Variation of the Apparent Dissociation Constants of Carbonic Acid With Magnesiu01 and Calci111n Concentrations in Seawater diageneses of magnesian-calcite and

The effects of calcium and magnesium· ion concentrations in artificial seawater (ASW) on the equilibrium state of the system H2C03·H20 have been tested. The measured first and second apparent dissociation constants of carbonic acid, Ki and K�, increase with an increase in the concentrations of calcium and magnesium in ASW. The total and free activity coefficients of HC03-and CO i -at the ionic strength of 0.718 and temperature of 25°C decrease as a function of Mg:Ca concentration ratios in ASW. The results also show _that the calcium ion has a greater effect on the apparent dissociation constants of carbonic acid than magnesium, suggesting that the. calcium ion associates more strongly with bcarbonate and carbonate than the magnesium ion does. . . . . (Key

of calcium and magnesium in ASW. The total and free activity coefficients of HC03-and COi-at the ionic strength of 0.718 and temperature of 25°C decrease as a function of Mg:Ca concentration ratios in ASW. The results also show _that the calcium ion has a greater effect on the apparent dissociation constants of carbonic acid than magnesium, suggesting that the. calcium ion associates more strongly with bcarbonate and carbonate than the magnesium ion does. The apparent equilibrium constants of carbonic acid (Lyman, 1965;Mehrbach, 1973;Pytkowicz e.t al., 1974) are of practical value (Feely and Chen, 1982;Chen and Drake, 1986) as long as they remain constants in the processes being considered. Such processes are photosynthesis, precipitation and dissolution of calcium carbonate, which have small · effects on the major ion composition of· seawater. In seawater, the apparent dissociation constants depend on the major ion composition of seawater within the pH range of oceanographic interest (Ben-Yaakov and Goldhaber, 1973;. In sediment reservoirs where there are physico-chemical processes that cause notable changes in the major ion composition, such as magnesium, there is a variation in the apparent dissociation constants. These processes include the diageneses of magnesian-calcite and ( 1) where x is akin to the thermodynamic activity of hydrogen, a H, but differs from it because the liquid junction and asymmetry potentials of pH electrodes change when they are transferred from dilute buffers to seawater (Hawley, 1973;Pytkowicz, 1983b). A further difference having a small effect, which is neglected here, occurs because an assumption is made about the activity of chloride ions when a pH is assigned to the buffer solution (Bates, 1973). Then, X is related to a H as follows: where k is constant within the reproducibility of the pH measurements. The reproducibility is high if the same types of glass electrode are used (Johnson et al., 1977). K� is also deter1nined by the method used by Hawley (1973) and Pytkowicz and Hawley (1974).
The theory behind measuring the value of ]{� K� originated from the fact that when the solution of interest is at equilibrium and the increase in HC03 does not affect the equilibrium of pH, the ratio of the carbonate alkalinity to total carbon dioxide, CA/� C0 2 , is one, and pH = -log x 0.5(pK� + pK� ).

( 2)
This pH value is defined as pHe in this phase of work and is equivalent to point b in Figure 1. At this pHe, the reference level of the solution is HC03 and H 2 0, and the proton condition ( 3 ) The function F( x )' introduced by Weyl (1961), is: H2co; 10 11 12 1. pC-pH diagram of carbonic acid in seawater of 35 salinity, total CO n is 2.3 mmole kg-1 SW, K� = 9.972x 10-7 and K� = 7.651x10-1 (from Mehrbach, 1973) and Kw = 2.399x 10-1 4 (Culberson et al., 1970), showing the various equivalent points.

