Cornelius T. Moynihan California State College at Los Angeles California 90032
I II
I
A Low Temperature Fused Salt Experiment The conductivity, viscosity, a n d density o f molten calcium nitrate tetrahydrate
The study of molten salt systems is currently receiving the attention of enough investigators that it may be considered to have graduated to the ranks of the "established" fields of physical chemistry.' As such, the topic deserves some treatment in the nndergraduate curriculum and, more particularly, might he appropriately introduced as the subject of a laboratory experiment for the physical chemistry course. A description of one such fused salt experiment, illustrating acid-base reactions in molten nitrates, has already appeared (6).%I n this communication a low temperature fused salt experiment involving the measurement of the transport properties viscosity and conductance as a function of temperature is described. The obvious drawback to a molten salt transport property experiment for the physical chemistry laboratory is that typical fused salts are high temperature liquids. Since the transport properties are strong functions of temperature, a well insulated tube furnace of fairly high heat capacity, or a well regulated high temperature bath, is required if precise data are to he obtained. Neither of these items is generally a part of the normal stock of undergraduate laboratory equipment. Likewise, the excessive amount of time required for a tube furnace and sample to come to thermal equilibrium places a further limitation on the amount of data that can be collected in a three or four hour period. A solution to this problem was seen, however, in the recent reports of C. A. Angell (6, 7) which assert that highly concentrated solutions of salts of high field cations in which the water content is insufficient to satisfy more than the first coordination sphere of the cation can he considered as molten salts of large complex cations, M(H,O)."+. The molten salt analogy is further enhanced by the fact that included in this class of solutions, which Angell termed "hydrate melts," are a large number of liquids arising from the fusion of low melting chemical compounds, e.g., Ca(NOs)2.4H20(mp 42.7"), CaC12.6Hz0(mp 30.2"), LiN03.3Hz0 (mp 29.g0), and i\4g(NO3),.6H,0 (mp 89.9"). Angell based his conclusion of the molten salt nature of such systems primarily on a correlation of the behavior of their electrical conductances as a function of This work was supported in part by a National Science Foundation Institutional Grant. 'For a brief introduction to molten salt chemistry the reader is referred to the review articles which appeared in T R I ~JOURNAL in 1962 (I, 8). Two recent hooks ( 3 , 4 ) of a considerably more advanced nature me also available on the subject. EDITOR'SNOTE: See also the article on the electromotive force of molten salt concent.ration cells and association equilibria J., THIS JOURNAL, 44, 223 (1967). in solution by BRAUNSTEIN,
temperature with that of other, higher temperature anhydrous systems by means of a free volume theory of transport. He also noted that these melts exhibit another property common to most fused salts, the ability to dissolve large amounts of other salts of a fairly similar nature. It was reported, for instance, that KN03can he dissolved in molten Ca(N03)z.4H20to the extent of 68 mole % at 100' (7) ; the corresponding solubility of KN03 in water at that temperature is only 30 mole %. Further evidence of the usefulness of considering these hydrate melts as fused salts is found in the work of Braunstein and coworkers (8, 9) who demonstrated the utility of the quasi-lattice model of molten salts in interpreting ion association equilibria in liquid NH4N03.2Hz0and Ca(N0a)2.4H20. Finally, Livingston and coworkers (10,ll) have shown that solutions of simple salts in numerous hydrate melts are nearly ideal out to concentrations of a few mole percent, yet another property characteristic of many molten salt solvents. The low liquidus temperatures of these hydrate melts thus make possible a fused salt experiment for the physical chemistry laboratory which avoids the time consuming difficulties inherent in higher temperature work. Calcium nitrate tetrahydrate, Ca(NO&.4H20, rras chosen as a working substance for a low temperature molten salt experiment because of its inexpensiveness and ready availability as a commercial product of high purity and nearly stoichiometric water content. The transport parameters of viscosity and electrical conductivity as well as the densities necessary for viscosity and ment and are thus suitable for an experiment in vhich a large amount of data is to be collected in a short period of time. The conductivity cell, viscometer, and density sample tube can all be mounted in the same hot water bath, and the three experiments conducted simultaneously. The procedure described below has been tested in the physical chemistry laboratory course at the author's institution and can he carried out by a pair of hard-working individuals in a single three to four hour period if all the necessary equipment and chemicals are set out beforehand. A tabulation of some typical results, a discussion of their significance, and some suggestions for student treatment of the data follow the experimental section. Experimental Procedure
A well stirred hot water bath in a 20 liter Pyrex container serves as a heat source for this experiment. If a Volume 44, Number 9, September 7967
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531
