CRYOSCOPIC BEHAVIOR OF SOLUTES IN MOLTEN ALKALINITRATES
2493
Cryoscopic Behavior of Selected Solutes in the Molten Alkali Nitrates.
I.
Molten Lithium Nitrate’
by R. E. Isbell, E. W. Wilson, Jr., and D. F. Smith Department of Chemistry, University of Alabama, University, Alabama
(Received January 18, 1966)
Freezing point measurements were taken on dilute solutions of several salts in molten lithium nitrate as a solvent. It was found that many of these solutions exhibit ideal behavior as evidenced by excellent agreement of the experimentally obtained freezing point constant for lithium nitrate with that obtained using the reported heat of fusion for lithium nitrate. Thermodynamic stability constants were determined in lithium nitrate and lithium nitrate-sodium sulfate or sodium chloride mixtures for CdS04, PbSOd, CuSO4, CoCI2, CoS04, and CdF2. It was noted that the copper sulfate-lithium nitrate and cadmium sulfate-lithium nitrate systems may contain complexes of the type C U ( S O ~ ) ~ ~ and Cd(S04)22-. Finally, it was found that the cadmium fluoride-lithium nitrate system did not appear to have any complexes formed in the concentration ranges investigated.
than those afforded by the pure salts alone. It is the purpose of this paper and the succeeding ones in The determination of stability constants for complex this series to present new data concerning stability ions in fused-salt media, and in particular the alkali constants of complex ions formed from the addition of nitrates, has been the subject of a substantial number inorganic salts to molten lithium, sodium, and potasof papers during the past few years. The methods emsium nitrate, in order to complement and enlarge upon ployed for gathering the necessary data have included existing information. This will be done using the polarographic peak height a n a l y s i ~ s, ~ p e~c~t r o ~ c o p y , ~ ~ ~ general experimental technique of Van Artsdalen. galvanostatic measurements,6electromotive force meas-
Introduction
urements,’ solubility,* vapor pressure measurements, and cryoscopy.lo Although electromotive force measurements are by far the most popular method, the cryoscopic technique has been used on various fusedsalt systems in many instances.11~*2 One of the earliest papers concerned with the existence of complex ions in an alkali nitrate solvent was that of Van A r t ~ d a l e n who , ~ ~ measured the depression of the freezing point of sodium nitrate due to the addition of the chlorides of cadmium, lead, copper, and zinc. The investigation indicated that these solutes were only partially dissociated in the solvent system studied. Van Artsdalen then proceeded to derive expressions to calculate the “ionization constants” of these substances in sodium nitrate and in mixtures of sodium nit>rateand sodium chloride. Most investigators in the references cited have preferred to use as solvents the eutectic mixtures of the alkali nitrates, presumably in order to work at lower temperatures
(1) This work was supported by Grant No. (40-1)-2065from the Atomic Energy Commission. (2) Yu. K. Delimarskii and X. F. Grischenko, Ukr. Khim. Zh., 29, 507 (1963). (3) J. H . Christie and R. A. Osteryoung, J . Am. Chem. SOC.,82, 1841 (1960). (4) D. M. Gruen and R. L. McBeth, J . Phys. Chem., 63, 393 (1959). (5) I. V. Tananaev and B. F. Dahurinskii, Dokl. Akad. Nauk SSSR, 134, 1374 (1960). (6) D. Inman and J. 0. M. Bockris, Trans. Faraday Soc., 57, 2308 (1961). (7) J. Braunstein, M. Blander, and R. M. Lindgren, J . Am. Chem. Soc., 84, 1529 (1962). (8) F. R. Duke and M. L. Iverson, J . Phys. Chem., 62, 417 (1958). (9) J. L. Barton and H. Bloom, Trans. Faraday SOC., 5 5 , 1792 (1959). (10) E.R. Van Artsdalen, J . Phys. Chem., 60, 173 (1956). (11) J. Goodkin and G. J. Janz, “Cryoscopy and Constitution of Molten Salt Mixtures,” AFOSR-TN 58-736, 1958. (12) B. R. Sundheim, Ed., “Fused Salts,” McGraw-Hill Book Co., Inc., New York, N. Y., 1964.
