2688
The Journal of Physical Chemistry, Vol. 82,No. 25, 1978
Eliezer et ai.
obtained by the method of Schreinmakers.14 Crystallographic Data f o r 3 and 4. 3. The crystals of enantiomer are monoclinic' with a = 6.766 A, b = 9.949 A, c = 8.121 A, p = 114.62'; space group P2,, Z = 2. The crystals of racemate are monoclinic with a = 6.743 A, b = 10.025 A, c = 8.085 A, /3 = 114.20'. The space group is either P21 or P2,/m, Z = 2. 4. The crystals of enantiomer are orthorhombic8bwith a = 8.089 A, b = 10.097 A, c = 12.404 A; space group P212121,Z = 4. The crystals of racemate are orthorhombic with a = 8.037 A, b = 10.119 A, c = 12.488 A. The space group is either Pnma or Pna&, Z = 4. Refinement of the Solid Solution Structures.20 The enantiomer molecular model is used. A coordinate system S is attached to the molecular group and defined as follows: origin N(1); Ox parallel to N ( 1 ) - 0 ( 6 ) ; Oy parallel to C(2)-C(5). The position of the group in the cell is given by the crystallographic coordinates uluzu3of the origin of S and three orientation angles 818283. S being in coincidence with-the cell system, a rotation of 0, around a' then e2 around b and d3 around c' lead S to its real orientation in the cell. Intensity data were collected on the Siemens four-circle diffractometer of the Laue-Langevin Institute (Grenoble). The final R value are for 3: R = 0.10, R , = 0.11 (700 intensities, 27 parameters, unit weights) and for 4: R = 0.09, R, = 0.09 (600 intensities, 36 parameters, unit weights). References and Notes
Cesario, M.; Guilhem, J.; Pascard, C.; Collet, A.; Jacques, J. Nouv. J. Chim. 1976, 2,343. Leiserowitz, L.; Weinstein, M. Acta Crystallogr., Sect. 6 1975, 37, 1463. (a) Chion, B.; Lajzerowicz, J.; Collet, A.; Jacques, J. Acta Ctystalbgr., Sect. 6 1976, 32,339; (b) Collet, A.; Jacques, J.; Chion, B.; Lajzerowicz, J. Tetrahedron 1976, 31, 2243. Chion, B.; Lajzerowicz, J. Acta Crystallogr., Sect. 61975, 37, 1430. Chion, B. Cryst. Structure Commun., 1978, 7 , 395. (a) Ament, S. S.; Wetherlngton, J. B.; Moncrieff, J. W.; Flohr, K.; Mochizuki, M.;Kaiser, E. T. J. Am. Chem. Soc. 1973, 95,7896; (b) Wetherington, J. 8.; Ament, S.; Moncrleff, J. W. Acta Crystallogr., Sect. B 1974, 30,568. Roozeboom, H. B. W. 2. Phys. Chem. 1899, 28,494. Bordeaux, D.; Lajzerowicz, J. Acta Crystahgr., Sect. 8, 1977, 33, 1837. (a) Baert, F.; Fouret, R. Cryst. Structure Commun. 1974, 4 , 307; (b) Kroon, J.; Van Gurp, P. R. E.;Onk, H. A.; Baert, F.; Fouret, R. Acta Crystalogr., Sect. 6 1976, 32,2561; (c) Oonk, H. A,; Kroon, J. ibid. 1976, 32,500. (a) Rozantzev, E. G. "Free Nitroxyl Radicals" (English translation); Plenum Press: New York, 1970; p 203; (b) Berliner, L. "Spin Labelling"; Academic Press: New York, 1976; p 183. The liquidus and solidus curves corresponding to a continuous solid solution (dotted line Figure 2) were calculated using the following data: enthalpy of fusion and melting point of the pure enantiomers, AH,' = 6.3 kcal mol-', T L = 391.5 K; melting point of the racemic form, T,' = 386 K. Details on this calculatlon will be given in a later publication. Jacques, J.; Gabard, J. Bull. SOC.Chim. Fr. 1972, 342. Ramasseul, R.; Rassat, A.; Rey, P. Tetrahedron, 1974, 30, 265. Andre, D.; Fourme, R.; Renaud, M. Acta Crystalbgr., Sect. 6 1971, 27,2371. Kitaigorodskii, A. I. "Organic Chemical Crystallography", Consultant Bureau, New York, 1967,p. 230. Bondi, A. "Physical Properties of Molecular Crystals, Liquids and Glasses"; Wiley: New York, 1968; p 453. The crystals of this solid solution contaln equimolecular populations of right- and left-handed conformations of the molecule; a fast conformational exchange in solution precludes the actual resolution of this compound. Lists of intensity data, hydrogen coordinatgs, and thermal parameters are available on request.
