Solubility and Activity Coefficients of Salts in Synthetic Seawater
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
2693
pressures, one can estimate that the equilibrium constant is about 0.28 at 1000 K and 1 atm pressure. The thermodynamic data in Table I show KIooo= 0.58 for the reaction
Acknowledgment. This work was supported by the United States Department of Energy under Contract No. EF-77-C-01-2524.
2KA1Si206(c,leucite) KA1Si308(c,sanidine)+ KA1Si04(c,orthorhombic)
(1) N. Eliezer, R. A. Howakl, M. Marinkovic, and I. Eliezer, J. Phys. Chem., 82, 1021 (1978). (2) J. F. Shairer and N. L. Bowen, Am. J . Sci., 253, 681 (1955). (3) I. Eliezer and R. A. Howald, Hiah TemD. Sci., 10, 1 (1978). (4) I. Eliezer and R. A . Howald, J.-Phys. Chem., in press. (5) I. Eliezer and R. A. Howald, High Temp. Sci., 9, 119 (1977). (6) R. A. Robie and D. R. Waldbaum, U . S . , Geol. Surv., Bull., 1259 (1968). (7) Kracek, Neuvonen, Burley, and Gordon, Annual Report of the Director of the Geophysics Laboratory, Geophysics Laboratory Paper 1215, 69-75 (1953). (8) K. K. Kelley, C. H Shomate, F. E. Young, B. F. Naylor, A. E. Salo, and E. H. Huffman, U . S . , Bur. Mines, Tech. Pap., 688 (1946). (9) R. Barani and L. H. Adami, U . S . , Bur. Mines, Rep Invest., 6873 (1961). (10) P. Gross, J. Christie, and C. Hayman reported in A. B. Thompson, Contrib. Mineral. Petrol., 48, 123 (1974). (11) J. L. Holm and 0. J. Kieppa, Am. Mineral., 51, 1608 (1966); T. Yokokawa and 0. J. Kleppa, J . Phys. Chem., 68, 3256 (1964). (12) J. P. Coughlin, J . Am. Chem. Soc., 78, 5479 (1956); P. Gross and C. Hayman, Trans. Faraday Soc., 66, 30 (1970). (13) A. B. Thompson, Contrib. Mineral. Petrol., 48, 123 (1974). (14) N. D. Chatterjee and W. Johannes, Contrib. Mineral. Petrol., 48, 89 (1974). (15) B. S.Hemingway and R. A. Robie, J. Res. U . S . Geol. Surv., 5,413 (1974). (16) K. K. Kelley, S. S. Todd, R. L. Orr, E. G. King, and K. R. Bonnickson, U.S., Bur. Mines, Rep. Invest., 4955 (1953). (17) E. R. Plante, C. D. Olson, and T. Negas, Int. Conf. Magnethydrodyn. Electr. Power Gener., 6th, Vol 11, 211 (1975). (18) T. Negas, private communication. (19) L. P. Cook, R. S. Roth, H. S. Parker, and T. Negas, Am. Mineral., 62, 1180 (1977). (20) F. E. Spencer Jr., J. C. Hendrie Jr., and D. Bienstock, Int. Conf. Magnetohydrodyn. Electr. Power Gener., Vol 11, 181 (1975). (21) Y. Seki and G. C. Kennedy, Am. Mineral., 49, 1267 (1964).
-
which is certainly of the correct order of magnitude, even allowing for a small difference in free energy between kalsilite and the orthorhombic crystals. The other curve, M in Figure 1, must represent vapor pressure equilibrium for some metastable system. One of the most likely nonequilibrium sets of solids is leucitetetragonal crystals-P-alumina for which the calculated liquid KOo.6activity a t 1700 K is 10-5.374, within a factor of 2 of the value for the M curve, 10-5.095. It is clear that the values proposed here for the thermodynamic quantities for the solid and liquid phases reproduce the major features of the ternary system KOo,6-A101,6-Si02. There are however enough discrepancies within a factor of 2 to indicate that better fits can be obtained in the future. However we have had to consider entropy values over a range of f 4 cal mol-l K-l, and factors of 2 present a substantial improvement over uncertainties of a factor of 8. In fact no thermochemical data a t all has been available for the tetragonal phase. Even such approximate values for the activities in the equilibrium liquids improve the thermodynamic characterization of the solids in complex ternary systems like this, and we can look forward to even better values as better enthalpy data and better computer programs for activity coefficients in multicomponent system become available.
References and Notes
Solubilities and Activity Coefficients of Calcium and Strontium Sulfates in Synthetic Seawater at 0.5 and 25
O C
C. H. Culberson," College of Marine Studies, University of Delaware, Newark, Delaware 19711
Glenn Latham, and Roger G. Bates Department of Chemistry, University of Florida, Gainesvllle, Florida 326 1 I (Received July 5, 1978) Publication costs assisted by the National Science Foundation
The solubility of CaS04.2H20was measured in water and synthetic seawater (23-45%0salinity) at 0.5 and 25 "C, and in sodium sulfate (0.23-1.64 rn) at 25 "C. The solubility of SrS04 was measured in water, synthetic seawater (%%o salinity), and in single salt solutions (NaC1, KC1, MgC12,CaClJ at 25 "C. Activity coefficients calculated from the solubility measurements are used to test the predictions of the Bransted-Guggenheim; Reilly, Wood, and Robinson; and Pitzer and Kim mixed electrolyte theories. In seawater at 25 "C and 35% salinity, the measured activity coefficients (y*(SrS04)= 0.140, y*(CaS04) = 0.136) are 8-17% lower than the theoretical values.
