2750
0. J. KLEPPAAND S. V. MESCHEL
their thanks to Mr. G. A. JIuccini for his assistance in obtaining and interpreting the inass spectral data,
Tiol. 67
and to RIr. Timothy Pierce for assisting with the experimental work in the summer of 1962.
THERMOCHEMISTRY OF ANION MIXTURES IN SIMPLE FUSED SALT SYSTEMS. 11. SOLUTIONS OF SO&lE SALTS OF Mod- i4SD MO4-2 ANIONS IN THE CORRESPONDING ALKALI NITRATES BY
0. J. KLEPPAA S D
s. IT.R‘IESCHEL
Institute for the Study of Metals and Department of Chemistry, University of Chicago, Chicago 37, Illinois Received J u l y 8, 1963 Calorimetric measurements have been performed on the heats of solution and of dilution of potassium perchlorate in potassium nitrate, of sodium, potassium, rubidium, and cesium perrhenate in the corresponding nitrates, and of sodiums ulfate, chromate, and molybdate in sodium nitrate. From the results have been derived values of the interaction parameters for the liquid-liquid mixtures, and of the heats of fusion of the considered solutes a t the temperatures of the measurements. Eew, approximate values of the heats of fusion (at the melting points) of the perrhenates and of potassium perchlorate are derived from the measurements. The new interaction parameters are discussed and compared with values previously obtained for the solutions of alkali bromides and chlorides in the nitrates.
Introduction I n simple fused salt cation-cation mixtures (with a common anion) it is usually observed that the enthalpy of mixing is negative, and increases sharply in magnitude with increasing difference in size between the two cations.’ This is true both when the two cations have the same charge,l and when they have different charges.2 In the case of simple anion-anion mixtures (with a common cation) the situation appears to be more complex. Thus a series of equilibrium studies by Flood, et aL13have indicated that small positive deviations from ideality are common. On the other hand, negative departures are also observed in some cases. Recently, the present authors have initiated a series of calorimetric investigations of this problem. The first study covered the heats of solution and of dilution for monovalent chlorides and bromides dissolved in the corresponding nitrates.* It was found that the explored alkali halide-nitrate systems all have small positive enthalpies of mixing, the magnitude decreasing somewhat in the sequence S a > .K > Rb > Cs. These results were interpreted in terms of the “radius ratio effect,” well known from the crystal chemistry of simple ionic solids. It is believed that this effect, which arises from the repulsion between the second nearest neighbor anion cores, may very well explain whg’ simple anion-anion mixtures often tend to show positive mixing enthalpies. In the present work, we explore a series of other anion solutes in liquid nitrates. In order to reduce as far as possible the influence of steric factors we have restricted our attention to solute anions which have tetrahedral symmetry. All the considered anions are larger than the nitrate ion, and in some cases they are doubly charged. They also cover a significant range of chemical character from the ‘Lsimplel’sulfate and perchlorate ions to the more “complex” perrhenate, chromate, and molybdate ions. The calorimetric equipment which was available for the present investigation has a maximum operating temperature of about 500’. This is also near the (1) (2) (3) (4)
0. J. Kleppa and L. S. Horsh, J . Chem. Phys., 34, 351 (1961). 0. J. Kleppit, J . Phys. Chem., 66, 1668 (1962). H. Flood, Pure A p p l . Chenz., 5, 529 (1962). 0. J. Xleppa a n d S. V. Meschel, J . Phys. Chem., 67, 6G8 (1963).