Volume 70, Number 8 Augzlet 1966
R. E. ISBELL, E. W. WILSON,JR.,AND D. F. SMITH
2494
0
Experimental Section Materials. The chemicals used in this study were of high quality reagent grade and were used without further purification. All substances were dried to constant weight just below their melting points. In the case of the hydrates, after the salts were heated to a constant weight, an analysis was made to check that the stoichiometric composition was correct. Lithium nitrate was used as the solvent, and this salt was dried at 200" in an oven for 20-24 hr, then placed in a Marshall tube furnace and kept in a molten state for 10-12 hr. Apparatus. The freezing point determinations reported in this study were carried out in a Marshall ceramic tube furnace, 6.0 cm in diameter X 32.0 cm in length. A stainless steel inner liner of 5.80-cm outside diameter and 5.1-em inside diameter was inserted into the furnace to smooth out thermal gradients and to increase the heat capacity. The sample was contained in a Pyrex glass tube, 5.0 ern in outside diameter and 25.4 cm in length, which seated snugly into the liner cup when cold. A constant-temperature zone was obtained in the furnace by use of shunts of resistance wire. -4n infrared lamp placed near the mouth of the sample tube helped keep the top of the melt from freezing too quickly. Stirring was accomplished with a reciprocating stirrer constructed from Inconel. The stirrer had a 1.5-in. stroke and was driven at a rate of 60 strokes/ min. It was of simple construction and consisted of two arms welded perpendicularly to a 0.5-in. nut at the top and to an assembly of four parallel and coplanar Inconel washers 0.25 in. apart at the bottom. The washers contained 0.25411. holes which produced turbulence and hence stirring on moving the stirrer up and down in the melt. The temperature of freezing was measured by means of a 28-gauge platinum-platinum-lOO/o rhodium thermocouple. The cold junction of the couple was sealed into a 6-in. Pyrex tube and placed in a stoppered 33 X 7 cm dewar flask filled with crushed, distilled waterice. The hot junction of the thermocouple was encased in a 6-mm Pyrex glass tube and placed near the center of the solution and arranged so that its position remained unchanged from one run to the next. The emf produced by the thermocouple was fed into a Leeds and Northrup Type E(-3 potentiometer and opposed by a potential 1-50 pv smaller. The net emf was then amplified by a Leeds and Northrup stabilized dc microvolt amplifier (Model 9835-A), and the magnitude of the signal recorded on a Leeds and Northrup Type G, 1-10 mv Speedomax recorder. The recorder plotted emf vs. time, thereby Oracing cooling curves The Journal of Physical Cherni8tl.y
- 0.5
- 1.0 - 1.5
Y G -2.0
-2.5
-3.0
1
I
I
1 Solute,
\,
I
7%
Figure 1. Freezing point depression by certain salts in lithium nitrate.
directly. The temperature was calculated from the emf obtained from the recorder and the known bucking potential. This arrangement gave consistent results, and duplicate freezing points could be reproduced to 0.03' and measured to 0.01". Procedure. Enough previously dried lithium nitrate (weighed to 0.01 g) was melted to give a liquid which covered the stirrer a t the height of its stroke by about 1 cm. A reproducible cooling rate from run to run was obtained by heating the sample to the same temperature each time (about 12" above the melting point). Two or more determinations were made on the pure solvent until successive freezing points were found to agree within 0.02'. After satisfactory check determinations were obtained on the solvent, samples of solute (weighed to 0.0001 g) were added in succession and the freezing points were determined after each addition. Usually six to eight additions were made in each solvent sample. Repeated measurements were made using a fresh sample and a new solute. In those cases where it was desirable to study ionic association in the presence of an excess of complexing ligand, almost the same procedure was used. First, the freezing point of the pure solvent was determined. Next, a suitable amount of the salt furnishing an ion common to the solute was added. This was to act as a driving
CRYOSCOPIC BEHAVIOR OF SOLUTES IN MOLTEN ALKALINITRATES
2495
0
force for complex formation. Successive freezing point determinations were made on the salt solution until a constant value was obtained. The solute salt was then added as previously described.
