Bicarbonate and carbonate model of seawater at 25°C ion-pairs R. M. Pytkowicx and J. E. Hawley School of Oceanography, Oregon State University, and a Corvallis 97331 Abstract The apparent (stoichiometric) association constants for the formation of ion-pairs between bicarbonate and carbonate and the major cations of seawater at 25°C were dctcrmined experimentally. The results wcrc used, in conjunction with earlier data on sulfate of the major species present in scawatcr. ion-pairs, to calculate the concentrations Here we measured the apparent (stoichiometric) association constants for the formation of bicarbonate and carbonate ion-pairs with sodium, calcium, and magnesium ions at 25°C and 0.72 ionic strength. The results were used, in conjunction with the sulfate association constants determined by Kester and Pytkowicz ( 1969)) to detcrmine the major ionic species present in seawater at 25°C and 34.8z0 salinity. We will show later that the proportions of ion-paired and free species are insensitive to the salinity. Activity coefficients are lower and solubility products higher in some mixed elcc.trolyte solutions such as seawater than in chloride solutions ( Kester and Pytkowicz 1969). This is usually attributed to ionic interactions, which can range from the formation of ion-pairs (outer sphere interactions due to electrostatic attraction) to that of true complexes (inner sphere bonds with loss of water of hydration). Partial molal volume data (Kestcr 1969) and results from Raman spectra (Daly et al. 1972) suggest that the major ions of seawater may form although the potentiometric ion-pairs, method we used does not distinguish between ion-pairs and complexes. Ionic interactions are important because, by affecting the charge distribution of solutes, they influence properties such as electrical conductivity, osmotic pressure, solubility of minerals, and sound attenua‘This work was supported by National Science Foundation Grants GA-17011 and (X-36057X and by Office of Naval Research Contract N00014-07A-0369-0007. LIMNOLOGY AND OCEANOGRAPHY tion. The effect of interactions on activity coefficients can be successfully accounted by two approaches; the specific interaction model of Br@nstcd ( 1922) and Guggenheim ( 1935)) in which interaction terms of an unspecified nature arc measured in bi.nary solutions and are applied to seawater ( Leyendclkers 1972; Robinson and Wood 1972; Whitfield 1973) and the ionpair concept of Bjerrum, which was introduced to oceanography by Carrels and Thompson (1962), and in which association constants are determined and applied to seawater. The two methods differ in their algebra but have much in common bccause they both require measurements in simple solutions and their application to seawater by the use of an extended ionic strength principle, namely, that interaction coefficients and association constants are independent of the medium composition at a given ionic strength. The validity of this principle was tested successfully (Pytkowicz and Kcster 1969; Kcster and Pytkowicz 1969; ILeyendekkers 1972; Robinson and Wood 1972; Whitfield 1973) because species distributions and activity coefficients calculated from measurements in binary solutions agreed with results in seawater, and because apparent association constants were found to be independent of composition at a given ionic strength. Both methods are compatible with Harned’s rule (Pytkowicz and Kester 1969) and lead to successful predictions of activity coefficients (Leyendekkers 1972; Whitfield 1973). It should be emphasized that, although apparent association constants can be mea- 223 MARCH 1974, V. 19(2) 224 Pytkowicx sured in simple binary solutions and applied to seawater, resulting total activity coefficients and species distributions are functions of the medium composition. Theoretical grounds for the invariance of stoichiometric constants and the concepts of free versus total activity