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Celestite (SrSO4(s)) solubility in water, seawater and NaCl solution
Gnxhimiad
C~ia
0016.7037/87/$3.00 + .oo
Adn Vol. 51. pi. 63-12
0papmonJaMllrLtd.1987.Rimcdinu.s.A.
Celestite (SrsO,)
solubility in water, seawater and NaCl solution E. J.
REARDON
and D. K. ARMSTRONG
Department of Earth Sciences, University of Waterloo, Waterloo, Ontario N2L 3G 1, Canada (Received May 5, 1986; accepted in revisedform September 26, 1986) Abstmct-Celestite solubility measurements have been conducted in pure water to 90°C. Equilibrium was achieved with respect to a crysmlhne solid phase from supersaturated solutions. The measurements show that the solubiity undergoes Log K values for the solubility reaction are adequately described by the following perature range 283.15 to 363.15 R -log K= -35.3106+0.00422837T+318312/T2+
at temperatures from 10 both undersaturated and a maximum near 20°C. expression over the tem-
14.99586 log T.
The following thermodynamic values for the dissolution reaction of SrSOqsj at 25’C have been derived: AGP = 37852 f 30 J mol-’ Ma = - 1668 f 920 J mol-’ &a=-132.6+3.2JK-‘mol-I. C&stite solubility measurements were also determined in NaCl solutions up to 5 m concentration and from 10 to 40°C. These data are in good agreement with the work of STRUBEL (1966), who reports solubility measurements to temperatures of IOO’C. The application of the Pitmr relations and the solubility constants determined in this study to calculate cekstite sohmility in Nail solutions yields excellent agreement between predicted values and experimental measurements over the entire range of temperature and NaCl concentration conditions. For the limited number of solubiiity m eesunmentri in seawater-type solutions and mixed-salt brines, the agreement using the Pitxer relations is witbin three percent of the measured solubiity. INTRODUCIlON
in this tabulation, STRUBEL( 1966), also reports data on celestite solubiiity to temperatures of 350°C. SrSO~NaCI-Hz0 system. The publishaI data on akstite solubility in NaCl solutions are leas extensive than in pure water. The available data are tabulated in Table 2. STRflBEL ( 1966) is the only worker who mported extensive alestite solubility data at temperatures other than 25°C. From an inspection of the reported solubihties in both pure water and NaCl solution, it can be seen that there is a wide variability in results at any particular temperature. At least two principal factors may account for this rather Large dis cordancy in solubility data. The tirst mlates to the welldocumented effect of particle sixe on celeatite sohrbility. This e&t has been extensively studied by ENUSTUNand TURKEVICH ( 1960), who in a series of aiestite solubility experiments with materialofvaryingsixedistribmionsshowedthatthesmalkstsized particks present appeamd to control the solubility. They reported the following expression which relates the observed solubiity enhancement to the minimum particle size present:
THE PROPERTIES OF celestite that have rendered it a highly suitable substance for studying the process of ptipitation are also the properties that account for the rather large disparity in reported solubilities for this material. Such properties include the long term stability of its supersaturated solutions (CAMPBFLL and Coorc, 1935); the propensity for surface poisoning effects (CAMPBELLand NANCOLLAS,1969); and the functional control on solubility by particle sixe, (ENOsToN and TURKEVICH,1960). Many of the earlier studies on celestite solubility did not thoroughly address these problems and so have not tinnly demonstrated the attainment of final equilibrium. In this study, we have tried to pay close attention to these potential problems and have demonstrated through approach to saturation from both supersaturated and undersaturated solutions, the attainment of equilibrium with respecttoauystaUinesolidphase.Wepresenttheresults of solubility experiments both in pure water and Nail solution and apply both the ion pairing and the Pitzer model to describe specilk ion interactions in solution.
PREVIOUS
log a/a,, = 1.61.~
(1)
whacaistbeobsavedactivityofthe~lidphasc;~ispctivity for the pure solid in macroQystauine form; and x is the minimum particle sixe in nanometers, For a sohmility experiment to reflect the actual &hility of wne c&&e, it would be necesmry to ensure that a/a,, does not exceed that value which could arise from analytical uncertainties alone. For example, if a water were satmati with respect to macroq3tallinecelestitebuttherewasa+ 1%combinedanalytical error in strontium and sulpham a conesponding a/p0 ratio of 1.01 would reauit. Using this value in Eqn. (1) reveals that acompambleenhancementinthesolubiJitywouldoccurif m0teriolwerepnrentwhoreparticlesizewrrsO.3~morlas. Asecondfhctorwhichmayaccountforthelargediq&ty in publiskl solubiiity data for alestitc rdates tothesuscep tibilityofthi8mat<osurhcepoisoning.Thi.%e&ctcan essentially shut down the approach to saturation from both
WORK
SrSOwH# system. The published data on ales&e solubilityat 1 barprwtmretotemperammsoflOO°Caremcorded inTable 1.Thebulkofthestudieareportsolubihtydataata single temperature, generally 25°C. but several of the studies (KOHLRAUSCH,1908; GALLQ 1935; and STRUBEL,1966) report data at a number of temperaturea. Although not shown 63
64
E. J. Reardon and D. K. Armstrong Table data
1. in
Published pure
Author
celestlte
water
at
Temperature
various
solubility temperatures. Solubility
(uoles/KK
f-c)
OfIll0 (1935)
5 10 20 30 40 50 80 70 80 90 95
0.859 0.702 0.719 0.751 0.773 0.746 0.724 0.686 0.646 0.648 0.837
Kohlraurch (1909)
2.95 11.4 32.3
0.617 0.823 0.826
strilbe1 (1988)
22 30.5 50.0 75.5 95.5 100.5
0.821 0.817 0.598 0.492 0.404 0.361
Dwia and Collins (1971)
25
0.821
Salivanova and Zubova (1958)
25
0.762
YUller
25
0.892
2
0.829
(1985)
20
0.119
Cupbell and Cook (1935)
30
0.897
Belfiori
20
0.821
26
0.822
Campbell and 25 N~~oollna (lSS9)
0.848
(1960)
North (1974) LIe8er
(1940)
Harden (1916)
Culberron et al.(lWL))
25
the experiments. When double-distilled water was used in its place, all inhibitory effects on dissolution and precipitation were removed.
Ii.01
0.844 i 0.001 over 22 ropllceter
EXPERIMENTAL Previous studies of celestite solubihty used either crushed natural material or material synthesized by reaction of a sulfate salt, usually Na2S0, and a strontium salt, usually SrQ. In this study, to ensure as pure a solid phase as possible, celestite crystals were synthesized by titrating 10 I of a 0.003 molal H2S0, solution with a strontium hydroxide solution to a pH of 5.7. The strontium hydroxide solution was filtered through a 0.2 pm filter as it was added to the sulphuric acid solution. This was done to remove particulate SrCOws~which immediately forms upon preparation of a strontium hydroxide solution. The concentration of HrSO, used was selected so as to be between the minimum molal concentration of SrSO, in solution that results in spontaneous nucleation, 0.00 12 molal (CAMPBELL and COOK, 1935) and the minimum molal concentration that results in the rapid mce of a precipitate, 0.015 molal (ENUSION and TURKEVICH, 1960). All reactant
and equilibrating solutions used in this study were prepared using distilled de-ionixed water with a mewred conductance of cl.8 fi cm-‘. AAer titration with Sr(OHk, the solution was stored for three days whereupon the solid phase was recovered and repeatedly washed with saturated SrSO, solution to remove fines. After a final rinse in reagent-grade acetone
Table 2. Published solutioa at various NaCl are expressad SrSO. are expressed Striibel
(1966)
T’C/NaCl(s)
0.1006
0.5029
1.082
2.285
20 30 40 50 80 IO 80 90 Boiling
1.524 1.506 1.434 1.401 1.328 1.239 1.149 1.044 0.918
2.912 2.838 2.807 2.888 2.529 2.385 2.199 2.009 1.803
3.815 3.758 3.700 3.551 3.398 3.186 2.995 2.751 2.415
5.244 5.131 5.008 4.950 4.750 4.398 4.080 3.033 3.660
Miller
pt.
(1980)
arlwoaaofrtrmtium~ of4oto5o%.Thiaw8atbecaeeevellmadutknuwbelnoaly largepatideawerepmm~i.e.tbepamccofpmkkeixes leaathan1juncouklncabeokfved.lnoneexpe6ment.a
Gall0
25°C
(1935)
Sk-SO.
T-C
NaCl
srso.
0.429 0.859
2.89 4.01
20 9
1.901 1.901
3.56 3.90
1.716 2.575 3.432 4.291 5.148 8.178
5.79 6.60 1.64 8.SO 10.48 12.34
NaCl
Nid COOK(1935). ThCSCNtllDlSllO!A!dCOSUpkkSlldOWlOfcryrUniution
celestite solubllity data In NaCl teaperatures. Concentrations of in aolality and COnceatratiOns of In sillfaolslity.
~.
Culberson
arpmrtunriwTbacauboslat~ Davis
and
Collins
(1971)
NaCl
SPSO.
0.010 0.015 0.025 0.050 0.068 0.172 0.257 0.431 0.869 1.771
0.730 0.811 0.937 1.085 1.448 1.813 2.298 2.881 3.875 4.283
25°C
et
al.
(1978)
NaCl
SrSO.
0.700
3.23
25°C
65
c&stite so1ubility the material was dried under vacuum. Two batches of this material were produced during this study and no di&tence in their solubility behaviour was observed. The prepamd celestite was composed of crystal aggregates ranging in sixe from about IO to 50 pm. Individual particles ofthecompositecrystabwereontheotderof5to lOlrm(see Fii 1). Suspensions of the celestite always settled rapidly (less than five minutes) leaving a clear super&ant solution which indicated an absence of ultrafine submicron particles. In addition, analyses on un6hered and filtered (0.2 rem) aliquots of the supematant alter solutions visibly cleared revealed no differences in strontium concentration. Before the solubility experiments were conduc@ a test was performed to determine if surface poisoning effects would pose a problem to the approach to saturation from either supersaturated or undersaturated conditions. SrSOtisj crystals were added to an undersaturated solution of SrSO, (0.4 mihimolality) maintained at 250°C. The electrical conductance was then monitored over time. Once the conductance levelled off and it was believed that equilibration had been achieved, fresh seed crystab were added to the reaction vessel. No change in conductance was observed over a five-hour period. The solution was then spiked with a supematumted solution of !&SO, to produce a 40% supersaturated solution and again the conductance was monitored. The results of this experiment are shown in Fig. 2 and demonstrate the absence of any inhibitory effects to the approach to saturation. The return electrical conductance
lW.1.Photomkqmphsshowingclystalsixeandaggmgate appearance of the c&&e pmpared for the solubility experiments. Scale bars are 1 pm long.