temperature controller which is easily reset is not available, the temperature of the bath can be maintained to better than +0.05" a t temperatures up to 70' by means of a 450 watt knife blade heater whose output is regulated with an autotransformer. Bath temperatures are measured with a 100" mercury thermometer marked off in0.1" divisions and calibrated at the ice point. The experiment, is most conveniently conducted by beginning measurements a t high temperatures (around 70"). This allows t,he Ca(NOs)?.4Hn0to be loaded in solid form into the conductivity cell, viscometer, and density sample tube and fused directly in the bath prior to the start of measurements. The bath can be cooled rapidly by passing cold water through copper cooling coils immersed in the bath; a cooling of 10-12" and the attainment of a new equilibrium temperature requires only ten minutes. To save initial beating time, it is suggested t.hat.an auxiliary 450 watt heater be provided or that the bath heater be turned on one or two hours prior to the &art of the laboratory period. An auxiliary 2.5' const,ant t.emperat.urebath is required for the conductivity ?.ell calibrat,ion. Alternatively, these calibrations can be performed a t the end of the experiment in the same bat,h by inserting into the bath a thermoregulator preset for 25' and connecting the heater to the regulator relay. Alallinekrodt AR quality Ca(NO& .4H20was used in all experiment,^. The freezing points of the salt taken from several different bottles used up by the students during the laboratory course were all identical to within a few hundreths of a degree and agreed with the literature value of 42.7"C. The melt compositions may be accurately interpolated from the precise density versus composition det,erminations of Ewing and Mikovsky (12); student densit,y results showed that the H,O/Ca(XO& mole rat,io of the commercial salt was quite reproducible from bottle to bottle at 4.02 0.02. I n a period of three to four hours it was found that measurements a t five to six bath equilibrium temperatures could be performed. The determinations described below were made in the range 25-70', and thus 10" temperature increments are of a convenient size. Conductivities were determined at 1000 cps with a Leeds and Korthrup 467qWheatstone bridge. A set of crystal headphones served as a null detector. The Pyrex conductivity cell, shown in Figure 1, was in the form of a U-tube, 24 cm in height, with the two arms connected by a 2 Figure 1. Conductivily cell for cm length of 2 mm id molten Co(NOalr. 4H10.
*
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capillary. The electrodes were 1 cm2pieces of platinum foil connected to the lead wires via a Pyrex-to-Pt seal. The electrode tubes themselves were sealed to ground glass joints which capped the two arms of the cell and allowed accurate vertical positioning of the electrodes. The cell constant was 56.6 cm-I, which keeps the measured resistances in the convenient 1000 to 10,000ohm range. The cell constant itself is determined almost entirely by the dimensions of the capillary. Rotation of the electrodes by 90" produced no detectable changes in the cell resistance, and vertical displacement of one of the electrodes by 1cm changed the measured resistance by only 0.7%. The conductivity cell was calibrated at 25' with a 0.1000 demal KC1 solution, which should be furnished for the students. A iyf decade capacitor was used to balance cell capacitances; these weregenerally small or completely negligible. Viscosities were measured with a Cannon-Ubbelohde Capillary Viscometer. The viscometer constant was 0.285 centistoke/sec, and observed efflux times were in the range 60 to 600 see. I t is suggested that either a calibrated viscometer be purchased or that the viscometer be calibrated with a standard oil which may be obtained from the National Bureau of Standards or the Cannon Instrument Co. Likewise, because of time requirements, it is convenient to supply the value of the viscometer calibration constant for the students. Densities were measured by means of a Westphal balance mounted on a laboratory jack next to the water bath. The density sample was contained in a 25 X 200 mm test tube. Results
Smoothed values at several temperatures of the conductivity, viscosity, and density of Ca(NOs)2.4H20obtained in a typical run are listed in Table 1, along with the values of various quantities calculable from the measurements. The conductivity (7, IS), viscosity (IS), and density (12,lS) of fused Ca(N03)2.4Hz0have all been reported previously. The values reported in Table 1 and the literature values for conductivity and viscosity agree within a few percent; the discrepancies arise mainly from small variations in the water content of the melt, since the transport properties are fairly sensitive to water content in this composition region. For the same reason typical student results for conductivity and viscosity agree with one another only within about 3 4 % . The resistances in the conductivity experiment and the viscometer efflux times can both be measured with a precision of about 0.2%; combination of this figure with the temperature uncertainty (0.05' = 0.2-0.3%) and the precision of the density measurements (0.05%) yields an overall precision of 0.5-0.6% for both equivalent conductance and viscosity. The scatter of data points from smooth curves drawn through them, as shown in Figure 2, is of about this magnitude in a typical run. Fortunately, slight variations in water content of the melt affect only the magnitude of the conductivity and the viscosity and not their temperature coefficients, which are discussed below. The equivalent conductances, A, tabulated in Table 1 were calculated from the conductivities, K, and densities, p, via the equation:
Figure 2.