Results and Discussion Freezing point depression measurements in molten lithium nitrate were made for a series of salts. The change of freezing point as a function of concentration for several solutes is shown in Figure 1, The lx, 2x, and 3x lines represent theoretical lines for one-, twoand threefold lowerings and are calculated from the known value of the heat of fusion of lithium nitrate. The data for several of the salts, which gave linear plots, are given in Table I. The slopes of the curves are easily recognized as the molal freezing point constant of the Raoult-van’t Hoff equation
AT = (vRTo2/1000Lt)m
- 0.5
P -1.0
(1)
where AT is the freezing point depression, v is the number of ions “foreign” to the solvent furnished by one molecule of the solute, R is the gas constant in calories per mole per degree, To is the absolute freezing point temperature of the pure solvent, Lt is the heat of fusion per gram of the pure solvent, and m is the concentration of the solute in moles per 1000 g of solvent. The data of Table I show a depression constant of 6.3’ per mole of foreign ions per 1000 g of solvent. This value agrees excellently with the value of 6.2” per mole of foreign ions per 1000 g of solvent calculated by use of 88.5 cal/g as the heat of fusion of lithium nitrate.la This agreement indicates that the salts behave ideally in molten lithium nitrate over the concentration range investigated.
- 1.5
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
cuso4, m. Figure 2. Effect of added sodium sulfate on the freezing point depression by copper sulfate in lithium nitrate.
Table I: Freezing Point Depressions in Lithium Nitrate One foreign ion
T w o foreign ions
Kr,
Kr,
Salt
NaN03 KNOa LinSOd LiCl LiF
“C
6.3 6.3 6.3 6.5 6.5 Average
Salt
OC
NaCl KCl Cas04
12.5 12.8 12.5
Three foreign ions Kf,
Salt
OC
Na2S04 18.8
per foreign ion 6 . 3 i 0 . 1
It is apparent that most of the salts shown in Figure 1 exhibit ideal behavior; ie., they show complete dissociation. However, some anomalous results have been obtained with nickelous salts and with potassium thiocyanate.
0
0.1
0.2 Na2SO4, 1)1.
0.3
Figure 3. Plot of cryoscopic number at infinite dilution us. concentration of sodium sulfate.
A study of the effect of added sulfate on the freezing point depression of the sulfates of cadmium, lead, copper, and cobalt was undertaken. All of the excess sulfate ion was added in the form of sodium sulfate. The results of this study are shown in Figures 2-6. In these plots AT represents the lowering of the freezing (13) “International Critical Tables,” Vol. V, p 131.
Volume 70,Number 8 August 1966
R. E. ISBELL, E. W. WILSON,JR.,AND D. F. SMITH
2496
0
0
- 0.5
-0.5
9
9
G
G
- 1.0
- 1.0
\ - 1.5
\\
- 1.5
I 0.02
0
I 0.04
I 0.06
I 0.08
I
I
0.10
0.12
\9 0.14
0
0.04
0.02
CdSO4, m.
0.06 cOs04,
Figure 4. Effect of added sodium sulfate on the freezing point depression by cadmium sulfate in lithium nitrate.
0.08
0.10
0.12
0.14
m.
Figure 6. Effect of added sodium sulfate on the freezing point depression by cobaltous sulfate in lithium nitrate.
point by added cadmium, lead, copper, and cobalt sulfates beyond the initial depression caused by the excess sodium sulfate. It is evident there is a tendency toward association in all of the cases mentioned. A reasonable explanation of the results may be found if one assumes the following mononuclear, stepwise reactions to take place
0
- 0.5
9
where M is the divalent copper, lead, zinc, or cobalt ion. The charges have been omitted for simplicity. If the experimentally determined line is on or below the theoretical lx depression line, as in the cases of the lead and cobalt systems, shown in Figures 5 and 6, it is possible only reaction 2 takes place. If the experimentally determined lines fall above the theoretical lx line, as in the cases of the copper and cadmium systems, shown in Figures 2 and 4, then it is possible that both reactions 2 and 3 and higher order, complexforming reactions exist. The corresponding stability constant expressions for reactions 2 and 3 are
h-
- 1.0
- 1.5
I
0
1 0.02
I 0.04
I I 0.06 0.08 PbSO4, m.
I 0.10
I 0.12
0.14
Figure 5. Effect, of added sodium sulfate on the freezing point depression by lead sulfate in lithium nitrate.