Introduction In the past decade, there has been increasing emphasis on the theoretical calculation of activity coefficients in seawater, 'and Reilly et al.,I Whitfield,* and Pitzer and Kim3 have proposed models for mixed electrolytes which allow calculation of the thermodynamic properties of seawater. The confidence with which we accept these calculations rests on the extent to which they agree with experiment. At present, comparison of theory and ex-
periment has been made in only a few cases: for the osmotic coefficient of ~ e a w a t e r ,and ~ for the activity coefficients of N a C P and Na2S04.7 For HC1,8 such a comparison is possible but has not yet been published. The theoretical equations correctly predict the osmotic coefficient of seawater and the activity coefficients of NaCl and Na2S04. Based on this agreement, particularly for Na2S04which is ion paired, it has been concluded that these models correctly predict the activity coefficients of
0022-3654/78/2082-2693$01.00/00 1978 American Chemical Society
2694
The Journal
c. H. Culberson, G. Latham, and R. G. Bates
of Physical Chemistry, Vol. 82, No. 25, 1978
Thermistor Probe
Solution
TABLE I: Initial Composition of Synthetic Seawater (35" ) Used in the CaSO, *2H,0 and SrSO, Solubility Measurementsa
Ball
ion N a+
K+
chlorinity ratio molality (g-ion/g-CP / o o ) (X 1000) 0.55553 0.0206 0.066795 0.02131 0.41 mg/g
Mg2+ Cazt SIz+ Mg2+t Ca2+ c10.998906 HC0,7.487 mg/g
485.23 10.58 55.18 10.68 0.09 65.95 565.78 2.46 568.24
comments
Cast replaced Srz+ in all seawaters
Cl- replaced HC0,- in all neawaters
Br-
3.473 mg/g 0.87 0.0675 mg/g 0.07 so, * 0.1400 29.27 1.327 mg/g 0.43 B(OH), a The ratio of calcium t o magnesium was varied while holding the sum of their molalities constant at its seawater value. Total solids = 35.12 g/kg solution.
F-
43
-Teflon
Metering Valve
U Figure 1. BrCnsted saturator used for CaSO4.2H,O and %SOl measurements. The internal diameter of the solubility column was 1 cm. The thermistor probe controlled the water bath temperature via a proportional temperature controller.
rated for 2 min at an aspiration rate of 3 mL/min, and the spectrophotometer output was recorded by a digital printer. The test solution was prepared by weight and divided the major constituents of seawater. into three aliquots. The first aliquot was used for the Becauseof the importance of the alkaline earth sulfates solubility measurement, the second for the standards, and in processes such as sound absorption (MgSO,) and the third to determine the strontium blank in the test mineral formation (CaS04, SrS04, and BaS0,) we measolution. After passing through the saturator, the satusured the solubilities of CaS04.2H20 and SrS0, in synrated solutions were collected in four preweighed 50-mL thetic seawater and in single salt solutions at ionic strength mixing cylinders, diluted to a strontium concentration of 0.7. In this paper, the activity coefficients of CaS04 and approximately 100 pm with distilled water, and made SrS0, calculated from our solubility measurements are 0.1000 m by adding 0.25 M HC1. The saturated solutions, used to check the ability of mixed electrolyte models to standards, and blanks were diluted by exactly the same predict the activity coefficients of 2:2 salts at the ionic amounts. strength of seawater. The measured values are from 8 to Two standards, with strontium concentrations 5% 17% less than the theoretical values. higher and 5% lower than the saturated solution, were Experimental Section prepared from the second aliquot by diluting the test solution with the required amounts of SrC12, HC1, and The solubilities of SrS04 and CaS04.2H20were meadistilled water. An amount of H2S04equivalent to that sured with the Bransted solubility column shown in Figure of SrCl, was added to the standards for the measurements 1. To prevent channeling, the saturator was inverted in distilled water and in single salt solutions to eliminate several times, and the solid allowed to resettle before each any matrix effects due to sulfate. Sulfuric acid was not solubility measurement. Temperature of the column was added to the seawater standards, due to the large amount controlled to rt0.05 "C with a proportional temperature of sulfate already present in the seawater. Samples and controller. standards were run in the order: low standard, saturated The composition of the synthetic seawater used in the solution, high standard; and this sequence was repeated experiments (Table I) was identical with natural seawater three to five times for each of the four unknowns. The except that NaCl replaced NaHC03, to prevent precipitransmittance of each standard was obtained at the time tation of carbonates, and CaC1, replaced SrC1,. Unless of the unknown by linear interpolation, and the concenotherwise noted, the synthetic seawater was prepared from tration of the unknown was then calculated by linear reagent grade salts. The MgC12, CaCI,, and SrCl, stock interpolation between the transmittances of the two solutions were filtered through a 5-pm fritted glass filter standards. and then standardized gravimetrically as silver chloride. The strontium blank in the test solution was determined Strontium Sulfate: The saturator was filled with 11cm of SrS0, prepared by the method of Lewin and V a n ~ e . ~ ~by the method of standard additions. Aliquots of the test solution were weighed into pairs of 50-mL mixing cylinders, Strontium sulfate, prepared by mixing solutions of SrC12 the second aliquot was spiked with 5 ,um SrC12,and both and Na2S04, was placed in the extraction thimble of a aliquots were diluted with HC1 and distilled water. These Soxhlet extractor and dissolved by reaction with constant two solutions were then run against a distilled water blank. boiling HC1. The HC1 in the reaction chamber of the Due to the lack of a technique for determining low conextractor gradually became supersaturated with SrS04and centrations of sulfate, we assumed that the sulfate blank large well-crystallized particles of SrS04precipitated. in the single salt solutions was negligible. The NaC1, Dilute HC1 (0.25 M) and H2S04(0.055 M), prepared Na2S04,NaF, KC1, and KBr used in the SrS0, solubility from constant boiling HC1 or from reagent grade conmeasurements were recrystallized from reagent grade salts centrated H2S04,were standardized against 0.1000 M to reduce the concentration of any strontium and sulfate NaOH using methyl red as the indicator. impurities. Strontium was measured on a Perkin-Elmer Model 303 The effect of flow rate on the measured solubility was atomic absorption spectrophotometer using a single slot small, In pure water, increasing the flow rate from 0.14 burner and an air-acetylene flame. Samples were aspi-