Arrhenim plots of molten CaINOlln.4H20 conductance and
vircolity.
where E is the mass of melt containing one gram equivalent of salt (118.08 g/eq for Ca(NO8),.4H,O). Discussion of Results
temperatures, which appears to be a phenomenon characteristic of almost all molten salts (14), and that the activation energies exhibit an accelerated increase in magnitude with decreasing temperature. This second phenomenon turns out to be a rather common characteristic of a large variety of liquids. At high temperatures and over fairly short temperature ranges, Arrhenius-type equations adequately describe experimental liquid transport data. At low temperatures, particularly temperatures below the equilibrium freezing point of the liquid, and over long temperature ranges, however, substantial deviations from Arrhenius behavior occur, and always in a direction corresponding to an apparent increase in activation energy with decreasing temperature. A different theory of liquid transport which explains the non-Arrhenius behavior of transport properties at low liquid temperatures assumes that migration takes place only when a void or hole occurs in the proximity of a migrating particle, which hole is of sufficient size to accommodate the particle. The void or hole is formed without any overall change in the total energy of the liquid from the liquid free volume, where the freevolume is taken to be the difference between the observed liquid volume at the temperature of interest and the random, close packed volume of the same liquid. The free volume theory predicts that the temperature dependence of liquid transport properties should be well described by equations of the form:
The temperature dependence of liquid transport properties such as equivalent, conductance and viscosity is often described by two parameter Arrhenius equations of the form: A = A, exp (-En/RT)
(1)
n = no exp (EdRT) EAand E, are the activation energies for conductance and viscosity. According to the Eyring theory of absolute reaction rates, En and E, may be interpreted as the height of the potential energy barrier over which a migrating particle must pass to make its way from one equilibrium position in the liquid to another, and/or the energy required to form a hole or vacancy in the liquid large enough to accommodate a migrating particle. Equations (1) imply that a plot of log A or log q versus l/T(OK) should be linear with slope -EA/2.3R or E,/ 2.3R. Such plots are shown in Figure 2 for a typical set of data; they obviously do not fulfill the linear require, mems 01" eqn. 11). One way to interpret such results is to consider EAand E, themselves to be functions of temperature. The activation energies listed in Table 1 for Ca(N0&.4Hz0 were calculated on this basis from the s l o ~ e of s the Arrhenius plots in Figure 2. Two notable features of these activation energies are that E, is greater than EAa t all
,.
.
Table 1.
A
=
7 =
A exp
(+)
(T)
A' esp
=
B'l'
=
A e x pv (- 2vo )
~ ' e x p(no)
(2
B'VO
where A , A', B, and B' can be considered as adjust,able constants, V,(= V - 17,) is the liquid free volume, P is t,he observed volume of the liquid, and V ois the random, close-packed volume of the-liquid. Transport equations of this form were first rigorously derived by Cohen and Turnbull (15) and have been used successfully to describe the temperature dependence of transport properties in hydrocarbons and simple organic liquids (15, 16), fused borates and silicates (17), anhydrous fused salts (IS), and hydrate melts (6, 7, I S ) . For glassforming oxides and silicates it was found (17) that Poin eqns. (2) could be taken as the volume of the glass a t temperatures well below the glass transition. For most liquids, however, density information on the glass is lacking and Voin eqns. (2) must be treated as a third adinstable ~arameter. (IR), eqns. (2) can be If we let V = l / p and Vo= cast in the equivalent form: log A = lo,. and
lug 7,
=
'
BP - 2.3(po - P )
,*~
is1
B'P log A ' + 2 . 3 ( ~ 0- P )
Transport Properties and Densities of Molten C a ( N 0 3 ) ~ 4 H ~ 0
t("C)
~(ohm-1om-')
A(cm4/ohmeq)
n(cp)
p(g/cma)
En(kcal/mole)
E,(kcal/rnole)
25 30 40 50 60 70
0.00470 0.00643 0.01080 0.016'44 0.0246 0.0337
0.318 0.436 0.735 1.158 1.691 2.33
285 203 110.1 66.9 43.3 29.8
1.748 1 . i43 1.735 1.727 1.718 1.710
12.0 11.3 10.0 9.0 8.2 7.6
13.5 12.5 11.0 9,7 8.7 7.9
Volume 44, Number 9, September 1967 / 533
recent theory of liquid transport (19,80) which emphasizes the role of configurational entropy, rather than that of free volume, in determining the temperature dependence of transport properties leads to expressions of the form of eqns. (5). Hence it may well he that eqns. (5) are more fundamental than eqns. (2). The equivalent conductance and viscosity of molten Ca(N0&.4H20 are compared in Table 2 with similar Table 2.