(1) (a) Collet, A,; Brienne, M. J.; Jacques, J. Bull. Soc. Chim. Fr. 1972, 127; (b) /bid. 1977, 494; (c) Secor, R. M. Chem. Rev. 1963, 63, 297. (2) A compilation of ca. 60 examples of solid solutions of enantiomers is being prepared for publication.
Calculation of Activities in the System KOo.5-A101,5-Si02 Isaac Eliezer," Naomi Ellerer, Reed A. Howald, and Mary C. Verwolf Department of Chemistry, Montana State University, Bozeman, Montana 59715 (Received Aprll 10, 1978) Publication costs assisted by the U S . Department of Energy
The vapor pressure of potassium has been measured as a function of temperature in the A101.5- and Si02-rich regions of the KOo,5-A101,5-Si02system. Combining this data with the known solubility relations in the system and mathematical analyses of activities in the binary subsystems leads to calculated activitiesfor all three species as a function of temperature and composition for liquids in the system KOo,5-A101,5-Si02.These calculations provide refinements in the phase diagram and in the thermodynamic properties of K2Si409,KAlOp, sanidine, leucite, and KA1Si04.
Introduction A ternary system can be analyzed thermodynamically if the activity of one component can be measured over the full range of compositions. We have measured potassium pressures over SiOz-rich liquids in the KOo,5-A101,5-Si02 system using atomic absorption measurements of the vapor diffusing from a sample cell. The technique and apparatus are described in an earlier paper on the KOo.5-Si02binary system-l However no single technique can provide accurate vapor pressure measurements over the range of pressures covered in this ternary system at a single temperature, or over the whole range of temperatures required by the high melting points of leucite, KA1Si04, KA102, corundum, and mullite. Our vapor pressure measurements over systems of three coexisting solids in the high A101.5 region of the 0022-3654/78/2082-2688$0 1.OO/O
phase diagram have confirmed the stability' of the leucite-corundum-orthorhombic KA1Si04 set of three solids, which shows an activity of 10-5.92for liquid KOo.5 a t 1700 K. Shairer and Bowen2have found that this set of three solids is in equilibrium with the liquid ternary of composition X K O o 6 = 0.2514, XA10S6 = 0.3303 a t 1826 K, a t which point the three liquid activities are calculated to be aKOos = 10-5.46 , aAIOl = 0.522, and aSiOz = 0.360. It is thus possible to obtain ah three activities at temperatures and compositions for the liquid where it is in equilibrium with three solids, and the thermodynamic analysis of the liquid should include this data. We have analyzed the liquids in the binary subsystems KOo.5-Si02,1 KOo.5-A101,5,3and A101,5-Si024 using the Redlich-Kister power series with terms through the fourth
0 1978 American Chemical Society
Calculated Activities in Ternary Systems
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978 2609