limit of thermal stability for the four alkali metal nitrates used in the present work. However, with one exception (NaReOS , the considered solutes have substantially higher melting points. Therefore, we were able to study only a limited range of concentrations, and adopted the heat of solution-heat of dilution approach used in our earlier woik on the halide-nitrate s y ~ t e m s . ~As a “by-product” of our study of the liquid mixtures, we also obtained some new information relating to the heat of fusion of the solutes. Experimental and Materials The calorimetric equipment used and the experimental procedures adopted in the present work have been described before.’ The sodium and potassium nitrate, potassium perchlorate, and sodium sulfate, chromate, and molybdate n-ere Mallinckrodt A.R. grade. They were used without further purification after appropriate drying. The rubidium and cesium nitrates were purchased from Millmaster Cheniical Corp. as “99.970 pure.’’ Both compounds were recrystallized twice from distilled water before use. The sodium and potassium perrhenates were of reagent grade purchased from the Chemistry Department, University of Tennessee. On the basis of the supplier’s analysis, these salts also were used without further purification. We prepared the rubidium and cesium perrhenates from ammonium perrhenate (University of Tennessee) plus rubidium and cesium salts (99.97, from Millmaster). The relatively low solubility of these perrhenates assured a good yield. The melting points of all the perrhenates were checked by thermal analysis and were found t o be in excellent agreement with the literature values.6 In order to check the thermal stability of the varioiis fused salt mixtures, separate samples were prepared and maintained a t the temperature of the calorimeter for about 24 hr., after which the loss in weight was determined. I n all cases the weight losses were found to be small, characteristically of the order of 2-3 parts per thousand or less. I n the course of the present study, two types of calorimetric experiments were performed. (1) Solid solute liquid nitrate solution experiments. The heat effects associated with theae were quite large, and the results accordingly are associated with small relative errors (about =I=1%). ( 2 ) Liquid-liquid maxzng (?rTaRee4-NaSC&) and dzlutaon experiments. I n the latter, concentrated liquid solutions of the solutes in the corresponding nitrate were diluted with pure liquid nitrate in the calorimeter. The resulting net heat effects mere small, sometimes even less than 0.1 cal. As a result the relative uncertainties resulting from the stirring of the mixtures and the breaking of the break-off ampoules Rere fairly large. This is reflected in the scattering of the data.
+
(5)
W.T. Smith, Jr., a n d 8. H. Long, J. Am. Chem. Soc., 70, 354 (1948).
THERMOCHEMISTRY OF BNIOK MIXTURES IN FUSE~D SALTSYSTEMS
Dec., 1963
KC104 In KN03
NaReOq-NONOS 8.2
2751
0400"
A4Wo
2
0 4
08
5
0 450'
P
0 440"
(7.961
0
*
L d 0.1
o
0.2
03~.'
-o, 0
0.1
0.2
Re0 ;1
KReOl -KN03 0453' e3540
t
-I j
".
I 0
I
I
0.1
0.2
1
-:
0
0,I
m
No2MoO4 in NoN03 0 480' 0 450'
~p--o,~;1
1
,
I 0
0.1
0.2
0
0.1
0.2
$ ~ x ~ , o h ~ l " ' tt' axReozlf,noj l~
Re02
Fig. 1.-Heat data for solutions of alkali perrhenates in the corresponding liquid nitrates: left part, A H " / X R , O ~ -from direct liquid experiments; right part, interaction parameters solid from mixing and dilution experiments.
+
Some of the solid pluo liquid solution experiments were performed a t two different temperatures. This permits a crude estimate to be made of the temperature dependence of the heat of fusion of the solute (AC',f).
Results The experimental data are presented in Fig. 1 and 2. On the left-hand side of these figures are plotted the quantities AH"/X vs. X. AHn3:is the molar enthalpy change associated with the formation (from liquid solid solute) of a melt with a solute mole nitrate fraction of X. On the right-hand side of Fig. 1 we give complete heat of mixing data for the liquid system XaRe04KaSOa and heat of dilution data for the other three perrhenate systems. The latter consist in experimental valuesof 4(4H"/X)/AX, plotted vs. l/Q(X(final) X(initia1)) . 4 Within the limits of experimental error achieved in the present work, these slopes appear to be independent of composition (and of temperature). Thus, we may write
+
+
AH"/X
4Hf(l)
+ a(1 - X)
Here 4Hf(t), the intercept a t X = 1, is the heat of fusion of the pure solute a t t o , while the slope of
xsoiute
Fig. 2.-Heat data for solutions of potassium perchlorate in liquid potassium nitrate, and for sodium sulfate, chromate, and molybdate in liquid sodium nitrate: left part, AHY/X,,l,te from direct solid liquid experiments; right part, interaction parameters from dilution experiments.
