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The ion-association model and the buffer capacity of the carbon dioxide system in seawater at 25°C and 1 atmosphere total pressure Michael Whitfield The Laboratory, Citadel Hill, Plymouth PLl 2PB, England Abstract The ion-association model of Berner has been extended to calculate the contributions of the various ion-pair formation reactions to the buffer capacity of the carbon dioxide system in seawater. These reactions are shown to make the major contribution to the equiof the pH libriunz buffer capacity at pH values greater’ than 8. However the indifference to quite large changes in solution composition arises, not from any pH-statting effect, but because the metal-carbonate ion-pairs form only a small proportion of the total cation concentration under normal conditions. ing the relative merits of the thermodynamic and a,pparent constants ( Wangersky 1972a,h; Pytkowicz 1972) in describing the carbon dioxide system is not considered here. Wangersky (1972a) has suggested that the buffer capacity of the carbon dioxide system in seawater is significantly influenced by the existence of a network of ionic interactions that can be conveniently described in terms of an ion-association model (e.g. Garrels and Thompson 1962). In particular he stated that Ion-association The existence of ion pairing in such proportions suggests that reactions linking the CO:! system with each of the major ions in seawater must be considered as taking part in the control of seawater pH. [Wangersky 1972a, p. 21 If control of pH in seawater occurs through this whole web of equilibria, a change in the proportions of the major elements in seawater should lead to a change in ion pairing and finally to a change in pH. [Wangersky 1972a, p. 31 MfXeMX. Here I propose to use an extended ionassociation model to look, in a quantitative manner, at the buffer capacity of the carbon dioxide system in seawater under equilibrium conditions to test this hypothesis and to see how far it is possible to explain Wangersky’s observations in terms of a conventional ion-pairing approach. I am concerned in this instance with a precise analysis of the role of ion-pairing in the buffering of the carbon dioxide system at equilibrium and not with the relative importance of the complementary buffer mechanisms described by Pytkowicz (1967) and Sill&r ( 1961). The associated discussion concernLIMNOLOGY AND OCEANOGRAPIIY model The ion-association model takes as its starting point values of the thermodynamic formation constants ( KB) of ion pairs thought to be formed in the solution. The free activity coefficients (fx) of the various components are then calculated on the basis of some hypothesis (Whitfield 1973a) and the corresponding stoichiometric constants are used to describe ( K+ = =‘f~fx/fux) the individual equilibria. The final distribution of the dissolved species is calculated by an iterative procedure involving the values of K+ for each ion-pair and equations defining the total concentration of each stoichiometric component. The procedure is described in detail by Garrels and Thompson (1962) who used the metal chlorides as model unassociated salts and defined the free single-ion activity coefficients according to the MacInnes’ convention ( MacInnes 1919). Their model has been updated by Berner ( 1971) who used more recent values for the activity coefficients of the model salt solutions and for the formation constants (KO) . His model is extended here to cover a wide 235 MARCH 1974, V. 19(S) 236 Whitfield Table 1. Thermodynamic ion-pair constants used in the ion-association pressed as logier). formation model (ex- Table 2. Free single-ion activity used in the ion-association model. = H+ OH- SO 2- 4 HC03- CO32- B(OH&- 6.366" 10.329" 9.236* 13.999* l-99" 1.27.1 1.06f -0.25-t Na+ 0.961 .K+ 2.36t 1.16.b 3.4t Mg2+ 2.1* H+ ca2+ 2.31t - 1.26t 3.2 t - pH range using the assumptions forr- = ~2~(NaOII)/fxa+, (14 (lb) an d f B(OIT),-= fur- = ~2*(Imr)/fK+. Na+ K+ Mg 62: OH- so 24 0.95 0.71 0.63 0.29 0.26 0.65 0.17 * Taken as value + Taken as value * Sill& and Martell (1964). t Garrels and Thompson (1962). * Berner (1971). f11+ = ~2~(IICl)/fC1-, coefficients (14 The calculations were carried out with the computer program HALTAFALL (Ingri et al. 1967) using the input data shown in Tables 1 and 2 and the solution composition of Garrels and Thompson (1962). The analysis is confined to 25°C and 1 atm pressure. In their original paper Garrels and Thompson effectively fixed their seawater at pH 8 by defining the ratio [ HC0,7-] T/ [ COS2-] T = 2.38 x lo-“/2.69 x lo-” = 8.85. Calculations using this value in Berner’s model ( Berner 1971) give results that are identical with calculations based on the present variable pH model at a pH of 8 (Table 3, columns B and F), indicating the compatibility of the two approaches. The Garrels and Thompson model has a number of weak points; the most conspicuous of these being the assumptions made in assigning activity coefficients to the ion-pairs and to the free ions (Whitfield 1973a,h). Quite large variations in HCO 2- CO3 H2c03 HS04cl- B(OH)4- 0.68* 0.20 1.13t 0.68 0.63 0.65 - for singly charged ion-pairs. for uncharged ion-pairs. the activity coefficients of the uncharged ion-pairs (Table 