TABLE I: Thermodynamic Values Selected for Solids and Pure Liquids
H"zss,akcal
kcal @ looo,b cal CPC mol- * mol-' mol-' K-* A B C D -43.2 -36.2 18.09 9.097 0.96 KOJc) -40.628 -32.128 19.4526 11.45 1.8 KOOS(1) SiOAc. cristobalite) -216.417 -206.4 18.1108 16.72175 2.05366 -1.6518 0.6463 sialic; quartz) ' -217.7 -206.86 16.899 16.48 0.0024 3.2268 1.2384 -215.74 -205.40 18.1766 16.61 SiO,(l) 12.2175 14.908 2.3471 -1.2727 0.34615 -200.25 -190.933 ~ 0 1 ,1s ~ 17.312 d -190.358 -182.152 16.555 ~Ol.S(l) -1047.818 -991.060 101.339 85.081 9.0876 -3.1173 K,Si,O,(c) -0.77932 25.819 2.752 33.5537 25.819 -304.8457 -288.8287 KSi02.5(c) KAlO,( c ) -272.9628 -256.6458 31.3415 24.005 KAlSi,O,(c, sanidine) -945.686 -898.786 85.78 75.5 10.0 56.5 3.14 KAlSi,O,(c, leucite) -726.210 -688.280 68.585 KAISiO,(c, orthorhombic) -506.870 -479.770 50.161 42.5 KAlSiO,( c, kalsilite) -508.0846 -480.9846 50.474 42.5 -241.2315 26.478 21.6357 0.4629 -0.17804 0.04846 K0.57A10.57si%43 O2(') -255.1689 a PTis defined as ~ H f o , , ~ t , , ~J ~ ~ ~dT. . , ~@ ~ isCfree ~ energy function defined as ST- (HQT - P , , , ) / T . Heat capacities are expressed by the power series C, = A + B x 10'YT - 1000) t C x 10'6(T - 1000)zt D X lO+(T - 1000)3. At temperatures over 2000 K the values are changed to A = 27.66 and B = -2.96.
power of mole fractions. If the full ternary can also be treated with reasonable accuracy with only terms through the fourth power, this is a particularly favorable situation, since there are only three additional independent terms for a ternary system through the fourth power beyond the terms known for the binary subsystems. We have chosen5 to label these Ba321,Ca321, and Cb321 and to write the contributions to the excess free energy of mixing as Ba321 xlXZx3, Ca321X1X& (1- X3), and Cb321X1X& (XI X 2 ) , The three unknowns B'321, Ca321, and Cb321 can be evaluated from the three known activities for a liquid in equilibrium with three known solids as in the above example. As expected, the experimental errors in the equilibrium temperatures and compositions together with uncertainties in the thermodynamic properties and compositions of the solids lead to substantially different values for Ba321, Ca321, and Cb321 from different liquids even a t similar temperatures. The major discrepancies in the first calculation were in the reported2 eutectic composition for sanidinetridymite-mullite and in the relative SiOz activities for two liquids, one in equilibrium with sanidine-leucite-KzSi2O5 and the other with sanidine-K2Si05-K2Si40g. Liquid compositions near the sanidine-tridymite-mullite eutectic are so viscous2that substantial experimental errors in the solubility data are not unexpected, and the uncertainities in Si02activities can be resolved by reasonable adjustments in the thermodynamic values for K,Si40g, sanidine, and leucite, as described in this paper.