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F ( x) (CA/�C0 2 ) -1. (4) Thus equation (4) shows that F ( x) = 0 at pHe. F ( x ) was modified in this work to calculate K� directly after K� ]{� was measured. The following equation was used: (5) K � was also detennined from the graphical plot of x versus l/CA, · following the ap proach developed by Hawley (1973). This approach is only applied to low pH, where only C0 2( aqueous) • H 2 C03 and HCOJ species, are dealt with, and where CO�-is negligible. Since the concentration of CO�is almost zero, carbonic acid can be treated as a monoprotic acid, making the following modification and definitions applicable: where (H 2 C03)* is the sum of(H 2 C03)+(C0 2 ) in solution, and the subscript T refers to total concentrations. In ASW, the total alkalinity is defined as TA (HC03 )r + (oH-)r -(H + ) r .
Equations (6) and (8) TAO, Vol.6, No.2, June 1995 Plotting x versus I/CA gives a straight line, with the intercept at I/CA = 0 a negative value of Ki , and the slope � C0 2 Ki .

EXPERIMENTAL PROCEDURE
(Mg 2 + ), (Ca 2 + ) and (H3B04)-free artificial seawater (ASW) was· prepared following the fo1mula of Kester et al., (1967). This ASW with the ionic strength of 0.498M was equilibrated with laboratory pC0 2 by bubbling air through the solution for about two days. Bubbling was stopped when the measured pH was at steady-state and was not changed by further bubbling. From this ASW and the prestandardized MgCI 2 · · and CaCl 2 stock solutions by Mohr titration (Blaedel and Meloche, 1957), five test solutions were prepared to obtain (Mg 2 + )-to-(Ca 2 + ) concentration pairs of O-to-0, O-to-0.01, O.Ol-to-0.01, 0.03-to-0.01 and 0.05-to-0.01 (refer to Table 2 for concentration units), for the determination of the dissociation constants of carbonic acid. These solutions had different ionic strengths, so varying amounts of reagent grade NaCl were added to maintain the ionic strength of 0.718M. · . A cell was constructed from a beaker fitted in a water jack for carbonic acid equilibrium constant determination. The cell included a pH electrode (R adiometer #K2401), a reference electrode (R adiometer #G202c), a cut-off glass syringe that was gradually pushed out as the titrant was added to maintain constant pressure, a glass tube with a stopcock to serve as a passage for flushing out any excess volume, and a hole for the micrometer syringe burette (Gilmont Sl200). The cell which has a volume of 82.894±0.031ml is shown in Figure 2. The water jacked beaker was connected to a water bath (VWR 1140) to maintain the temperature at 25.00±0.05°C. The electrodes were connected to a Radiometer PHM84 Research pH Meter.
Before any titration was conducted, the electrodes were standardized in two buffer solutions (NBS buffer 180f having an assigped pH of 4.006 at 25°C and buffers 186-1-C and 186-11-C having an assigned pH of 7.415 at 25°C). The slope, S, of the electrode pair expressed in m V /pH was determined. The measured slope was compared with the theoretical_ one (s = 59.155 mV/pH at 25°C), and if it was higher than 99%, the theoretical one was usually used. The measured slopes for five different measurements are shown in Table 1.
The measured pH, pHm, was calculated from the equation: where pHb is the pH of the standard buffer solution, Em and Eb are the electrode potentials in the test solution and in the standard buffer solutions, respectively, and s is the slope of the electrode pair.  For the detennination of Ki K�, the titration cell previously described was completely filled with the solution to avoid the exchange of C0 2 . The pH of the test solution was dropped to approximately· -0.05 pH units lower than the 0.5(pK� + pK�) by the addition of a few tenths of a ml of O. lN HCI. Then, about 5 to 8 mg reagent grade NaHC03 was placed in a dry 2.5 ml Hamilton syringe, and about 0.5 ml of C0 2 -free distilled water was pulled into the syringe to dissolve the salt. The solution in the syringe was injected slowly into the test solution through the hole in the stopcock while stirring was maintained. After the solution was stirr�d for about two to three minutes, the electrode potential was recorded for two to three minutes without further stirring. Usually, about five to seven additions of HaHC03 were made to achieve a constant pH. The final total alkalinity of the test solution ranged from 3.49 to 5.75 meq kg-1 ASW .

