J . Phys. Chem. 1990, 94, 1175-1179
1175
Vapor-Liquid Phase Equilibria of Potassium Chloride-Water Mixtures: Equation-of-State Representation for KCi-H20 and NaCI-H,O Jamey K. Hovey, Kenneth S. Pitzer,* John C. Tanger IV,' Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
James L. Bischoff, and Robert J. Rosenbauer US.Geological Survey, Menlo Park, California 94025 (Received: July 26, 1989) Measurements of isothermal vapor-liquid compositions for KCI-H20 as a function of pressure are reported. An equation of state, which was originally proposed by Pitzer and was improved and used by Tanger and Pitzer to fit the vapor-liquid coexistence surface for NaCl-H20, has been used for representation of the KC1-H20 system from 300 to 410 "C. Improved parameters are also reported for NaC1-H20 from 300 to 500 OC. Introduction The equation of state proposed for mixtures of NaCl and H20 by Pitzer and co-workers'-" has provided very useful results over the entire range of NaCl concentrations at vapor + liquid saturation pressures and temperatures from 300 to 600 "C. The universality of the equation, however, has not been tested to date because of the lack of accurate measurements obtained over substantial ranges of temperature, pressure (or density), and composition for other aqueous salt systems. The present work reports new precise experimental isotherms for KCl-H20, both in the near-critical region and along the three-phase line, and an application of the equation of state to these data. Recently, more precise measurements have been reported5 for NaCI-H20 in the range 380-41 5 "C, and the entire array of experimental data for that system has been critically evaluatede6 This new information has been used to refine previously reported value^^.^ for the NaCl-H20 equation-of-state parameters over the temperature range of the evaluation6 (300-500 "C). Thermodynamic properties of single and mixed aqueous salt solutions in the critical region are very important theoretically and for numerous applications in geochemistry and engineering. This study presents a comparison of the equation-of-state parameters for the KCl-H20 and NaC1-H20 systems at conditions ranging from subcritical to supercritical for pure H20. The similarity of the thermodynamic behavior of these systems leads to simple suggestions regarding expected behavior for the ternary system NaCI-KCI-H20. Experimental Methods Experimental methods were similar to those described in Rosenbauer and Bischoff and Bischoff and Rosenbauer* except that a larger (26.5 mL) Rene 4119 pressure vessel was used. This vessel was equipped with larger (0.125-in. 0.d.) sampling and adjustable-dip tubes that were fitted with Inconel-600 wire inserts to reduce the dead volume through the sampling valve to 0.2 mL. Temperature was maintained by a vertically positioned two-zone Marshall resistance furnace and controlled by a Research Inc. Microstar dual-channel PID controller (Model 828B). Temperature gradients were minimized by a large copper block machined to the contours of the pressure vessel and a system of resistance shunts in the furnace that allows fine tuning of the temperature profile. The maximum temperature gradient from the bottom to the top of the pressure vessel was 0.2 "C. Temperature was measured by two 100-Q platinum RTD's (Yellow Springs Instrument Co., Inc.) individually calibrated to an NBS standard and monitored by using an Instrulab 4200 digital readout. Total error of the temperature measurements was deemed to be f0.02 OC. Temperature variations during the course of a single Present address: Simulation Sciences, 1051 W. Bastanchury Rd., Fullerton, CA 92633.