Literature Values for the Thermodynamic Properties of the Solids The three major potassium aluminum silicates at high temperatures are sanidine (KA1Si308),leucite (KA1Si206), and orthorhombic KA1Si04. Heat of formation values for all three compounds are listed in the standard compilation of Robie and Waldbaum.6 These values must be recalculated on the basis of revised enthalpies of formation of the secondary standards used for aluminum compounds, We have recalculated the enthalpies of these three compounds from the original data7-9using improved heats of formation for gibbsite,'O y-alumina,'l and A1C13.6H20.'2 Our value of AHfo298 = -726.21 kcal mol-' for leucite is based upon comparison to gibbsite, instead of A1C13.6H20 as in the original calculations of Barani and Adami12and the recalculation of Thompson.13 For KA1Si04 and sanidine our recalculated values are in agreement with previously published values recalculated by Thompson13
and Chatterjee and Johannes,14 respectively. The values we have used in our calculation are given in Table I. The KA1Si04 and leucite values in Table I are within 100 cal of the value tabulated by Hemingway and Robie,15 and the discrepancy between this compilation15 and Thompson13 for sanidine is now only 660 cal mol-l. There are third law entropies available now for these three compositions: KA1Si308 (as adularia),16 KA1Si2O6 (c, leucite),16and KAlSi0t6 (as a synthetic material called kaliophilite). Natural kaliophilite cannot be synthesized, and the temperature of synthesis and reported X-ray data indicate that this entropy value actually applies to the orthombic forms of KA1Si04. We attempted to use these third law entropies (uncorrected) for sanidine, leucite, and orthorhombic KA1SiO4. However these values would allow sanidine to disproportionate into cristobalite and leucite a t 1200 K, and are therefore not satisfactory. Even the small excess entropy (0.79 eu) used by Chatterjee and Johannes14 is not sufficient stabilization for sanidine. = 85.38 for sanidine is sufficient to prevent Using disproportionation of sanidine before its incongruent melting point, but it leaves leucite as the third solid in equilibrium with K2Si40gand K2Si205at 900 K in contradiction to phase diagram data of Shairer and Bowen.2 If the free energy function of sanidine is increased by 2 or 3 cal mo1-l K-', leucite disproportionates unless its entropy is increased relative to that of kaliophilite as well. We concluded that both leucite and sanidine may have substantial entropies of mixing due to AI-Si disorder, and we have relied on equilibrium measurements to evaluate the entropies. There is more entropy of mixing in sanidine than in leucite or KA1Si04. We have considered @looO values for sanidine from 85.38 to 90 cal mol-I K-'. The calculated excess entropy of mixing (4.4cal mol-' K-l) used by Robie and Waldbaum6 for sanidine corresponds to a value = 87.76 cal mol-' K-l which is in the middle of this range. The final value for sanidine in Table I is = 85.78 cal mol-' K-l. This value was obtained by using six of the best activity coefficient data which were independent of the absolute entropies of the potassium aluminum silicates to get a first set of estimates for Ba321, Ca321,and Cb321,and calculating aSD2(= 0.360) for the liquid present at the 1826 K eutectic for orthorhombic KA1SiO4, leucite, and corundum. The thermodynamic properties of the solid potassium silicates' and of mullite4 have been discussed in connection with the corresponding binary systems. There is not much
2090
The Journal of Physical Chemistry, Vol. 82,
No. 25, 1978
TABLE 11: Redlich-Kister Coefficients for the Binary Subsystems system quantity A B KO,,-SiO,
log ylOm -17.4226
-1.010074
Si02-A10,,, log y l w
-0.212799
0.096297
KOo,,-AIO,.,
-4.4601 -25264
1.330516 6400 log ylw0 - 1 3 . 3 8 0 5 enthalpy - 7 5 7 9 2
al.
C
-10.64114 -53000.
enthalpy - 9 0 0 0 0 CP 8
Eliezer et
enthalpy
data available for potassium aluminate, KA102, but its properties are fixed fairly closely by the vapor pressure measurements of Plante el al.17 Thus at 1400 K KA102 in equilibrium with 0-aluminate has a potassium pressure of 5.608 X lo4 atm, corresponding to an activity of KOo,@) of 4.598 X 10". The corundum-@-alumina system at this temperature has a much lower KOo.5 activity: 2.700 X The activity of alumina also varies with the composition of the 0-alumina to satisfy the Gibbs-Duhem relationship. The ratio of mole fractions is somewhere between 0.1/0.9 = 0.111 and 0.167/0.833 = 0.200. For a 0-alumina in equilibrium with KA102 at this temperature, a, = 4.598 X and a2 = 0.319 f 0.118. When the calculation is repeated at another temperature, we have both enthalpy and entropy of KA102 fixed at least approximately to the values shown in Table I. The melting point of KA102 is approximately 2373 K.18 From the compositions of the solid and liquid in equilibrium at 2096 K19 we have estimated the equilibrium constant for the reaction of KA102(s) KA102(1)as 0.834, and the heat of fusion as 12.92 kcal mol-l. This fixes the Redlich-Kister A values for enthalpy and log y for the K00.5-A101.5binary liquid system. The B values also shown in Table I1 are arbitrarily picked as 1/3A, so that Rl and log y reach maxima at X1 = 0, because this is closer to the behavior found for the KOo,,-Si02 systems than setting the B values equal to zero.