3, column C, cf. Table 2,) have little effect on the distribution of the various ion-pairs and will not seriously alter the conclusions reached here. The use of a different convention for fixing the single-ion activity coefficients (Lafon 196!3; Table 3, column D) produces a significant change and gives a distribution for the sulfate ion-pairs that is in better agreement with the experimental measurements of Kestcr and Pytkowicz ( 1969) (see Table ,3, column G). The predictions of Lafon’s model and mine can be compared directly with the experimental data of Hansson (1973a) by calculating the total concentrations of the components of the carbon dioxide system as a function of pH. The value of [H&03”] ( the total concentration of uncharged species in solution, i.e. [CO,] + [H&03] ) is obtained directly and the values of [C0s2-:]T and [HC03-lT1 can be calculated from the equations [ COs2-] T = [ C032-]p + [ NaCOs-] + [ MgCOs”] + [ CaCOsO] (2s.) an d [ HCOs-] T = [ HCOs-] p + [ NaHCO:iO] + [ MgHC03+] + [CaHCOs+], (2b) where [Xl, and [X] T indicate the free and total concentrations of component X. The predictions of this model are in close agreement with the experimental findings Buffer Table pairs. 3. Ion-association models capacity of CO2 in seawater for seawater* 23rl 1(298”K, 1 atm, 35%, S, pH 8). Distribution $ anion as ion-pair? E C D of ion- Anion Ion-pair A+ F G so 24 NaSO4MgSOd CaSO4' 18.3 0:6 22.7 3.2 21.9 o-7 23.5 3-7 19-Y 0.6 29.0 5*1 37.6 0.4 19.6 2.7 24.7 0.8 24.2 3*9 21.9 o-7 23.5 3.7 37.2 0.4 19.4 4-o Free 55.2 50.2 54*5 39*5 46.4 50.2 39-o NaC03M&o3' caco3o 17.5 67.0 6.6 19.1 63.3 7.1 15.1 68.2 8.4 17.8 63.0 8.8 21.4 59.0 7*3 19.1 63.4 7.1 17.3 67.3 6.4 8.9 10.5 8.3 10.4. 12.3 10.5 Y-0 8.3 14.5 3.2 8.4 14.1 3.1 8.0 CaHCO3" 8.6 17.1 3.4 9*5 3.4 8.2 12.4 2.8 8.3 14-5 3.2 8.6 17.8 3.3 Free 70.9 74.0 74.4 79*1, 76.6 74-o 70.3 co 23 KS04- Free HC03- NaHC03' MgHCOJ+ * Seawater composition Na+ (0.4752), B (molalities, K+ (O.OlOO), Carrels Mg2+ (0.0540), and Thompson 1962). Ca2+ (0.01.04), cl- (0.5543), so42- (0.0284), COAX- (0.000269), HCO~- (0.00238). q Recalculated for HALTAFALL (Ingri the composition shown above using the computer program parameters from the following et al. 1967) and the appropriate references. F A. Garrels and Thompson (1962). the uncharged ion-pairs as dipoles 'MgX' P 0.8, (Kester D. Lafon (1969) using 1969) and B. Berner (1971). C. Berner (1971) treating rather than neutral molecules, i.e. with yc,x" = 0.72 (Yeatts and Marshall 1969). the supporting electrolyte convention for defining values used to single-ion activity coefficients. E. As for A but Y -t@Cl) calculate fx were oalculated from a specific interaction model (Whitfield 1973b) 2+ F. Calculated from the variable for the mixture Na+ - K+ - Mg - Ca2+ - Cl-. composition is as shown in pH model described here at pH 8. The solution except Pytkowicz (1969) with experimental standard seawater CT = 2.4 mM and [H~BO~]~ = 0.43 footnote* values for mM. gulfate G. Kester and &n-pair formation in a solution. of Hansson ( Fig. 1) and with the calculations of Lafon ( 1969), indicating that the different distributions of the sulfate species in the two models produce only small changes in the stoichiometric equilibrium constants for the carbon dioxide system. The equilibration of the ocean with the atmosphere ‘may be simulated by allowing 238 Whitfield ‘-‘2C4 -log HCO, co,‘- [Xl, 6 8 4 6 8 10 PH Fig. 1. Comparison of the total concentrations of the components of the carbon dioxide system (HGOS, HCOs-, CO,“-) in seawater at 25”C, 1 atm pressure, and 35% S calculated by different procedures. Experimental data of Hansson (1973a) -solid lines; ion-association model (this paper)0; ion-association model ( Lafon 1969)-X. the model seawater to equilibrate with carbon dioxide at a partial pressure of 3.3 X lo-” atm (Fig. 2). If the carbon dioxide solubility data of Murray and Riley ( 1971) in acid solution are used, then the total concentration of carbon dioxide in solution can be calculated as a function of pH. Typical total concentrations of carbon dioxide in seawater (0.002 to 0.0027 mol kg-l) give rise to pII values in the range 8.2 to 8.3, indicating that the behavior of the open system has been successfully predicted. Since the modified ion-association model gives a reasonable account of the behavior of the system at equilibrium it can be used to look at the influence of ion-pair formation on the buffer capacity of the system. The discussion will focus on the solution phase and will not include the precipitation of calcium carbonate at this stage. Closed systems I used the ion-association model to construct a logarithmic distribution diagram (Fig. 3) for the free components using pH as the master variable (Sill& 1967; Stumm 4 6 8 PH Fig. 2. Calculated variation of total carbonate concentration (CT) with pH for an artificial seawater in equilibrium with carbon dioxide at a partial prcsure of 3.3 x lo-” atm. CT is defined by the equation CT = [HzC0~*1 + [HCO,IT + [COa2-l T. The horizontal line indicates a typical value for CT in the open ocean (~0.0027 mol liter-‘). and Morgan 1970). The plots exhibit considerably more curvature than the corresponding plots showing the total concentrations ( e.g. Fig. 1) so that the diagram cannot be constructed