0022-3654/90/2094- 1 175$02.50/0
experiment were f0.05 "C and between experiments f0.3 "C. Pressure was measured simultaneously by three redundant strain gauge transducers (Setra Systems Model 204E, Precise Sensors Model SC450 and FLW Model 2004), each dead weight calibrated and accurate to * O S bar. Variations among the three readouts are included in the reported pressure interval for each sample. Liquid samples were taken from the bottom and vapor samples were taken from the top of the reaction vessel and were analyzed for K by atomic absorption (Perkin-Elmer Model 370) and C1 by chloride titrator (Radiometer/Copenhagen Model cmtl0). Relative precision of the analysis is 1% for concentrations of K and C1 above 0.5 wt %, 2% for concentrations between 0.5 and 0.05 wt %, and 5% for concentrations below 0.05 wt %. Experimental Results The KCI two-phase boundary was determined in the critical region for two isotherms at 380 and 410 "C. Measured pressures and compositions extend from the critical point down and along each vapor and liquid limb about 10-12 bar in order to define the apex of the curve. Tables I and I1 show the individual experimental points; pressures are averages of the sampling intervals, and the f values indicate the sizes of the intervals. The temperature-pressure relations of the three-phase assemblage from 350 to 480 "C are shown in Table I11 and are consistent with the study of KeeviL9 Three vapor compositions along the triple point curve are shown in Table IV. The large uncertainty associated with these compositions is due to kinetic effects and not analytical error. These errors are larger than for a similar study with the system NaC1-H20S and appear to be due to sluggish kinetics of vapor-liquid equilibration during sampling. Apparently, such equilibration is significantly slower for KCl-H20 than for NaCl-H20. Equations The equation of state used here results from a simple expansion about the critical point of water.' The effect of the electrolyte is expessed by a very small number of temperature-dependent terms in increasing powers of the amount of salt added and of the density difference from the critical density of HzO. It is convenient to take as a basis 1 mol of H 2 0and y mol of salt; thus, (1) Pitzer, K. S.J . Phys. Chem. 1986, 90, 1502. (2) Pitzer, K. S.; Bixhoff, J. L.; Rosenbauer, R. J. Chem. Phys. Let?.1987, 134, 60. (3) Pitzer, K. S.;Tanger, J. C., IV Int. J . Thermophys. 1988, 9, 635. (4) Tanger, J. C., IV; Pitzer, K. S . Geochim. Cosmochim. Acfa 1989,53, 973. (5) Bischoff, J. L.; Rosenbauer, R. J. Geochim. Cosmochim. Acra 1988, 52, 2121. ( 6 ) Bischoff, J. L.; Pitzer, K. S.Am. J . Sci. 1989, 289, 217. (7) Rosenbauer, R. J.; Bischoff, J. L. Geochim. Cosmochim. Acta 1987, 51, 2349. (8) Bischoff, J. L.; Rosenbauer, R. J. Earrh Planer. Sci. Lett. 1984, 68, 172. (9) Keevil, N. B. J. Am. Chem. SOC.1942, 64, 841.
0 1990 American Chemical Society
1176
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
TABLE I: KCI Content of Vapors and Liquids as a Function of Pressure along the Two-Phase Solvus at 380.1 f 0.3 O C " vapor liquid f wt % KCI Plbar f wt % KCI Plbar 235.5 0.6 0.381 235.0 0.3 0.84 1.04 235.2 0.6 0.350 234.8 0.3 0.89 0.5 0.279 234.6 0.4 235.0 1.17 0.5 0.3 234.9 0.278 234.5 1.32 234.6 0.4 0.209 234.1 0.3 1.25 234.4 0.4 0.179 234.0 0.3 1.44 234.3 0.4 0.172 233.8 0.5 1.58 234.1 0.4 0.156 233.5 0.5 1.72 234.0 0.4 0.149 233.1 0.5 1.92 233.9 0.4 0.147 232.6 0.7 2.85 233.8 0.4 231.4 0.4 0.156 2.94 0.4 233.8 0.5 0.133 231.3 2.95 233.6 0.6 0.132 23 1.2 0.4 3.08 0.4 0.136 23 1 .O 0.4 233.5 3.18 0.4 0. I37 230.9 233.4 0.3 0.124 230.5 3.40 233.2 0.5 0.4 230.1 3.50 233.1 0.4 0.5 0.133 3.81 0.129 229.8 233.0 0.6 0.5 3.98 0.127 299.4 232.8 0.4 0.6 0.1 18 228.9 4.26 232.8 0.5 0.6 0.122 228.0 5.12 232.4 0.4 0.3 5.20 0.113 227.8 232.2 0.6 0.4 0.115 227.5 5.32 232.0 0.4 0.4 0.104 227.2 5.54 231.6 0.5 0.5 5.71 0.110 227.0 231.5 0.5 0.5 5.94 0.099 226.7 230.8 0.7 0.5 0.4 0.101 226.3 6.10 230.3 0.5 0.090 226.0 0.5 6.36 229.8 0.5 0.9 0.093 225.5 6.59 229.6 0.5 0.8 7.65 228.8 0.3 0.088 224.0 0.2 7.80 0.086 223.8 228.8 0.4 0.3 0.083 223.6 7.96 228.4 0.4 0.9 0.084 223.4 8.18 228.2 0.4 0.8 0.08 1 8.38 227.6 0.4 223.1 1.4 8.40 0.072 223.0 226.4 0.5 0.068 0.9 222.5 8.58 226.2 0.5 0.066 0.9 222.4 8.78 224.6 0.4 0.061 1.7 222.9 9.36 223.8 0.5 "f"represents the pressure range during sampling