10-7'
,
,
,
,
,
,
,
,
,
a0
6b
.
,
,
65
\ ,
\
,
.
,
, 70
io4/ T, K-' Figure 1. Four lines of potassium pressure vs. l/Tobserved for high alumina samples in the system KOo 5-A101.5-Si02.
used, the activity of liquid Si02 in equilibrium with the two solids at 968 K is too low, only 0.250. It appears that the narrow temperature range between 1043 and 1015 K is not sufficient to give the enthalpy accurately enough to extrapolate down to 968 K. The phase diagram of Shairer and Bowed shows the K2Si205-K2Si409liquid curve a t higher Si02 mole fractions and activities than the leucite-sanidine liquid line. While most of the adjustment to bring about agreement has been in the entropies of leucite and sanidine, we have also adjusted the enthalpy of K2Si409to reduce AH for the reaction
-+
Adjustment of the Thermodynamic Values for K2Si409,Sanidine, Leucite, a n d KA1Si04 We have measured vapor pressures of potassium over systems of three coexisting solid phases in the alumina-rich region of the ternary phase diagram. Three reproducible pressure vs. temperature curves were observed in addition to that for the 0-alumina-corundum system known from the binary system. These four lines of log P vs. 1/T are shown in Figure 1,labeled as L, B, M, and H in order of increasing activity of KOo.&They correspond to activities for liquid KOo,5at 1700 K of 10-5.921,10-5.705, 10-5.095,and 104sM, respectively. One of these values should correspond to equilibrium with leucite and orthorhombic KA1Si04. The third law entropy values for these solids gave U K O ~ = for the leucite-orthorhombic KAlSi04-coruhdum system at 1700 K, which is between the values for the L and M curves. We have tried adjustments of the entropy values to bring the liquid activity to 10-5.921for KA1Si04-leucite-corundum or to 10-5.095for KA1Si04leucite-p-alumina. The first of these assignments is not only consistent with the solubility data of Shairer and Bowen,2 but provides an overall better (smaller positive deviations from ideality for Si02) set of activities and activity coefficients over the full range of compositions for the ternary system. Solid KzSi,O9 melts at 1043 K and appears in the phase diagram in equilibrium with liquid down to the eutectic with K2Si205at 1015 K. At 1015 K the activity of liquid Si02in equilibrium with these two solid potassium silicates is about 0.323. Although this value should decrease with decreasing temperature, if the enthalpies from ref 1 are
,
-
1/2K2Si409(c) 1/2K2Si205(~) + Si02(l)
~
down to 1.3 kcal mol-l (instead of 7.3 kcal mol-I). With this adjustment, the activities of SiOz and KOo.5in the equilibrium eutectic liquid at 968 K are aSiOz = 0.313 and uKOos = 0.269 X lov9. Thus, two of the activity coefficients in this liquid are known even if the entropy of sanidine is uncertain. In the course of a long series of trials on this ternary system we came to the conclusion that the most reliable equilibrium data of Shairer and Bowen for liquid in the presence of three solids was at 1826 K, with the values at 968, 1083, and 1588 K the next most reliable data. The 1083 K equilibrium with sanidine, leucite, and K2Si205is extremely dependent upon the values selected for sanidine and leucite, but the other three points each supply two clearly established activities and activity coefficients. In principle, six values are enough to calculate the values and temperature dependence of B'321, Ca321, and Cb321. However in practice, the least-squares treatment had to be limited to fewer unknowns to avoid magnification of random errors. We have arbitrarily assumed that each of these values has a temperature dependence such that a linear plot of Ba321, Ca321, and Cb321vs. 1 / T passes