•
The purity of the reagent grade N aHC03 is represented by the sample value of CAI� C0 2 . Pure bicarbonate has a value of one, while a sample contaminated with carbonate has a value of more than one. Since by defi nition, the primary standard's CA/EC0 2 is exactly one, its steady-state pH is equal to 0.5 (pK� + pK�). The steady-state is some value greater than 0.5 (pKi + pK�) due to contamination with carbonate. The values of K� K� and K� in 0.72M NaCl (Hawley and Pytkowicz, 1973) were substituted in the following equation: The value of CA/�C0 2 for HaHC03 used in this work as calculated from equation (11) was 1.0057. This was equivalent to a value of 0.0117±0.001 pH unit between pHe and 0.5(pK� + pK�).
The same cell was also used for the deter1nination of Ki . The cell was completely filled with the test solution, and the electrodes were allowed to equilibrate until the potential was changed by less than 0.1 mv hr-1 . Then, the solution was titrated with standard HCI (0.1001 N) from a calibrated syringe burette (Gilmont #S 1200). The initial titration alkalinities in the titration cell were calculated from the weight of the test solution. The titration alkalinity at each point during the titration was obtained from the equivalents of alkalinity initially present minus the equivalents of HCI added. x versus l/CA indicated by equation (9) is shown in Figure 3. The departure from linearity was tested from the first three titration points using the slop� of x versus 1/CA as calculated by the least squares method. Then the fourth data point was combined with the first three, and when the slope from the successive calculation changed less than 0.5 percent, the value of the slope obtained, 2';C0 2 K� , was used to calculate K� . K� was calculated at each point on the titration curve from the expression K � = (�C0 2 Kf /CA)-x , and K� was taken as the mean of the individual values.
From each test solution, at least two aliquots were brought to different pH values with HCI, and re-weighed amounts of sodium bicarbonate were added to ·the test solution. The change in the pH was recorded, and the amount of acid or base, z, required to produce the same change in pH was obtained from the titration curve of the same test solution. This had been done before. l/F ( x ) was calculated from the moles of (HC03 ) and (H + ) added per kg ASW, where F (x) =moles of (H + )/moles of (HC03 ) (acid-base comparison) (Weyl, 1961). Then the I<i K� values of the test solution obtained from pH steady-state were used to calculate K� , as follows: The K� value obtained from equation (12) was introduced into the expression: ( F ( x) -K � K � -x2)/(x2 + xl{� + K � I< � )and modified to obtain � = 0. The results of pHe and Ki K� are shown in Table 2. The values of the first apparent dissociation constants, determined by the modifi ed Weyl's (1961) F (x ) function after the mean of the Ki K� values in Table 2 was taken, and those values from the graphical plot of x versus I/CA are shown in Table 3.
The data in Table 3 shows that there is an increase in the K� value with an increase in the (Mg 2 + )-to-(Ca 2 + ) concentration ratios in solution. The results of Ki! { � in Table  2 indicate a relationship with (Mg 2 -+ )-to-(Ca 2 + ). Both Ki and Ki K� show a positive co11elation with the metal concentration in the solutions of constant ionic strength ( Figures  4 and 5). The curvature in Figure 4 may be due to the formation of triple ions (Hawley, 1973). This is usually attributed to the formation of ion-pairs which decreases the activity coefficients and increases the solubility products in the same electrolyte solution Kester and Pytkowicz, 1969;�tkowicz, 1969 and l 983a;Pytkowic and Hawley, 1974). The data also show that (Ca 2 + ) was relatively more effective with dissociation constants than (Mg 2 + ), which suggests that Ca 2 + associated with bicarbonate and carbonate more strongly than Mg 2 + does. This was illustrated by the higher shift of the·first and second ionization fractions, a1 and a 2 , of carbonic acid in Figure 6, when only Ca 2 + = 9.73 mmole 1-1 was added to the test solution compared to the shift that was produced when (Mg 2 + ) = 29.56 mmole 1-1 was added in the presence of (Ca 2 + ). In the foqner, the shift increased and became obvious when the concentration of (Mg 2 + ) was five times more than that of (Ca 2 + ).