TABLE 11: KCI Content of Vapors and Liquids as a Function of Pressure along the Two-Phase Solvus at 410.2 f 0.2 OC" liquid vapor Plbar f wt % KCI Plbar f wt % KCI 309.2 0.7 3.62 309.3 0.3 4.42 309.1 1.5 3.90 308.6 0.5 2.41 308.5 0.5 2.22 308.6 0.4 5.52 0.5 1.97 308.3 308.0 0.5 6.21 307.8 0.6 1.80 308.1 0.4 5.8 1 307.4 0.5 1.78 308.0 0.3 6.58 307.3 0.7 1.70 307.9 0.5 6.82 307.1 0.6 1.62 307.6 0.4 6.99 306.7 0.7 I .47 307.4 0.4 7.22 306.5 0.7 307.2 0.4 7.42 I .49 306.4 0.7 1.42 0.4 7.77 306.7 306.0 8.12 0.6 1.32 306.2 0.4 305.4 0.7 1.24 305.7 0.5 8.43 305.2 0.7 1.16 305.1 0.4 8.89 304.6 0.7 1.11 302.5 0.6 10.51 304.3 0.7 302.0 0.5 10.94 1.03 304.0 0.8 1.05 301.6 0.5 1 1.05 303.5 0.8 0.98 301.3 0.5 11.23 303.1 0.7 0.93 301.0 0.5 11.36 302.4 0.7 0.88 300.6 0.5 11.62 302.2 0.8 0.88 300.3 0.5 11.71 301.4 0.6 0.78 299.8 0.6 12.01 300.7 0.6 0.72 299.3 0.5 12.23 298.9 0.6 12.57
Hovey et al. TABLE III: Temperature and Pressure Relations of the Three-phase Assemblage Vapor-Liquid-Sylvite rl°C Plbar tl°C Plbar t/"C Plbar 347.5 82.1 399.7 126.5 459.8 178.4 377.5 107.1 419.1 143.9 480.1 193.4 398.5 125.5 439.4 161.7 TABLE IV: Temperature, Pressure, and KCI Content of Vapor in Equilibrium with Liquid and Sylvite rpc Plbar wt % KCI 398.8 f 0.2 125.7 f 0.1 0.0013 f 0.0005 458.3 f 0.2 177.5 f 0.2 0.0053 f 0.0002 498.7 f 0.2 205.1 f 0.1 0.0128 f 0.0020
weight fraction salt) and define the reduced density d = p(H20)/p,(H20), with p,(H20) the critical density of pure water. Then one writes for the pressure
P=
PH20(T,d)+ y[b,o + bl,(d - 1)
+ ...I + y2[b20+ ...I + ... (1)
where PH20represents the pressure of pure water at T and d as derived from any appropriate equation of state for pure water; we use the Haar-Gallagher-Kell'o (HGK) equation. It has been demonstrated that only three parameters (namely, bIo, 611, and b20)are required to yield results to within reasonable estimates of uncertainties of experimental results. Higher terms could be included but were not required for the extensive range of data for NaCl-H,O. The physical significance of each of the parameters has been discussed by Pitzerl and Tanger and P i t ~ e r . ~Clearly, .~ the blo and b l l terms arise from the hydration of the electrolyte, the blo term is for water of critical density, and the bll term is for the effect of change from critical density. At zero concentration, the salt will be fully dissociated so that this should be the sum of the hydration effects for the ions. We know, however, from the conductance measurements of Quist and Marshall,, that NaCl in critical H 2 0is a weak electrolyte and that it is largely associated to ion pairs at the concentrations we consider. Thus, the blo term actually represents the hydration effect of a distribution of ion pairs together with some separated ions and the b,, term gives the combined effect of a change in density of water on the hydration process and on the degree of association of the salt. The y2b2,,term, which is included, becomes important only for quite concentrated liquids where various binary solute interactions will be present. As done by Tanger and Pitzer,jy4 the Helmholtz free energy can be derived from the original equation (1) by appropriate integration, (dA/ad)T= Pu,/&, introduction of an ideal mixing term, and addition of a temperature-dependent term proportional to the salt concentration but independent of density:
Here u, is the critical volume and uH is the molar Helmholtz free energy of pure water at the conditions of interest. The Gibbs free energy of 1 mol of solution is given by G/(nHzO + nKCI) = (1 - x)gH20(T,d)+ RT[X In X + (1 x ) In (1 - x)] + xu,bll(l + In d ) + xg*KCI(T)(3) Determination of the P-x isothermal coexistence curve starts with calculating the reduced density as a function of concentration of salt using eq 1 (with appropriate equation-of-state parameters). Then, substitution of these results into eq 3 yields the molar Gibbs free energy of the solution as a function of the mole fraction of the salt. The compositions of vapor and liquid phases in equilibrium can then be characterized by equating chemical potentials
represents the pressure range during sampling.