220
SPIKE SrS04 ,’ SOLUTION ADDED h
FRESH
loo
0
CRYSTALS
I
I
20
40 TIME
I
I
I
I
60
aD
loo
120
(Ill
FIG. 2. Results of exnetiment to demonstrate absence of from both superband undemat&ed solution conditions. The plot illustmtes conductance changes with time upon dissolution to equilibrium and the return to equihbtium conditions upon addition of a spike supersaturated solution of Sr!I04.
reading recorded 50 h following addition of the spike solution was within 1% of the value recorded immediately before the addition. The reaction vessels used in the actual sohmility runs were 20 ml glass vials into which suthcient SrSoqs~ (generally 100 mg)wasadded16~~~atleastatactorofttnmonsolid material than would dierolve during the course of the experiments. To prevent reduction in partide sixe due to grind@ effects the solutions were not stirred during the reactions. In~thereactionvesselswemlashedtotheoutsideofaplastic rod, immetsed hotixontally in a water bath and heki in position by two rods athxed by needles to the centre points of each endofthecentralpIasticcore.TbeetIhtentI?omthecirculator pump was then dire&d towards this sample carousel. The force of the effluent was stdhcient to induce a rotational speed of from 10 to 20 RPM. This resulted in a gentle tumbling action to the precipitate within each reaction vessel during the equilibration period. Solid phase equilibration was approached horn both undersaturated solutions and supersaturated solutions to demonstrate reproducibihty of the solubility measurements and to verify attainment of equilibrium. This was achieved by repeating solubiity measurements at a number of temperatures; once as the temperature was progmsively increased (approach to equilibrium by precipitation) and again, as the temperature was pmgmssively decmased (approach to equilibrium by dissolution). Strontium analyses were performed on acidified samples using a Varian@ Model 1475 Atomic Absorption Spectrophotometer. In order to suppress interferences and ionization in the air-acetylene flame, 2% by weight LaCl, and 2% KNO, were added to all samples, standards and blanks. Despite this precaution, there was still a small but significant suppression in the strontium signal due to the presence of sodium ion for samples from the celeatite solubihty runs in NaCl solution. ThiswascorrecMforbypreparingstandardsattheapproptiate Nail concentrations as the sample soh&ms. Strontium analyses could be reproduced for all solution compositions to better than I %. Sulphate was determined on selected samples from the NaCl solution runs using a Dionex@ Auto Ion Model 12 ion chromatograph. Analytical uncertainties are much
E. J. Reardon and D. IL Armstrong
66
where “m” refers to molal concentrations.
pKSrS0.'
PKs5rso,(S)
0.813 O.Sl3
2.211 2.212
5.531 * 6.529 "
0.540
o.soo
2.255
5.522 "
Km: refers to the dissociation constant of the SrSO~ ion pair. Values of this constant in pK form at each temperature are recorded in column four (Table 3) and were taken from the work of &ARJ3ON (1983) who determined the temperature dependence of K-z from 10 to 60°C. Activity coefficients for Srr+ and SO:- were calculated using the Deybe-Huckel equation, The mean molal activity coefficient for SrSO, is recorded in column three (Table 3). We used a value of unity for $!jrSO~, but it makes no difference to the calculated solubility product if any of the available equations describing a functional dependency with ionic strength are used. The calculated solubility products that are recorded in Table 3 above a temperature of 60°C are somewhat in doubt because Ksrso~ values used tn the calculations were obtained by extrapolating the data of REARDON (1983) above this temperature. A limited number of runs were made to determine the effect of NaCl on the solubility of celestite at various temperatures. These data which cover a range of NaCl concentrations from 0.05 to 5.0 molal and temperatures from 10 to 40°C are recorded in Table 4. These data are not amenable to an ion pairing model treatment to calculate solubility products because of the uncertainties in the calculated activity coefficients using the Deybe-Huckel equation at high ionic strengths. Instead, we applied the Pitzer relations to determine activity coefficients, the results of which ate presented later in this paper. The results presented in Table 4 indicate a reversal in the solubility of celestite between 2.0 and 5.0 molal NaCl. To document this reversal and to determine better at what concentration it occurs, we performed a series of more detailed solubility measurements at 25°C after the first set of data were collected. These were performed on a second prepared batch of celestite at NaCl concentrations from 2.0 to 4.2 molal These additional experimental results are recorded in Table 4.
0.541 0.543
0.509 0.500
2.292 2.290
5.534 s 5.532 u
DISCUSSION
29.5
0.531
0.509
2.314
6.550 u
40.0 39.3
0.555 0.507
0.510 O.SlO
2.353 2.350
5.559 s 5.557 "
40.5 49.5
0.555 0.574
0.510 0.511
2.405 2.407
5.724 e 5.735 "
50.0 30.5
0.534 0.531
0.513 0.514
2.450 2.440
5.500. 5.504 "
76.5
0.475
0.515
2.511
6.593 "
59.3
0.402
0.524
2.550
7.035 "
gmaterfortheanalysisofsulphatethan forstromium(wmpare *5?6 VS.fO.S%). However, the sulfate analyses served as a check that substantial substitution of Cl- for eand Na+ for S? in the solid phase did not occur during the equilibrati0Il.X A2 a further check that the solid phase in contact with the NaCl solutions showed little or no solid substitution, all solid phases were mcovered at the end of the experiments and analysed for their sodium content. For this analysis the material was repeatedly washed id a sodium-free saturated solution of MO, and then dried under vacuum. Samples of the solid phase were dissolved in 0.14 m HCl and analysed for sodium by AA. Sodium concentrations were below detection for all samples indicating sodium contents of the c&stites at less than 0.1%.
RESULTS The TcsuI1s of the celestite solubility measurements indisUd&ionizedwateratvarioustempemtumsare recorded in Table 3. The negative logarithms of the solubility product of celestite QX-3 are shown in the last column. These were calculated using an ion pairing model. The relevant equations that were iteratively solved to a constant ionic stmngth in order to calculate p& were simply:
mS12+= mSrror - mSrS(X mS60! = &&y~~(mSti+mSOi-
(2) - TS~~+YSO:~ (3)
msof- = m!P+
(4)
C5155t1t5 S5tcb *1. PC
S?SO. rolsdKSIl.0
10.3 10.4
0.533 0.531
20.2 25.4 25.0
1 f srS0.
Ce1mtits SW&l 82 39.3
0.510
0.509
2.350
5.554 "
40.5
0.577
0.511
2.407
5.734 "
50.5
0.535
0.513
2.4.9
a.797 "
73.5
0.472
0.517
2.511
5.809 "
89.3
0.410
0.522
2.355
,.02l "
Figure 3 presents the published data on celestite solubility in pure water along with the results of this study as a function of temperature. Our results are in Rood agreement with those of KOHLIUU~CH ( 1908), STROBEL (1966), CAMPBELLand NANCOLLA~(1969) and CULBER~~Nei al. (1978) at temperatures near 25°C. Over the entire temperature range our data are in very close agreement with those of STROBEL (1966). Our data are not in agreement with those of h&RUEN (19 16), GALLO ( 1935), and SELIVANOVA and ZUBOVA (1956). These data are all at higher concentration and it is possible that either surface poisoning effects, or particle size effects were contributory to the enhancement in so1ubility observed in their Studies. The calculated solubility products for o&Mite determined in this study are plotted as a function Oftemperature in Fii. 4. The data were fitted through regreS_ sion analysis to an equation of the form:
67
cdestite 201ubiiity
Cela~tltc 2atcb
21
NaCl
(aolality)
TW
0.0501
0.2020
0.4793
1.074
4.977
10.3 20.2 25.4 25.0 29.8 40.0
1.10 1.18 1.17 x.14 1.17 1.12
1.84 1.81 x.80 1.86 1.87 1.84
2.62 2.74 2.69 2.m 2.06 2.65
4.62 4.77 4.60 4.62 1.5s 4.4s
4.50 4.87 4.5s 4.4a 4.32 4.41
6.55 T”pewlturL
- 25.1-c
NRC1
WSO. (BIlllDalallty)
mcllalityl
t 6.401 0
1.981 2.397 2.640 3.076 3.538 4.184
4.71 4.90 4.95 4.92 4.89 4.68
l~K=a+~T+cfT’~dl~
0.7
I
T+e/T
(5)
t
o.s
is ;i o,4
+
0.3 0
the temperature range of the experiments, 10 to 90°C. The four term and five term expressions are: -log J&o, =-35.3106+0.00422837T+318312/T2 + 14.99586 log T
(6)
-log Ks,sc,, I=14805.9622 + 2.46609241” + 40553604f T2 - 5436.3588 log T - 756968.533/~
srs0ys,+
$
(7)
0 0
0 Q
0
0 0
20
40
OO
3
GALL0 fi935) CAMPMLL a alix tle3sl ~ECFIORI f 1940) S&LWANOVA 4 ZWOVA flSS6t MULLER lt9601 LIES R (1969) STR 5; EL (I9661 CAMPBELL 6 NANCOCLAS (I9691 WRTH (1974) CUL&iRSON .I d. (1976) DAVIS 6 COLLINS (19711 THIS ,SYUDY , I
60
sr2+
+ so24-
(8)
we obtain the following values at 298 K, AG: = 37852 -+ 30 J mol-‘; AH$ = -1668 + 920 J mol-‘; and AS% = -132.6 it 3.2 J K-r mol-‘. The uncertainties attached to these values are based on an assumed total analytical uncertainty in log K at temperatures near 25°C on the order of 0.005 log K units.
a XO
a K0ilLRWSCH wD61 @ MARDEWt1916) 0 _ 0 * X 0 6 _ A 0 m 0 0
-1 100
where T is expressed in Kelvin. Using l&r. (7) and its derivative to calculate the~~~arni~ properties for the reaction:
0
” E
I 60
FIG. 4. Calculated pK values for the solubility of celcstite determined in this study versus temperature; (+) equilibria approached fkom supersatumtion; (0) equilibria approached from undersaturation. Solid curve represents values determined from Eqn. (7).
0.9
-2
I 60
I 40
T OC
which is derived from a formulation to express fke energy data to high temperatures presented by HAAS and FISHER (1976). Consideration of only the first four terms of this expression yields a less cumbersome expression requiring only single precision calculations. Omission of the 6fI.h term, however, yields a somewhat inferior reproduction of the data at temperatures near 25°C. The maximum difkence between tire two expressions, however, is only 0.007 log K units over
0.6
I 20
AP~~~~N OF THE PllZER MODEL TO CELlSPITE ALES DATA IN Na SOLUTION
i
* A
I
I
60
IO0
T oc FlG. 3. CMe5titcsolubility plotted against temperature for data co&ted in this study in comparison with previous pub lished data.
Comments on compuatiorud procedures. The rather involved set of relations for computing activity coefficients using the Pitxer model am not presented hem, but some comments on the computational procedures used in this study am nv. We adopted the HARVIE and WEARE (1980) formulation of the Pitzer relations in this study. For calculating temperature etfects on the single electrolyte parameters, the following expression was used:
68
E. J. Reardon and D. K. Armstrong
the temperature functional expressions for @“, 8”) and C* given by DE LIMA and ~TZER ( 1983) and ROGERS and PITZER (198 1). These are:
(T- 298) T-298
(T- 298)2
(9)
where x = PO), fl’), f12)or C*. Because ions of different charge occur in the NaCISrCkH20 system, the assymmetric mixing theory of PITZER (1975) was used to improve the description in high ~n~n~~on solutions. This entailed calculating the func~ons E@&Z)and E&{Z> where the subscripts “c” and “a” refer to cation and anion, respectively. The values of these functions are given by complex integrals and can be either evaluated and tabulated for each pair of ion charge type at various ionic strengths or approximated by a numerical technique given by PITZER (1975) as presented by M~XVNINand SCHO~ (1984). For programming simplicity we adopted the latter and equally accurate approach.
Paramererization in the NaCI-SrSO&O
system.