on the basis of simple rules ( Sill&n 1959; Butler 1964) but must be derived from detailed calculations. IIowever, once constructed, the diagram presents a simple pattern. The curves for the carbonate and bicarbonate complexes lie parallel to the lines representing the free ligands ( Fig. 3). Their displacement from the line of the free component can be deduced from log ~hcOs = log [MIICO;,] - log [Ml&T -- log [ IICOs-] [?, so that log [ MHCOR] - log [ HCO&l log Khl~O, + log = CMl p; ( 3a > similarly log [ MCOJ log - log [ co32-.] = K*iwco, + log UN,. (W Buffer capacity of CO, in seawater rI80 PX 60 O. / cT 40 8 8 6 4 10 PH Fig. 3. Logarithmic distribution diagram for the components of the carbon dioxide system in seawater at constant CT. pX = -log [Xl,. The letters identify equations in Table 4 that describe the formation of the various components. For the distribution of example curve e describes MgCOe” as a function of pH. The medium ions exert their greatest influcncc on the carbon dioxide system at high pH values (pH > 9) where the metalcarbonate complexes become the predominant species in solution (Fig. 4). Calculation of the buffer capacity As Pytkowicz (1972) has pointed out, the buffer capacity of the carbon dioxide sys tern in seawater can be accurately described in terms of the total concentrations of the solution components. On this basis the buffer capacity of the carbon dioxide system in seawater can be defined by the equation (Stumm and Morgan 1970; Butler 1964) /3r/ln 10 = c&K,” [ I-I’] ( [H+12-I- 4&*[H+] + &*K2*) ( [Hk12 -l- KI”[H+] + KI*K2*)2 = [H’] + [OH-] + w2co3*l[I-IcoL+ + [HCO& D32CQ3*3 [HCO&[C032-]T + [ I-ICo/J~ + [C032-]/ (4) 6 8 6 10 PH Fig. 4. Distribution of the components of the carbon dioxide system cxprcssed as a percentage of CT. The letters identify equations in Table 4 that describe the formation of the various components ( cf. Fjg. 3 ) . where Kz* = [HC03-].[H+]/[H2C03*] and K2* = [C032-.]T[H~]/[HCO~-]~. The values of pT calculated from the ion-association model and from the experimental dissociation constants ( Hansson 1973a) using equation 4 will be virtually identical (see Fig. I ) . The buffer capacity curve (Fig. 5) shows maxima at pH values where [H&03’k] = [IIC03-]T and [HC03-lT = [ COs2-]1r. From equation 4 the value of these maxima is given by (PT)mnx = CT In 10/4, (5) where CYl represents the total concentration of all carbon dioxide species (Fig. 2). The buffer capacity associated wjth the selfionization of water is predominant at pH values <4 and >lO (Fig. 5). Although it is possible to ascribe differences between Fig. 5 and the corresponding picture for carbon dioxide in freshwater ( Stumm and Morgan 1970) to ion-pair formation, it is inaccurate to assume that the buffer capacity of the system is extended in any way 240 Whitfield Table 4. Reactions considered the buffer capacity of the carbon in seawatm. in calculating dioxide system Ionization fractions (al and cxo) can be defined so that for reaction A al(A) Reaction a b c d e Ca*+ Mg*+ H,c03 Nat Mg*+ f Ca*+ Na+ HCOf H20 g h i -log, ,K + H2CO3 4CaHCOf -I- H2CO3 eMgHC03+ s H2CO3 C-l HC03- e HC03- * I-Ico3-6 -I+ -i+ e e + II+ + H' t H+ mo3NaHC03+ t H+ W03’ caco3o NaC03Zco3 OH- = [MX]/Cx (94 ao ( A ) = [ HX] p/G, 5.450 5.502 6.124 and for reaction w B f%(B) = PWG 6.745 (lo4 a0 ( B ) = [ HX] zP/C,Y. -I- H+ 7.665 + Ii+ 7.913 + H+ 9.186 + H+ . g.776 (lob) It can be shown (Stumm and Morgan 1970) that the total buffer capacity of reactions A and 13 in water can be calculated from + H+ 13.791 beyond the capacities calculated from equation 4. Calculations of the buffer capacity from the ion-pair model represent a redistribution of the contributions to pT but do not result in the introduction of any additional terms. According to the ion-association model the metal ions contribute to the buffering capacity of the carbon dioxide system via the reactions (Table 4) + I-I+ (6a) M”’ + II&O:1 e ALU-ICO~@-~)-+ + d[OH-] P-P-. dpI1 d[H+] dpH P-> Considering the first term, al(A) and a0 (A) can be expanded to give ( combining 7, 9a, 9b, and the appropriate version of 8 for each complex) al(A) = K$,JM]P( K&s + ~K?ux[M]i.-t- [II:; )-I so(A) = [H+](K&s+ and ~K*,,~ey[M]p+ Al ( 12) [I-I+])-‘. ( 13) M”- + I-IC03- = AJEO:,‘“-~)+ + II+. (6b) The buffer capacity of such a system of reactions can be approximated by considering the general buffer reaction M + 11X = MX + I-I-’ (B) The total concentration of ligand X( =C032or IIC0,7-) is given by Cx = [Xl, + [HXIF + x[MX] Al (7) for a system containing M cations (M = Na-+, Ca2+, Mg2+) forming ion-pairs with X. The stoichiometric constant for reaction A is given by K?KS = [MX][H+]/[M]~[IIX]p. (8) equations 12 and 13 for reac- (K:$,, + ~KLJ,,y[M]. AI = CsdaL/dpH. (4 where 11X may also dissociate according to the equation HX = I-I’ + x. Combining tion A, + [I-r-+])-” (14) Therefore from the definitions of al(A) and cyo( A) ( equations 9a and 9b), c d49 - x dpH = 2.3[MX] [E[X]p,‘Cx; (15) = 2.3[X]1,JHX]p,‘C,s. (16) similarly c d%(B) ~ x dpH When these values are combined with the corresponding derivatives for [OH-] and [H+] (Stumm and Morgan 1970) the total buffer capacity becomes Buffer capacity Table 5. Feature B/;“lO x104 Condition a Approx buffer capacity [:H+] First maximum Second minimum Second ('H*COJ = rMfy1 [H2C03] + bfC031' [:H,C03] = [MCOJ] [H2C03] + @CO31 Third minimm 10 fea- First minimum maximum PJ1q 6 of predominant capacity curues. Identification tures on the buffer 4 241 of CO, in seawater = ~-ICO~]~’ = CMCOJ [:mco31 = [OH-I [MHCOs + [H+] [MCOJ] + [OH-] [MHCO~] + [OH-] PH Fig. 5. The buffer capacity of the carbon dioxide system in seawater as a function of ~1-1. The solid line follows ,& calculated from the experimental data of Hansson ( 1973a) using equation 4. The results of calculations from the ionpair model using equation 17 are shown as open circles. The individual contributions of the magnesium complexes (equations b and e: Table 4) and the free ligands (equations c and 32: Table 4) are shown as broken lines. Prl,/ln 10 = [I-I+] + [OH-] + ~[HX]~~~[Xl./CX (17) This solution is approximate in that the individual reactions have been treated independently. The buffer reactions (Table 4) can be treated in this way provided that their equilibrium constants are adequately separated. The error will not be more than 5% provided that the ratio of successive constants is not greater than 100 ( Stumm and Morgan 1970). Clearly reactions a to CZcan be treated independently from reactions e to h with little error, but the ‘reactions within each group will not bc mutually i.ndependent so that the resulting value of prP will be in error, particularly in the region of maximum buffering. However, the calculated curve follows the experimental curve quite closely (Fig. 5). The maximum error observed in pIP using equation 17 is about 15% in the region of the second buffer maximulll (Fig. 5). The profile of the first buffer maximum is accurately reproduced. Much greater errors of * M E Na, Mg or Ca. For the contribution the free components substitute [HCOJ-&, for 2[MHC03] and [CO3 ], for [MC03]. The corresponding pH values and buffer capacities can be read off from Fig. 3. arc introduced if plr/‘ln 10 is calculated from the logarithmic distribution diagram ( Fig. 3) by summing the concentrations of all components rcprcscnted by lines with slope SL oi -1 (Stumm and Morgan 1970) since the lines in the present diagram show marked curvature, particularly in the region of maximum buffering. A more exact but far more complex solution can be obtained by following through the derivation given by Stumm and Morgan ( 1970) for a multicomponent system. It is sufficient, for the present purposes, to use equation 17 to calculate the relative contributions of the various reactions (Table 4) to the total buffer capacity. Since equations 4 and 17 are two alternative descriptions of the same system pY1=pII, if both descriptions are valid. The predominant features of the buffer capacity curves associated with the various postulated reactions (Table 4; see aZso Fig. 5) can be estimated quite simply from the logarithmic distribution diagram (Fig. 3, Table 5). From the relative contributions of the various reactions to the total buffer capacity it is clear (Fig. 6) that, if the ionassociation model is to be espoused, the reactions resulting in the formation of metal-carbonate ion-pairs (reactions e to g : 242 Whitfield 3 80 0 /B0 a 60 1 2 IP 40 PH 6 20 io PH 1 4 Fig. 6. Percentage contributions of the various reactions listed in Table 4 to the buffer capacity of the carbon dioxide system in seawater as calculated from the ion-association model. The letters on the curves refer to the reactions listed in Table 4. The positions of the maxima and minima shown in Fig. 5 are indicated by arrows. Table 4) make major contributions to the buffer capacity of the system in seawater above pH 7.5. The formation of MgCO:,O contributes more than 50% of the total at pH 8.5. Influence of seawater composition the buffer capacity on The effect of solution composition on the buffer capacity can be illustrated by the simulation of acid-base titration curves for seawater of different compositions and by studying the effect of variations in composition on the pH of a standard seawater solution. The concentration of free magnesium ions in solution can be altered either by changing the total magnesium concentration (maintaining the charge balance by the addition or subtraction of sodium ions) or by changing the total sulfate concentration (maintaining the charge balance by the addition or subtraction of chloride ions) so as to alter the proportion of magnesium complexed by sulfate ions. Both procedures were used by Wangersky (1972a). Titration curves simulating the addition of strong acid or strong base to seawater (Fig. 7) were calculated from the ionassociation model. The value of CT (see equation 5) was held constant in all titra- ‘\\r 4 I a I 24 meq strong acid I L 1 40- 56 x 10 Fig. 7. Calculated curves corresponding to the titration of seawater with strong acid. The acid used in the calculations was sufficiently concen trated ( 20 M ) to make concentration corrections negligible. Crr was kept constant throughout the titration. The system was out of contact with the atmosphere and initially contained only 10-l” MII’. Solution compositions were as follows (with charge balance maintained as described in the text) l-artificial seawater (see F in Table 3); 2-artiIicial seawater with [Mg”+]T x 2; 3-artificial seawater with [Mg”‘] T x 0.5; 4-artificial