J . Phys. Chem. 1986, 90, 3009-3013 or for the pure fused salt reference state (In yJ)DH= -z,~ A,((2/p) In [(I z,q1
+ ~ Z , l / ~ ) / ( +l p(z,0)1/2)] + - 2Z,/Z?)/(l + pZ,'/2)] (37)
Here Z," is the ionic strength of the pure fused salt which is 2;/2 for the MX type. One may note that when z; reduces to zero, eq 36 and 37 reduce to eq 3 1. W e have written these equations for ions of charge zJ for general interest even though our applications will involve only singly charged ions. For a single solvent of known properties and a defined value for p, the various Debye-Huckel terms are fully determined and the only disposable parameters are those in the short-range-force function. Also, as noted above, there is a relationship between p and these last parameters. Consequently, the value of p and the form of the extended Debye-Huckel expression should be stated clearly in all cases. The situation is more complex for systems with more than one neutral species, Le., for mixed solvents. If one accepts the macroscopic dielectric constant of the mixed solvent, as seems best, and takes M a s the mean molecular weight of the solvent, then A, is determined by eq 33. But A, is now a function of the solvent composition. Thus, differentiation of the excess Gibbs energy,
3009
eq 32, will introduce derivatives of A, into the expression for the activity coefficient of a particular solvent species. The physical picture related to these composition derivatives of D and of A , is a preferential solvation of ions by one species of solvent. This is primarily a short-range effect which is also represented by terms for short-range forces as given in the previous section. If the excess Gibbs energy is taken as the basic expression, the results for the various activities will be consistent, but the equations become complicated. The best procedures should be explored for real systems involving electrolytes in mixed solvents. It should also be mentioned that this entire treatment is designed for liquid systems well removed from the critical region. Near the critical point or critical curve the compressibility becomes very large and special effects arise. Also the Debye-Hiickel derivation basically involves the Helmholtz energy and the ionic concentrations. The simple conversion to Gibbs energy and mole fraction is a satisfactory approximation only for relatively incompressible fluids.
Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Division of Engineering and Geosciences of the US. Department of Energy under Contract No. DE-AC03-76SF00098,
Thermodynarnlcs of Multicomponent, Miscible, Ionlc Systems: The System LiNO3-KNO3-H,O John M. Simonson* Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
and Kenneth S . Pitzer Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: September 17, 1985; In Final Form: January 24, 1986)
Vapor pressures of water over KN03-H20 and LiN03-KN03-H20 (50.34 cation 7% Li) are reported in the temperature range 373 C T/K C 436. Water activities calculated from these vapor pressures and other available results are fitted to an equation appropriate for multicomponent electrolyte solutions which are miscible to fused salts. The resulting equation gives the excess Gibbs energy over the complete composition range of the three-component system. Parameters for the binary fused salt mixture are determined from aqueous solution data and compared with approximate values calculated from phase diagrams. Excess thermodynamic properties, including solute activity coefficients and excess enthalpies, are calculated from the model.
Introduction Electrolyte-molecular solvent systems which are miscible at moderate temperatures from dilute electrolyte to the fused salt are relatively uncommon, but are of interest for both theoretical and practical reasons. There are electrolytes of industrial or geological interest which become extremely soluble in water at high temperature and pressure. Any new type of system is of theoretical interest. Thus we chose to investigate a prototype system. Mixtures of metal nitrates, with relatively low melting temperatures and high solubilities in water, have been the most extensively studied systems of this type. Solvent activities in these solutions have been determined by direct vapor pressure,'** isopiestic: differential transpiration," and dew point methods.' A
complete, consistent description of the measured thermodynamic properties of very concentrated systems has not been available due to limitations in the composition range of the experimental results and the lack of a comprehensive set of modeling equations appropriate for multicomponent mixtures of electrolytes in molecular solvents. In this work we report the results of water vapor pressure measurements over K N 0 3 solutions near 393 and 423 K,and over the mixed electrolyte system LiN03-KN03-H20 near 373, 393, and 436 K. These results are combined with other available data and treated with equations developed in an accompanying paper to give a consistent and comprehensive representation of the thermodynamic properties of the LiN03KN03-H20 system.
