Ml(L(i) 1”. yMLlij yM ‘L(i) total n-1 i-1 n 2. Percent uncomplexed metal ion: %(M) = lOO/ 1 t 2 k P (i),(L (il I” n=l i=l yML(i) n 1 3. Percent complex ML(i)” : lOOP(iln (L (i) 1’ ‘M ‘L;i) ‘v ’ ML(i) n %(ML(i), ) = 4 J ‘AA 1 +C C P(il,(L (i) )n. - ‘L”(i) n=l i=l Y ML(i) n to calculate the concentrations of the un- complexed metal ion and each complcxcd spccics as pcrccntagcs of the total metal concentration. The metals were consid- ered to be in the divalent state in seawa- ter. Interactions bctwecn a cation and an anion were assumed to result only in the formation of mono- (ion pairs), di-, tri-, and tetra-ligand complexes. Polynuclcar complexes such as Cu2 ( 011) z2+, mixed- ligand complexes such as Cu( OH) ClO, and organic chelates were not included in the model. All calculations arc made for sea- water of chlorinity 19%, at 2% and 1 atm total pressure. Thermodynamic cquilib- rium was assumed to exist. Calculation of the distribution of species To calculate the distribution of chemical spccics, a mass balance equation is writ- ten for each metal under consideration. Thus, for any given metal M WI total [Ml + i i [ML(i),,], (1) n=1 =1 where [M] totnl = total metal concentration, [ M ] = uncomplcxed and/or hy- drated metal ion concen- tration, [ML(i) ?%] concentration of the nth order complex bctwecn the metal M and the ith ligand L(i), J = total number of ligand types (i.e. anions ) in- cluded in the model. The concentration of the complex ML(i), can be expressed in terms of its overall formation constant, p(i),, the uncomplexcd ligand and uncomplexcd metal ion con- centrations and their respective activity cocfficicnts, and the activity coefficient of the complex. Thus,  CIIEMICAL SPlXIATION OF METAL IONS 663 [ML(i Jn] = P(i)18[M] [L(i)]“* ~yyr’(“, (2) whcrc /l(i)% = overall formation constant for the complex ML(i) 12, YM = thermodynamic activity CO- efficient of the uncom- plcxcd metal ion M, YMi) = thermodynamic activity co- efficient of the uncom- plexed ligand L(i), yMT,(i), = thermodynamic activity co- efficient of the complex ML(i).. Equation (2) is obtained simply by rcar- rangement of the conventional expression for the formation constant. By combining equations (1) and (2) the mass balance equation can bc rcwrittcn as the first cxprcssion in Table 1. The second and third equations in Table 1 arc, respectively, the concentrations of the un- complcxed metal ion and the complcxcs cxpresscd as pcrcentagcs of the total metal concentration. The former was obtained by rearrangement of the first equation in Table 1 and the latter by dividing cqua- tion (2) by the expression for the total metal concentration [equation (l), Table 11, Expressions (2) and (3) in Table 1 arc independent of the total metal concentra- tion, Concentrations of the ligands HCOS-, COa2-, and OH- obviously dcpcnd on the pH of the system. Insertion of appropri- ate pII-dependent cxprcssions for their concentrations (see Table 3) into the cqua- tions for the percent concentrations pcr- mits one to calculate the distribution of chemical spccics as a function of pH. Activity coefficients Values for the individual