+
4Hn1/X us. X is --a, the negative of the "interaction parameter" for the liquid-liquid mixing process. In all cases the slopes of the curves drawn on the lefthand side of Fig. 1 and 2 are based on the dilution measurements. Note that a constant slope for AHMIX us. X is equivalent to a simple parabolic expression for AHM in the liquid-liquid mixing process. For the special case of T\'aReOmNaNO8the essential validity of such a relation is confirmed by the complete set of heat of mixing data contained in Fig. 1. Within experimental error the plot of AH"IX(1 - X) vs. X gives a constant value of a. From the experimental results contained in Fig. 1 and 2 we have in Table I prepared a summary of thermochemical data for all the binary systems covered in the present work. I n the third column of this table will be found the limiting heat of solution of the solid solute in "pure" liquid nitrate (4Hf(t) a) ; the fourth column gives the experimental interaction parameter a obtained from mixing or dilution experiments, while the fifth column gives the (extrapolated) value of the heat of fusion of the solute a t the considered temperature, AHf(t). Among the solutes used in the present work we were able to find in the literature heat of fusion data orily for
+
0 . J. KLEPPA ASD
2752
ST31IIIARY O F
Temp., System
OC.
S.V. MESCHEL
TABLE I THERMOCHEMICAL D A T S FOR SOLCTE-NITRATE
+ a, koal./mole
AH%)
a, kcal./mole
1701.
67
hfrXTVRESa
AH‘(t), kcal./mole
AH‘(rn.p.), kcal./mole
ACP*, cal./deg. moleb
400 8.27 +0.56 f 0.02 (450”) 7.7 ... 6 353 (7.96) (7.4) . 6 5 f .I 8.9 ... I((Re04-NOa) 453 0.58 4 354 (9.20) (8.5) Rb(Re04-S03) 447 4.61 . i s f .1 3.8 9 397 (4.14) (3.3) Cs(Re04-KOa) .59 f .1 6.56 .. 450 7.1.5 - .29 f . I 3.6 ... K( ClOn-KOa) 450 3.88 8 440 (3.8) Xa( SOc-NOa) 479 5.08 .os iz . 2 5.0 5.8” (884) 9(2) 450 (4.81) (4.8) Na( Cr04-N03) 480 5.40 $1.3 i . 2 4.1 6 , 2d (792) (7) Na( MoO4-NO3) 480 8.00 +2.14 f .15 5.9 4.6d (698) 11(-6) 450 (7.67) (5.5) Quoted uncertainty limits are estimates of experimental errors. Values in parentheses from a comparison of data given in columns G. Petit and C. Bourlange, 5 and 6. Other values based on own data alone. National Bureau of Standards Circular 500, 1952. Compt. rend., 246, 2865 (1958); SazNIo04undergoes solid state phase transiormat.ions a t about 585 and 623” (“International Critical Tables,” Vol. 4, p. 7). This accounts for t.he wide discrepancy between the ti%-ovalues of ACP* for this salt,.
Na( Reo4-NO3)
+
+ + -
sodium sulfate, chromate, and molybdate. These data are quoted in column 6 of Table I. Finally, we give in this table approximate values of ACpf derived from our own heat data if these were obtained at two different temperatures. These values are based on the assumption that the interaction parameter is independent of temperature. For sodium sulfate, chromate, and molybdate we also estimate ACDf by comparing our own heat data (at 450-480”) with the literature values of AHf a t the melting point. Where a comparison can be made, the agreement between the two values of ACPf is poor. This underscores the need for further work on the enthalpy of fusion of simple inorganic salts (see also footnotes in Table I). It is for this reason that we present in Table I1 new, approximate heat of fusion data for the remaining five solutes. The quoted values have been obtained from AHf(t)(Table I) and our own values of ACPf. L‘kl”2ROXIMATE HEATS AND
TABLE I1 ESTROPIES OF FCSIOK
O F THE -4LK.4Ll
PERRHEKATES B N D O F POTASSIU\I PERCHLOR.4TE
AHf (in.p.), Salt
h1.p.. OK.