'
(3) K 1 values were determined from the plot of x versus 1/CA. Two successful approaches have been used to account for the effect of the interaction on activity coefficients. First, in the ionic-pair concept, as introduced to the mixed electrolyte solution by Garrels and Thompson (1962), association constants are detertnined and applied to seawater. Second, in the specific interaction model of Bronsted (1922), Guggenhiem (1935 and Pitzer, ( 1971 ), the interaction terms of an unspecifi ed nature are measured in a binary solution and applied to seawater (Leyendekkers, 1972;Robinson and Wood, 1972;Whitfi eld, 1973).
The total activity coefficients of bicarbonate and carbonate, (/ HCO� )T and (/ co ;-)T at different magnesium-to-calcium concentration ratios were calculated following the method of : . . . .
(15) The thermodynamic dissociation constants, Kf and K2, used here were from Hamed and Davies (1943) and from Hamed and Scholes (1941). The activity coefficient of C0 2 was obtained from the expression:  where s DW and s sw are the Bunsen coefficients of distilled water and seawater respectively, as deter1nined by Murry and Riley (197 1). The solutions were treated as seawater with different salinities. The computed activity coefficients of the C0 2 of the solutions and the values of 8, the factor which was used to convert the concentrations from mole kg-1 SW into mole kg -1 H 2 0, are shown in Table 4. The activity of water, aw , as a function of salinity, S, in the solutions was deter1nined from the equation of Robinson (1954) by: The factor k was estimated from the following equation: The value of K�' was found to be l.105x 10-6 at the ionic strength of 0.718 from Hamed and Bonner (1945) and that of (! tt + ) was 0.866. The value of k was 1.140 for the test solutions  Table 5 and indicate a decrease in the total activity coefficients with an increase in the major ions in the solutions resulting from the for1nation of ion pairs in the electrolyte solution.  Additionally, the free activity coefficients of bicarbonate and carbonate ions were esti mated following the relationships: (1 HC03 ) F (1 HC03 )r(HC03 )r/(HC03 )F, and (1 9 ) _ (20) Tl)e total concentration of bicarbonate, (HC03 )r, and carbonate, (COi -)r , were calculated from the pH and TA measurements. The concentrations of free bicarbonate, (HC03)F, and carbonate, (CO�-)p, were calculated using the MICROQL program (Westall, 1979). The association constants of ions pairs f or1ned in the test solutions are shown in Table 6.   m · sedime nm�· wf 1Cte0tne�co1 1 cet-r�-,, . . ,.,,. ,, , _ _ � trations of magnesium · and calcium in pore water are affected by various chemical processes. According to Drever, (1974), Holland, (1978, and Pytkowicz, (1983a) these processes in clude: the uptake of Mg 2+ during dolomitization, ion exchange of Ca 2+ on exchange sites of clays by Mg 2+ , Na + and K + formation of illite as sinks for Mg 2+ in oceans, uptake of buricite between silicate layers of monotmorillonites, gibbsite-chloride transformation and the precipitation of sepiolite. There is also the input of Mg 2+ , such as in evaporite deposits. Sayles et al., (1973) have concluded that there is about a 16% decrease in the Mg 2+ con centration in the sediment. Therefore, according to the results in this study, a 16% drop in Mg 2 + in the sediment causes a decrease of about 1.3% in the value of ](� and about a 14.1 % drop in the value of K�.

S. CONCLUSIONS
The variation in the apparent dissociation constants of carbonic acid which has been shown in this study, and probably that of other acids, depends upon the major ion composition of the solution at constant ionic strength. This variation is attributed to the for1nation of ion pairs such as CaHcot , CaCO�, Ca 2 co; + , MgHCOj , MgC03 and Mg 2 co; + . This supports the validity of the ion association model as an adequate for1nal representation of the behavior of the activity coefficients and equilibrium constants (Pytkowicz, 1983b).