Application of the full deveiopment of the Pitzer relations to predict stoichiometric aotivity coefFi&nts in the NaCl-S&&-H20 system requires data for the single ekctroiyte parameters @, ,@!, PJ and C$, tkirtempemture derivatives, as well as the mixture interaction terms %I=, %,, $_ and 1L,. We have ignored the possible temperature dependence of these interaction terms. It has been pointed out that this is a reasonable assumption over a modest temperature range (MONNIN and won, 1984). The values s&e&d for ah required parameters are recorded in Table 5. Not shown in Table 5 are the electrolyte parameters for NarSO,. We used
0.0765 0.2&M
Na-Cl
ar-clb sr-so.C
WlXturt
0.2681 1.067 3.1873
0 2000
Interaction
o.oo127 -o.w1so -54.24
Parmeters
se Na-Cl-SO. Sr-Ci-SO CI-Na-S h so,-ma-srd
0.02 0.02 0,011 0.031
Y 0.0014 -0. oe21
Ns-Cl
0.7159 -,.,*o 0.7008 2.1rs.e
-0.lO54 0.1454~
St-t.3
sr-SO,=
0.711 2.840
s..*
-0.510
/3”’ = - 1.03611 x IO-‘T’ + 0.0300299T 175.4 - 14.3441 In T- nT_263)
-~+g1.5@43
(101 8”‘= -3.2355 X 10-4+0.576552T54.17 - nT--263)’
188.769111T
9.9786 X IO*_- 2326&f T(680 - Tf T + 1w2’77
(11) C*=5.14316XlO-‘T+
90.9428 flT- 263) -y-0.094327.
(12)
Use of the above expmsskns accurately fit the availabie activity coefficient data for NatSO, solutions from 25 to 350°C. Values for all other single electrolyte pamme&m exoept &SO, and most of the mixture intemction terms were t&n from the extensive compilations pzovkkd by~R(1979)and~Mptal.(1984).~sioOle electrolyte parameters for SrSO, and values for $s,w, $Q.and #so_-, however, are not included in these compilations. Fortunately, the cakulated sohmility products for celeetite in NaCl solutions are insensitive to tire choice of values for an”, 8(l), 8(3) and 0. This is a retlection of the rather Iow SdubiJity of celestite in NaCl solution and the fact that Srr” and Sof- ate always in low concentrations relative to Na’ and Cl-. For example, we computed mean values for andtheirtempemture ~~~~~~~ derivatives for other bivalent metal sulphate s&s Ifs&d in &IXER (1979). In the application Ofthe Pk&er equations to determine celestite solubility products in NaCl solutions, each of these parameters was adjusted by two standard deviations of their mean value end were found to impart a 0.0 1 variation or less in the cakt&ed log K for celestite solubility for all solution compc& tions at all tcmpratures. In the actual c&uktiOnq we used the single electrolyte parameters repcHad by ROGERS(I98 I ) for C&O, as an approximation for the SrSo, values. The values for the mixing parameters &jrand $~_-NcScanbesafSBfdysettozeroinaj&ingtheFitzer relations to celestite equilibria in NaCl solutions. The importance of the contribution of these terms to the cakulation of activity coetkknts is w to the product of the molalities of the indicated ions. For these two w the concentrations of two Of the indicated ions, S?’ and 5XX are always low, mIRktkg the contribution of these two parameters t&i&k for all solution compositions. This is not the case for &,_-, however, because only one of the indkUed ions is always at low concentrations. This parameter,
C&stite solubiiity
69
derivedfrom the w&esin addition to ‘ew&, WBS~&BTIGIM &OIB EMF mea* IT&KS of sew and $sion analyses along with their standard error are 0.05 1 smcnts on binary mixtures of NaCl-SrCl~reported it 0.003 and -0.0021 s 0.0010, respe&vely. by~(l%S)usingaprocM~outhedby~R Thereissome confusion in the fiterature over the aodKIM(1974).Thaeauthors~thattbe~~nce in the experimental activity coe@ients for a salt MX use of the terms $6and 8. In the ~rn~tion of I%Rm ef d ( 19&t), thetabulated Bvaluesare actually‘@values in a &$X&Xmixture and the values calculated us@ of PrTzER(1975). For the Pitzer equations witb the parameters eyed &WZV according to the t~inolo~ pairs of ions of identical valence no union is netsettozeK,isn~~to~ewiluesofthese~eters essary, since se is synonymous with Bbecause the term, through the following expression: %(Z>, in Eqn. (14) equals zero. For pairs of ions of ~~ valence, however, se is not condom with f?. HARYIE et d. (1984) chose not to distinguish these ( 13) = I?,,+ Y&rl.X+~Z~ZX~~~~ values in their ~b~tio~ and equation formation wtlereu- vM+ ux (i.e. the sum of the moles of ions using the general label, 8, throughout. It can be argued, contributed by one mole of salt MX) and, 2, and 2~ however, that this distinction should be maintained, refer to the charges on the ions. A plot of the quantity otherwise the impression may be given that all e values on the left-hand side of Eqn. ( 13)against the coefficient listed in PKTZER (1979) are inte~~ble with Bvalof qxMMshould be linear with intercept rt,, and dO@! ues listed in HARWEet al. (1984). Cleariy, this is not &,N. PITZER and KIM( 1974) the case, In addition, because the threeentre inter~~~e~u~ butifthe actions terms $a and J/1ocare determined simultaterms are included in the ~mpu~tion of A In ‘y~x neously with Bor SB,diflbrent values for these paramum eters will be obtained if the asymmetric mixing theory valuesto account forasymmetricmhing the am yields values of se(RTZER,1975). Values is applied than if it is not. Thus, the values listed in relmxi t0 e ~4~3 thmgh the expression: HARVIE ef al. ( 1984) ared.so not interchangeable with values tabulated in FITZER (1979) unless they refer to 8 = c + “@(I). (141 mixtures of ions with identical valences. The measured TNa data Of hNIER (1965) Were Celestite solubilityin NaCI solutions.The results of treatedin the above manner and the results are plotted our celestite solubility measurements in NaCl solution in Fig. 5. The data cover an ionic strength range from at 25’C along with the results of previousworkers are 1 to 6. There is a we~develo~ linear tread with shal- plotted in Fig. 6. The solid curve is the predicted sot low slope over most of the range of abscissa values ubility behaviour at 2YC using the Pitzer relations with incre&ng scatter for the lower caption data with the parameters provided in Table 5. A c&s&e points. Scatter is expected to increase towards solubility product of 10-6.632 at 25°C (see Table 3) was ionic stmugths because the A In y term should used in the solubility cakulations. Aside front the Salapproach zero making expezimental ~n~nti~ in ubility donation reported by MOLLERf196O), the measuti activity amend yield &!er uncer- there is excellentagreementamong aUworkers.In adtainties in the value of the lefi-hand side of Eqn. ( 13). dition, the predictedvolubilitybehaviourbasedon the MONNINand SCH~ (1984) recommended ouly using F5tzerformation offers a superb ~p~n~~on of data above an ionic strength of 1 to 2. The single dis- the actual solubility measurements to concentrations parate data point in Fig. 5 is at an ionic streng& of 1.O of 5.0 m NaCl, Mtiller’ssolubility data are much higher and was not included in fitting the regression line. The at the high concentration end than either STR~EL (19~~,DAv~andC0~1~~~197l)orour~n~~a~ do not document a reversal in the solubility behaviour Of6 betweeu 2.0 and 5.0 m NaCl as predicted by the Pitzer t fo~ulation and as observed in this study. MOJ_I.ER ( 1960) useda EDTA complexometric technique to deINTERCEPT 0.051 io.003 SLOPE termine strontium ~n~n~tioos and it is possiblethat -0.002 to.uw minor ~u~e~ng of sodium ion by EDTA at these high NaCl concentrations resulted in anomoiously high strontium ~~~n~tions. This problem of possible matrix effects influencing the determination of strontium was not addressed by MULLER(1960). Figure 7 presents the solubility data of STROBEL (1966)and this work at IO,20,30 and 40°C and other data of SlWBEL (1966) at selected temperatures. It can be seen that the predict& soiubility behaviour using the Pitzer equations accurately and ~~e~~y npresents the actual solubility measurements over the entire concentration of 0.05 to 5.0 m NaCl and tem~tu~ from XO*Cto 90°C. The ~ment is
E. J. Reardonand D. K. Armstrong
70
12 -
,*_
X
X 0
MijLLER STRhEL
I19601 lW66t
0
DAVIS 8 COLLINS IlP?i) X
~7 CUL8ERSON lt O! 11676) + TWS STUOY
i 0
I I
I
2 NOCI
I
3 I lnoktlity)
1
I
J
4
s
6
FIG. 6. Resultsofcehstite sohtbiity measummentsin N&l solution at 25’C from this study along with previouslypub ~~~~~~~~~~~~~ basedon the PitrerFormulationas describedin the text.
indeed superb, and attests to the ~~~ of these reiations to predict mineral ~lu~ti~ in hi&Iv saline waters. CELRSTiTR S0LUBiLITY IN SEZELWATER AND MIXED&ALT SOLUTIONS cbs%SON
et al. (1978) conducted celestite solu-
bihty measurements at 25 ‘C in synthetic seawater and in three additional saline waters with chemical cornpositions simi& to seawater. The synthetic seawater was 0.4852 mNa+, 0.01058 mK+, OAHO68 mCa*+, 0.05518 mMgz+, 0.5682 mCK- and 0.02927 msd;. The other three waters di&ed from seawater oniy in the relative ~~~ of calcium and magnesium. Table 6 lists these chemical di&renoes and the rest&s of the sohibihty meesutements. Although it is not known to what extent solid sohttion e&ct.s may play in a&cting celestite solubihty in mixed-s& systems like seawater, the Fitaer relations can be applied to caicufate the solubihty of pure c&s&e in these &IItions as a comparison with the ex&ntal values. All the additional parameters totiythe Pitxer model that are not inch&d in Table 5 were taken directly from T%itvIEef al. (1984). cVLf3~t60~ etal.(1978) aiso applied the Pitaer reMions to cornpam the predicmd with the measured fifty for one of their synthetic seawaters. Their pmdicted vahie is includedin Table 6 along with the values calcuiated in this investigation. There is a large difference between the pmdicted solubility of celestite in seawater calcu;iatadby_ERSON er al. (1978) and our value, compare 0.345 vs. 0.403 miRimoIa1. We are not sure exactIy why this should be the case. However, a somewhat &Brent set of interaction parameters were used in this study based on the more recent compilations by PITZER ( 1979) and
HARVIEet al. (1984) and the experimental work of I&YEER( 1965). This, coupled with the fact that higherorder electrostatic terms incorporating asymmetric mixing effects were not considered by CULBERSON d al. (1978), may account for this difference. ROGERS (198 1) also used the Pitzer formulation to compare predicted celestite solubihties with Cuiberson’s data. These values are recorded in the last column of Table 6. ROGERS(1981) used a somewhat higher solubility product for celestite than determined in this study (compare ~15:of 6.614 vs. 6.632). It is seen that our vahtes are siigbdy lower and hers slightly higher than the actuai measured values. The differences between predicted and measured solubi~ities for seawater-type solutions using the Pitzer formulation thus appears to be at the Ievel of uncertainty in the solubility product used in the calculations. CULBERSON et al. (1978) made four additional solubihty measurements of celestite in various solutions at the same ionic strength as seawater. Table 6 shows a comparison of the predicted and experimental vaiues. In these solutions, the solubihties are about an order of magnitude higher than in the seawater solutions because of the absence of sulphate in the original equilibrating solutions. Again, however. the agreement between predicted and measured values is excellent for all solutions with the maximum deviation being on the order of three percent. 6 6O.C 0
6
6r
PIG.7. Results of cekstite solubility measurements in NaCl sohuiotu determiacd in this study (A’s) and thoseof !3W.U@%
( 1966) (o’s) at vwiouss&cctedUmpcrptuns. The wiid curve in usch of the gmpbs 3xpftsmt.9the solubilitykehatiow as
predicted by
the
t?trer equattons
celdte
lolobility
Results of csleatite conducted by Culberaon Tabulated aolubilitiea. millimolalitiea.
meaaurehenta in Svntbetic et al. (1978) aa cmmred t0 predicted expreaasd in concentrationa are
Table 6. amwater
Solution
ca
Sewatcr Saline 1 Saline 2 Saline 3
10.78 0.0 27.95 44.91
55.19 05.98 38.01 20.99
0.416 0.414 0.423 0.422
0.7 mNac1 0.7 mKc1 0.233 nCaC1. 0.233 JIgCl.