seawater with [SO~~‘-IT x 0.5; S-artificial seawater with [SO:,“-IZ~ X 2. A solution with [Mg*+]T x 0.5 und [SO.,%]T X 2 would follow curve 3 initially and then curve 5 at low pII. tions so that the maximum buffer capacity of the system will be unaffected by change:< in solution composition. However the titration curves will be displaced from one another since changes in sohrtion composition are likely to influence the stoichiometric cons tan ts ( K1 *, Kz*) and the details of the buffering process (Fig. 6). Although the [Mg”+], : [SOd2-lT ratio was altered from 0.48 to 7.61 (cf. 1.90 for normal seawater) as suggested by Wangersky (1972aI1, the titration curves show very little alteration in the buffer capacity of the system (Fig. 7). Alterations in [ S042-]21 show the greatest influence at low pH values where the reaction S0.12- + H+ * HSO,- will play a significant role in the buffering process. Variations in [Mg2+]T have most effect at high pH values where, according to the ionassociation hypothesis, the formation of Buffer capacity of CO, in seawater PH I I o-04 0.08 ml ‘ti tranf’ Fig. 8. The influence of changes in solution composition on the pH of standard seawater. I. Starting solution contains 0.0054 M [Mg”]T and Each 10 ~1 of titrant increases 0.5724 M [ Na’]r. [M~“]T by 0.02 M and decreases [Na+]T by 0.04 M. II. Starting solution contains 0.00284 M [SO.?.]T Each 10 ~1 of titrant inand OX054 M [Cl-IT. creases [SO,‘-]T by 0.01 M and decreases [Cl-IT by 0.02 M. III. Starting solution as defined in Table 3 (see F), Each 10 ~1 of titrant increases [SO?-IT by 0.005 M and [Na+]T by 0.01 M and decreases [Cl-IT by 0.01 M and [Mg2’lT by 0.005 M. 0 ther components have the concentrations listed in Table 3 and these arc maintained constant throughout the titration. MgC0,70 ion-pairs dominates the buffering process (Fig. 6). The overall effect is small and would appear at first to support his proposal (Wangersky 1972a, p. 5) : The effects of fairly large variations in composition are in fact fairly small. This is only to be expected if the entire mass of inorganic solutes in seawater is involved in the equilibria. However the differences between the various titration curves are small simply because magnesium is always present in large excess over carbonate so that the actual concentration of the MgCOsO complex is not greatly affected by the changes in solution composition shown in Fig. 7. Since [ Mg2+],, does not appear in the buffer capacity equation, changes in its value are only indirectly felt. 243 This point is more clearly made if much larger excursions in the [Mg2’] r : [ SO4”-]21 ratio are considered. From the acid-base titration curves (Fig. 7) it was observed that, using the present model, 2.55 mM of strong acid are required to adjust the seawater to pH 8 in a closed system. To study the effect of changes in [Mg”+], on the pH of seawater this amount of acid was added to a seawater with the usual composition (Table 3) but with only a tenth the normal magnesium concentration (i.e. 5.4 mM ) and with the sodium concentration adjusted accordingly to maintain the charge balance. The pH of the resulting solution was then calculated together with the distribution of species in the carbon dioxide sys tern ( represcntcd in Fig. 3). The solution composition was then altered by adding magnesium ions and removing sodium ions to maintain the charge balance and the same parameters were calculated. The results are shown as a titration ( curve I: Fig. 8) for clarity. Each 0.01 ml of the hypothetical titrant changes the magnesium concentration by an increment of 0.02 M and decreases the sodium concentration by a step of 0.04 M. Therefore the normal seawater co:mposition is attained after the addition of about 0.025 ml giving a pH of 8. The titration was continued until the Vahe Of [ Mg2-I-1, was more than five times the normal seawater concentration (i.c. 0.2854) and the sodium was almost totally depleted ( [ Na] T = 0.0124). The ionic strength varies from 0.659 to 0.939 M during the course of the titration. The effect of this variation on the free ion activity coefficients (Table 2) is small and has been neglected. The pI1 of the system is remarkably resistant to changes in [ Mg2-c]T (Fig. 8: curve I). A shift of [Mg2-b]II from a tenth to five times the normal seawater concentrations results in a decrease in pH (reaction e: Table 4) of only 0.55 pI1 units. It is instructive to look at the influence of this change in composition on the distribution of species in the carbon dioxide system. From the buffering point of view the most important parameters at this pH are 244 Whitfield h [MCO,l B 0.10 - 0*05 c I 0.05 I 0.10 W41 T Fig. 9. Variation in concentration of metalcarbonate ion-pairs accompanying the titrations shown in Fig. 8. The solid lines show the variation of [MCOJ during the titration. The vertical line indicates norm‘al seawater composition. A. Corresponds to curve I, Fig. 8. The dashed lines show the variation that would be expected over the corresponding pH range if [ M]~~ were held constant. The curve marked z corresponds to the sum [NaCO;] + [MgC030]. B. Corresponds to curve II, Fig. 8. the concentrations of the MgC030 and NaCOs- ion-pairs ( Fig. 9A, cf. Fig. 6). In the natural situation, magnesium removal