coefficients were discussed by Pytkowicz (1969) and by Kester ( 1969). Main features of the model estimated by Garrels and Thompson (1962) have been confirmed (Berner 1965; Thompson 1966; Thompson and Ross 1966; Pytkowicz and Gates 1968; Pytkowicz and Kester 1969; Kester and Pytkowicz 1968, 1969) but there are significant differences for several species concentrations, especially anionic ones. This occurs because Garrels and Thompson used estimated singIe ion activity coefficients which are uncertain, especially in the case of sulfate ions, as these are associated in all solutions that could be used for the mean salt method, and because they assumed, as a result of the scarce data available at the time, that the activity coefficients of charged ionpairs were equal to those of bicarbonate while those of ion-pairs with zero net charge were the same as those of nonelectrolytes, even though ion-pairs are dipolar entities. We avoided questionable assumptions about activity coefficients in our choice of experimental methods as far as possible. In the earlier sulfate work we used ratios of activity coefficients of cations, thus canceling errors in part, and at no time did we have to resort to estimating activity coefficients of anions and of ion-pairs. The difficulty of estimating such coefficients accurately makes it difficult to apply the thermodynamic association constants determined by Hostetler (1963), Nakayama ( 1971), and Reardon and Langmuir (in prep.) to seawater. In the sulfate work chloride solutions were used as reference solutions (in which association does not occur) and cation activities were compared in chloride and seawater to determine the extent of ion-pairing. In this work on bicarbonate and carbon- and Ha&e y ate ions, changes in the dissociation equilibria of carbonic acid with composition at constant ionic strength provide the ion.pairing information. We have used reference electrodes with salt bridges and assumed that liquid junc,tion potentials, to a first approximation, are independent of composition at a given ionic strength rather than avoiding salt bridges and having to make assumptions about the activity coefficient of chloride ions. Either approach has to be viewed with caution and the results considered tentative until confirmed by other independent methods. Our assumption about liquid junction potentials appears justified, within the precision of the method, because the association constants that we determined for sulfate ion-pairs (Pytkowicz and Kester 1969) and for bicarbonate ion-pairs ( this work) are independent of composition and lead to a successful prediction of the activity coefficients of cations (Kester and Pytkowicz 1969). In the case of ca:cbonates we are forced to invoke triple ions to explain the measurements although the experimental results may reflect changing liquid junction potentials. Still, the relative strength of the several triple ions will be justified from an energetics viewpoint and the extent of carbonate association shown to be compatible with data on carbonic acid dissociation and on calcium carbonate solubility. Earlier workers did not find triple ions because they did not measure the concentration dependence of the association. The ion-pair concept is used in preference to the specific interaction model because data on sound attenuation (Fisher 1967) and from Raman spectroscopy (Daly et al. 1972) indicate that ion-pairs may indeed exist. Still, the specific interaction model is a valuable tool for the study of multielectrolyte solutions. Details of experimental and calculation procedures not presented here are available in Hawley ( 1973). We thank C. Culberson and S. Ingle for assistance in this work and. S. Williams for Bicarbonate typing and proofing the manuscript. related to yIIco,, the free activity coefficient which applies only to the nonassociated ions, by (Pytkowicz et al. 1966; Pytkowicz 1969) the many