Solubility and Activity Coefficients of Salts in Synthetic Seawater
to 0.67 mL/min caused the strontium concentration to decrease from 648.2 to 643.9 wm, a decrease of only 0.7%. For convenience, our solubility measurements were made at a constant flow rate of 0.3 mL/min. Calcium Sulfate. The saturator (Figure 1)was filled to a depth of 12-15 cm with reagent grade CaS04.2H20which had been digested twice in boiling distilled water and then stored in contact with distilled water for 6 months at room temperature. To prevent significant changes in the ionic strengths of the samples, the calcium and magnesium concentrations of the synthetic seawaters were adjusted until the change in calcium concentration upon passing through the saturator was less than 0.3% of the sulfate concentration. Calcium was determined by a compleximetric titration using EGTA as the titrant and (glyoxal-bis(2-hydroxyanil)) as the i n d i ~ a t o r .In ~ ~the concentration range 13-51 mm, the relative standard deviation of 33 sets of triplicate determinations was 0.09%. A 10-mL calibrated buret, graduated in 0.02-mL divisions, was used to deliver the EGTA titrant. The solubility was determined by the following procedures. One kilogram of synthetic seawater (or Na2S04 solution) was prepared and divided into two parts. The first part was used to standardize the EGTA and the second part was passed through the solubility column. For standardization, triplicate 10-g portions of synthetic seawater were weighed into 50-mL mixing cylinders and titrated with EGTA. The solution reservoir was filled with the second half of the test solution and the solubility column rinsed with 40 mL of the new solution. The flow rate was adjusted to 0.7 mL/min. Triplicate 10-g portions of the effluent from the saturator were weighed into 50-mL mixing cylinders and the calcium concentration determined by titration with EGTA. Solubility measurements in pure water were made in the same way, except that 20-g portions were used and that the EGTA was standardized with pure CaC1, solution. The CaClz stock solution was standardized gravimetrically as silver chloride and by EGTA titration against primary standard grade CaC03. The two standardizations agreed to foal%. Solubility measurements in Na2S04 were similar to those in seawater except that the NaZSO4solutions were filtered through a 5-pm fritted glass filter before use to remove particulate matter (the concentrated Na2S04solutions were yellowish before filtration), and the standards were prepared by adding CaClz to the first aliquot of NaZSO4.A blank determination was run on each NaZSO4solution. The average blank was equivalent to 0.006 mol % calcium in the Na2S04. The effect of flow rate on the measured calcium concentration was checked in pure water. The calcium concentrations measured for flow rates of 0.55 and 1.34 mL/min were identical with the calcium concentration of a water sample which was presaturated with CaSO4.2Hz0 at room temperature and then run through the solubility column at 0.58 mL/min.
Results The measured solubilities and activity coefficients of SrS04 and CaSO, in pure water, synthetic seawater, and single salt solutions are listed in Tables I1 and 111. The thermodynamic solubility products of SrSO, and CaS04.2H20 are defined as K0srSo, = ( r + ( S r S 0 4 ) ) 2 ( m ~ , ) ( m ~ ~ ~ ) (1) ~
C
~
=S (ra(CaS04))2(mc,)(m~04)(a~z~)2 O ~ (2)
where r,(MX) is the mean ionic activity coefficient of MX,
The Journal of Physical Chemistry, Vol. 82,No. 25, 1978 2895
TABLE 11: Solubilities and Activity Coefficients of SrSO, a t 25.0 "C molality x
lo6
na
Srz+ SO,,- r t ( S r 9 0 , ) 16 642.4 i O S b 642.4 H,O 6 646.1 i 0.9 646.1 average 644.3 0.7636' 3227d 0.1524 0.7000 NaCl 1 4 3231 ?: 21 3421d 0.1438 0.7000 KCl 14 3421 f 16 3742d 0.1315 0.2333 MgCl, 12 3743 i 6 4101d 0.1193 0.2333 CaCl, 12 4144 * 6 1 3 413.8 i 1.0 29679 0.1404 seawater-le 1 6 415.8 i 2.2 29682 0.1400 seawater-2 18 422.7 ?: 2.2 29689 0.1389 seawater-3 seawater-4 15 422.1 ?: 4.4 29689 0.1390 Uncertainties represent i:2 a Number of replicates. standard deviations of the mean. ' Activity coefficient of The difference CaSO, from Pitzer and Mayorga.'O strontium blank. e The synthetic sea((Srz+)- (SO,2-,)).=, waters had the initial composition given in Table I. Molal ionic strength after saturation = 0.725. The magnesium and calcium concentrations were (molal X 1000): SW-I, Mg2+= 65.98, Ca2+= 0.00; SW-2, MgZf= 55.19, Caz+= 10.76; SW-3, Mg2+= 38.01, CaZt = 27.95; SW-4, Mgzt = 20.99, Ca2+= 44.97. solution
TABLE 111: Solubilities and Activity Coefficients of CaS04.2H,0 in Pure Water, Synthetic ' Seawater, and Na, SO,a molal X 1000
T, " C
I, m
equiv salinity
ri-
Ca2+ SO,,-
(CaSO,)
15.24 15.24 0.3304b 0.05 0.06095 H,O 0.5562 27.15 50.75 22.53 0.1510 48.54 29.28 0.1360 0.7228 34.99 46.46 38.09 0.1226 0.9397 45.02 0.50 i 0.05 0.05140 H,O 12.85 12.85 0.3645' 0.4727 23.17 43.15 19.16 0.1648 0.7231 35.01 41.21 29.30 0.1373 0.9391 44.99 40.29 37.93 0.1227 25.06 k 0.05 0.7224 0.2266d 10.66 0.9986 0.3178 11.30 1.9986 0.6481 13.56 2.6973 0.8792 14.90 2.9998 0.9794 15.43 3.9993 1.3105 16.91 5.0002 1.6429 17.90 a The equivalent salinity is the salinity of natural seawater that has the same molal ionic strength as the synthetic seawater. The composition of the synthetic seawater at 35"/00 salinity is given in Table I. The concentration of magnesium in the synthetic seawaters was as follows a t 25 "C, Mg" = 0.00, 17.42, 39.30; at 0.5 "C, Mg" = 0.000, 24.79, 45.34. Salinities other than 35"/00 were prepared by adding or removing water from the formula in Table I. Activity coefficient of pure CaSO, from Pitzer and Mayorga.'O ' Activity coefficient of pure CaSO, a t 0.5 "C calculated from the freezing point measurements of Brown and Prue'' using the equations of Pitzer and Mayorga." Molality of Na,SO,. 25.06
i:
aHzOis the activity of water, and m iis the stoichiometric molality of calcium, strontium, or sulfate. The mean ionic activity coefficients of strontium and calcium sulfate can be calculated from eq 1 and 2 if the concentrations of the relevant ions are measured at saturation, and if the thermodynamic solubility products, KOsp,at infinite dilution in pure water are known. In practice, we calculated KOspfrom our solubility measurements in pure water and then calculated the values of r*in the test solutions from KO, and the measured solubilities in the test solutions. &rontium Sulfate. There are few reliable measurements of the solubility of &SO4 in aqueous solutions. Our value in pure water (Table 11) is 0.3% lower than the
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The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
solubility measured by Campbell and Nancollasg using conductance measurements. Our value for ya(SrS04) in seawater is 12% smaller than the value calculated from the solubilities measured by North3' a t 2 "C. The reproducibility of our measurements can be seen by comparing the solubilities in pure water which were measured over a 2-month period. The precision of the measurements was less in salt solutions than in pure water because the flame became less stable as the burner became clogged with salt deposits. The thermodynamic solubility product, KOSrSO4,in water at 25 "C was calculated from the average of the measured solubilities in pure water using eq 1. Unfortunately, the activity coefficient of SrS04 in its pure saturated solution is not known. Therefore, we substituted the value (0.7636) of ya(CaSO4) at the same ionic strengthlo for y+(SrS04). This substitution should introduce an uncertainty of less than 2% in the subsequent calculations of y+(SrS04) because, at the ionic strength of the pure saturated solution, the maximum range in the activity coefficients of the seven divalent sulfates listed by Pitzer and MayorgalO is only 2%. Hence K0sr~o4 = (0.7636)2(6.443X 104)2 = 2.421 X lom7 (3) The activity coefficient of SrS04in each of the solutions of high ionic strength (Table 11) was calculated from eq 1 and 3 and from the concentrations of strontium and sulfate in the saturated solutions. The synthetic seawaters in Table I1 differ only in their ratio of calcium to magnesium; the sum of the calcium and magnesium concentrations was held constant at the value for natural seawater. Seawater-2 has the normal calcium and magnesium concentrations. The solubility of SrS04is so small that no attempt was made to hold the ionic strength and sulfate concentration of the synthetic seawater at their initial values. Theoretical calculations, using the equations of Pitzer and Kim: show that y+(SrS04)in our seawaters is within 0.1% of its value in natural seawater at the same ionic strength. Calcium Sulfate. Our values for the solubility of CaS04.2H20in pure water at 25 "C (15.24 mm) and at 0.5 "C (12.85 mm) are in good agreement with the measurements of Yeatts and Marshallll (15.23 mm, 25 "C), Briggs and Lilley12 (15.18 mm, 25 "C), and Marshall and Slusher13 (12.8 mm, 0.5 "C). At Na2S04concentrations between 0.25 and 1.69 m, solubilities interpolated from our measurements in Na2S04average 0.2 % larger that those reported by Briggs and Lilley.12 The solubility of CaSO4.2Hz0 in natural seawater is 0.0214 m14 at 25 "C and 35%0salinity. Saturating natural seawater with CaSO4.2Hz0increases the ionic strength by 12%, the concentration of alkaline earths by 32%, and the sulfate concentration by 73%. The changes in composition that occur on saturating seawater with gypsum mean that activity coefficients of CaS04 based on solubility measurements in natural seawater are not representative of their values in unaltered seawater. To eliminate changes in the ionic strength and in the sulfate concentration, we replaced some or all of the magnesium in our synthetic seawaters with calcium while keeping the total alkaline earth concentration (Mg2++ Ca2+) constant. Gilbert and Gilpin15 performed an experiment similar to ours at 20 "C. They measured the solubility of gypsum in natural seawater in which Mg2+was replaced by Ca2+ by adding calcium oxide to the seawater: CaO(s) Mg2+ H 2 0 = Mg(OH),(s) + Ca2+ (4) They do not give the salinity of their seawater, but the Mg2+, Ca2+, and S042- concentrations of their initial
+
+
C. H. Culberson, G.Latham, and R. G.Bates
seawater correspond to a salinity of 34.9 f O . ~ % O . Their value for the solubility should be comparable to ours because the solubility of gypsum in seawater changes less than 2% over the temperature range 18-30 OC,lpl' Their measured solubility, in seawater similar in composition to our synthetic seawater, is 1.2% lower than our value. The thermodynamic solubility products of gypsum a t 0.5 and 25 "C were calculated from the measured solubility in pure water by eq 2. A t 25 "C, the osmotic and activity coefficients in the saturated solution were calculated from the parameters in Pitzer and Mayorga.lo The activity and osmotic coefficients at 0.5 "C were calculated from the freezing point measurements of Brown and Prue18 using the equations of Pitzer and Mayorga.lo Thus, for CaS04 25 "C K0caso4= (0.3304)2(0.015237)2(0.9996)2= 2.532 X (5) 0.5 "C KOcasO, = (0.3634)2(0.012850)2(0.9997)2 = 2.179 X (6) The activity coefficient of CaS04 in the synthetic seawaters (Table 111) was calculated from eq 2 using the values of KOcdol from eq 5 or 6 and the measured calcium and sulfate concentrations a t saturation. The activity of water in the synthetic seawaters was calculated from the isopiestic measurements of Robinson4 and the freezing point data of Doherty and Kester.lg Calculations using the specific interaction model2 showed that replacing magnesium by calcium in seawater would change the water activity by less than 0.01%. The major source of error in activity coefficients calculated from eq 2 is the value of y+(CaS04)in the pure saturated solution. The activity coefficient of CaS04 in its saturated solution calculated from the data of Pitzer and Mayorga'O is 2.3% lower than the value measured by Lilley and Briggs.20 Activity coefficients calculated from eq 2 are directly proportional to the assumed value of ya(CaS04) in the pure saturated solution. Therefore, the uncertainty in the pure water value of y+(CaS04)means that activity coefficients calculated from eq 2 using Lilley and Briggs'20data will be 2.3% larger than the values we report in Table 111.