is likely to be compensated for by an increase in the sodium concentration so that the total buffer capacity resulting from the formation of metal-carbonate ion-pairs will only be slightly affected, even by the total depletion of magnesium (Fig. 9A). Large increases in the magnesium concentration will also have a small effect on the buffer capacity, not because of any compensation from the concomitant decrease in sodium ion concentration, but bccause the concentration of MgC030 iortpairs is limited not by the value of [ Mg2+]21 but by the availability of carbonate ion:;. If it were postulated that some other species (e.g. K+) that did not form ion-pails with carbonate were introduced to maintain the charge balance, the buffer capacity would not be markedly affected unless the magnesium concentration was depleted to such an extent that [ Mg2+lT became the limiting factor in the formation of MgC030 ion-pairs (i.e. about a tenfold depletion of [ Mg2+] Ip would be required). The ovcral!l effect agrees, in a qualitative manner, with Wangersky’s postulates, but the introduc:tion of the concept of an interlinked pHstatting system would appear to be superfluous. This is clearly illustrated in Fig. 6 where the minimum in the buffering capacity is shown to coincide with the situation where most of the reactions listed in Table 4 play a significant role in the bufferin:: process. Where the buffer capacity is at a maximum the buffering process is dominated by a single reaction. Wangcrsky (1972a, p, 5) suggested that since three-fourths of the sulfate present in normal seawater is tied up in ion pairs-in competition with carbonate and bicarbonate for cations-a change in sulfate concentration should be directly and strongly reflected in pH change. procedure has also bee::1 A “titration” used to study the effects of alteration in the sulfate concentration on the pH of sea.water. In this instance the starting point was a seawater containing 0.00284 M sullfate and 0.6054 M chloride. Each O.Ol+J increment of titrant increases [ S0,2-] T by 0.01 M and decreases [Cl-] by 0.02 M. The titration was continued until [ S042-]yl Rufjer capacity 245 of CO, in seaumter reached five times the normal value (0.143 M ) . The change in ionic strength throughout the titration (0.682-0.819 M ) was small and its influence on the activity coefficients was neglected. The overall shift in pII ( -I- 0.11 units curve II : Fig. 8) is only a fifth of the value observed for corresponding alterations in [Mg”-‘] T. There is evidence (Berner 1972) that the sulfate budget of the ocean is in a state of imbalance and that the present value of [ SOh2-lT may be doubled in 14 million years. My calculations indicate that much larger excursions in sulfate concentrations will result in only a small change in the pH of seawater due to shifts in the ion-associCalculations of the conation equilibria. centrations of MgCO,?O and NaCO:$- (Fig. 9B) indicate that a decrease in the concentration of MgCOso (because of competition with the formation of MgSOdO) is almost compensated by a simultaneous increase in the concentration of NaC03- resulting from the release of carbonate ions from the magnesium ion-pairs. Depletion of magnesium and increase of sulfate concentration both tend to increase pH (Fig. 8), and the largest effects are expected at low magnesium concentrations (Figs. 8 and 9A). However, a tenfold depletion of magnesium accompanied by a threefold increase in sulfate only results in a pH shift of 0.25 units ( curve III: Fig. 8). The pH of seawater is therefore particularly resistant to changes in the composition of the major electrolytes. Wangersky ( 1972a) supported his arguments by presenting experimental data on the influence of variations in the partial pressure of carbon dioxide on the pH of various artificial seawaters. These conditions will now be simulated with the aid of the ion-association model, Open systems The procedures used to analyze the carbon dioxide equilibria in closed systems can also be applied to open systems (e.g. Fig. 2) provided that care is taken to treat the gaseous and aqueous phase components on the same concentration scale. From the measurements of Murray atid Riley ( 1971) the concentration of I-I&OS* is related to the partial pressure of carbon dioxide ( PcO,) by the equation, as = [II2C~O:I”l/~co, = 289 x 10-d mol liter-l atm-l (18) at 25°C and 1 atm total pressure. For the purpose of my calculations the concentration of carbon dioxide in the gaseous phase [ COJg was expressed in units of mol liter-l using the expression, [CO& = Pco, x V/RT = 0.0409 PcoZ mol liter-l. (19) The master variable diagram at constant P analogous with Fig. 3 for closed systc?ZZ, indicates that over most of the pH range the concentrations of the bicarbonate and carbonate species may bc represented by two systems of parallel lines with slopes +l and +2 (Fig. 10). The cquations of these lines can be simply calculated. For carbonic acid ( equation c: Table 4) log [ IICOn-] JY= (log [H&Ioi7*] + log K&o,) + pH. (20) The term in brackets is constant. Similarly for the formation of the metal-bicarbonate ion-pairs log [MHCOs] (log [M]F = + log ~%mco, + log [H2C03*]) + PI-I, (21) where the formation constant refers to the relevant equilibria a, 79,or d (Table 4). For the carbonate complexes log [ co,2-]Io = (log [H2C03*] an d log [MCOJ = (log [H2C03*] + log K:~oo,) + 2 pH (22) + log ZU,,o, -I- log [Ml,) + 2 pH. (23) The equilibrium constants used in equations 22 and 23 refer to reactions derived by summing equation c (Table 4) with equations h and e to g respectively. At high pH vahies the carbonate complexes represent significant proportions of 246 Whitfield t seawgter -.