Equivalent Conductances and Viscosities of Molten Salts Near Their Melting Points
Salt
Figure 3.
Free volume plots of molten CoINOalr.4H10 conductance ond
YisCOIity.
If the small temperature dependence of the density, p, in the numerators of the second terms on the right side of the equations is ignored, eqns. (3) predict that plots of log A or log 7 versus l/(p, - p) should be linear, provided po is appropriately chosen. Plots of this sort are shown in Figure 3 for the Ca(N03)2.4H,0data in Table 1, where po was taken to be the density a t temperature To= 200°K and was obtained by extrapolation of the linear density versus temperature plot for the melt. As predicted, the plots are linear within experimental error. It is significant here that the same value of p, linearizes both the log A and the log 7 plots, since this effectively eliminates one of the three adjustable constants in eqns. (3). Students are a t first apt to be somewhat surprised to find the temperature dependence of the transport properties desrribed by expressions such as eqns. (3) in which temperature does not even appear explicitly. It appears, however, that the densities of liquids are very generally linear functions of temperature of the form p=a-bT
(4)
If eqn. (4) is substituted into eqns. (3), equations are generated in which temperature appears explicitly: Log A = log A log n = log A'
- 2.3b(TBP- T o ) = log A
+ 2.3b(TB '-p To)
=
k
-T
- To
+
k'
log A'
'"I
where k and k' may be considered constants if the small temperature dependence of p is neglected, and To may be interpreted as the temperature a t which the free volume of t,he liquid disappears and liquid transport becomes impossible. It should be pointed out here that a 534
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Journal o f Chemical Education
t
(TI
n(crns/ohm ea)
n
ieol
values for higher temperature systems near the melting points of the salts. At first appearance it may seem that the equivalent conductance of Ca(iV03)2.4H20is rather low and the viscosity rather high in comparison to other, more typical fused salts. However, Table 2 shows that this is in accord with a general trend of decreasing cor~ductanceand increasing viscosity with decreasing liqnidus temperatures for ionic melts. Indeed, Figure 3 can be used to estimate the conductance and viscosity of Ca(NOa)2.4H20at higher temperatures. Values estimated in this fashion for 300" are shown in parentheses in Table 2 and are of a magnitude eomparable to those of anhydrous fused nitrates in this temperature range. Thus what is unusual about Ca(N03)2.4H,O is not the difficulty of ionic migration a t low temperatures, which would be expected from the low thermal energy of the ions and the small liquid free volume, but rather the low liquidus temperatures themselves. Table 2 further illustrates the general tendency among molten salts of a given charge type toward decreasing liquidus temperatures with increasing complexity of ions. Thus alkali nitrates have lower melting points than alkali halides, and the melting point of Ca(H20)r+2(N03-)2is predictably lower than that of Ca+2C12-by a considerable degree. The reason for this trend inmelting points is not clear at this time, although the problem has been explored in some detail by Ubbelohde ($1). One way to approach this problem is in terms of the thermodynamic equation Tr,.
=
A H d A
Sf,,
Some appropriate thermodynamic data are given in Table 3. With reference to their respective chlorides, it is clear that the low melting point of LiN03 is due priTable 3.