Theoretical Calculations In this section we use the theories of Reilly, Wood, and Robinson1 (eq A-9), Whitfield* (eq 6), and Pitzer and Kim3 (eq 15) to calculate the activity coefficients of NaC1, HC1, Na2S04,CaS04, and SrS04 in mixed electrolytes at the ionic strength of seawater. The equations of Reilly et a1.l and Pitzer and Kim3 are complex, and the reader is referred to the original papers for the actual equations used to calculate the activity coefficients. The theoretical models require the activity and osmotic coefficients of salts in their pure solutions at the ionic strength of the mixture. Previous calculations2,21,22 used pure solution data from several sources.10~23-25 To be internally consistent, we have used the same pure solution data10~26~26 in all of our calculations. The activity coefficient of SrC12 in its pure solution was calculated from the osmotic coefficients of pure SrC1,27using eq 2 and 3 in the paper of Pitzer and Mayorga.26 The values of the parameters in these equations are PoSrCl = 0.2918, P1srcl 1.5603, C'SrCl = -0.00446. In the theoretical calculations for y*(SrSO4) and ya(CaS04)we have included the concentrations of Br- and F- along with that of C1-. Whitfield. The interaction coefficients required in the specific interaction model were calculated from eq 6 in
Solubility and Activity Coefficients of Salts in Synthetic Seawater
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978 2697
TABLE IV: Measured and Calculated Values of Mean Molal Ionic Activity Coefficients in Synthetic Seawater and Single Salt Solutions at 25 O C and Ionic Strength 0 . I a
salt
technique
NaCl
electrodes
ionic strength
activity coefficient meas
s p . I.
Pitzer
RWR
comments/ref
-
0.718 0.695 0.723 0.673 0.718 0.723 0.723 0.725
0.672 0.664 0.667 0.665 ref 5 0.668 ref 6 HCl electrodes 0.627 0.684 0.712 0.688 ref 8 , seawater 0.729 0.719 0.730 0.726 ref 8 , sulfate-free seawater Na,SO, electrodes 0.385 0.37 1 0.369 0.370 ref 7 CaSO, solubility 0.1360 0.1556 0.1588 0.1587 (Ca'-) = 48.52 mrn 0.1373 (at 0.5 "C) 41.21 SrSO, solubility 0.1404 0.1519 0.1538 0.1523 (CaZ-)= 0.00 m m 0.1400 10.76 0.1389 27.95 0.1390 44.97 0.713 0.1524 0.1604 0.1743 0.1628 0.700 NaCl 0.714 0.1438 0.1537 0.1588 0.1487 0.700 KCI 0.715 0.1315 0.1494 0.1331 0.1384 0.2333 MgCI, 0.717 0.1193 0.2333 CaCl, 0.728 0.1568 ref 37, 35.2°/00salinity, 2 "C a The columns labeled Sp. I., Pitzer, and RWR are the values calculated from the equations given by Whitfield,2 Pitzer and Kim,3 and Reilly et al.' The activity and osmotic coefficients of pure solutions required in the equations of Whitfield' and Reilly et all were calculated from the equations of Pitzer and M a y ~ r g a 'and ~ ? ~Pitzer ~ et aLZ6
rectly predict yk(HC1) in the absence of sulfate (Table IV), but with sulfate present they yield values which are intermediate between the measured values in seawater with and without sulfate. This discrepancy is undoubtedly due to HS04-formation since 26% of the hydrogen ions in seawater are associated with sulfate.8 The value of y*(HCl) in seawater is 16% less than its value in the sodium/ potassium/magnesium/calcium chloride solution. The b0,2(1/2)+ b0,3(12/3) g M N x = b0,l equations of Reilly et a1.l and Whitfield2 seem to underestimate the effect of ion association on r+(HCl). Pitzer where bo,l, and bo,3can be calculated from Scatchard's et al.'sZ6equations explicitly exclude the effects of HS04and neutral electrolyte equations.'' The values of bo,l, formation, and their model predicts a value for y*(HCl) used in our calculations are listed in Table VI (supin seawater that is close to its value in sulfate-free seawater. plementary material). Interaction parameters involving The values of y*(Na2S04) in seawater reported by calcium or strontium and sulfate have not been measured Platford and Dafoe7 are based on activity coefficients of because the low solubilities of CaS04-2Hz0and SrS04 pure NazS0:8r39 which are about 2% smaller than recent preclude measurements over a range of calcium or value^.^^^^^ Recent theoretical calculations of y*(NazS04) strontium concentrations if constant ionic strength is in seawater2J1 are based on activity coefficients of pure maintained. Where possible, we have substituted the NaZSO4from Robinson and Stokes.23 From the comMg/S04 parameters for those of Ca/S04 and Sr/S04. parison of Platford and Dafoe's7 original results with Pitzer and Kim. The interaction parameters, 0 and $, theoretical calculations,2121it has been felt that there was required in Pitzer and Kim's3 equations were taken from agreement the measured and calculated their paper and from more recent ~ o r k . Values ~ ~ ~ ~excellent ~ ~ ~ ~ - ~between ~ values. In fact, the measured values are 4% larger than of 0 and $ taken from sources other than Pitzer and Kim3 the calculated values when they are referred to the same are listed in Table VI1 (supplementary material), which pure solution data (Table IV). All three models yield also lists our assumptions about the value of parameters almost identical results for yk(NazS04) in seawater. for which experimental data are not available. The calPlatford and Dafoe7 quote a relative standard deviation culated activity coefficients are compared to the measured of f4.3% for