versions of Theoretical The methods used to determine the apparent ( stoichiometric) association constants are based on the variation of K’1 and K’2, the apparent dissociation constants of carbonic acid ( Lyman 1956)) with the major ion composition of the test solutions at constant ionic strength. The equations presented below were used to derive the working relation for the determination of the association constants. The first apparent dissociation constant is related to the first thermodynamic dissociation constant, K1, by K’ I = kf~o,a&G/f-tI~o,; 1. Equations ’ K1 * aH20f referred = KI/1 = ~IICO,(HCOs-) = fmo,( HCOa-) T; (2) aII00, ( HC03-) and ( HC03-) T are the molal concentrations of the fret and the total (free plus ion-paired) bicarbonate ions. (I-ICOS-)T is given by ( HCOa-)T = ( IIC03-) + ( NaHCOSO) + (MgI-ICOs+) + ( CaHC03+). (3) The apparent association constant for a generic ion-pair MHCOSC-l, where c is the charge of the cation MC, is (MHCO$-l) K” (1) k is the correction in aII, the hydrogen ion activity, which results from pH measurements in concentrated solutions ( Hawley and Pytkowicz 1973)) fee, is the activity coefficient of molecular COa, arI,o is the activity of water, and frrcc, is the total activity coefficient of bicarbonate. fIIeO, is Table 225 and carbonate ion-pairs MIICO, = (M”)(HCOa-) = yMyI-Ico3 K YIIco,. (4) YMIICO, Equation 5 in Table 1, the relation used by us to determine K*~~rree3, was obtained from equations 1 through 4. ZV1 = kK1/ levee, was determined experimentally as to in the text. 1 t K” NaHC03 (Nat) + K*Mg,Ico (W2’) ( Ca2+) + K*CaHCO CO2 (5) 3 3 I K;K’2 = K’;KN * aH20E 1 tK* 2 (Nat) NaCo + K*Mgco 3 CO2 = KP;K/Z (Ms2+) t K*caco (Nat) 1 t KxcNaCO 3 t K* MgGO 3 * K CaCO (Ca2f) 3 K* Ca CO (Ca2t)2 2 3 Ws2? (6) lCa2’) 3 I + 3 + K*Mg (Mg2+)’ co 2 t 3 ’ K*MgCaCO (Mg2’)( 3 (8) Ca2+) I 226 Pytkowicx will be shown below. Equation 6 in Table 1, the working relation for the determination of K*dlCO, was obtained from a set of equations similar to 1 through 4 but with the use of K’lK’z instead of just K’, . K”l K”z in equation 6 is kSKIKz/yco,. The values of K*;lIITTCOy,K”,, K*cc,, and K”lK”2 were determined by measuring K’1 and K’,K’2 in a series of solutions of varying composition but the same ionic strength. This led to a system of equations such as 5 and 6 which could be solved for the desired quantities, although the solution of the equations for K*c,,-,, required extra terms. K’l and K’lK’2 were obtained by the methods used by Kester and Pytkowicz (1967) for the apparent dissociation constants of phosphoric acid. In essence, K’1 was determined by titrating the solutions with I-ICI and using the equation and Hawley LY!5r&d+ 0 Magnesium 0.20 Concenlrotion , mold 0.:!4 Fig. 1. K’JuH,o~co~as a function of magnesolutions at sium concentration in NaCl-MgCb 25°C and 0.72 ionic strength. this assumption. For ASW, fco, was calculated from the solubility data of Murray and Riley ( 1971). aiI,o was obtained from osmotic coefficient data ( Robinson and TC02 K’l Stokes 1968 ) and the additivity relation of ~ - Kfl Robinson and Bower ( 1965). ar1 = -CA It can be shown that, in the absence of where CA = ( HC0,7-) T + 2( COcj2-) Il is the triple ions, K’~/aI120f~0, should vary linearly carbonate alkalinity. TC02, the total dis- with the concentration of cations. This solved inorganic carbon, was held con- can be proven by introducing the ionic stant by filling the cell completely with strength relationship into equation 5 for solution. K’1 remains constant as long as binary solutions and eliminating all ion the major ion composition of the solutions concentrations but one. A linear relationremains essentially constant ( Weyl 1961; ship was indeed found in the case of bicarKester and Pytkowicz 1967; Pytkowicz bonate association, as illustrated in Fig. 1 1969). K’lK’2 was obtained by adjusting for a NaCl-MgC12 solution, This did not the solution to a ~1-1 that