through the origin. For example Ba321(r) = Ba321(looo)/(lOOO)/ T. These assumptions applied to our six selected data points gave B'321 = 0.75, Ca321 = -1.30, and Cb3z1 = -5.58 at 1000 K. With these values, we calculated usion = 0.360 for the eutectic liquid at 1826 K, of composition Xsio2 = 0.417, XAIO1,S = 0.330, and XKOo6 = 0.252. This fixes the free energy function values for orthorhombic KA1Si04 and leucite at the values shown in Table I. The value for sanidine is then determined by the sanidine-leuciteK2Si205liquid equilibrium at 1083 K. Once these values are fixed, the four major points give a total of 12 activity coefficient values. A new least-squares treatment of these
Calculated Activities in Ternary Systems
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978 2691
TABLE 111: Comparison of Thermodynamic Values at 298.15 K for High Sanidine from Recent Work kcal mol-'
H"298,
this work ref 14 Z = 0.0984 2 = 0.1607 ref 15
s",,,, cal mol- ' K' I
-945.686
54.96
-945.521 -945.686 -046.350
53.38 53.26 55.664
TABLE IV: Extended Redlich-Kister Coefficients for the Ternary Liquid System KO,,-AlO,,,-SiO, H,,,,kcal C, cal term log Y lnnn mol-' mol'' K-I
A13 B13
-13.3805 -4.4601 -1 7.422 66 -10.64114 -1.010074 1.330516 -0.212799 0.096297 1.4667 -2.4659 -4.8201
-7 5.7 92 -2 5.264 -90.000 -53.000 0 6.4 0 0 6.711 -11.283 -22.055
0 0 8 0 0 0 0 0
.32 0 0
12 values gave the final values Ba321 = 1.4667, -2.4659 and C"321 = -4.8201 a t 1000 K.
Ca321
=
Sanidine occupies a position in a great variety of equilibria of geological and technical importance. Thus there have been and will continue to be heated arguments in the literature on the best interpretation of the available thermodynamic and equilibrium data. We are making the point in this paper that solubilites and vapor pressures in the K00,5-A101,5-Si02system provide data on these values, but we do not wish to discount the information from hydrothermal equilibria or even calculations of the temperature dependent disorder present in the crystals. The important point to be established now is that information from a great variety of sources is becoming available, and the remaining uncertainties are getting smaller. Thus we feel that Table 111, comparing our values with other recent p a p e r ~ , will ~ ~ Jbe~ of more value than arguing the relative merits of the differing values. Extended Redlich-Kister Coefficients for the T e r n a r y System As mentioned in the Introduction, since the binary subsystems are represented with reasonable accuracy with two or three Redlich-Kister coefficients, we can expect that we can do a similarly adequate job for the entire ternary using only terms through the fourth power in mole
fractions. This is convenient because it leaves only the three terms Ba321,CR321,and Cb321 to be evaluated at a particular temperature, and this can be accomplished from three activity coefficients for a single liquid. Thus, those liquid compositions found by Shairer and Bowen2 to be in equilibrium with three solids of differing stoichiometry take on special significance. Shairer and Bowen2 have identified eight such liquids, and it is possible to calculate values for Ba321, Ca321, and Cb321for each one. Unfortunately the calculated values are very sensitive to the entropy values used for the solid potassium aluminum silicates, and it was necessary to get estimates for the three terms from the few activity coefficients independent of these entropy values. The values were then refined by least squares to give the final values in Table IV. The enthalpy coefficients are fixed by the form of the temperature dependence which was assumed (Ba123(T)= Ba12,(1000) [ l O O O / T I , etc.). The single heat