(1) Trudelle, M.-C.; Abraham, M.; Sangster, J. Can. J. Chem. 1977, 55,
Experimental Section Lithium nitrate was prepared by neutralizing a hot-filtered solution of lithium hydroxide (Fisher Scientific) in distilled water
1713. (2) Campbell, A. N.; Fishman, J. B.; Rutherford, G.; Schaefer, T. P.;Ross, L. Can. J. Chem. 1956, 34, 151. (3) Braunstein, H.; Braunstein, J. J . Chem. Thermodyn. 1971, 3, 419. (4) Tripp, T. B.; Braunstein, J. J. Phys. Chem. 1969, 73, 1984. (5) Tripp, T. B. J . Chem. Thermodyn. 1975, 7, 263.
0022-3654/86/2090-3009$01.50/0
(6) Tripp, T. B. Proc. In?. Symp. Molten Salts, Princeton, NJ 1976, 560. (7) Sacchetto, G. A.; Bombi, G. G.; Ma-, C. J . Chem. Thermodyn. 1981, 13. 31.
0 1986 American Chemical Society
3010 The Journal of Physical Chemistry, Vol. 90, No. 13, 1986
To Vocuum
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Simonson and Pitzer
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TABLE I: Measured Water Vapor Pressures and Calculated Activities T IK
PlkPa
XI
f/kPa
folkpa
ai
102.95 97.70 102.83 105.11 99.66 99.20 98.59 99.61
0.9100 0.8560 0.7442 0.7297 0.5676 0.4516 0.2983 0.2609
374.03 372.55 373.99 374.62 373.1 1 372.98 372.80 373.09
0.8977 0.8485 0.7540 0.7401 0.6110 0.521 1 0.3948 0.3593
F = 0.5034 95.00 93.68 84.70 83.63 77.39 76.52 77.57 76.70 57.05 56.57 45.10 44.80 29.54 29.41 26.09 25.99
392.66 392.10 392.67 390.99 392.26 392.79 39 1.61 392.55
0.9043 0.8170 0.7983 0.6985 0.6386 0.6087 0.5380 0.7217
F=O 180.04 176.29 164.88 161.71 164.35 161.22 142.49 140.09 140.72 138.41 136.98 134.80 124.70 122.87 153.25 150.53
191.01 187.68 191.07 181.23 188.63 191.79 185.16 190.35
0.9229 0.8616 0.8438 0.7730 0.7338 0.7029 0.6636 0.7908
393.49 393.36 393.78 393.69 393.54 393.64 393.84 393.96
0.8832 0.8022 0.7079 0.6246 0.5043 0.3856 0.3409 0.2925
F = 0.5034 177.05 173.46 157.85 154.99 136.79 134.65 114.91 113.40 85.52 84.68 58.01 57.62 49.02 48.75 40.72 40.52
196.02 195.21 197.81 197.25 196.35 196.94 198.18 198.89
0.8849 0.7939 0.6807 0.5749 0.43 13 0.2926 0.2460 0.2038
426.40 422.50 421.85 423.91 423.36 422.45 421.76 422.25
0.8480 0.8355 0.6284 0.5234 0.4409 0.3335 0.6730 0.3865
F=O 442.71 427.12 401.83 388.46 318.45 309.97 292.43 285.41 255.25 249.86 212.70 208.92 325.47 316.59 218.10 214.12
497.34 449.45 441.78 466.32 459.66 448.88 440.71 446.43
0.8588 0.8643 0.7016 0.6121 0.5436 0.4654 0.7184 0.4796
436.35 435.98 435.96 436.09 435.91 435.18 436.04 435.87 436.15 436.13 435.96
0.9298 0.8803 0.8334 0.7420 0.6926 0.6147 0.4885 0.3766 0.2554 0.21 14 0.1800
F = 0.5034 619.34 591.86 579.19 555.04 548.17 526.50 475.03 458.74 429.71 416.33 366.32 356.50 274.96 269.46 196.78 193.95 117.83 116.82 93.77 93.12 75.57 75.15
637.53 631.87 631.50 633.47 630.72 619.65 632.78 630.08 634.41 634.17 631.50
0.9284 0.8784 0.8337 0.7242 0.6601 0.5753 0.4258 0.3078 0.1841 0.1468 0.1190
I
El
Figure 1. Block diagram of vapor pressure apparatus: (a) pressure indicator; (b) capacitance manometer; (c) temperature indicator; (d) valve manifold; (e) prepressurization cell; (f) sample cell; (g) oil bath; (h) platinum resistance thermometer; (i) magnetic stirrers; (j)air oven (thermostat); (k) stirring motor.