-.~ PX 6 8 4 6 8 PH Fig. 10. Logarithmic distribution diagram for the components of the carbon dioxide system in seawater at constant Pco,. The letters identify the equations in Table 4 that describe the formation of the various components. For example curve f represents the distribution of CaC,Ono as a function of pH. pX =-log [Xl,. The curve marked CT corresponds to Fig. 2 and the horizontal line marked “seawater” indicates the typical open ocean situation. the total metal concentration so that the free metal concentrations in equations 21 and 23 are no longer constant and the plots deviate from linearity ( Fig. 10). The curvature becomes noticeable above pI1 8.5. Comparison of equations 3a and 3b with equations 20 to 23 indicates that below this pH the relative contributions of the various equilibria to the total buffer capacity will be the same in both open and closed systems. The deductions drawn from Fig. 6 may therefore be used in the discussion of open systems. Wangersky (1972a) considered the influence of solution composition on the pH of open systems equilibrated with various partial pressures of carbon dioxide. I have reconstructed his experimental conditions here on the assumption that the system reached equilibration in the course of his experiments. The calculated curve for a.rtificial seawater ( curve 2: Fig. 11A) runs parallel to that obtained experimentally by Wangersky (curve 1: Fig. 1lA) but is djsplaced into the more alkaline region by one pII unit. The calculated curve would a:ppear to be in better agreement with the accepted properties of seawater, in that tyI)ical atmospheric values for pcoe give a PI-I of 8.2 to 8.3 whereas Wangersky’s data give a pH of 7.2 to 7.3. The reason for this djscrepancy is unclear as Wangersky giv#es few experimental details. Th,e influence of varying [ Mg2 ‘1Il : [SOL~2-]~~ratios on the curves (Figs. 11A and 11B) is in accord with the deductions drawn from calculations on closed systems. As Wangersky suggests the effects are small, but my calculations failed to reproduce in detail the behavior that he observed. A decrease in [Mg2+], should produce a shift to high pH and an increase a shift to low pH (Fig. 1lA: curves 4 and 3; cf. Fig. 8). Wangcrsky observed this behavior only at low values of PcO,; in all other cases the curves were shifted to higher pH values by an alteration in [ Mg2+lT. This behavior is not readily explained. Both the model system and the experimental system show similar shifts in pH when [ S042-] T is altered ( Fig. 11B ) , although the marked shift observed by Wangersky to lower pH when the sulfate concentration is decreased is unexpected. The calculation and the experiments are in close agreement when the effects of simultaneous variations in [ Mg2+lIT and [SOd2-] T are considered ( curves 4 and 15: Fig. 11B). Conclusions There can be no doubt that the composition of the ionic medium influences the buffer capacity of the carbon dioxide system since the experimental equilibrium constants ( apparent or stoichiometric j are observed to alter when the medium changes ( Ben-Yaakov and Goldhaber 1973; Hansson 1973a). Stoichiometric constants of high preci- Buffer capacity of CO, in seawater 247 seawaters with various compoFig. 11. The influence of variations in PCO~ on the pH of artificial sitions. Changes in the magnesilrm concentration are accompanied by complementary changes in the Similarly changes in the sulfate concentration sodiun concentration to maintain the charge balance. are balanced by changes in the chloride concentration (see text). A. l-Artificial seawater ( Wangersky 1972a); 2-artificial seawater (this paper); 3-[Mgz’], X 2; 4-[Mg2+]T X 0.5. The h orizontal lines mark the normal range of pcoa in the atmosphere. B. l-Artificial seawater (this naner): 2-rSOi”-]~ X 0.5; 3-[S0.?-]~ X 2; 4-[SO42-]r X 0.5, [Mg”], x 2; 5-[SO4’-]T x 2, [Mg’+& x 0.5. - ’ ’ - sion are now available (Hansson 1973a) together with a pH scale for seawater as an ionic medium (Hansson 19731>). Ruffcr capacities calculated from these stoichiometric constants can be accurately reproduced, at 25°C and 1 atm pressure, by a modified ion-association model, If for geochemical or physicochemical reasons we wish to break down the total buffer capacity of the system into its component parts, the ion-association model provides us with a convenient summary of the various interactions in solution. Using this model we can show that, at normal pH values, the formation of MgCOn” makes the major contribution to the buffer capacity of the system in seawater. Quite large variations in [Mg2+lT cause only slight alterations in the pH and the buffer capacity because the concentration of the magnesium carbonate ion-pair represents only a small proportion of [Mg2+lTT. Only at very low magnesium concentrations is the effect significant and, in the natural situation, it