capacity value, Ba321(Cp) = -32 cal mol-l K-I was selected to cancel most of the contribution from B13 = +8 along the Si02-Ko.5Al,,50 join. With these values we can calculate the activities of all three components for any selected temperature and composition for the liquid phase. Table V shows a comparison of the activities for the liquids found by Shairer and Bowen in equilibrium with three solids of different compositions. The agreement for the 1826 K point is very good, while the values for the other three points included in the least-squares procedure are within &35%. The fit at the 968 K eutectic is the least satisfactory. It can however be improved considerably by a small adjustment in the temperature and composition (from 968 K, X1 = 0.356, X2 = 0.0346, X 3 = 0.6409 to 973 K, Xi = 0.372, X2 = 0.045, X3 = 0.583). For the points not included in the least squares in Table V (generally at higher mole fractions of Si02), the agreement is not as good. Shifting the compositions to less Si02 generally improves the fit, but it is also clear that using this set of Redlich-Kister coefficients exaggerates the positive deviations from ideality shown by Si02. The calculation does come quite close to the measured cristobalite solubilities at higher temperatures, but apparently this set of parameters gives too large a temperature dependence for log ysio ; the values of Ifsiozare too large. Since the major contribution to Ifsio2in this region is from B13, it is clear that an improved fit of these points will require more accurate enthalpy data for the KOn,-SiO, binary system. (This may be obtainable from dataon heat capacities and heats of solution of glasses in the NaOo.,-Si02 ternary system.) Nevertheless, this set allows calculations of reasonable accuracy (h50%)over much of the composition range.
TABLE V: Comparison of Calculated Activities for Liquids in Equilibrium with Three Solids of Three Different Compositions S R symbol C A P N U 968 1083 1178 temp, K 1826 1588 983 1413 solids present leucite leucite sanidine leucite sanidine sanidine sanidine kalsilite mullite quartz leucite KAlSiO, K2Si,09 leucite mullite corundum K,Si,O, K,Si,O, corundum corundum K,Si,O, liquid compn XI 0.2524 0.3559 0.3730 0.4467 0.1655 0.2720 0.1471 0.3303 0.1526 0.03462 0.05689 0.2035 0.04078 0.08192 0.4173 0.4713 0.6310 X, 0.6094 0.5702 0.7003 0.6873 Calcd from Properties of Solids U , X 109 3468 0.2688 27.15 17.87 4.730 68.01 0.0817 0.00076 0.00021 0.3450 0.00036 0.000274 0.2340 a2 0.5216 0.3134 0.3033 0.3644 0.4912 0.7672 0.7004 a3 0.3604 Calcd from Redlich-Kistler Coefficients a,X l o 9 3824 0.1613 3.354 95.92 185.9 11.46 0.0312 0.2214 0.3085 0.00033 0.00259 0.5290 0.00060 0.00021 (12 0.4060 0.3047 0.05243 1.065 0.9310 1.004 a3 0.3721
x,
M 1258 sanidine tridymite mullite 0.1159 0.1229 0.7612 0.3727 0.1351 0.7757 1.157 0.2119 1.123
2692
Eliezer et al,
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
1 2200
2000
-5 1800 n. m
-6 1600
-7
I
I
7
6
5
1400
1&/T
Figure 2. Comparison of measured and calculated (solid lines) pressures of potassium atoms. The diamonds and upper line are for a composition = 0.36, XM,, = 0.04,XsD, = 0.60. The circles and the lower of XKoos = 0.13, XAIOls = 0.07,Xslo, = 0.80. line are for a sample with XKOod
H,,, kcal log Y low
mol-'
A' B
-3.343539 4.023792 -0.411118
-16.0933 20.4465 -0.7052
c'
6
.4 xs102
.2
'"
0
K.541.50
Flgure 3. A calculated portion of the phase diagram from leucite to KA102.
TABLE VI: Redlich-Kister Coefficients for the
,530,-K,,AI,,OPseudobinary Subsystem term
1200
C,, cal mol-' K-l
0
4 0
Figure 2 shows a comparison of the calculated and experimental potassium pressures for two selected compositions in the high SiOz region.