ion activity cocfficicnts of HCOs- and COs2- are 0.68 and 0.20 (from Garrcls and Thompson 1962). The value of ycl- was assumed to be equal to that of ycIccI and was taken to bc 0.64 (from IIarncd and Owen 1958). The value for SOd2- is 0.21 (Kcstcr and Pytkowicz 1968). An activity coefficient value was not required for OH- since its activity was obtained directly from TABLE 2. Molal concentrations of uncomplexecl HCO,- ancl COs”- in seawater at 25C and I-atm pressure as a function of pll HCO, co:- PH (x 10-y (x 10-61 7.0 1.62 2.60 7.1 1.61 3.25 7.2 1.58 4.00 7.3 1.57 4.99 7.4 1.55 6.21 7.5 1.52 7.70 7.6 1.49 9.50 7.7 1.46 11.65 7.8 1.41 14.21 7.9 1.36 17.20 8.0 1.29 20.64 8.1 1.22 24.52 8.2 1.14 28.82 8.3 1.05 33.45 8.4 0.96 38.32 8.5 0.86 43.29 8.6 0.76 48.19 8.7 0.66 52.87 8.8 0.57 57.16 8.9 0.48 60.93 9.0 0.40 64.06 I____~__---._ ---- --..-. - Individual activity coefficients for the metal ions and their complcxcs wcrc calculated from the Davies modification of the Dcbye-Huckcl expression (Davies 1962) : 1% Ya = -0.51x2 1 Frl ( ~-0.301 ) > (3)  664 ALRERTO ZIRINO AND SACIIIO YAMAMOTO TABLE 3. Expressions for the total concentrations of potassium, sodium, calcium, magnesium, ancl sulfate in seawater and for titration alkalinity* 1. Total potassium concentration: K, = (K+)r,+ - - t yK+ K,, 2- .y 4 so,2- ’ (SO, 2-l /Y,04 2- 1 2. Total sodium concentration: NaT= NatlYNol $1 ’ KNaHCO” HCO I 3 ;(HC03-) /YNoHCO 0 + KNaOHoAOH-/YNaOHo 3 +K NaCO< ‘y,,;-(c032-) /Y,,,, - + K 1 N SOd- .YS04’- (so42-) /YNaSO, - 1 3. Total calcium concentration: Ca T = (Cu 2+)YCa2i 1 -tK YCaZ’ CaHCO,’ ’ Y HCO.,- +-‘COJ /YcaHco 3 + + KCaCO o ~~co3~.~~~32-~~-ycacoi’ 3 3 t Kc~so~‘?so~- I( S0,2-) /YcaSO,O + KC~OH’ eAOH-/YCaOHt 1 Total magnesium concentration: Mg, = ( Mg2+)Y I 1 Mg=+ y tK MgHCO,+ .Y Mg” k,co3-( HC03-)/~Mg,,co+ “/,.jgco o~yC,2-(co~-1’yMgCOo 3 3 3 3 + K MgSO.: =%O., z-( SO42’) /Y MgSO,” + KMgOH’ ’ AoH- / YMgOH+ I 5. Total sulfate concentration: so,,= ( so42-)Y,,;- [ + so:- + KKSO ; ‘7,’ ( Ktl /‘KsO,;’ KNaso,- “Na’ ( NatI /yNaSO, +K MgSO,’ *Y Mg?’ ( Mg2t) /YMgsoAot KcaSO,” ‘Ycayt( Ca 2t) /‘CaSO,(’ I 6. Titration alkalinity: Yco32- AH +(COS2-) T.A. = 1 t K NaHCOs’ -Y K -.?HC03- HCO; “N a+ ” Nat’ “NaHCO “tKCaHCO+*YHC03- 3 3 HC03 ‘ycal+( Ca2-+) IYcaHcO + + KMgHco+ ‘yHco- ” 3 3 3 Mg’+( w+vMgHCo~ - - I + 2 ( cog-)Yco2- 1 qo2- [ t KNaCO --YNa+(Nat 1 3 /‘YNaco +K 3 CaC030 %o z+(Ca’+) /YcaCO 0 3 3 +K MgCO,’ -yMg2’(Mg2+) /YMgcoo t (Ke’ *2.2’10-5’cl%o) / (AH++ KB’) 3 I I 1 t (AOH-- AH+) t KNaOHo (Na+)‘YNat ‘AOH--/ NaOH o+K CaOH+ (Ca2+)yca2 t l AOH-/Y CaOH’ ’ ’ MgOH+ (Mg2+I * YMg2t ’ AOH- /YMgoH+ -___----. -- * Key to symbols: 1 I = concentration; YM 3 YL’ YML = individual ion and ion pair activity coefficients; K ML = stability constants of metal M and ligand L; K ncoo- II second dissociation constant of carbonic ncicl; AOH’ AI-I+ T.A. Cl%” K’n = hydroxyl ion activity; = hydrogen ion activity; = titration alkalinity; = chlorinity in parts/thousand; = apparent dissociation constant of boric acid in seawater.  