a "f"
y is the mole ratio and the mole fraction x = y / ( 1 + y ) . We use the density of water in the system, p(H20) = p(solution)(l -
(10) Haar, L.; Gallagher, J. S.; Kell, G. S. NBS-NRC Sreom Tubles; Hemisphere: Washington, DC, 1984. (11) Quist, A. S.; Marshall, W. L. J . Phys. Chem. 1968, 72, 684.
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1177
Vapor-Liquid Phase Equilibria of KC1-H20 of the solute and solvent in the two phases, which is conveniently done by using the double-tangent method with the G x expression. The beauty of this simple equation of state is the ease by which other thermodynamic quantities can be derived. The present equation of state has been used to derive the following expressions for the chemical potential, p, entropy, S, internal energy, U,and isochoric heat capacity, C,:
R T In (1 - x ) (5)
of the three parameters, it was possible to carry out a regression of selected and weighted experimental points and to obtain improved parameters for NaCl-H20 and new values for KCl-H20. In general, the experimental data for NaCl-H20 were taken from the critical evaluation of Bischoff and Pitzer6 while the data for KCl-H20 were those of Tables I-IV with additional values from several s o ~ r c e s . ~ J ~ - ~ ~ It was convenient to generate equations for properties on the three-phase line. Specifically, separate equations were developed for the pressure, the liquid composition, and the vapor composition as functions of temperature. The details are given in the Appendix. NaCl-H20 and the General Method. At each temperature in the NaCl-H20 system for which critically evaluated data were available from Bischoff and Pitzer: four sets of equation-of-state parameters were used to calculate four separate isotherms. The first set consisted of the original parameters listed by Tanger and Pitzer,“ while each of the other three sets corresponded to a small finite shift in one of the three parameters. Normally, vapor and liquid roots were determined for seven or eight pressures a t each temperature for which evaluated data were available.6 These calculations led directly to a series of equations of the form a116b10 + a126bll + a136b20 = a 1 4
+ an26b11 + an36b20 = an4 where each matrix coefficient on the left was derived by observing the change in the logarithm of the composition (mole fraction of vapor or liquid) that the corresponding 66 effected, where all 66 values are referenced initially to the values generated with the original NaCl parameters. As an example, all can be calculated from the equation 1% (XI.2) - 1% (XI,I) (14) *I1 = anlablo
( y;)]
T-db20) + ( d l n d + -1) b l l - T dT
+yh*KCI(r) (7)
(9)
Apparent molar volumes, 4V, enthalpies, @L,and heat capacities, W p ,can also be calculated from the following relations:
{ln d +
:)% + “p
=
bll(l
1
+ In d) + h*Kcl(T) (12)
(g) P
where d,,, and dH represent the reduced densities for water in the solution and for pure water, respectively, at the specified temperature and pressure. Evaluation of Equation-of-StateParameters It is not feasible to obtain the parameters by a direct regression of experimental points on an isothermal coexistence curve. Rather, some type of iterative procedure must be used. In this case, we had relatively good starting values from refs 3 and 4 and assumed that the effects of a small adjustment in any parameter would be linear. With these linear relationships determined for each
6blO where x1,2and xl,l are mole fractions of the liquid root at some specified pressure for the coexistence curve generated by 610 + 6bl0 and blo, along with identical bll and b20values, respectively. All coefficients correspond to the differences required (on a log basis) for the composition calculated from the original parameters to agree exactly with experiment. The final matrix for NaCl-H20 had the dimensions 230 X 4 and was used in a weighted least-squares procedure to derive appropriate temperature dependences for each equation-of-state parameter optimized as 66 = b(T,new) - 6[ T,NaCl(original)]. A sequential fitting of the temperature dependences of the parameters from optimizations at specific temperatures proved unsatisfactory because of the interdependence of all parameters. The global optimization of all parameters simultaneously considering all available experimental data proved best. The total error of fits with smoothed parameters (weighted sums of squared deviations) was only about 15% higher than with unconstrained fits at each temperature. The selected equations that represent the temperature dependences of all parameters for the NaCl-H20 system are similar to past equations4 and are given by the following: bl0 = 592539.86 - 845.47387 + 0.3928056P - 1.383656 X 10*/T (15) bll = 21251.84- 29.70891T-9.716411 x l O I 4 / P (16) b2o = 44637.41 - 63.27050T - 9.769747 X 1O2O/P (17) (12) Benedict, M.J . Geol. 1939, 47, 252. (13) Khaibullin, Kh.; Borisov, N. M. Teplofiz. Vys. Temp. 1966, 4, 489 (English translation). (14) Zarembo, V. I.; Antonov, N. A.; Gilyarov, V. N.; Ferdorov, M. K. Zh. Prikl. Khim. (Leningrad) 1976, 49, 1259 (English translation). (IS) Wood, S. A.; Crerar, D. A,; Brantley, S. L.; Borcsik, M. Am. J . Sci. 19114. 