y+(Na2S04).Thus, the difference between values in Table IV. the calculated and measured values, although larger than Discussion previously thought, is probably not significant at the 95% Measured and calculated values of activity coefficients confidence level. in synthetic seawater and in single salt solutions at ionic An additional uncertainty in Platford and Dafoe's7 strength 0.7 are listed in Table IV. This table includes measurements is due to the unknown solubility of PbS04 experimental data from the literature in addition to our in seawater. Calculations of lead speciationN suggest that solubility measurements. the solubility of lead sulfate in seawater at pH 5 and 25 The measured and calculated values of the mean ionic "C is approximately 0.6 X low3m. At higher pH the activity coefficient of NaCl are in excellent agreement. solubility would be larger. Platford and Dafoe7 did not This agreement might be expected because, as a first consider the effect of PbS04 solubility on the concentration approximation, seawater can be considered a slightly of sulfate in their calculations. An increase of 0.6 X low3 perturbed NaCl solution. Platford5 showed that y*(NaCl) m in the sulfate concentration would cause their calculated in seawater is only 1.2% larger than its value in pure NaCl values of y*(NaS04) to be 0.7% too large. at ionic strength 0.72. The measured activity coefficient of SrS04 in calcium The activity coefficients of HCl calculated from the free synthetic seawater is compared with theoretical equations of Reilly et a1.l and Whitfield2 are about 10% calculations in Table IV. In making this comparison, it larger than the measured value. These two models corwas necessary to assume that the interaction parameters Whitfield.z The interaction coefficients for Ca/S04 and Sr/S04 at an ionic strength of 0.7 cannot be calculated due to the low solubilities of CaS04.2Hz0 and SrS04. In our calculations, we have substituted the Mg/S04 interaction coefficient for those of Ca/S04 and &/SO4. Reilly, Wood, and Robinson. The interaction parameters, gMNX, in eq A-9 in ref 1 are defined as28
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The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
TABLE V: Activity Coefficients of Alkaline Earth Sulfates in NaCl at Ionic Strength 0.72 m and 25 Ca NaCl molality salt 0.5695 0.7200 comments/ref MgSO, 0.140 0.144 ref 4 3 0.141 0.142 ref 44 CaSO, 0.136 (0.139) ref 13 at 25 "C 0.5 "C, m(NaC1) = 0.5806, 0.137 I = 0.72 SrSO, 0.152 this work, I = 0.713 ref 42 0.139 ref 37 at 2 "C,I = 0.672 0.165 BaSO, 0.120 ref 45 0.134 ref 42 a The trace activity coefficient of CaSO, in 0.72 m NaCl was extrapolated using the average concentration dependence for MgSO,. Pure solution activity coefficients from Pitzer and Mayorga.'O
for strontium and sulfate were equal to the parameters for magnesium and sulfate. This assumption is unlikely to cause large errors in the calculated values for several reasons: (1) The interaction parameters are multiplied by the concentrations of strontium and sulfate which are low relative to the concentrations of sodium, magnesium, and chloride. (2) The activity coefficients of all divalent sulfates are nearly equal when compared at constant ionic strength (ref 10 and Table IV). (3) The association constants of MgS040 and C a s 0 2 (and presumably SrSO:) are nearly equal at ionic strength 0.7.41 (4) The measured value of y+(SrS04)changes only 1% when 45 mm magnesium is replaced by calcium in synthetic seawater (Table IV). The comparison in Table IV shows that the measured activity coefficient is about 9% lower than the calculated values. In this case, as for HC1, it seems that the mixed electrolyte theories underestimate the effects of ion association on mean ionic activity coefficients. To better understand the differences in the measured and calculated values for y*(SrS04)in synthetic seawater, the activity coefficient of strontium sulfate was measured in a series of single salt solutions at ionic strength 0.7 (Table IV). The results are easier to interpret in this case because strontium and sulfate are present in trace concentrations and the strontium/sulfate interaction has little effect on the value of yk(SrS04). The calculated activity coefficients are consistently larger than the measured values, although in certain cases (Pitzer for MgC12, Reilly for KC1) there is fair agreement. In addition, the differences between the theoretical models are more pronounced in single salt solutions than in seawater. Calcium sulfate is moderately soluble, and to keep the sulfate concentration at its seawater level it was necessary to increase the calcium concentration of the synthetic seawater. This was done by replacing most of the magnesium by an equivalent amount of calcium (Tables I, 111, and IV). The theoretical and measured values of y+ (CaS04) are compared in Table IV. In performing the calculations it was necessary to assume that the calcium/sulfate interaction parameters were equal to the magnesium/sulfate parameters. Because of the higher calcium concentrations this assumption is not as good as the corresponding assumption for SrS04. Nevertheless, the substitution of Mg/S04 parameters for Ca/S04 parameters should not cause serious errors in the calculated values of y*(CaSO4) for the same reasons given in the