CHEMICAL SPFKXATION OF METAL IONS 665 TABLE 4. Stability constants for copper SpWif%. All values are logarithms and unless otherwise in&cat& were obtained from Sillen ancl Martell (ltM4) and are fo-r 25C and infinite chtion Anion IWP, log& logo, log P4 cl- 0 -0.7 -2.2 -4.4 SOA*- 2.3 -* - - OH- 6.3 14.3 15+ 16+ HC03- 2.7* - - - cos2- 6.77 10.0 - - . * Dashes indicate that the stability constants were un- available, or the species were not included in the calcula- tions, or both. t Schindler 1967. jz Estimated from the stability constant of CuCO,O as- suming log Bc,,co,o/lo~ BcUncos+ = 2.5. whcrc x is the ion charge and I is the ionic strength. The following values of activity coefficients arc obtained from equation (3) for seawater which has an cffcctive ionic strength of 0.67 (Kestcr and Pytkowicz 1969) : 70 = 1.0 for neutral species, yI = 0.74 for monovalent ions, and yrr = 0.34 for divalcnt ions. Concentrations Total metal concentration values were not rcquircd since all the results were obtained as pcrccntagcs. All anion con- centrations wcrc exprcsscd in terms of molalitics. The concentration of Cl- was taken to bc 0.554 molal (Goldberg 1965) and that of SOJ2-, 0.0284 molal (Garrcls and Thompson 1962). The concentration of OH- was assumed to be fixed by the pH at which the calculations were made. The concentrations of unassociated HCOs- and COs2- used in the computations, shown in Table 2, were calculated as a function of pI1 as follows. The Garrels and Thompson (1962) model was rewritten in terms of the six pH-dc- TAULE 5. Stability constants for zinc species. All values are logarithms and unless otherwise in&- cated were obtained fTom Sillen ad Mad1 (1964) and are for 25C and infinite dilution Anion lo& I42 log 03 log P4 Cl- 0.4 0.61 0.53 0.2 Sod*- 2.3 -* OH- 4.4 12.89 14 15 HCO,- 2.1 + - co,*- 5.37 - - - * Dashes indicate that the stability constants were un- available, or the species were not included in the calcula- tions, or both. t Obtained from the estimated stability constant of ZnCOsa assuming log ~e,coso/log BznncOs+ = 2.5. :I: Estimated from the dissociation constant vs. electro- negativity curve (Fig. 1). pcndcnt equations presented in Table 3. The sixth equation in the table is the titra- tion alkalinity expressed in terms of the bases in the first five equations plus the borate alkalinity (Harvey 1956). The ti- tration alkalinity was assumed to remain constant at 2.34 X low3 cquiv/kg over the entire ~1-1 range; this is a good approxi- mation to natural seawater conditions (Harvey 1956). All stability constants and activity cocfficicnts wcrc obtained from the Garrcls and Thompson (1962) model with the cxccption of KNncTro which was obtained from Sillcn and Martcll (1964) and YNnOII", ycuo11+, and yMgcII.+ which were set at 1.13, 0.68, and 0.68. Stability constants Stability constants used in the calcula- tions arc shown in Tables 4-7. The values arc presented as the logarithms of the association constants. Nearly all of the stability constants for the chloride, sulfate, and hydroxide com- plexcs were obtained from Sillcn and Mar- tell (1964). Exceptions wcrc those for Cu( OH)s- and Cu( OH)b2- from Schindler
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