284. -.- ., - ., 668. - - -. (16) Benrath, Von A.; Gjedebo, F.; Schiffers, B.; Wunderlich, H. Z . Anorg. Allg. Chem. 1937, 231, 285. (17) Potter, R. W.,11; Babcock, R. S.; Brown, D. L. J . Res. US.Geol. Surv. 1977, 5, 389.
Hovey et al.
1178 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
1
I80 160-
0 NaCI.VLS. Bischoff and Pitzer (1989) 0 NaCI. Bischoff and Pilzer (1989) A KCI (smoolhed). present work
'c3' x K C I . Zorembo eroi 11976) 0 KCI. Khoibullen and Bor~sav119661 3 NoCI. Bischotf and Pitier A KCI. VLS
\a
100
A KCI, V L S - NaCI. present work .__ _work KCI. _ present
(19891 350°C
I--
N a C " Tanger and Pitzer 11989)
- 300 - 260 - 220
220 -
- 180
180-
- 140
140\
h
40
A
,
1
IO-*
IO-'
IO-I
I
X
Figure 1. Fitted vapor and liquid compositions along the 300 and 350
OC isothermal coexistence curves for KC1-H20 and NaCI-H20. Also shown are the results of the original equation-of-state parameters for NaCI-H20 from Tanger and P i t ~ e r . ~ Each parameter has the dimension pressure and is in bar. KCI-H20. An identical treatment was used to generate equation-of-state parameters for the KCl-H20 system except that because of the lack of reliable data over wide ranges of temperature, calculations were performed at the four temperatures stated below. Initial analyses using the KCl-H20 data from Khaibullin and Borisov13 from 250 to 440 OC proved unsatisfactory because of uncertainties in these data. The only coexistence data chosen for analysis, in addition to the present results, corresponded to temperatures with extremely well defined liquid compositions and vapor compositions that can be regarded only as rough estimates. KCl-H20 coexistence data at 300 and 350 OC from Khaibullin and Borisov,I3 Zarembo et al.,I4 and Wood et al.I5 were used in addition to the results presented in Tables 1-111, and equations listed in the Appendix, to derive temperature-dependent equation-of-state parameters for this system over this temperature range. The vapor-phase compositions along the three-phase line were determined by interpolation of the data given in Table IV and were estimated outside of this range as described in the Appendix. The differences in parameters between the KCI-H20 system and the new smoothed expressions for NaCl-H20 were fitted by the matrix mfficient/global optimization scheme described above. The differences were constrained to be of an identical form for each of the parameters described by eqs 15-17. These difference expressions lead directly to the following equations that describe the temperature dependence of the KCI-H20 parameters from 300 to 410 OC. b,o = 116989.96 - 157.8381 T
+ 0.06641785P - 3.039773 X 10717- (18)
b l l = -4452.32 b20
= -37956.21
+ 2.11429T-
+ 45.321673-
1.958284
1.831384
X
X
I O i 4 / 7 " (19)
1020/76
(20)
Results The results of the present analysis are shown clearly in Figures 1 and 2 for the 300, 350, 380, and 410 OC isotherms. Depicted in these plots are curves rqpresenting the present fits to both NaCI-H20 and KC1-H20 coexistence curves and comparison with Although the results from the previous s t ~ d yfor ~ ,NaCl-H20. ~ parameter values in the temperature-dependent equations differ substantially between KCI and NaCI, the values of blo, b , , , and bzo at any given temperature are quite similar. As described earlier, the present equation-of-state representation, in terms of expressions for the temperature-dependent parameters, can be used to generate various thermodynamic functions. Many of the most important functions were calculated previous19 for the NaCI-H20 system. We have not repeated these
Figure 2. Fitted vapor and liquid compositions along the 380 and 410 "C isothermal coexistence curves for KC1-H20 and NaCI-H20. Also shown are the results of the original equation-of-state parameters for NaC1-H20 from Tanger and Pitzer4and smoothed KCI-H20 coexistence data at rounded pressures as derived from Tables I and 11.