C. H. Culberson, G. Latham, and R. G. Bates
discussion of y*(SrS04). The calculated values in Table IV are about 16% larger than the measured value, in agreement with the results for SrS04. There are three significant features of the above comparisons: (1)The calculated and measured values for yJNaC1) and y*(NazSO4)agree, even though sulfate ion (39% free) is extensively associated with the major cations in seawater.41 (2) The model of Pitzer et al.,26which explicitly includes the HSO, equilibria, correctly predicts the value of y* (HCl), while the equations of Reilly et al.,l and Whitfield,2 which implicity include HSO, formation through their use of H2S04pure solution data, do not predict correct values. (3) All three models predict values for y*(SrS04) and y*(CaS04) which are 8-17% too large. These differences are not simply due to the amount of ion pairing in solution. If the error in the calculations for HCI, CaS04, and SrS04 is due to ion association, then yh(Na2S04)should also be in error. This is not the case. The association constants at infinite dilution for the NaS04-, HS04-, and CaS040 ion pairs are as follows:22 PoNaSOa= 7; PoHso = 100; PoCaSOa = 200. The difference between the calculated and measured values of y+ seems to be related to the free energy of the ion association reaction. The models correctly predict yk(Na2S04),for which the energy of association is small, whereas they are in error for HCl, CaS04, and SrS04which form stronger complexes with sulfate. Only in the case of HC1, for which the equations of Pitzer et aLZ6explicity recognize the HSO, equilibria, is there agreement between measurement and theory. Due to the lack of Ca/S04, Sr/S04, and Ba/S04 interaction parameters it is difficult to predict trends in the activity coefficients of the alkaline earth sulfates at constant ionic strength. In Table V, we have collected data on the activity coefficients of the alkaline earth sulfates at an ionic strength 0.72 in NaC1. The experimental data for SrS04and BaS04 are scattered, but there is no obvious trend in the measured activity coefficients at infinite dilution in 0.72 m NaC1. Our value for y+(SrS04)in NaCl is 9% larger than that calculated from the data of Davis and Collins42and is 8% smaller than North's3' value at 2 "C. The data for CaS04in Table IV suggest that the effect of temperature on yk(SrS04) is small. Our value for y*(SrS04)in NaCl is 9% larger than our measured value in seawater. This is consistent with the theoretical models which predict that y+(SrS04)is 6-13% larger in NaCl than in seawater. Acknowledgment. This research was supported by NSF Grant OCE76-24384 and by ONR contract N00014-77C-0290. We thank J. B. Macaskill and K. H. Khoo for use of their unpublished data and calculations. Supplementary Material Available: Table VI containing values of the interaction parameters in eq 7 for use with the equations of ref 1 and Table VI1 containing the values of the interaction parameters in the equations of ref 3 (2 pages). Ordering information is available on any current masthead page. References and Notes (1) P. J. Reilly, R. H. Wood, and R. A. Robinson, J . Phys. Chem., 75, 1305 (1971). (2) M. Whitfield, Deep-sea Res., 21, 57 (1974). (3) K . S. Pitzer and J. J. Kim, J . Am. Chem. Soc., 96, 5701 (1974). (4) R. A. Robinson, J. Mar. Biol. Assoc. U . K., 35, 449 (1954). (5) R. F. Platford, J. Mar. Res., 23, 55 (1965). (6) J. M. T. M. Gieskes, Z . Phys. Chem. (FrankfurtamMain),50, 78 (1966).
Determination of Hydration Number of an Electrolyte (7) R. F. Platford and T. Dafoe, J . Mar. Res., 23, 63 (1965). (8) K. H. Khoo, R. W. Ramette, C. H. Culberson, and R. G. Bates, Anal. Chem., 49, 29 (1977). (9) J. R. Campbell and G. H. Nancollas, J. Pbys. Chem., 73, 1735 (1969). (10) K. S. Pitzer and G. Mayorga, J . Solution Chem., 3, 539 (1974). (1 1) L. 8. Yeatts and W. L. Marshall, J. Chem. Erg. Data, 17, 163 (1972). (12) C. C. Briggs and T. H. Lilley, unpublished work. (13) W. L. Marshall and R. Slusher, J . Pbys. Chem., 70, 4015 (1966). (14) B. Elgquist and M. Wedborg, Mar. Chem., 3, 215 (1975). (15) F. C. Gilbert and W. C. Gilpin, J. Soc. Chem. Ind., 65, 111 (1946). (16) A. Manuelli, Ann. Chim. Appl., 5, 13 (1916). (17) E. Posnjak, Am. J . Sci., 238, 559 (1940). London, Ser. A , 232, (18) P. G. M. Brown and J. E. Prue, Proc. R. SOC. 320 (1955). (19) B. T. Doherty and D. R. Kester, J. Mar. Res., 32, 285 (1974). (20) T. H. Lilley and C. C. Briggs, Proc. R. SOC.London, Ser. A , 349, 355 (1976). (211 R. A. Robinson and R. H. Wood. J. Solution Chem.. 1. 481 (1972). (22j M. Whitfield, ”Chemical Oceanography”, Vol. 1, 2nd ed, Academic Press, London, 1975, Chapter 2. (23) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions”, Butterworths, London, 1968. (24) K. S. Pitzer, J . Chem. SOC.,Faraday Trans., 68, 101 (1972). (25) K. S. Pitzer and G . Mayorga, J . Phys. Chem., 77, 2300 (1973). (26) K. S.Pitzer, R. N. Roy, and L. F. Silvester, J. Am. Chem. Sac., 99, 4930 (1977). (27) C. J. Downes, J. Chem. Thermodyn., 6, 317 (1974). (28) W. W. Watson, R. H. Wood, and F. J. Millero, ACS Symp. Ser., No. 18, chapter 6 (1975). (29) Y. C. Wu, R. M. Rush, and G. Scatchard, J. Phys. Chem., 72, 4048 (1968).