was invariant to happen, however, for carbonate association, the addition of NaHC0,7. The relation as the corresponding plots were curved. pH = 0.5 ( PK’~ + PK’~) is valid when this We were led therefore to add triple-ion pH is obtained. terms to equation 6, as is shown in equation 8 (Table 1). Triple ions involving (COs2-)2 f co, was calculated from the relation fco = So/S, in which So and S are the solu- were not required because the concentrabihties of CO2 in distilled water and in the tion of carbonate ions was much lower than test solution, and the solubility data of those of the cations, rendering the probMarkham and Kobe ( 1941). We assumed ability of such triple ions negligible. Also, that the activity coefficient of CO2 in the the data fit equation 8 better without the solutions was the same as that in a NaCl term K*C112c;o,( Ca2+) 2, as was expected beof calcium ions solution of the same ionic strength and cause the concentration tested this assumption in NaCl-MgCl2 solu- was kept low relative to those of the other of calcium tions. WC found ftJo, = 1.20 2 0.04 in 0.72 cations to prevent precipitation carbonate. m NaCl, 1.20 * 0.04 in 0.36 m NaCl-0.12 The fitting of the measured values of K’1 m MgClz, and 1.14 c 0.04 m in 0.24 m and K’lK’3 to the systems of equations such MgC12. Also, as will be shown later, the as 5 and 8 was done by solving for K”‘1, results for bicarbonate are compatible with Bicarbonate Table Composition 2. Test solution numbe r of the test solutions in molal units. (NaHC03)TQ (CaC12JT ---- --.,- 0.7200 0.4800 0.2400 ---0.0800 0.1600 0.2400 ------0.1900 0.1400 0.0400 -m-w 0.2200 0.0597 0.3702 Added 227 (Na2S04)T 2 3 4 5 6 7 8 9 10 11 12 ASW hk and carbonate ion-pairs ---- ---” ---- ---- ---- 0. 6300 0.4800 ---- ---- --se -m-w 0.6000 0.5700 ---------- -m-m 0.0315 as Na2C03 due to the reaction varying pairs, 0.4659 but expressed with amounts C02. as NaHC03 because When the solutions of NaHCO 3 were w--- ------------0.0300 0.0800 0.0500 0.1000 ---0.0500 0.0200 0.01195 of the c:onversion were used for of C032- the study added to find the pH which x 103 5. 00 5. 00 5.00 5. 00 5. 00 5. 00 5.00 5. 00 5. 00 5.00 5.00 5.00 5. 00 to HC03 - of carbonate was invariant ion- to further additions. K”lK”2, and the association constants, with the condition that these quantities had to be positive. The calculation procedures used to determine the distribution of species were similar to those of Kester and Pytkowicz ( 1969). A system of equations of the type (Na+)T = (Na+) + (NaS04-) + ( NaHCOso) + ( NaC03-) K* (9) (NaSOd-) Nas04= (Na-‘)(S(-&2-) (10) extended to all the species present was solved for the concentrations of free ions, ion-pairs, and triple ions. Experimental procedures The compositions of the test solutions are shown in Table 2. The solutions were prepared by weight, corrected to weight in vacuum. Reagent grade NaCl and NagSO4 were dried and weighed as solid salts while MgC12, CaCl2, and Na2C03 were added from stock solutions standardized by the Mohr titration (Blaedcl and Meloche 1957). The standard Na&03 solution was prepared by weight from Mallinckrodt primary standard Na2COs (99.96% pure) which had been dried for 2 hr at 280°C an d cooled in a vacuum desiccator. The I-ICI titrant was standardized by potentiometric titration of primary standard Na2C0s. Electrode potentials were measured using a potentiometric circuit similar to the one described by Kester and Pytkowicz ( 1967). The sensitivity of the system was within ~O.OI mV. Titrations for the determination of K’1 were performed in the cell shown in Fig. 2, constructed from a 200-ml Berzelius beaker fitted with a water jacket to allow temperature control of +O.O3”C. The barrel of a 5-ml ground glass syringe was cut off and mounted horizontally in the cell with epoxy cement. The piston of the syringe was displaced as titrant was added, eliminating the need for an air space to take up the titrant volume; it displaced about 4 ml of test solu- 228 Pytkowicx and Hawley Thermomeier TO E/et fronfcs GiUSS E/ecrook ‘1 ,.