calculations. Since the present parameters for NaCl-H,O do not differ greatly from the previous values, however, the general conclusions from the earlier calculations remain valid.
Discussion The close similarity of the vapor-liquid coexistence surfaces for NaCl-H20 and KC1-H20 is not surprising. The critical pressures at 380 and 410 OC are slightly higher for KC1, as is the breadth of the coexistence curves in the near-critical region, but only very precise measurements can demonstrate such small differences. There is a marked difference, however, for the equilibria with the solids. KCl is more soluble, which yields a lower three-phase pressure for KCl-H20 than for NaCI-H,O. It is interesting to consider the three-component system NaCl-KC1-H20. In that case, eq 1 becomes P = PH20+ y , [ b ( $+ b\',)(d - l ) ] + y,[b('d + b\?)(d - l)] + y126&') + + 2~Iy2b&~'(21) where y , and y 2 are the mole ratios of NaCl and KC1 to H 2 0 , respectively, and the superscript numbers indicate parameters for NaCl and KC1 in a corresponding manner. Equation 21 can be integrated to yield the Helmholtz energy and further manipulated to yield other quantities including the chemical potentials of each component in a manner corresponding to that of eqs 2-13. All of the parameters of eq 21 except that for the cross term bib2)are known from the binary systems. It would be reasonable to take bib2)as either the arithmetic or geometric mean of b&') and b$i2);in this case, either choice would yield about the same result. Since the KCI-H20 and NaCl-H20 parameters are near1 the same, it is apparent that eq 21, with a mean value for bi012r, will predict nearly ideal mixing of the two salts on a molal basis. It will be interesting, however, to test the precise predictions of eq 21 for the ternary system at 380 and 410 OC when separate values are available for the KC1 parameters. The new equation for NaCl-H20 fits the improved data base more accurately in several regions than the old e q ~ a t i o n ,al~,~ though perfect agreement is not possible from such a simple equation. The new fitting procedure reduces considerably the maximum deviations on the vapor side. The agreement on the liquid branch is good for both old and new equations. Since we gave less weight to the critical pressure than before, we do not expect improvement for that particular quantity. The largest change is for the vapor composition at temperatures below the critical point of H 2 0 and at pressures from 80% to 90% of the vapor pressure of H20. The vapor is very dilute and measurements are very difficult in this region. The old equation yielded vapor compositions that were much larger than the experimental values, and the improvement with the new equation is very apparent in
Vapor-Liquid Phase Equilibria of KC1-H20 600
1
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1179 TABLE V: Coefficients for Eq A-1-A-3
500T
P%
i
NoCl
1 2 3 4 5 6
Bischoff and Pltzer (1989)
400
r
bi
0,
-308.19 5.01055 -3.13178 X lo-' 9.29982 X -1.19918 X lo-' 5.46864 X IO-"
6.50905 X lo6 -2.91285 X lo4 41.2623 7.59889 X lo-*
n
ci -6.6887 9.6353 X lo-)
,
\
a 300
KCI (vapor) Vapor + Liquid +Solid (soturation pressures)
200
500 IO0
t/'C
10-8
10-2
10-6
-
I
0 present work
'NoCI
Figure 3. Fitted vapor and liquid compositions along most of the crit-
ically evaluated isothermal coexistence curves for NaCI-H20.6 4
,
1
'
3oot
1
4
KCl(liquid) Vapor + Liquid +Solid (saturation pressure)
wt %
t
i
400t
I
0 Benedicl (19391
Keevil (1942) A Poller et ol (19771 - - - H a l l e/o/ (19871 C 3