3.23 3.42 4.14 3.74
a Calculated from Culbcraon using the Pitzer relationa 6.616 at 25-C. b
Calculated in pK for cclaatits
c
Calculated
Sr(pradka
Sr(m*aa)
Ng
2 t ? *_
t ? +_ +
0.001 0.001 0.002 0.004
et and
(1981)
0.345 -
using
PERFORMANCE OF THE PITZER FORMULATION FOR DILUTE SOLUTIONS In electrolyte solutions where there are strongly associating pairs of ions such as is o&n the case with 2:2 or higher valence type electrolytes, it is often not possible to accurately represent activity coefficient behaviour in dilute solutions (CO. 1 m) with the Pitxer formulation. This problem was first addressed by PITZER and MAYORGA (1974) who introduced the addition of the 8”’ term to the second virial coefficient expression. It can be shown on a theoretical basis that 8(‘) is equal to -K/2 at infinite dilution, where K is the association constant for the ion pair or complex. Op-
Sr(prad)=
0.408 0.403 0.411 0.416
0.429 0.426 0.430 0.434
3.18 3.33 4.16 3.83
al.‘a their
A final test of the formulation can be made with the celestite solubility data of DAMS and COLLINS( 197 1). They measured celestite solubility in three mixed-salt NaCl-type brines. The compositions and the measured and predicted solubilities are reported in Table 7. In performing the calculations we added the small concentrations of Br to the Cl concentration. The maximum ditkence between the measured and predicted celestite solubilities mcorded in Table 7 is 2.5%. Putting it in another way, the ditkrence between measured and predicted solubilities would correspond to an uncertainty in the solubility product of celestite used in the calculations of less than 0.01 pK units.
Table 1. mixed-salt (1971). aolubilitiea
sr(prsd)b
0.01 0.02 0.01 0.01
this atudy uaiag the of 6.632 at 25-C.
by Rogera
71
Bolubility
tabulated calculated
Pitter
pK for
relationa
cclsatitc
‘L.,. pK fo9
value obtained ccleatitc of
and our
of
aatimated
8.814.
emtionally, however, a”’ is treated as a titting parameter in the mgression analysis of osmotic or activity coefficient data at low concentrations. Latge negative values of 8”’ indicate strong ion association. I-IARVIEef cf. (1984) discussed at length the limitations of this ap preach and suggest& in the case of 2:2 electrolytes, that for flz) values lower than about -250, a superior fitofthedataisachievedby recog&ing the ion pair or complex as a separate species. This greatly increases the complexities of the computations, however, and in addition, nquires an iterative solution in applying the model. Computationally, it is clearly advantageous if this approach need not be taken. We present a test of the parametem for SrSO, adopted in this study to describe the dilute solution behaviour in Fig. 8. The diffiia in the negative logarithms of the solubility products for the pure water solubility runs calculated using the ion pairing model (see Table 3) and the Pitxer formulation am plotted versr4.stemperature. The ditferences are seen to be very small ranging from 0.0 15 pK units near 25°C to 0.025 pK units at higher temperatures. We have found that all differences can be removed by adopting a f12)value of -78 and a temperature derivative value of -9.2. A 8”’ value of -78 is seen to be well above a value of -250 at which consideration of a separate species, i.e. Sa, would be recommended.
Comparison of meaaured and predicted celaatite lolubility In NaCl-type brinea. gxperimental data from Davis and Collins All concentrations ace axpreaasd ln lolalitiea. SFSO. are erpreaaad in lillimolslity.
NO
I%
wcr
K
Cl
nr
SrSo. meaa
srS0, prod
Brine
1
1.218
0.0250
0.0206
0.0051
l.SO2
0.013
4.43
4.33
Brine
2
1.140
0.0374
0.0023
0.0051
l.s65
0.019
5.02
4.92
Brine
3
2.436
0.0499
0.0411
0.0193
2.011
0.025
5.22
5.09
72
E. J. Reardon and D. K. Armstrong 0.02
of saturated electrolyte mixtures of NaCl with Na#& and with MgCl* J. Solution Chem. 12, 187- 199. ENOSTUN B. V. and TURKEVICHJ. ( 1960) Solubility of tine particlesof strontium sulfate. J .4mer. Chem. Sot. 82,4502-
r
4509.
e 8 -0.04 t - 0.06 1 0
I 20
I 40
I 60
I 80
I 100
T *C FIG. 8. A plot of the difference between p&o, calculated using the Pitzer relations and pK_ values recordbd in Table 3. Use of &,,, of -78 and afl’)/~?Tof -9.2 reduces the differences to zero at all temperatures.
We must point out that we cannot unequivocally recommend a set of interaction parameters for SrXh atthistime.Idcally,they&auldbedetamincdthrough regrc%ion analyses of activity codE&nt data or solubility&tainsystemswhereslleastoneoftheions Sr” or amay be vuiai over a wide concentration
range such as the ternnry sywms Na2SOrSrS04 or SrClrSrS04. The sohhility data in the !3rSOcNaCl system is not approprh inthisnprdDuctoalack of data or a lack of data of su&icnt quality in the appropriate systems, this analysis cannot be made at this time. Until such time as thoa data become available the adoption of the C&JO, parameters as a proxy for SrS04 should yield reaa~nable predictions of the solubility of c&&c in mixad-& solutions. Acknow/e&emenfs-The
authors woti IiLe to extend their apprcci&ontoG.MicbardfbrtbecditorirlbandIinpPndto the anonymous reviewers whooe very cIose reading and detailed critique aided con&erably in the lwiaion oftbe manuscript. This project was funded by the National Science and Engineering Research Council of Canada. Editorial handling: G. Micbard
RJwERENcEs P. ( 1940) The dfcct of alkali nitrites on several difficulty solubie sulfa- Ann. Chim. Applicata 30.233-237. CAMPBELL A. N. and COOK E. J. R. (1935) A study of the precipitation from supnlaunted solutions of strontium stite. J. Amer. C/tern. Sac. S7,387-390. CAMPRELLJ. R. and NAN~~LLASG. H. (1969) The crystallization and dissdution of strontium sulfate in 4ueous solution. J. Phys. Chem. 73, 1735-1740. CUL-N C. H.. LATHAMG. and BATESR. G. (1978) Solubilities and activity co&cieats ofcalcium ti strodtium sulphata in synthetic sawltaat O.S”C aad 25-C. 1. Pbys. Chem. 82.26932699. DAVISJ. W. and COLLINS A. G. (197 I) Solubi.lity of tium and strontium s&fates in strong eJectmlyte solutions. Env. Sri. and Techn. 5, 1039-1043. DE LIMAM. C. P. and PITTERK. S. (1983) Thermodynamics BELRORI
GALLOG. (I 935) Equilibrium of strontium sulfate and water at various temperatures. ‘4nn. Chim. .4pplicata 25, 628631. HAASJ. L. and FISHERJ. R. (1976) Simultaneous evaluation and correlation of thermodynamic data. Amer. J. Sci. 276, 525-545. HARVIE C. E. and WEARE J. H. (1980) The prediction of mineral solubilities in natural waters: The Na-K-Mg-CaCI-S0,-H210 system from zero to high concentration at 25°C. Geochim. Cosmochim. Acta 44,98 l-988. HARVIE C. E., ~LLER N. and WEARE J. H. (1984) The prediction of mineral solubilities in natural waters: The NaK-Ma-Ca-H-Cl-SO‘-OH-HCOXO,-COT-H,0 svstem to high ionic strength; at 25°C. 6eociim. i’osmoc& Acta 48,723-75 1. KOHLRAUSCHF. ( 1908) Saturated aqueous solutions of sparingly soluble salts (II). The solubilities and their change with temperature. 2. Physik. Chem. 64, 129-169. LANIERR. D. (1965)Activity coefficients of sodium chloride in aqueous three-component solutions by cation-sensitive glass electrodes. J. Phys. Chem. 69,3992-3998. LIE~ERK. H. (1965) Radio&n&he Messungder Lijslichkeit von Erdalkalisulfaten in Wasser und in Natriumsulfatl& sungen. Z. Anogr. Allgem. Chem. 335,225-23 I. MARDENJ. W. ( 19 16) Solubilities of the sulfates of barium, strontium, calcium and lead in ammonium acetate soh~tions at 25” and a criticism of the present mahods for the sep aration of these substances by means of ammonium acetate solution. J. Amer. Chem. Sot. 38, 310-316. MONNIN C. and SCHOTT1. (1984)Determination of the solubility products of sodium carbonate minerals and application to trona deposition in Lake Magadi (Kenya). Geechim. Cosmochim. Acta 48,Y 1-58 1. MOLLERG. (1960) Die Liislichkeit von Coelestin (SrSOI) in w&serigen NaCI- und KCI-Liisungen. Neues Jahrb. Mineral. Mon. 1960, 237-239. NORTHN. A. (I 974) Pressure dependence of SrSO, soiubiiity. Geochim. Cosmochim. Acta 38, 1075-108 I. PITZERK. S. (1975) Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms. J. Solution Chem. 4,249-265. PITZER K. S. (1979) Theory: Ion interaction approach. In Activity Coejicients in Electrolytes Solutions, Vol. I (ed. R. M. PYTKOWICZ~. DD. 157-208. CRC Press inc. PITZERK. S. and KJM J. J. (I 974) Thermodynamics of electrolytes. IV. Activity and osmotic coefficients For mixed electrolytes. J. Amer. Chem. Sot. 96, 5701-5707. PITZERK. S. and MAYORGAG. (1974) Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2-2 electrolytes. J. Solution Chem. 3, 539-546. REARDONE. J. (1983) Determination of SrSa ion pair formation using conductimetric and ion exchange techniques. Geochim. Cosmochim. Acta 47, 1917-1922. ROGERSP. S. 2. ( 1981) Thermodynamics of geothermal fluids. Ph.D. thesis, Univ. of California, Berkeley, 243 p. ROGERSP. S. Z. and PITZER K. S. (198 I) High-temperature thermodynamic properties of aqueous sodium sulfate solutions. J. Phys. Chem. 85,2886-2895. SELIVANOVA N. M. and ZUBOVAG. A. (1956) Polarography and thermodynamics IV. Thermodynamic properties and solubility of strontium sulfate. Trudy Moskov.Khim.-Teknol. Inst. im. D.I. Mendeleeva 1956, 38-46. SILVESTERL. F. and PITZERK. S. (1977) Thermodynamics of electrolvtes. 8. High temperature properties, including enthalpy and heat c&city, with application to sodium chloride. J. Phvs. Chem. 81. 1822-1828. STROBELG. (1966) Die hydr&hermaie Laslichkeit von Cislestin im System SrSO,-NaCl-H20. Neues Jahrb. Mineral. Mon. 1966,99-107. I,
.