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(30) C. J. Downes and K. S. Pitzer, J . Solution Cbem., 5, 389 (1976). (31) J. Padova and D. Saad, J. Solution Chem., 8, 57 (1977). (32) K. H. Khoo, C-Y. Chan, and T. K. Lim, J. Solution Chem., 6, 651 (1977). (33) K. H. Khoo, C-Y. Chan, and T. K. Lim, J . Solution Chem., 6, 855 (1977). (34) J. B. Macaskill, D. R. White, R. A. Robinson, and R. G. Bates, J. Solution Chem., in press. (35) S.Z. Lewin and J. E. Vance, J . Am. Chem. Soc., 74, 1433 (1952). (36) S.Tsunogai, M. Nishirnura, and S.Nakaya, Talanta, 15, 385 (1968). (37) N. A. North, Geochim. Cosmochim. Acta, 38, 1075 (1974). (38) H. S.Harned and J. C. Hecker, J. Am. Chem. Soc., 56, 650 (1934). (39) R. A. Robinson, J. M. Wilson, and R. H. Stokes, J. Am. Chem. Soc., 63, 1011 (1941). (40) A. Zirino and S. Yamarnoto, Limnol. Oceanogr., 17, 661 (1972). (41) D. R. Kester and R. M. Pytkowicz, Limnol. Oceanogr., 14,686 (1969). (42) J. W. Davis and A. G. Collins, Envlron. Sci. Techno/.,5, 1039 (1971). (43) Y. C. Wu, R. M. Rush, and G. Scatchard, J. Phys. Chem., 73, 2047 (1969). (44) R . F. Platford, Can. J. Chem., 45, 821 (1967). (45) C. C. Ternpleton, J. Chem. Eng. Data, 5, 514 (1960). (46) J. B. Macaskill, R. A. Robinson, and R. G. Bates, J. Solution Chem., 6, 385 (1977). (47) R. M. Rush and R. A. Robinson, J. Tenn. Acad. Sci., 43, 22 (1968). (46) R. A. Robinson and V. E. Bower, J . Res. Natl. Bur. Stand., Sect. A , 70, 313 (1966). (49) R. A. Robinson and A. K. Covlngton, J. Res. Natl. Bur. Stand., Sect. A , 72, 239 (1968). (50) C. J. Downes, J. Solution Chem., 4, 191 (1975). (51) R. A. Robinson, R. F. Platford, and C. W. Childs, J. Solution Chem., 1, 167 (1972).
Determination of Hydration Number of an Electrolyte by Vapor Pressure Measurements Chai-fu Pan Department of Chemistry, Alabama State University, Montgomery, Alabama 36 10 1 (Received January 6, 1978; Revised Manuscript Received June 28, 1978) Publication costs assisted by Alabama State University
By using the Stokes-Robinson model of hydration with mathematical derivations, it can be shown that the limiting value of the ratio of the measured vapor pressure of an electrolyte solution to the calculated vapor pressure of an “ideal Debye-Huckel solution” equals the ratio of the mole fraction of water if the hydration effect is considered to the mole fraction of water if hydration is ignored. A hydration number for the electrolyte is thus obtained.
Introduction The thermodynamic properties of electrolyte solutions are determined by several physical factors which are believed inseparable. From the activity coefficient point of view, Stokes and Robinson’s theory1 was important. They proposed a model for electrolyte solutions up to a few molal in concentration in which the Debye-Huckel treatment of interionic interactions was combined with the idea that the solute species in solution are hydrated ions. However, the hydration number h in their parameter equations has lost its original meaning. In fact, the hydration numbers of individual ions or electrolytes resulting from different measurements and interpretations of various properties of solutions are considerably different. Bockris and Reddy,2 Robinson and stoke^,^ as well as Hinton and ami^,^ have given detailed surveys of the results obtained by investigators using various concepts and methods. By using Stokes and Robinson’s concept of hydration,l the hydration number of an electrolyte can be derived from the experimental vapor pressure data. The detailed procedure is presented in this communication. 0022-3654/78/2082-2699$0 1.OO/O
Derivation and Application For a nonassociative dilute aqueous electrolyte solution, the measured vapor pressure of the solution usually deviates from that of the “ideal Debye-Huckel solution”. According to Stokes and Robinson’s idea,l this is primarily due to the hydration of the ions. The so-called “ideal Debye-Huckel solution” is just a hypothetical solution which may be defined in this way: “It is an electrolyte solution which deviates from an ideal solution only because of the interionic interactions. It follows the Debye-Huckel law exactly.” The Debye-Huckel law may be expressed by the following equation5
in which fk,DH is the mean rational activity coefficient calculated from the Debye-Huckel equation, m is the molality of the solution, and K1 and K2 are constants. For aqueous solutions a t 25 “C,for 1:l electrolytes, K1 = -1.17604, K2 = 0.3286186, and for 2:l electrolytes, K1 = 0 1978 American Chemical Society