Thermodynamic Properties of the Tetragonal Phase The data of Cook et al.19 on the SiOz-KA1O2 join in this ternary system show that there is a tetragonal phase with 4302 in equia composition approximately K0,j7A10.57Si0 librium with orthorhombic KA1SiO4 at 1700 K. Thus one expects to find vapor pressure readings for the set of three and we have solids KA1Si04-Ko,57Alo,j7Sio,430z-~-alumina, assigned the free energy of K0,57A10,57Si0.430z at 1700 K to fit the observed KOo,5activity on the H curve, 10-4.544, for this equilibrium set of solids. The X-ray dataz0 clearly indicate that the tetragonal phase is a high temperature material, so the reaction 0.43KA1Si04 + 0.14KA102 K0.j7A1057Si0.4302
-
is expected to be endothermic. If it is endothermic by as much as 2 kcal mol-' the calculated melting point for K0.57A10,j7Si0.430z is too high (over 2300 K). The enthalpy and entropy values in Table I for K0.57Al057Si0.4302 are assigned assuming AH = 1 f 1kcal mol-I for this reaction.
Calculations of Phase Equilibria on the Si02-Ko,sAlo.50 Join The extended Redlich-Kister coefficients in Table IV allow one to calculate Redlich-Kister coefficients for various pseudobinary mixtures within the ternary phase diagram, The Si02-Ko.5Alo50pseudobinary is one of the most important of these because of the number of potassium aluminum silicates found along it. The Redlich-Kister coefficients calculated for this pseudobinary are listed in Table VI, and Figure 3 shows a calculated phase diagram for the low SiOz region along this join where the melting points are so high that they are not well established. The excessive positive deviations from ideality calculated from these values at lower temperatures and
high SiOz mole fraction introduce substantial distortions of the phase diagram for XsiOz> 0.6, so this region is not shown in the figure. Leucite, KA1SiO4, and K0,j7A10,57Si0.4302have been treated as stoichiometric compounds for this calculation, although they all have been shown to have somewhat variable compo~ition.'~ The solubility of SiOz in K0,5A10,50 is so substantial that it has been necessary to assign Redlich-Kister parameters for the K0,5Alo.50 cubic phase: Ala = 1.499 and B I Z= 5.934. These values were selected to give a eutectic between Ko.sAlo.jOand the tetragonal phase at 2100 K, and they give calculated equilibrium compositions for Ko~jA1o~jO at lower temperatures in substantial agreement with the X-ray data.19 The liquidus curve for Ko,5A10.50saturated with SiOz is very sensitive to the melting point of pure Ko.5Alo.50and the assumption made concerning its heat of fusion. Therefore the lines are likely to be substantially in error and are shown as dotted lines in Figure 3. They are excessively steep because the assumption we have used requires SiOz to stabilize solid Ko~jAlo,jO more than the liquid, and thus suggests that SiOz addition may raise rather than depress the melting point of potassium aluminate. This possibility is worth considering in interpreting the scanty data available on the melting point of potassium aluminate.1s~20
Potassium Vapor Pressures in the High A101.5Region In the course of these calculations we have assigned three of the four observed potassium pressure vs. temperature curves in Figure 1 to equilibrium sets of three solid materials as follows: L curve, leucite-KA1Si04-corundum; B curve, KA1Si04-corundum-~-alumina; and H curve, KA1Si04-tetragonal phase-&alumina. These assignments serve to fix the thermodynamic properties of these solids, so the agreement between calculated and observed potassium pressures must be good. One can however check the assignments using any other equilibrium measurement on the solids. Seki and Kennedyz1 have studied the disproportionation of leucite 2KA1SizOG(c,leucite) KAlSi,O&c,sanidine) + KA1Si04(c,kalsilite) as a function of temperature and pressure. Knowing the volume change for this reaction and the equilibrium +
Solubility and Activity Coefficients of Salts in Synthetic Seawater
The Journal of Physical Chemistry, Vol. 82, No. 25, 1978
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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).
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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