.
C~ia
0016.7037/87/$3.00 + .oo
Adn Vol. 51. pi. 63-12
0papmonJaMllrLtd.1987.Rimcdinu.s.A.
Celestite (SrsO,)
solubility in water, seawater and NaCl solution E. J.
REARDON
and D. K. ARMSTRONG
Department of Earth Sciences, University of Waterloo, Waterloo, Ontario N2L 3G 1, Canada (Received May 5, 1986; accepted in revisedform September 26, 1986) Abstmct-Celestite solubility measurements have been conducted in pure water to 90°C. Equilibrium was achieved with respect to a crysmlhne solid phase from supersaturated solutions. The measurements show that the solubiity undergoes Log K values for the solubility reaction are adequately described by the following perature range 283.15 to 363.15 R -log K= -35.3106+0.00422837T+318312/T2+
at temperatures from 10 both undersaturated and a maximum near 20°C. expression over the tem-
14.99586 log T.
The following thermodynamic values for the dissolution reaction of SrSOqsj at 25’C have been derived: AGP = 37852 f 30 J mol-’ Ma = - 1668 f 920 J mol-’ &a=-132.6+3.2JK-‘mol-I. C&stite solubility measurements were also determined in NaCl solutions up to 5 m concentration and from 10 to 40°C. These data are in good agreement with the work of STRUBEL (1966), who reports solubility measurements to temperatures of IOO’C. The application of the Pitmr relations and the solubility constants determined in this study to calculate cekstite sohmility in Nail solutions yields excellent agreement between predicted values and experimental measurements over the entire range of temperature and NaCl concentration conditions. For the limited number of solubiiity m eesunmentri in seawater-type solutions and mixed-salt brines, the agreement using the Pitxer relations is witbin three percent of the measured solubiity. INTRODUCIlON
in this tabulation, STRUBEL( 1966), also reports data on celestite solubiiity to temperatures of 350°C. SrSO~NaCI-Hz0 system. The publishaI data on akstite solubility in NaCl solutions are leas extensive than in pure water. The available data are tabulated in Table 2. STRflBEL ( 1966) is the only worker who mported extensive alestite solubility data at temperatures other than 25°C. From an inspection of the reported solubihties in both pure water and NaCl solution, it can be seen that there is a wide variability in results at any particular temperature. At least two principal factors may account for this rather Large dis cordancy in solubility data. The tirst mlates to the welldocumented effect of particle sixe on celeatite sohrbility. This e&t has been extensively studied by ENUSTUNand TURKEVICH ( 1960), who in a series of aiestite solubility experiments with materialofvaryingsixedistribmionsshowedthatthesmalkstsized particks present appeamd to control the solubility. They reported the following expression which relates the observed solubiity enhancement to the minimum particle size present:
THE PROPERTIES OF celestite that have rendered it a highly suitable substance for studying the process of ptipitation are also the properties that account for the rather large disparity in reported solubilities for this material. Such properties include the long term stability of its supersaturated solutions (CAMPBFLL and Coorc, 1935); the propensity for surface poisoning effects (CAMPBELLand NANCOLLAS,1969); and the functional control on solubility by particle sixe, (ENOsToN and TURKEVICH,1960). Many of the earlier studies on celestite solubility did not thoroughly address these problems and so have not tinnly demonstrated the attainment of final equilibrium. In this study, we have tried to pay close attention to these potential problems and have demonstrated through approach to saturation from both supersaturated and undersaturated solutions, the attainment of equilibrium with respecttoauystaUinesolidphase.Wepresenttheresults of solubility experiments both in pure water and Nail solution and apply both the ion pairing and the Pitzer model to describe specilk ion interactions in solution.
PREVIOUS
log a/a,, = 1.61.~
(1)
whacaistbeobsavedactivityofthe~lidphasc;~ispctivity for the pure solid in macroQystauine form; and x is the minimum particle sixe in nanometers, For a sohmility experiment to reflect the actual &hility of wne c&&e, it would be necesmry to ensure that a/a,, does not exceed that value which could arise from analytical uncertainties alone. For example, if a water were satmati with respect to macroq3tallinecelestitebuttherewasa+ 1%combinedanalytical error in strontium and sulpham a conesponding a/p0 ratio of 1.01 would reauit. Using this value in Eqn. (1) reveals that acompambleenhancementinthesolubiJitywouldoccurif m0teriolwerepnrentwhoreparticlesizewrrsO.3~morlas. Asecondfhctorwhichmayaccountforthelargediq&ty in publiskl solubiiity data for alestitc rdates tothesuscep tibilityofthi8mat<osurhcepoisoning.Thi.%e&ctcan essentially shut down the approach to saturation from both
WORK
SrSOwH# system. The published data on ales&e solubilityat 1 barprwtmretotemperammsoflOO°Caremcorded inTable 1.Thebulkofthestudieareportsolubihtydataata single temperature, generally 25°C. but several of the studies (KOHLRAUSCH,1908; GALLQ 1935; and STRUBEL,1966) report data at a number of temperaturea. Although not shown 63
64
E. J. Reardon and D. K. Armstrong Table data
1. in
Published pure
Author
celestlte
water
at
Temperature
various
solubility temperatures. Solubility
(uoles/KK
f-c)
OfIll0 (1935)
5 10 20 30 40 50 80 70 80 90 95
0.859 0.702 0.719 0.751 0.773 0.746 0.724 0.686 0.646 0.648 0.837
Kohlraurch (1909)
2.95 11.4 32.3
0.617 0.823 0.826
strilbe1 (1988)
22 30.5 50.0 75.5 95.5 100.5
0.821 0.817 0.598 0.492 0.404 0.361
Dwia and Collins (1971)
25
0.821
Salivanova and Zubova (1958)
25
0.762
YUller
25
0.892
2
0.829
(1985)
20
0.119
Cupbell and Cook (1935)
30
0.897
Belfiori
20
0.821
26
0.822
Campbell and 25 N~~oollna (lSS9)
0.848
(1960)
North (1974) LIe8er
(1940)
Harden (1916)
Culberron et al.(lWL))
25
the experiments. When double-distilled water was used in its place, all inhibitory effects on dissolution and precipitation were removed.
Ii.01
0.844 i 0.001 over 22 ropllceter
EXPERIMENTAL Previous studies of celestite solubihty used either crushed natural material or material synthesized by reaction of a sulfate salt, usually Na2S0, and a strontium salt, usually SrQ. In this study, to ensure as pure a solid phase as possible, celestite crystals were synthesized by titrating 10 I of a 0.003 molal H2S0, solution with a strontium hydroxide solution to a pH of 5.7. The strontium hydroxide solution was filtered through a 0.2 pm filter as it was added to the sulphuric acid solution. This was done to remove particulate SrCOws~which immediately forms upon preparation of a strontium hydroxide solution. The concentration of HrSO, used was selected so as to be between the minimum molal concentration of SrSO, in solution that results in spontaneous nucleation, 0.00 12 molal (CAMPBELL and COOK, 1935) and the minimum molal concentration that results in the rapid mce of a precipitate, 0.015 molal (ENUSION and TURKEVICH, 1960). All reactant
and equilibrating solutions used in this study were prepared using distilled de-ionixed water with a mewred conductance of cl.8 fi cm-‘. AAer titration with Sr(OHk, the solution was stored for three days whereupon the solid phase was recovered and repeatedly washed with saturated SrSO, solution to remove fines. After a final rinse in reagent-grade acetone
Table 2. Published solutioa at various NaCl are expressad SrSO. are expressed Striibel
(1966)
T’C/NaCl(s)
0.1006
0.5029
1.082
2.285
20 30 40 50 80 IO 80 90 Boiling
1.524 1.506 1.434 1.401 1.328 1.239 1.149 1.044 0.918
2.912 2.838 2.807 2.888 2.529 2.385 2.199 2.009 1.803
3.815 3.758 3.700 3.551 3.398 3.186 2.995 2.751 2.415
5.244 5.131 5.008 4.950 4.750 4.398 4.080 3.033 3.660
Miller
pt.
(1980)
arlwoaaofrtrmtium~ of4oto5o%.Thiaw8atbecaeeevellmadutknuwbelnoaly largepatideawerepmm~i.e.tbepamccofpmkkeixes leaathan1juncouklncabeokfved.lnoneexpe6ment.a
Gall0
25°C
(1935)
Sk-SO.
T-C
NaCl
srso.
0.429 0.859
2.89 4.01
20 9
1.901 1.901
3.56 3.90
1.716 2.575 3.432 4.291 5.148 8.178
5.79 6.60 1.64 8.SO 10.48 12.34
NaCl
Nid COOK(1935). ThCSCNtllDlSllO!A!dCOSUpkkSlldOWlOfcryrUniution
celestite solubllity data In NaCl teaperatures. Concentrations of in aolality and COnceatratiOns of In sillfaolslity.
~.
Culberson
arpmrtunriwTbacauboslat~ Davis
and
Collins
(1971)
NaCl
SPSO.
0.010 0.015 0.025 0.050 0.068 0.172 0.257 0.431 0.869 1.771
0.730 0.811 0.937 1.085 1.448 1.813 2.298 2.881 3.875 4.283
25°C
et
al.
(1978)
NaCl
SrSO.
0.700
3.23
25°C
65
c&stite so1ubility the material was dried under vacuum. Two batches of this material were produced during this study and no di&tence in their solubility behaviour was observed. The prepamd celestite was composed of crystal aggregates ranging in sixe from about IO to 50 pm. Individual particles ofthecompositecrystabwereontheotderof5to lOlrm(see Fii 1). Suspensions of the celestite always settled rapidly (less than five minutes) leaving a clear super&ant solution which indicated an absence of ultrafine submicron particles. In addition, analyses on un6hered and filtered (0.2 rem) aliquots of the supematant alter solutions visibly cleared revealed no differences in strontium concentration. Before the solubility experiments were conduc@ a test was performed to determine if surface poisoning effects would pose a problem to the approach to saturation from either supersaturated or undersaturated conditions. SrSOtisj crystals were added to an undersaturated solution of SrSO, (0.4 mihimolality) maintained at 250°C. The electrical conductance was then monitored over time. Once the conductance levelled off and it was believed that equilibration had been achieved, fresh seed crystab were added to the reaction vessel. No change in conductance was observed over a five-hour period. The solution was then spiked with a supematumted solution of !&SO, to produce a 40% supersaturated solution and again the conductance was monitored. The results of this experiment are shown in Fig. 2 and demonstrate the absence of any inhibitory effects to the approach to saturation. The return electrical conductance
lW.1.Photomkqmphsshowingclystalsixeandaggmgate appearance of the c&&e pmpared for the solubility experiments. Scale bars are 1 pm long.