is liable to be compensated for by complementary changes in the concentration of NaC03- as the charge balance is maintained. Indirect changes in the free magnesium concentration brought about by alterations in the sulfate concentration have a very small effect, partly because of the influcnces noted. above and partly because the carbonate ions, relcascd as magnesium sulfate ion-pairs are formed, are taken up by the sodium ions. All of thcsc effects can be treated quite effectively in closed or open systems by the ion-association model and no new mechanisms are required. In fact, unless the cation concentrations become severely depleted, the indiffercncc of the seawater pH to changes in solution composition arises because the major cations are only slightly complexed rather than from their involvement in the whole network of equilibria. Pytkowicz (1972) agrees that the formation of ion-pairs influences the effective concentrations of the carbonate and bicarbonate ions in seawater and therefore in turn affects the apparent constants, the pH, and indirectly the buffer capacity. He emphasizes, however, that the ion-pairs do not buffer seawater and that this is still 248 Whitfield done by the classic reaction, 2IICO3-, total * H&OS* + COS2-, total. This contention is stated quantitatively in equation 4. However, if the ion-association model is to help us understand the reason why the buffer capacity of the carbon dioxide system is different in seawater from that in distilled water, then it is valid to express the total buffer capacity in terms of the relative contributions of the various ion-pair formation reactions (equation 17, Figs. 5 and 6). The difference between this view and that of Pytkowicz is purely one of semantics. References BATES,R. G. AND R. M. PYTKOWICZ. 1969. Sodium, magnesium, and calcium sulfate ion-pairs in seawater at 25C. Limnol. Oceanogr. 14: 686-6912. LAFON, G. M. 19169. Some quantitative aspect; of the chemical evolution of the oceans. Ph.D. thesis, Northwcsteln Univ., Evanston, Ill. 137 p. MACINNES, D. A. 1919. The activities of the ions of strong electrolytes. J. Am. Chem. sot. 411: 1086-1092. MURRAY, C. N., AND J. P. RILEY. 1971. The solubility of gases in distilled water and seawater. 4. Carbon dioxide. Deep-Sea Re::. -, 1972. Determination of pH, theory and practice, 2nd ed. Wiley. BEN-YAAKOV, S., AND M. B. GOLDHADER. 1973. The influence of sea water composition on the apparent constants of the carbonate system. Deep-Sea Res. 20: 87-99. BERNER,R. A. 1971. Principles of chemical sedimentology. McGraw-Hill. 1972. Sulfate reduction, pyrite forma-. tion, and the oceanic sulfur budget, p. 3473,61. In D. Dyrssen and D. Jagncr reds.], The changing chemistry of the oceans. Almqvist and Wikscll. BUTLER, J. N. 1964. Ionic equilibrium, a mathematical approach. Addison-Wesley. GARI~ELS, R. M., AND M. E. TIIOMPSON. 1962. A chemical model for sea water at 25°C and one atmosphere total pressure. Am. J. Sci. 260 : 57-66. HANSSON, I. 19’73a. A new set of acidity constants for carbonic and boric acid in sea Deep-Sea Res. 20: 461-478. water. 1973b. A new set of pH-scales and -. standard buffers for sea water. Deep-Sea Rcs. 20 : 479-491. INCHI, N., W. KAKOLOWICZ, L, G. SILL$N, AND B. WARNQVIST. 1967. High speed computers as a supplement to graphical methods. 5. IIALTAFALL, a general program for calculating the composition of equilibrium mixtures. Talanta 141: 1261-1286. 19691. Ion association of sodium, KESTER, D. R. with sulfate in an d magnesium calcium solutions. Ph.D. thesis, Oregon aqueous State Univ., Corvallis. 19,772. Effect of ion pairing on the pH -. of seawater. Limnol. Oceanogr. 17: 959960. 18: 533-541. R. M. 1967. Carbonate cycle and the buffer mechanism of recent oceans. Gcochim. Cosmochim. Acta 31: 63-73. -. 1972. Comments on “The control of seawater pI1 by ion pairing” (P. J. Wangersky). Limnol. Oceanogr. 17 : 958-959. S~L,L~N,L. G. 1959. Graphic presentation cf equilibrium data, p, 277-317. In I. M. Kolthoff and P. J. Elving reds.], Treatise on ana.lytical chemistry, part 1, v. 1. Interscicnce. -. 1961. The physical chemistry of sca.water, p. 549-581. In M. Sears [ed.], Oceanography. Publ. Am. Assoc. Adv. Sci. 67. -. 1967. Master variables and activity scales, p. 45-56. In W. Stumm [ed.], Equilibrium concepts in natural water system::. Adv. Chem. Ser. 67. AND A. E. MARTELL. 1964. Stability coAstants of metal-ion complexes, 2nd ed. Chem. Sot. (Lond.) Spcc. Publ. 17. 754 p. STIJMM, W., AND J. J. MORGAN. 1970. Aquatic chemistry. Wiley-Interscience. WANGERSKY, P. J. 197’2a. The control of seawater pI1 by ion pairing. Limnol. Oceanogr. PYTKOWICZ, 17: l-6. -. 197%. Ion pairing and pH: A reply. Limnol. Oceanogr. 17 : 96&962. 1973~. Sea water as an electroWHITFIELD, M. lytc solution, in press. In J. P. Riley and G. Skirrow reds.], Chemical oceanography, 2nd cd. Academic. -. 1973b. A chemical model for sea water based on the Br$nsted-Guggenheim hypoth+ sis. Mar. Chem. 1: 251-256. YEATTS, L. B., AND W. L. MAIUILALL. 1969. Apparent invariance of activity coefficients of calcium sulfate at constant ionic strength and temperature in the system Ca2SO,Na,SO, -NaNOrHz0 to the critical temperature Df water. Association equilibria. J. Phys. Chem. 73: 81-90. Submitted: Accepted: 1 August 1973 5 December 1973