=; , I ) 0 I 2 3 5 I/CA Ground G/ass syringe Fig. 2. Water-jacketed titration cell. pH electrodc, Sargent S-30050-15C; reference electrode, Sargent S-30080-15C; syringe buret, Gilmont s 1200. tion and was lubricated by a thin film of solution. A pH electrode, a reference electrode having a porous ceramic plug liquid junction, and a thermometer were fitted tightly into a rubber stopper which had been machined to fit into the beaker. A small hole in the stopper held the syringe needle of the titration buret and allowed for overflow of test solution upon filling of the cell. Electrode potentials in a standard buffer solution were the same in the titration cell as in an ordinary thermostated beaker. The titration procedure was as follows. First, the pH electrode pair was standardized in buffer solution (National Bureau of Standards buffer 185d having an assigned pH of 4.008 at 25°C). Next, the titration cell was completely filled with test solution and the electrodes were allowed to equilibrate until the potential changed by less than 0.1 mV per hour. Then, the solution was titrated with standard HCl Fig. 3. UH versus l/CA from the titration of a 0.7200 m NaCl and 0.005 m NaHCO, solution with HCl. from a calibrated syringe buret. Finally, the electrodes were returned to the buffe:r solution and the amount of test solution titrated was determined by weight. The electrodes were thoroughly rinsed with the new solution when they were transferred. The linearity of a rI versus I./CA, expected from equation 7, is shown in Fig. 3. For the determination of K’,KIZ the cell was completely filled with ,test solution to avoid exchange of CO:! and the pH was adjusted to about 0.5( pK1 -t p&) by addition of a few hundredths of a milliliter of 0.02 N N&OS. This brought the alkalinity to about 0.005 meq liter-‘. Then lo-15 mg of reagent grade NaHCOs ‘were placed in a dry, gastight, 2.5-ml IIamilton syringe and about 0.3 ml of COZ-free distilled water was pulled into the syringe to dissolve the salt. The NaIICOs was injected slowly into the test solution. The solution was stirred for 5 min and the electrode potential was then recorded for 5 min in the absence of stirring. At least five additions of NaHC03 were made to establish that a constant pH had been obtained. The final total alkaIinity was about 3.5 meq liter-‘. The constancy of the pH, within the experimental precision of kO.003 pH units, was aster- Bicarbonate Table 3. Measured values of K’1 and K’s, calculated Kpa calculated from equations 5 and 8 and the speciation Test solution number K’l 1 x106 Measured / / KlK2xlO 1.161 1.161 1.072 1.084 1.085 1.140 1.160 1.199 1.243 1.244 1. 250 1. 278 1.145 1.170 1.290 1.307 4 5 6 7 8 9 10 11 12 ASW 229 and carbonate ion-pairs values of aIt,0 and fCOZ, and values of K’I and model. Calculated 16 2.070 2. 041 2.245 2. 239 8.120 7.860 16.79 17.01 16.65 28.16 28.54 6.390 34.52 K’l fC02 x 106 0.983 1. 292 1.160 2. 06 0.972 1.178 1.089 2.26 0.977 1.178 1.152 8.12 0.981 1,178 1.211 16. 8 0.986 1.178 1.274 28. 3 0.974 0.977 0.986 0.986 1.178 1.178 1.178 1.178 I. 122 1.176 1.290 1.302 6.71 34. 0 5.030 9.840 29.61 8. 02 1.094 1.140 1.136 1.143 This is the value calculated of the measured values. from 16 K’lK;xlO aH20 4. 84 9.70 29.7 7. 87” the model which agrees within 3 percent with the average Table 4. Values of the apparent (stoichiometric) association constants determined in this work 1(l), those based on the work of Garrels and Thompson (1962) (2), and those measured by Butler and IIuston (1970) (3) and by Dyrssen and Hansson (1973) (4). Ionic Strength (1) (2) 0072 0. 66 (3) (4) 0. 5 1.0 0. 39 0.21 NaH C03’ 0.280 o. 26 MgHC03+ 1.62 5.22 1.04 CaHC03+ 1.96 5.10 1.04 NaC03- 4. 25 4.16 MgC03’ W2C03 112 2-k CaC03’ MgCaC03 1.86 32.5 387 162 2t 160 1.38 1,040 78 32. 