220
SPIKE SrS04 ,’ SOLUTION ADDED h
FRESH
loo
0
CRYSTALS
I
I
20
40 TIME
I
I
I
I
60
aD
loo
120
(Ill
FIG. 2. Results of exnetiment to demonstrate absence of from both superband undemat&ed solution conditions. The plot illustmtes conductance changes with time upon dissolution to equilibrium and the return to equihbtium conditions upon addition of a spike supersaturated solution of Sr!I04.
reading recorded 50 h following addition of the spike solution was within 1% of the value recorded immediately before the addition. The reaction vessels used in the actual sohmility runs were 20 ml glass vials into which suthcient SrSoqs~ (generally 100 mg)wasadded16~~~atleastatactorofttnmonsolid material than would dierolve during the course of the experiments. To prevent reduction in partide sixe due to grind@ effects the solutions were not stirred during the reactions. In~thereactionvesselswemlashedtotheoutsideofaplastic rod, immetsed hotixontally in a water bath and heki in position by two rods athxed by needles to the centre points of each endofthecentralpIasticcore.TbeetIhtentI?omthecirculator pump was then dire&d towards this sample carousel. The force of the effluent was stdhcient to induce a rotational speed of from 10 to 20 RPM. This resulted in a gentle tumbling action to the precipitate within each reaction vessel during the equilibration period. Solid phase equilibration was approached horn both undersaturated solutions and supersaturated solutions to demonstrate reproducibihty of the solubility measurements and to verify attainment of equilibrium. This was achieved by repeating solubiity measurements at a number of temperatures; once as the temperature was progmsively increased (approach to equilibrium by precipitation) and again, as the temperature was pmgmssively decmased (approach to equilibrium by dissolution). Strontium analyses were performed on acidified samples using a Varian@ Model 1475 Atomic Absorption Spectrophotometer. In order to suppress interferences and ionization in the air-acetylene flame, 2% by weight LaCl, and 2% KNO, were added to all samples, standards and blanks. Despite this precaution, there was still a small but significant suppression in the strontium signal due to the presence of sodium ion for samples from the celeatite solubihty runs in NaCl solution. ThiswascorrecMforbypreparingstandardsattheapproptiate Nail concentrations as the sample soh&ms. Strontium analyses could be reproduced for all solution compositions to better than I %. Sulphate was determined on selected samples from the NaCl solution runs using a Dionex@ Auto Ion Model 12 ion chromatograph. Analytical uncertainties are much
E. J. Reardon and D. IL Armstrong
66
where “m” refers to molal concentrations.
pKSrS0.'
PKs5rso,(S)
0.813 O.Sl3
2.211 2.212
5.531 * 6.529 "
0.540
o.soo
2.255
5.522 "
Km: refers to the dissociation constant of the SrSO~ ion pair. Values of this constant in pK form at each temperature are recorded in column four (Table 3) and were taken from the work of &ARJ3ON (1983) who determined the temperature dependence of K-z from 10 to 60°C. Activity coefficients for Srr+ and SO:- were calculated using the Deybe-Huckel equation, The mean molal activity coefficient for SrSO, is recorded in column three (Table 3). We used a value of unity for $!jrSO~, but it makes no difference to the calculated solubility product if any of the available equations describing a functional dependency with ionic strength are used. The calculated solubility products that are recorded in Table 3 above a temperature of 60°C are somewhat in doubt because Ksrso~ values used tn the calculations were obtained by extrapolating the data of REARDON (1983) above this temperature. A limited number of runs were made to determine the effect of NaCl on the solubility of celestite at various temperatures. These data which cover a range of NaCl concentrations from 0.05 to 5.0 molal and temperatures from 10 to 40°C are recorded in Table 4. These data are not amenable to an ion pairing model treatment to calculate solubility products because of the uncertainties in the calculated activity coefficients using the Deybe-Huckel equation at high ionic strengths. Instead, we applied the Pitzer relations to determine activity coefficients, the results of which ate presented later in this paper. The results presented in Table 4 indicate a reversal in the solubility of celestite between 2.0 and 5.0 molal NaCl. To document this reversal and to determine better at what concentration it occurs, we performed a series of more detailed solubility measurements at 25°C after the first set of data were collected. These were performed on a second prepared batch of celestite at NaCl concentrations from 2.0 to 4.2 molal These additional experimental results are recorded in Table 4.
0.541 0.543
0.509 0.500
2.292 2.290
5.534 s 5.532 u
DISCUSSION
29.5
0.531
0.509
2.314
6.550 u
40.0 39.3
0.555 0.507
0.510 O.SlO
2.353 2.350
5.559 s 5.557 "
40.5 49.5
0.555 0.574
0.510 0.511
2.405 2.407
5.724 e 5.735 "
50.0 30.5
0.534 0.531
0.513 0.514
2.450 2.440
5.500. 5.504 "
76.5
0.475
0.515
2.511
6.593 "
59.3
0.402
0.524
2.550
7.035 "
gmaterfortheanalysisofsulphatethan forstromium(wmpare *5?6 VS.fO.S%). However, the sulfate analyses served as a check that substantial substitution of Cl- for eand Na+ for S? in the solid phase did not occur during the equilibrati0Il.X A2 a further check that the solid phase in contact with the NaCl solutions showed little or no solid substitution, all solid phases were mcovered at the end of the experiments and analysed for their sodium content. For this analysis the material was repeatedly washed id a sodium-free saturated solution of MO, and then dried under vacuum. Samples of the solid phase were dissolved in 0.14 m HCl and analysed for sodium by AA. Sodium concentrations were below detection for all samples indicating sodium contents of the c&stites at less than 0.1%.
RESULTS The TcsuI1s of the celestite solubility measurements indisUd&ionizedwateratvarioustempemtumsare recorded in Table 3. The negative logarithms of the solubility product of celestite QX-3 are shown in the last column. These were calculated using an ion pairing model. The relevant equations that were iteratively solved to a constant ionic stmngth in order to calculate p& were simply:
mS12+= mSrror - mSrS(X mS60! = &&y~~(mSti+mSOi-
(2) - TS~~+YSO:~ (3)
msof- = m!P+
(4)
C5155t1t5 S5tcb *1. PC
S?SO. rolsdKSIl.0
10.3 10.4
0.533 0.531
20.2 25.4 25.0
1 f srS0.
Ce1mtits SW&l 82 39.3
0.510
0.509
2.350
5.554 "
40.5
0.577
0.511
2.407
5.734 "
50.5
0.535
0.513
2.4.9
a.797 "
73.5
0.472
0.517
2.511
5.809 "
89.3
0.410
0.522
2.355
,.02l "
Figure 3 presents the published data on celestite solubility in pure water along with the results of this study as a function of temperature. Our results are in Rood agreement with those of KOHLIUU~CH ( 1908), STROBEL (1966), CAMPBELLand NANCOLLA~(1969) and CULBER~~Nei al. (1978) at temperatures near 25°C. Over the entire temperature range our data are in very close agreement with those of STROBEL (1966). Our data are not in agreement with those of h&RUEN (19 16), GALLO ( 1935), and SELIVANOVA and ZUBOVA (1956). These data are all at higher concentration and it is possible that either surface poisoning effects, or particle size effects were contributory to the enhancement in so1ubility observed in their Studies. The calculated solubility products for o&Mite determined in this study are plotted as a function Oftemperature in Fii. 4. The data were fitted through regreS_ sion analysis to an equation of the form:
67
cdestite 201ubiiity
Cela~tltc 2atcb
21
NaCl
(aolality)
TW
0.0501
0.2020
0.4793
1.074
4.977
10.3 20.2 25.4 25.0 29.8 40.0
1.10 1.18 1.17 x.14 1.17 1.12
1.84 1.81 x.80 1.86 1.87 1.84
2.62 2.74 2.69 2.m 2.06 2.65
4.62 4.77 4.60 4.62 1.5s 4.4s
4.50 4.87 4.5s 4.4a 4.32 4.41
6.55 T”pewlturL
- 25.1-c
NRC1
WSO. (BIlllDalallty)
mcllalityl
t 6.401 0
1.981 2.397 2.640 3.076 3.538 4.184
4.71 4.90 4.95 4.92 4.89 4.68
l~K=a+~T+cfT’~dl~
0.7
I
T+e/T
(5)
t
o.s
is ;i o,4
+
0.3 0
the temperature range of the experiments, 10 to 90°C. The four term and five term expressions are: -log J&o, =-35.3106+0.00422837T+318312/T2 + 14.99586 log T
(6)
-log Ks,sc,, I=14805.9622 + 2.46609241” + 40553604f T2 - 5436.3588 log T - 756968.533/~
srs0ys,+
$
(7)
0 0
0 Q
0
0 0
20
40
OO
3
GALL0 fi935) CAMPMLL a alix tle3sl ~ECFIORI f 1940) S&LWANOVA 4 ZWOVA flSS6t MULLER lt9601 LIES R (1969) STR 5; EL (I9661 CAMPBELL 6 NANCOCLAS (I9691 WRTH (1974) CUL&iRSON .I d. (1976) DAVIS 6 COLLINS (19711 THIS ,SYUDY , I
60
sr2+
+ so24-
(8)
we obtain the following values at 298 K, AG: = 37852 -+ 30 J mol-‘; AH$ = -1668 + 920 J mol-‘; and AS% = -132.6 it 3.2 J K-r mol-‘. The uncertainties attached to these values are based on an assumed total analytical uncertainty in log K at temperatures near 25°C on the order of 0.005 log K units.
a XO
a K0ilLRWSCH wD61 @ MARDEWt1916) 0 _ 0 * X 0 6 _ A 0 m 0 0
-1 100
where T is expressed in Kelvin. Using l&r. (7) and its derivative to calculate the~~~arni~ properties for the reaction:
0
” E
I 60
FIG. 4. Calculated pK values for the solubility of celcstite determined in this study versus temperature; (+) equilibria approached fkom supersatumtion; (0) equilibria approached from undersaturation. Solid curve represents values determined from Eqn. (7).
0.9
-2
I 60
I 40
T OC
which is derived from a formulation to express fke energy data to high temperatures presented by HAAS and FISHER (1976). Consideration of only the first four terms of this expression yields a less cumbersome expression requiring only single precision calculations. Omission of the 6fI.h term, however, yields a somewhat inferior reproduction of the data at temperatures near 25°C. The maximum difkence between tire two expressions, however, is only 0.007 log K units over
0.6
I 20
AP~~~~N OF THE PllZER MODEL TO CELlSPITE ALES DATA IN Na SOLUTION
i
* A
I
I
60
IO0
T oc FlG. 3. CMe5titcsolubility plotted against temperature for data co&ted in this study in comparison with previous pub lished data.
Comments on compuatiorud procedures. The rather involved set of relations for computing activity coefficients using the Pitxer model am not presented hem, but some comments on the computational procedures used in this study am nv. We adopted the HARVIE and WEARE (1980) formulation of the Pitzer relations in this study. For calculating temperature etfects on the single electrolyte parameters, the following expression was used:
68
E. J. Reardon and D. K. Armstrong
the temperature functional expressions for @“, 8”) and C* given by DE LIMA and ~TZER ( 1983) and ROGERS and PITZER (198 1). These are:
(T- 298) T-298
(T- 298)2
(9)
where x = PO), fl’), f12)or C*. Because ions of different charge occur in the NaCISrCkH20 system, the assymmetric mixing theory of PITZER (1975) was used to improve the description in high ~n~n~~on solutions. This entailed calculating the func~ons E@&Z)and E&{Z> where the subscripts “c” and “a” refer to cation and anion, respectively. The values of these functions are given by complex integrals and can be either evaluated and tabulated for each pair of ion charge type at various ionic strengths or approximated by a numerical technique given by PITZER (1975) as presented by M~XVNINand SCHO~ (1984). For programming simplicity we adopted the latter and equally accurate approach.