The Journal of Physical Chemistry
KI = (MSO,)’/(M)’(SO4)’
Kz
=
M (SO&’/ (MSOI) ’(SO,) ’
(4) (5)
CRYOSCOPIC BEHAVIOR OF SOLUTES IN MOLTEN ALKALINITRATES
2497
1 AT - 2 m ~ s 0 ,m
0
u=---
m‘Ys0,
K t
-
- ...
2m‘~(00,)~
mMsO,
(74 where m in the middle of eq 7a is the stoichiometric molality of the added divalent metal sulfate. The right-hand side of eq 7a may be rearranged to yield a “power series” in terms of the concentrations of the added components, through the use of relations 4 and
-0.5
9
0
F;
I
1
\
-1.0
1
1
I
1
0 p a CdFz 0 0.2946 6 Li? A 0.431s 6 2 0
B\“
0 0.5749 m L U
- 0.5
- 1.5
0
0.02
0.04
0.08 CoClz, m.
0.06
0.10
0.12
0.14
Figure 7. Effect of added potassium chloride on the freezing point depression by cobalt chloride in lithium nitrate.
9~.- 1.0 d
and, in general
- 1.5 Kn = [M(S04)n’]/[M(S04)n-l’] [(Sod’]
(6)
where the prime species denotes the actual or (‘free concentration.” Entities not primed are the stoichiometric concentrations. - 2.0 In deciding which of the various methods of ob0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 taining stability constants from cryoscopic measureCdFz, m. ments might be most suited to the present needs, only Figure 8. Effect of added LiF on the freezing point three methods in the literature seemed to a ~ p l y . ~ J O J ~depression by CdFz in LiN03. , ~ chosen because The method of Braunstein, el ~ l . was it provides the most direct method for obtaining the stability constants for our data. Both the method of 5. The stability constants become the coefficients of Van Artsdalen and Rossotti and Rossotti14suffer from the concentration terms. At infinite dilution of the the fact that the presence of more than two reactions divalent metal ions, the slope of the freezing point taking place simultaneously necessitates the use of curve of the lithium nitrate-sodium sulfate mixtures some sort of iterative procedure. is proportional to Briefly, the method of Braunstein, et al., consists of 2 - KmNazso, (K12 - ~ K ~ K ~ ) ~-I- N. . ~. ~(84 s o , ~ finding the cryoscopic number, vo, at infinite dilution of the divalent metal ion. Instead of working with where all the terms greater than second order are mole ratios as the units of concentration, as did Braunneglected. Now the series is compared with a Macstein, et al., it is simpler to use molality (moles of solute per 1000 g of solvent). The cryoscopic number, u, (14) F. J. C. Rossotti and H. S. Rossotti, J. Phys. Chem.,63, 1041 may be expressed as (1959).
+
Volume 70,Number 8 August 1966
R. E. ISBELL, E. W. WILSON,JR.,AND D. F. SMITH
2498
Laurin expansion of f(mMs04, mNa2s04)about and mNanS04 both equal to zero. f ( r n M S O r , rnNarSO4)
=
f(0,0)
~ M S O ~
Table 11: Summary of Calculations for the System Copper Sulfate-Sodium Sulfate-Lithium Nitrate
+ mMSo4(-)bmMso4 Qf +
cuso4
0.0
concn,
+ 1/2mMS042(b r n ~ 9)0 ~ ~+ . . . '~
O,O
O,O
(9)
Then, from eq 8a and 9 one can arrive at
rnNa2S04 = 0
Equations 10 and 11 may be used to evaluate the first and second stability constants, K1 and Kz. Equation 7a and hence 8a must be rewritten for a 2-1 electrolyte, such as cobalt chloride.
7
0.0000
m
0.0100 0.0200 0.0300 0.0400 0.0500 0.0600 0.0700 0.0800 0.0900 0.1000 0.1100 0.1200 0.1300 0.1400 0.1500
0.11 0.10 0.11 0.11 0.11 0.10 0.11 0.11 0.11 0.11 0.10 0.11 0.11 0.11 0.10 vo = 1.70
d(AT) NazSO4 concn, m 0.0918
0.1750
0.2696
0.085 0.080 0.071 0.064 0.060 0.054 0.047 0.042
0.078 0.071 0.064 0.061 0.056 0.055 0.048 0.044 0.042 0.039
0.053 0.053 0.054 0.053 0.052 0.052 0.054 0.054 0.052 0.053
1.42
1.23
0.84
Table 111: Summary of Cryoscopic Numbers a t Infinite Dilution
1 AT Kt m
v=--==
Concn of complexing
3 - KlmNacl -k (KI'
- 2KiKz)m~aci~ 4- . . .