5 230 Pytkowicx and Hawley Table 5. Chemical model for the major species in seawater at 25°C calculated from the sulfate association constants @ester and Pytkowicx 1969) and the bicarbonate and carbonate association c(?nstants (this work: Table 4). The constants for magnesium and calcium fluoride association were taken from Elgquist (1970). The number of significant figures is used for mass balance purposes and does not reflect the accuracy which is unknown because of the assumptions made. = N2 Total molality 0.4822 Mg 2f 0. 05489 Ca2 I0. 01063 97.70 89.11 88.35 % MS04 2.25 10.35 10.87 7’0 MHC03 0.05 0.24 0. 29 Yc MC03 0.01 0.17 0.41 “/c Free metal ‘-30Mg2C03 0.03 % MgCaC03 0.01 0.07 % MF 0.07 0.02 so42- cog2- HC03- d - 0.01062 100.00 F - Total molality “/c Free anion 0.02906 0. 00213 39.19 81.33 0.000171 7.99 % NaX 37.29 10.73 15.99 % MgX 19.55 6.44 43.86 “/c CaX 3.97 1.50 20.96 % Mg2C03 7.39 % MgCaC03 3.82 0. 000080 51.04 46.94 2.02 - tained after correction for dilution. The pH = 0.5( pK’1 + pE2) ranged from 7.231 to 7.845 in going from MgQ-CaC12 to NaCI solutions. The electrodes ( Fig. 1) were standardized with NBS buffers 185d (pH = 4.008 at 25°C) and 186-l-b and 186-11-b (pH =7.413 at 25°C). Results Values of K’l, K’JX’Z, aE120,and fee, are shown in Table 3. The values of the apparent association constants are presented in Table 4. The percentages of the ions present as free and as associated species are shown in Table 5. The calculations were made at pH 8.0 and 8.1 with no significant difference in the results. In Table 6 we present the model if an association constant for KS04- is added to the calculations. This constant should, however, be measured. Discussion The validity of the model was tested by measuring K’, K’ 2 in a solution (ASW in Table 3) with the cation composition of seawater and comparing it to K’,K’2 calculated from equation 8, used in conjunction with the association constants determined in the simpler test solutions. The measured value was 8.02 X lo-l6 while the calculated value was 7.87 x 10-l”; the two agree within 3%. In addition, the value of KllK’2 r’eccntly measured in seawater by Mehrbach et al. (1973) at 25°C and 35s0 salinity was Ca2CO:12+ 7.68 x 10-‘6. A model including yielded 8.13 X lo- Is; thus, it did not agree as well with measurements and, as the cal- Bicarbonate 231 and carbonate ion-pairs Table 6. Chemical model of Table 5 modified when an association the results of Garrels and Thompson (1962), is added to the calculations. theirs. Nat Mg 2-b constant for KHSO?, based on The values in parentheses are Ca2+ 97.71 (99) 89.15 (87) 88.39 (91) 70 MS04 2.24 (1.2) 10.31 (11) 10.82 (8) 7’0 MHC03 0.05 (0.01) % MC03 0.01 ( $J Free metal ) 0.24 (1) 0.29 (1) 0.17 (0.3) 0.41 (0.2) % Mg2C03 0.03 % MgCaC03 0.01 0.07 % MF 0.07 0.02 HC o3 - so4z% Free anion 39.01 (54) 81.33 (69) % NaX 37.13 (21) 10.73 % MgX 19.47 (21.5) 6.45 1.50 $3 CaX 3.96 (3) % Kx % Mg2C03 % MgCaC03 0.42 (0.5) cium concentration was kept low to prevent precipitation of CaCOs, was rejected. Another test of the validity of the model is that it can be used to explain the solubility of calcium carbonate in seawater. The apparent solubility product of calcium carbonate, K’sIJ is related to the thcrmodynamic solubility product, KxIJ, by the equation K’ w = &dfc,fco,. ye the free ion activity coefficient obtained by the mean salt method, is 0.255 as calculated by C. Culberson in our laboratory. The use of an equation such as 2 for carbonate ions yields fen= 0.225 as 88.35% of the calcium ions are free. f,&k2 = (KlKJK’lK’g) = 0.031 according to the ion assoan,0f co, ciation model. KNgp= 3.98 X 10-O (Langmuir 1968) and, thus, we calculate K’gp = 5.67 x 10-7. The experimental values of Kgp are 5.4 X 1O-i ( MacIntyre 1965) and 4.93 X 10d7 (Ingle et al. in press). The last value is expressed here as moles co3z- K+ 98.85 1.15 (99) (1) F- 7.98 (9) (8) 15.98 (17) (19) 43.86 (67) (4) 20.96 (7) 51.03 46.95 2.02 7.39 