Paramererization in the NaCI-SrSO&O
system.
Application of the full deveiopment of the Pitzer relations to predict stoichiometric aotivity coefFi&nts in the NaCl-S&&-H20 system requires data for the single ekctroiyte parameters @, ,@!, PJ and C$, tkirtempemture derivatives, as well as the mixture interaction terms %I=, %,, $_ and 1L,. We have ignored the possible temperature dependence of these interaction terms. It has been pointed out that this is a reasonable assumption over a modest temperature range (MONNIN and won, 1984). The values s&e&d for ah required parameters are recorded in Table 5. Not shown in Table 5 are the electrolyte parameters for NarSO,. We used
0.0765 0.2&M
Na-Cl
ar-clb sr-so.C
WlXturt
0.2681 1.067 3.1873
0 2000
Interaction
o.oo127 -o.w1so -54.24
Parmeters
se Na-Cl-SO. Sr-Ci-SO CI-Na-S h so,-ma-srd
0.02 0.02 0,011 0.031
Y 0.0014 -0. oe21
Ns-Cl
0.7159 -,.,*o 0.7008 2.1rs.e
-0.lO54 0.1454~
St-t.3
sr-SO,=
0.711 2.840
s..*
-0.510
/3”’ = - 1.03611 x IO-‘T’ + 0.0300299T 175.4 - 14.3441 In T- nT_263)
-~+g1.5@43
(101 8”‘= -3.2355 X 10-4+0.576552T54.17 - nT--263)’
188.769111T
9.9786 X IO*_- 2326&f T(680 - Tf T + 1w2’77
(11) C*=5.14316XlO-‘T+
90.9428 flT- 263) -y-0.094327.
(12)
Use of the above expmsskns accurately fit the availabie activity coefficient data for NatSO, solutions from 25 to 350°C. Values for all other single electrolyte pamme&m exoept &SO, and most of the mixture intemction terms were t&n from the extensive compilations pzovkkd by~R(1979)and~Mptal.(1984).~sioOle electrolyte parameters for SrSO, and values for $s,w, $Q.and #so_-, however, are not included in these compilations. Fortunately, the cakulated sohmility products for celeetite in NaCl solutions are insensitive to tire choice of values for an”, 8(l), 8(3) and 0. This is a retlection of the rather Iow SdubiJity of celestite in NaCl solution and the fact that Srr” and Sof- ate always in low concentrations relative to Na’ and Cl-. For example, we computed mean values for andtheirtempemture ~~~~~~~ derivatives for other bivalent metal sulphate s&s Ifs&d in &IXER (1979). In the application Ofthe Pk&er equations to determine celestite solubility products in NaCl solutions, each of these parameters was adjusted by two standard deviations of their mean value end were found to impart a 0.0 1 variation or less in the cakt&ed log K for celestite solubility for all solution compc& tions at all tcmpratures. In the actual c&uktiOnq we used the single electrolyte parameters repcHad by ROGERS(I98 I ) for C&O, as an approximation for the SrSo, values. The values for the mixing parameters &jrand $~_-NcScanbesafSBfdysettozeroinaj&ingtheFitzer relations to celestite equilibria in NaCl solutions. The importance of the contribution of these terms to the cakulation of activity coetkknts is w to the product of the molalities of the indicated ions. For these two w the concentrations of two Of the indicated ions, S?’ and 5XX are always low, mIRktkg the contribution of these two parameters t&i&k for all solution compositions. This is not the case for &,_-, however, because only one of the indkUed ions is always at low concentrations. This parameter,
C&stite solubiiity
69
derivedfrom the w&esin addition to ‘ew&, WBS~&BTIGIM &OIB EMF mea* IT&KS of sew and $sion analyses along with their standard error are 0.05 1 smcnts on binary mixtures of NaCl-SrCl~reported it 0.003 and -0.0021 s 0.0010, respe&vely. by~(l%S)usingaprocM~outhedby~R Thereissome confusion in the fiterature over the aodKIM(1974).Thaeauthors~thattbe~~nce in the experimental activity coe@ients for a salt MX use of the terms $6and 8. In the ~rn~tion of I%Rm ef d ( 19&t), thetabulated Bvaluesare actually‘@values in a &$X&Xmixture and the values calculated us@ of PrTzER(1975). For the Pitzer equations witb the parameters eyed &WZV according to the t~inolo~ pairs of ions of identical valence no union is netsettozeK,isn~~to~ewiluesofthese~eters essary, since se is synonymous with Bbecause the term, through the following expression: %(Z>, in Eqn. (14) equals zero. For pairs of ions of ~~ valence, however, se is not condom with f?. HARYIE et d. (1984) chose not to distinguish these ( 13) = I?,,+ Y&rl.X+~Z~ZX~~~~ values in their ~b~tio~ and equation formation wtlereu- vM+ ux (i.e. the sum of the moles of ions using the general label, 8, throughout. It can be argued, contributed by one mole of salt MX) and, 2, and 2~ however, that this distinction should be maintained, refer to the charges on the ions. A plot of the quantity otherwise the impression may be given that all e values on the left-hand side of Eqn. ( 13)against the coefficient listed in PKTZER (1979) are inte~~ble with Bvalof qxMMshould be linear with intercept rt,, and dO@! ues listed in HARWEet al. (1984). Cleariy, this is not &,N. PITZER and KIM( 1974) the case, In addition, because the threeentre inter~~~e~u~ butifthe actions terms $a and J/1ocare determined simultaterms are included in the ~mpu~tion of A In ‘y~x neously with Bor SB,diflbrent values for these paramum eters will be obtained if the asymmetric mixing theory valuesto account forasymmetricmhing the am yields values of se(RTZER,1975). Values is applied than if it is not. Thus, the values listed in relmxi t0 e ~4~3 thmgh the expression: HARVIE ef al. ( 1984) ared.so not interchangeable with values tabulated in FITZER (1979) unless they refer to 8 = c + “@(I). (141 mixtures of ions with identical valences. The measured TNa data Of hNIER (1965) Were Celestite solubilityin NaCI solutions.The results of treatedin the above manner and the results are plotted our celestite solubility measurements in NaCl solution in Fig. 5. The data cover an ionic strength range from at 25’C along with the results of previousworkers are 1 to 6. There is a we~develo~ linear tread with shal- plotted in Fig. 6. The solid curve is the predicted sot low slope over most of the range of abscissa values ubility behaviour at 2YC using the Pitzer relations with incre&ng scatter for the lower caption data with the parameters provided in Table 5. A c&s&e points. Scatter is expected to increase towards solubility product of 10-6.632 at 25°C (see Table 3) was ionic stmugths because the A In y term should used in the solubility cakulations. Aside front the Salapproach zero making expezimental ~n~nti~ in ubility donation reported by MOLLERf196O), the measuti activity amend yield &!er uncer- there is excellentagreementamong aUworkers.In adtainties in the value of the lefi-hand side of Eqn. ( 13). dition, the predictedvolubilitybehaviourbasedon the MONNINand SCH~ (1984) recommended ouly using F5tzerformation offers a superb ~p~n~~on of data above an ionic strength of 1 to 2. The single dis- the actual solubility measurements to concentrations parate data point in Fig. 5 is at an ionic streng& of 1.O of 5.0 m NaCl, Mtiller’ssolubility data are much higher and was not included in fitting the regression line. The at the high concentration end than either STR~EL (19~~,DAv~andC0~1~~~197l)orour~n~~a~ do not document a reversal in the solubility behaviour Of6 betweeu 2.0 and 5.0 m NaCl as predicted by the Pitzer t fo~ulation and as observed in this study. MOJ_I.ER ( 1960) useda EDTA complexometric technique to deINTERCEPT 0.051 io.003 SLOPE termine strontium ~n~n~tioos and it is possiblethat -0.002 to.uw minor ~u~e~ng of sodium ion by EDTA at these high NaCl concentrations resulted in anomoiously high strontium ~~~n~tions. This problem of possible matrix effects influencing the determination of strontium was not addressed by MULLER(1960). Figure 7 presents the solubility data of STROBEL (1966)and this work at IO,20,30 and 40°C and other data of SlWBEL (1966) at selected temperatures. It can be seen that the predict& soiubility behaviour using the Pitzer equations accurately and ~~e~~y npresents the actual solubility measurements over the entire concentration of 0.05 to 5.0 m NaCl and tem~tu~ from XO*Cto 90°C. The ~ment is
E. J. Reardonand D. K. Armstrong
70
12 -
,*_
X
X 0
MijLLER STRhEL
I19601 lW66t
0
DAVIS 8 COLLINS IlP?i) X
~7 CUL8ERSON lt O! 11676) + TWS STUOY
i 0
I I
I
2 NOCI
I
3 I lnoktlity)
1
I
J
4
s
6
FIG. 6. Resultsofcehstite sohtbiity measummentsin N&l solution at 25’C from this study along with previouslypub ~~~~~~~~~~~~~ basedon the PitrerFormulationas describedin the text.
indeed superb, and attests to the ~~~ of these reiations to predict mineral ~lu~ti~ in hi&Iv saline waters. CELRSTiTR S0LUBiLITY IN SEZELWATER AND MIXED&ALT SOLUTIONS cbs%SON
et al. (1978) conducted celestite solu-
bihty measurements at 25 ‘C in synthetic seawater and in three additional saline waters with chemical cornpositions simi& to seawater. The synthetic seawater was 0.4852 mNa+, 0.01058 mK+, OAHO68 mCa*+, 0.05518 mMgz+, 0.5682 mCK- and 0.02927 msd;. The other three waters di&ed from seawater oniy in the relative ~~~ of calcium and magnesium. Table 6 lists these chemical di&renoes and the rest&s of the sohibihty meesutements. Although it is not known to what extent solid sohttion e&ct.s may play in a&cting celestite solubihty in mixed-s& systems like seawater, the Fitaer relations can be applied to caicufate the solubihty of pure c&s&e in these &IItions as a comparison with the ex&ntal values. All the additional parameters totiythe Pitxer model that are not inch&d in Table 5 were taken directly from T%itvIEef al. (1984). cVLf3~t60~ etal.(1978) aiso applied the Pitaer reMions to cornpam the predicmd with the measured fifty for one of their synthetic seawaters. Their pmdicted vahie is includedin Table 6 along with the values calcuiated in this investigation. There is a large difference between the pmdicted solubility of celestite in seawater calcu;iatadby_ERSON er al. (1978) and our value, compare 0.345 vs. 0.403 miRimoIa1. We are not sure exactIy why this should be the case. However, a somewhat &Brent set of interaction parameters were used in this study based on the more recent compilations by PITZER ( 1979) and
HARVIEet al. (1984) and the experimental work of I&YEER( 1965). This, coupled with the fact that higherorder electrostatic terms incorporating asymmetric mixing effects were not considered by CULBERSON d al. (1978), may account for this difference. ROGERS (198 1) also used the Pitzer formulation to compare predicted celestite solubihties with Cuiberson’s data. These values are recorded in the last column of Table 6. ROGERS(1981) used a somewhat higher solubility product for celestite than determined in this study (compare ~15:of 6.614 vs. 6.632). It is seen that our vahtes are siigbdy lower and hers slightly higher than the actuai measured values. The differences between predicted and measured solubi~ities for seawater-type solutions using the Pitzer formulation thus appears to be at the Ievel of uncertainty in the solubility product used in the calculations. CULBERSON et al. (1978) made four additional solubihty measurements of celestite in various solutions at the same ionic strength as seawater. Table 6 shows a comparison of the predicted and experimental vaiues. In these solutions, the solubihties are about an order of magnitude higher than in the seawater solutions because of the absence of sulphate in the original equilibrating solutions. Again, however. the agreement between predicted and measured values is excellent for all solutions with the maximum deviation being on the order of three percent. 6 6O.C 0
6
6r
PIG.7. Results of cekstite solubility measurements in NaCl sohuiotu determiacd in this study (A’s) and thoseof !3W.U@%
( 1966) (o’s) at vwiouss&cctedUmpcrptuns. The wiid curve in usch of the gmpbs 3xpftsmt.9the solubilitykehatiow as
predicted by
the
t?trer equattons
celdte
lolobility
Results of csleatite conducted by Culberaon Tabulated aolubilitiea. millimolalitiea.
meaaurehenta in Svntbetic et al. (1978) aa cmmred t0 predicted expreaasd in concentrationa are
Table 6. amwater
Solution
ca
Sewatcr Saline 1 Saline 2 Saline 3
10.78 0.0 27.95 44.91
55.19 05.98 38.01 20.99
0.416 0.414 0.423 0.422
0.7 mNac1 0.7 mKc1 0.233 nCaC1. 0.233 JIgCl.