IK)
mo ("GI
Thermodynamic Fusion Properties of Salts
marily to a high entropy of fusion, while the low melting point of NaN08 is due to a low heat of fusion. The low liquidus temperatures of Ca(N0&..4H20 are due to its high entropy of fusion, possibly arising from the onset or increase of eomplex ion rotation on melting. A further interesting point to be gleaned from Table 1 is that the conductance and viscosity of Ca(N03)2.4Hz0 at 25" (which corresponds to a 14.8 N solution) diier by over two orders of magnitude from the infinite dilution conductance and viscosity of aqueous Ca(NO& at this temperature (130.9 cm2/ohm eq and 0.895 cp respectively). Most of the decrease in conductance and increase in viscosity occurs in concentration regions above 1 N where the dilute solution theories of electrolyte transport break down. Indeed, the effect of increasing concentration in increasing interionic attraction and decreasing ionic mobility becomes so pronounced in this region as to cause the electrical conductivity, x , to go through a maximum a t about 4.0 N and to decrease rapidly thereafter. Conductivity, vis-osity, and density data we available for Ca(NOa)2solutions in water up to moderately high concentrations (22). The author has found it instructive to direct the students' attention to this data to point out (1) the pronounced effect of composition on electrolyte solution transport properties at high concentrations, and (2) that concentrat,ed aqueous electrolyte solutions probably have more in common with anhydrous fused salts than with dilute aqueous solutions. A find point to be noted is that liquid Ca(NOa)v 4H20 is readily supercooled below it,s equilibrium freezing temperature; the measurements performed in this experiment extend well into the supercooled region. The experiment t.hus provides a nice illustration of the fact t.hat supercooled liquids are in no sense extraordinary. Rather, inspection of Figures 2 and 3 shows that t,he properties of the liquid change in a regular and continuous fashion as it passes into the metastable undercooled state. Conclusion
The author feels that the experiment described in this paper can serve as a useful addition to the undergraduate physical chemistry course. It provides, in one afternoon's experiment, an introduction t,o fused salt chemistry, an illustration of t,heoriesof liquid transport, and a familiarization with the experimental techniques of conductivity and viscosity measurement. I n some respect.s, the experiment raises more questions than it answers (the absolute reaction rate theory of transport versus the free volume theory, the need for a working theory of concentrated electrolyte solut,ions, etc.). However, this is probably a good thing in that it directs the students' attention to problems whose answers are being actively pursued today. Some of the points included in the discussion sectiou can be presented to the students during the regular lect,ureperiod or in the lec-
ture preceding the laboratory period. Alternatively and perhaps preferably, these points can be presented to the student in mimeographed form, and the student required to draw his own conclusions about the results of the experiment. The latter approach has been adopted at the author's institution and has worked out quite nicely. Finally, there are a large number of low-melting hydrates which for the sake of variation can replace Ca(N03)2.4H20in this experiment. A few of these have been mentioned in the introduction; the reader will discover a large number of others simply by thumbing through the section of the "Handbook of Chemistry and Physics" devoted to physical constants of inorganic compounds. There are likewise some ternary mixtures of inexpensive,readily availahleanhydroussalts with low liquidus temperatures (eg., 0.38 LiNOd.16 NaNOr 0.46 KN08 (f.p. 120') (23) or 0.26 LiN03-0.67 NH4N030.07 NH&l (f.p. 86') (24)) which might be investigated at slightly higher temperatures by replacing the water bath with an oil bath. Literature Cited (1) J A ~C., J., J. CHEM.EDUC.,39, 50 (1962). (2) LAITY,R. W., J. CHEM.EDUC.,39, 67 (1962). M., (Editor), "Molten Salt. Chernistw," Inter(3) BLANDER, science Publishers (Division of John Wilev & sons, Inc.1. New York, 1964. ( 4 ) SUNDHEIM, R. R.. (EdilOr), "Fused Salts," MeGmw-1-Till Rook Co.. New York. 1964 j. M., J. C & ~ E D U C . , 43,362 (1966). (5) SCHLEGE~, (6) ANGELL,C. A., J. Phgs. Chem., 69, 2137 (1965). C. A , J. E/eclrochem. Soc., 112, 1224 (1965). (7) ANCELL, (8)HESS, J. M. C., BRAUNSTEIN, J., AND RRAUMTEIN, IT., J . I m ~ gNuel. . Cham., 26, 811 (1964). J., ALVEREZ-FUNES, A. R., A N D BRAUNSTEIX, (9) RR.\UNSTEIN, H.. J . Phus. Chem... 70.. 2734 119661. LIVINGSTONE, J., MORG.