3.82 kg-I120-2; Ingle et al. present it in units of moles kg-SW-“. The agreement between the calculated and measured results is fair considering the uncertainties in the model and in the measurement of solubility products in seawater. Still, the differences suggest, when the data of Ingle et al. are used, that the percent free carbonate may be closer to 9.1% than to 8. This is a slight difference which could be resolved, for instance, if the extent of MgCOao association were off by only 2% of its value. The model of Garrels and Thompson ( 1962), although it yields a percent free carbonate of 9, does not lead to a satisfactory prediction of KfBP. They reported an d used yea = 0.28 and ycoI = 0.20 which, in conjunction with their model, yields for the total activity coefficients fCn= 0.91 x 0.28 = 0.255 and fCO, = 0.09 x 0.20 = 0.018 and results in Kap = 11.1 X 1O-7 instead of 232 Pytkowicx a value near 5 X 10-7. The error appears to arise because they used a rough estimate of YCO~, the free activity coefficient, by Walker et al. (1927). ‘Our value of ycos and Hawley evaluated because they did not examine all the possible pairs. It may be, however, that their results are low because ours explain the apparent dissociation constants is fco,( CO&/( C03) = 0.388. of carbonic acid and the apparent soluOur association constant for NaEIC030 bility of calcium carbonate. We found less is in good agreement with those of Garrels MgCOsO ion-pairing and considerably more and Thompson (1962) and of Butler and CaCOsO ion-pairing than was the case in Huston (1970) but the constants for the model of Garrels and Thompson (TaMgHCOs+ and CaHCOs+ differ from those ble 6). of Garrels .and Thompson ( 1962) and DyrsOur model is not complete. Ca2C0,7:!+ sen and Hansson ( 1973). Our results sug- triple ions were not detected because the gest that calcium associates more strongly concentration of calcium was kept low to than magnesium with bicarbonate, in con- prevent precipitation of CaC03. In additrast to those based on the estimates by tion, triple ions involving sodium may ocGarrels and Thompson (1962), and that cur but were not necessary to explain our the extent of association for both cations is results, in part because of the composition slighter than they predicted. Greenwald’s of the test solutions and in part because the ( 1941) calculations also indicate that cal- association of sodium is weaker than those cium .association with bicarbonate is of magnesium and calcium. stronger than magnesium association, and The association reactions possible when TKester and Pytkowicz (1969) found that triple ions form are of the following charge pK*cnso, was slightly larger than K*MgSO,. types : The relative strengths of magnesium and 2NA+ + COs2- = Na2C0,0; (11) calcium association probably reflect the radii of the hydrated cations, as was sug(12) Na+ + Mg2+ + COs2- = NaMgC03+; gestcd by Nancollas (1966). Robinson 2Mg”’ + COs2- = Mg2C03”+. (13) and Stokes (1968) presented hydration numbers and ion size parameters for MgC12 The important factor in determining the b and CaC12, derived from the hydration relative stability of triple ions is their tota. theory activity coefficients. These paraminteraction energy. Consider Na2C030 with eters suggest that the hydrated radius of a linear Na+-CO 32--Na-b configuration and calcium ions is smaller than that of mag- with the centers of the ions separated by nesium ions and, therefore, that calcium the distance r. Assuming point charges for ions should interact more strongly than rough estimates, the interaction energy is magnesium with anions, as we found to 2ZmZcop2 &&&” be the case. Again, we found K*C,C03 to + Ah,,co, = (14) be larger than KQAIgOO,in contrast to the Dr 2Dr ’ constants based on the results of Garrels where ZNn and Zco, are the valence charges, and Thompson (1962). The concentration e is the electronic charge, and D is the diof MgCO,O is larger