3.23 3.42 4.14 3.74
a Calculated from Culbcraon using the Pitzer relationa 6.616 at 25-C. b
Calculated in pK for cclaatits
c
Calculated
Sr(pradka
Sr(m*aa)
Ng
2 t ? *_
t ? +_ +
0.001 0.001 0.002 0.004
et and
(1981)
0.345 -
using
PERFORMANCE OF THE PITZER FORMULATION FOR DILUTE SOLUTIONS In electrolyte solutions where there are strongly associating pairs of ions such as is o&n the case with 2:2 or higher valence type electrolytes, it is often not possible to accurately represent activity coefficient behaviour in dilute solutions (CO. 1 m) with the Pitxer formulation. This problem was first addressed by PITZER and MAYORGA (1974) who introduced the addition of the 8”’ term to the second virial coefficient expression. It can be shown on a theoretical basis that 8(‘) is equal to -K/2 at infinite dilution, where K is the association constant for the ion pair or complex. Op-
Sr(prad)=
0.408 0.403 0.411 0.416
0.429 0.426 0.430 0.434
3.18 3.33 4.16 3.83
al.‘a their
A final test of the formulation can be made with the celestite solubility data of DAMS and COLLINS( 197 1). They measured celestite solubility in three mixed-salt NaCl-type brines. The compositions and the measured and predicted solubilities are reported in Table 7. In performing the calculations we added the small concentrations of Br to the Cl concentration. The maximum ditkence between the measured and predicted celestite solubilities mcorded in Table 7 is 2.5%. Putting it in another way, the ditkrence between measured and predicted solubilities would correspond to an uncertainty in the solubility product of celestite used in the calculations of less than 0.01 pK units.
Table 1. mixed-salt (1971). aolubilitiea
sr(prsd)b
0.01 0.02 0.01 0.01
this atudy uaiag the of 6.632 at 25-C.
by Rogera
71
Bolubility
tabulated calculated
Pitter
pK for
relationa
cclsatitc
‘L.,. pK fo9
value obtained ccleatitc of
and our
of
aatimated
8.814.
emtionally, however, a”’ is treated as a titting parameter in the mgression analysis of osmotic or activity coefficient data at low concentrations. Latge negative values of 8”’ indicate strong ion association. I-IARVIEef cf. (1984) discussed at length the limitations of this ap preach and suggest& in the case of 2:2 electrolytes, that for flz) values lower than about -250, a superior fitofthedataisachievedby recog&ing the ion pair or complex as a separate species. This greatly increases the complexities of the computations, however, and in addition, nquires an iterative solution in applying the model. Computationally, it is clearly advantageous if this approach need not be taken. We present a test of the parametem for SrSO, adopted in this study to describe the dilute solution behaviour in Fig. 8. The diffiia in the negative logarithms of the solubility products for the pure water solubility runs calculated using the ion pairing model (see Table 3) and the Pitxer formulation am plotted versr4.stemperature. The ditferences are seen to be very small ranging from 0.0 15 pK units near 25°C to 0.025 pK units at higher temperatures. We have found that all differences can be removed by adopting a f12)value of -78 and a temperature derivative value of -9.2. A 8”’ value of -78 is seen to be well above a value of -250 at which consideration of a separate species, i.e. Sa, would be recommended.
Comparison of meaaured and predicted celaatite lolubility In NaCl-type brinea. gxperimental data from Davis and Collins All concentrations ace axpreaasd ln lolalitiea. SFSO. are erpreaaad in lillimolslity.
NO
I%
wcr
K
Cl
nr
SrSo. meaa
srS0, prod
Brine
1
1.218
0.0250
0.0206
0.0051
l.SO2
0.013
4.43
4.33
Brine
2
1.140
0.0374
0.0023
0.0051
l.s65
0.019
5.02
4.92
Brine
3
2.436
0.0499
0.0411
0.0193
2.011
0.025
5.22
5.09
72
E. J. Reardon and D. K. Armstrong 0.02
of saturated electrolyte mixtures of NaCl with Na#& and with MgCl* J. Solution Chem. 12, 187- 199. ENOSTUN B. V. and TURKEVICHJ. ( 1960) Solubility of tine particlesof strontium sulfate. J .4mer. Chem. Sot. 82,4502-
r
4509.
e 8 -0.04 t - 0.06 1 0
I 20
I 40
I 60
I 80
I 100
T *C FIG. 8. A plot of the difference between p&o, calculated using the Pitzer relations and pK_ values recordbd in Table 3. Use of &,,, of -78 and afl’)/~?Tof -9.2 reduces the differences to zero at all temperatures.
We must point out that we cannot unequivocally recommend a set of interaction parameters for SrXh atthistime.Idcally,they&auldbedetamincdthrough regrc%ion analyses of activity codE&nt data or solubility&tainsystemswhereslleastoneoftheions Sr” or amay be vuiai over a wide concentration
range such as the ternnry sywms Na2SOrSrS04 or SrClrSrS04. The sohhility data in the !3rSOcNaCl system is not approprh inthisnprdDuctoalack of data or a lack of data of su&icnt quality in the appropriate systems, this analysis cannot be made at this time. Until such time as thoa data become available the adoption of the C&JO, parameters as a proxy for SrS04 should yield reaa~nable predictions of the solubility of c&&c in mixad-& solutions. Acknow/e&emenfs-The
authors woti IiLe to extend their apprcci&ontoG.MicbardfbrtbecditorirlbandIinpPndto the anonymous reviewers whooe very cIose reading and detailed critique aided con&erably in the lwiaion oftbe manuscript. This project was funded by the National Science and Engineering Research Council of Canada. Editorial handling: G. Micbard
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GALLOG. (I 935) Equilibrium of strontium sulfate and water at various temperatures. ‘4nn. Chim. .4pplicata 25, 628631. HAASJ. L. and FISHERJ. R. (1976) Simultaneous evaluation and correlation of thermodynamic data. Amer. J. Sci. 276, 525-545. HARVIE C. E. and WEARE J. H. (1980) The prediction of mineral solubilities in natural waters: The Na-K-Mg-CaCI-S0,-H210 system from zero to high concentration at 25°C. Geochim. Cosmochim. Acta 44,98 l-988. HARVIE C. E., ~LLER N. and WEARE J. H. (1984) The prediction of mineral solubilities in natural waters: The NaK-Ma-Ca-H-Cl-SO‘-OH-HCOXO,-COT-H,0 svstem to high ionic strength; at 25°C. 6eociim. i’osmoc& Acta 48,723-75 1. KOHLRAUSCHF. ( 1908) Saturated aqueous solutions of sparingly soluble salts (II). The solubilities and their change with temperature. 2. Physik. Chem. 64, 129-169. LANIERR. D. (1965)Activity coefficients of sodium chloride in aqueous three-component solutions by cation-sensitive glass electrodes. J. Phys. Chem. 69,3992-3998. LIE~ERK. H. (1965) Radio&n&he Messungder Lijslichkeit von Erdalkalisulfaten in Wasser und in Natriumsulfatl& sungen. Z. Anogr. Allgem. Chem. 335,225-23 I. MARDENJ. W. ( 19 16) Solubilities of the sulfates of barium, strontium, calcium and lead in ammonium acetate soh~tions at 25” and a criticism of the present mahods for the sep aration of these substances by means of ammonium acetate solution. J. Amer. Chem. Sot. 38, 310-316. MONNIN C. and SCHOTT1. (1984)Determination of the solubility products of sodium carbonate minerals and application to trona deposition in Lake Magadi (Kenya). Geechim. Cosmochim. Acta 48,Y 1-58 1. MOLLERG. (1960) Die Liislichkeit von Coelestin (SrSOI) in w&serigen NaCI- und KCI-Liisungen. Neues Jahrb. Mineral. Mon. 1960, 237-239. NORTHN. A. (I 974) Pressure dependence of SrSO, soiubiiity. Geochim. Cosmochim. Acta 38, 1075-108 I. PITZERK. S. (1975) Thermodynamics of electrolytes. V. Effects of higher-order electrostatic terms. J. Solution Chem. 4,249-265. PITZER K. S. (1979) Theory: Ion interaction approach. In Activity Coejicients in Electrolytes Solutions, Vol. I (ed. R. M. PYTKOWICZ~. DD. 157-208. CRC Press inc. PITZERK. S. and KJM J. J. (I 974) Thermodynamics of electrolytes. IV. Activity and osmotic coefficients For mixed electrolytes. J. Amer. Chem. Sot. 96, 5701-5707. PITZERK. S. and MAYORGAG. (1974) Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 2-2 electrolytes. J. Solution Chem. 3, 539-546. REARDONE. J. (1983) Determination of SrSa ion pair formation using conductimetric and ion exchange techniques. Geochim. Cosmochim. Acta 47, 1917-1922. ROGERSP. S. 2. ( 1981) Thermodynamics of geothermal fluids. Ph.D. thesis, Univ. of California, Berkeley, 243 p. ROGERSP. S. Z. and PITZER K. S. (198 I) High-temperature thermodynamic properties of aqueous sodium sulfate solutions. J. Phys. Chem. 85,2886-2895. SELIVANOVA N. M. and ZUBOVAG. A. (1956) Polarography and thermodynamics IV. Thermodynamic properties and solubility of strontium sulfate. Trudy Moskov.Khim.-Teknol. Inst. im. D.I. Mendeleeva 1956, 38-46. SILVESTERL. F. and PITZERK. S. (1977) Thermodynamics of electrolvtes. 8. High temperature properties, including enthalpy and heat c&city, with application to sodium chloride. J. Phvs. Chem. 81. 1822-1828. STROBELG. (1966) Die hydr&hermaie Laslichkeit von Cislestin im System SrSO,-NaCl-H20. Neues Jahrb. Mineral. Mon. 1966,99-107. I,
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.