with nitric acid (Mallinckrodt AR Grade). The resulting solution was concentrated and cooled to precipitate lithium nitrate trihydrate. The trihydrate was recrystallized twice from distilled water, then dried under vacuum over P205for several days to yield the anhydrous material. Potassium nitrate (Mallinckrodt AR Grade) was dried over P,05 in a vacuum desiccator before use. A mixed salt of 50.34 mol % L i N 0 3 composition was prepared by fusing weighed amounts of the dried lithium and potassium nitrates under vacuum. Samples for vapor pressure experiments were made up from this mixed fused salt or potassium nitrate and degassed distilled water. Appropriate amounts of water and salt were loaded into borosilicate glass sample cells, attached to a vacuum line, and degassed by repeated freeze-pump-thaw cycling. Degassed samples were frozen and transferred to the vapor pressure measurement apparatus, then evacuated while thawing for final sample degassing. The vapor pressure apparatus is shown schematically in Figure 1. The sample cell, a prepressurization cell containing degassed distilled water, and a stainless steel valve manifold were maintained at the temperature of the experiment in a double walled, forced circulation cylindrical air oven with a contact thermometer temperature regulator. Short-term temperature fluctuations of the sample were minimized by immersing the sample cell in a stirred oil bath. A calibrated platinum resistance thermometer was used to measure the oil bath temperature to fO.O1 K. Pressures were measured with an independently thermostated capacitance manometer (MKS Instruments, Model 315 BH lOo00). The pressure transducer and inlet line were maintained approximately 10 K above the sample temperature to prevent condensation. After temperature equilibrium was attained the prepressurization valve was opened and the pressure in the apparatus dead volume increased to near the estimated experimental vapor pressure. This prepressurization eliminated flashing of the solution, and minimized changes in solution concentration due to solvent vaporization. Vapor pressure and sample temperature were recorded at intervals over a period of time and, after attainment of equilibrium, the readings were averaged to give the temperature-pressure value for each run. Solution compositions were
determined by weight after the vapor pressure measurements. No corrections to solution concentration due to vaporization were necessary for these experiments.
Results Experimental results of this study are presented in Table I. The composition variable xIis the mole fraction of water on an ionized solute basis *1
=
nl/(nl
+ Zn,)
(1)
where the sum is over all ionic components. Vapor pressures of pure water and corrections for vapor nonideality necessary to calculate solvent activity from the measured vapor pressures were calculated from the equation of state of Haar, Gallagher, and Ke1LS Experimental error in the vapor pressure measurements, estimated from the internal consistency of calculated water ac(8) Haar, L.; Gallagher, J. S.; Kell, G. S. In Proceedings of the 8th Symposium on Thermophysical Properties; Sengers, J. V., Ed.; American Society of Mechanical Engineers; New York, 1981; Vol. 11, p 298. Proceedings of the 9th International Conference on the Properties of Steam; Straub. J . , Scheffler, K., Eds.; Pergamon: Oxford, UK, 1980: p 69.
The Journal of Physical Chemistry, Vol. 90, No. 13, 1986 3011
Multicomponent, Miscible, Ionic Systems tivities, is about &OS% for experiments at lower temperatures (to 393 K); the results at higher temperatures show a greater uncertainty of about *2%. Values of water activity for LiN03-KN03-H20 (50.34 mol % Li) near 373 and 393 K were compared with those calculated from the isopiestic molalities reported by Braunstein and Braunstein3 using LiCl reference solution activities taken from Gibbard and Scatchard9 at 373 K and from Holmes and Mesmer'O at 393 K. Agreement of the water activities is within the estimated uncertainty of our measurements. From the equations for mixed-electrolyte thermodynamic properties developed in the accompanying paper (specifically eq 26b and 31), the activity of water in the LiN03-KN03-H20 system is written as a function of solution composition as
TABLE II: Fit Parameters and Uncertainties ab
bb X 102/K
-3.582 (10.017) 0.759 (i0.050)
1.156 (10.041) 0.55 (10.10) -1.007 (f0.044) 0.899 (f0.070) 0.253c
parameter' wI,MX uI,MX wI,NX U1,NX
0.688 (f 0.019)
x: ; ;2
-2.865 (h0.073) -1.88 ( f O . l l )
1 = H20, M = Li', N = K', X = NO