than that of CaCOs”, electric constant. Thus, AUN~,CO, = -7e2,/ but this is because there is more magneDr. The interaction energies for all the possium than calcium in seawater. sible triple ions, taking the values of r in Our value for K*NaCO:,agrees with that centimeters, based on the effective hybased on Garrels and Thompson (1962) drated ionic diameters presented by Stumm but is larger than that of Butler and Huston ( 1970). Our values for K*MgCO,and K*c~co, and Morgan ( 1970)) are listed in Table 7. The free energy AF is AH-TAS which indicate significantly more ion association If it is assumed than those of Dyrssen and Hansson ( 1973). is approximately AU-TAS. The results of Butler and Huston and of that the entropy charge AS is roughly the same for all triple ions then, as AF = -RT Dyrssen and Hansson cannot be definitively Bicarbonate and carbonate ion-pairs Table 7. Interaction energies for triple ions calculated as explained in text. D is the dielectric constant and e is the electronic charge. Triple ion Na2C03 Interaction energy x lo8 D/e2 -0.83 NaMgC03 -1.29 NaCaCO3 -1.44 MgCaC03 -1.70 Mg 2C03 -1.54 Ca2C03 -1.87 233 constants of ion-pairs that have yet to be explained. An alternative theory to ion-pair formation, the specific interacTion theory of Br@nsted and Guggenheim, provides results comparable to those of the ion-pair theory. Both approaches are equally valuable numersound attenuation and ically; although Raman spectra data indicate the actual existence of ion-pairs. References coefficients’ of R. A. 1965. Activity bicarbonate, carbonate and calcium ions in seawater. Gcochim. Cosmochim. Acta 29 : 947-965. 1957. BLAEDEL, W. J., AND V. W. MELOCHE. Elementary quantitative analysis : theory rand practice. Row, Peterson. 1922. Studies on solubility. 4. BISONSTED, J. N. Principle of specific interaction, of ions. J. I Am. Chem. 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GIXEINWALD, I. 1941. The dissociation of calcium and magnesium carbonates and bicarbonates. J. Biol. Chcm. 141: 789-796. GUGGENIIEIM, 'E. A. 1935. The specific thermodynamic properties of aqueous solutions of strong clectrolytcs. Phil. Mag. 19: 588-643. I-IAWLIZY, J. E. 1973. Bicarbonate and carbonate ion association with sodium, magnesium and calcium at 25°C and 0.72 ionic strength. BERNER, In K, the triple ions with the larger absolute values of the interaction energy will have larger association constants and will be more stable. The interaction energies do not differ by much but the differences will be magnified in the association constants K because of the logarithmic term. The above calculation is very rough but indicates that triple ions with calcium and magnesium should be more stable than those involving sodium. Conclusions We derived a speciation model of seawater that confirms roughly that of Garrels and Thompson but shows significant differcnces for some ions. Our model represents progress because no assumptions were made regarding the activity coefficients of ion-pairs and of bicarbonate, carbonate, and sulfate ions, and because the compositional dependence of the ionic interactions was measured. Our results explain reasonably well the changes in the apparent dissociation constants of carbonic acid and in the apparent solubility product of calcium carbonate in going from distilled water to seawater. We do not claim, however, that our model is final. At this time the existence of triple ions must be considered tentative and, if they do indeed exist, then it will be necessary to characterize all the possible species. There are also discrepancies in the results of various investigators for the association t 234 -, Pytkowicx Ph.D. thesis, Oregon State Univ., Corvallis. 66 p. AND R. M. PYTKOWICZ. 1973. Intcrprctation of pH mcasuremcnts in concentrated clcctrolyte solutions. Mar. Chem. 1: 245- 25th HOSTETLER, nesium P. B. 1963. 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