(8b)
One of the difficulties with the cryoscopic method is that one cannot tell if complexes are really formed. The freezing point depression may be due to welldefined complexes, to associated species of varying composition, or to entirely different reasons. However, the preponderance of data gathered over the years would certainly indicate the existence of certain welldefined complex species present in systems such as those investigated in this study. One of the advantages of this method of calculation is that all of the values are obtained at infinite dilution at which point the ratios of the activities t o concentration approach unity. The calculations for the copper sulfate-sodium sulfate-lithium nitrate system (Figure 2) will be illustrated in order to clarify the method of calculation of K1 values. First, the values of AT were read from the concentration vs. AT plots a t intervals of 0.01 m. Next, the change in AT per 0.01 m amount of copper sulfate was plotted os. the concentration of copper sulfate and a straight line drawn through the points. The intercept of this line, corresponding to d(AT) at infinite dilution, was obtained. From this value and eq 7a one can calculate the value, vo, the cryoscopic number The J O U Tof~Physical ~ Chemistry
Solute
ligand, m
CdSOc
Nak3Oa 0.0000
80
0.1041 0.2091 0.2642
2.14 1.60 0.79 0.84
PbSOd
0.0000 0.1658 0.2665
1.62 1.32 0.92
CuSOa
0.0000 0.0919 0.1750 0.2696
1.70 1.42 1.23 0.84
0.0000 0,0890 0.1867
2.27 2.17 1.82
COS04
COClZ
KCl 0.0000 0.2026
CdFz
3.24 2.98
Completely dissociated at all concentrations studied
at infinite dilution. This information is summarized in Table 11. To obtain the value of K1 the values of vo are plotted
LIQUIDDIFFUSIVITIES IN THE GLYCOL-WATER SYSTEM
2499
us. the concentration of sodium sulfate.
The slope of this line at a concentration of sodium sulfate equal to zero is taken as K1 (Figure 3). Table I11 reports the values of the cryoscopic number, vo, at infinite dilution for the various systems studied. Table IV is a list of the values of K1 obtained from
the plots of the limiting slopes of the various systems studied. It should be noted that the cadmium fluoride does not appear to form any complexes at all in the concentration ranges investigated. Because of the error associated with K1 values obtained, it was decided the values of K 2 would be meaningless at the present time.
Table IV : Values of K , for Certain Salts in Molten Lithium Nitrate
Conclusion
Salt
Ki
CdSO4 PbSOc cuso, COClZ cos04 CdFn
5.3 f1.2 0.93 f 0 . 3 2.7 f 0 . 5 0.13 f ? 0.40 A 0 . 4 0.0 f ?
A variety of different salts have been added to lithium nitrate and lithium nitrate-sodium sulfate or chloride mixtures. It was found that all but copper sulfate, lead sulfate, cobalt sulfate, cadmium sulfate, and cobalt chloride were completely dissociated in lithium nitrate. For these five incompletely dissociated salts, K1, the thermodynamic stability constant was calculated, using the method of Braunstein, et al.
Liquid Diffusivities in the Glycol-Water System
by Charles H. Byers and C. Judson King Lawrence Radiation Laboratory and Departmnt of Chemical Engineering, University of California, Berkeley, California (Received January 26, 1966)
Mutual diffusion coefficients are reported for the system ethylene glycol-water over the entire range of compositions at temperatures ranging from 25 to 70". Differential coefficients were obtained by the use of diaphragm cells and a differential interferometer. It was found that the group Dv/T is temperature independent and varies linearly with the mole fraction of glycol present. The theoretical implications of these results are discussed briefly.
effect of concentration level upon diffusivity is limited to quite simple systems. Corrections for nonidealities have often been confined to instances where regular solution theory is postulated1 and the activity coeffi-
(1) R. J. Bearman, J . Phys. Chem., 6 5 , 1961 (1961). (2) D.L. Bidlack and D. K. Anderson, ibid., 68, 206, 3790 (1964). (3) D. K. Anderson, J. R. Hall, and A. L, Babb, ibid., 62, 404 (1958).
Volume 70, Number 8 August 1966