AHf (temp OK.)
A S f (mp.), kcal./mole cal./deg. mole
687 7.7 (673) NaReO4 KRe04 828 8 . 9 (726) RbReOe 877 3 8 (720) CsReO4 888 6 56(723) KClOi 883 3 6 (723) a Based on an assumed value of ACPf of
7 8 9 3
11 3 11 2 5 2 5 9 7.5“ 8.4” 4 9 5 5 +6 cal./moIe.
Discussion The Size of the Anions.-Our earlier discussion of the results obtained for the halide-nitrate systems was based on ideas relating to the relative sizes of cations and anions. We noted that in typical anion-anion mixtures, where the anion is substantially larger than the cation, the anions are not well separated either in the pure salts or in the mixed systems. Under these conditions, it is expected that the short range core repulsion between second nearest neighbor anions may make a significant positive contribution to the enthalpy of mixing. For the alkali metal and halide ions the radii of the ions are reasonably well established. Thus, the discussion of the relative sizes of the ions introduces no
particular difficulties. However, for nonspherical, complex anions, such as those considered in the present work, there is no really unambiguous way to calculate an ionic “radius.” Furthermore, one may expect that the effective radius of the ion niay have a somewhat different value in different media. In the “crystal-chemical” approach to the problem of the size of complex ions, the ionic radius is calculated from the lattice parameters of simple salts in which anions and cationsareassumed to be in contact. Knowledge of the cation radius then permits an evaluation of the anion radius (and vice versa). This method seems particularly appropriate in cases where the complex ion has some measure of “rotational” freedom, i.e., is able to assume, with comparable probability, several different orientations in space. This is believed to be the situation in the high-temperature cubic modifications of rubidium and thallium nitrate, from which Kleppa and Hershl estimated a crystal chemical radius of the nitrate ion of 2.19 8. Another approach to the problem of the sizes of complex ions is that of Kapustinskii and co-workers.‘j This method is based on the relation between the enthalpies of formation and the lattice energies of the considered salts. For five of the six anions considered in the present work, Kapustinskii gives the following “thermochemical” radii: NOs-, 1.89; C101-, 2.36; S04-2, 2.30; Cr04-2, 2.40; Mo04-?, 2.54 A. We have been unable to find any thermochemical radius for Reo4-. However, from the lattice parameters of the tetragopal, monovalent perrhenates (in which, however, the perrhenate ions presumably are not free to “YOtate”) we es!imate the radius of this ion t o be of the order of 2.6A. For the nitrate ion there is a very large discrepancy between the ciystal-chemical and the thermochemical radius. Presumably, this is in large measure due to its planar, trigonal shape. In order to throw some further light 011 this problem, we have initiated a series of calorimetric measurements on reciprocal salt pairs involving nitrate, bromide, and chloride ions in nitrate melts.’ These measurements, which are still in progress, snggest that the effective ionic radius of the nitrate ion in a (6) A . F. Iial,ustinskn, Quayt. Reo. (London), 10, 283 (195G). (7) S. V. hIesohe1, unpubllshed results.
Dec., 1963
THERMOCHEMISTRY O F ANION n/IIXTURES IN
liquid nitrate medium is slight& smaller than that of the bromide ion, ie., 1.90-1.95 A. ’Thisresult is in good agreement with Kapustinskii’s thermochemical radius of 1.89 A. For the other ions considered in the present work, which all have tetrahedral symmetry, it is expected that there will be better agreement between the crystalchemical and the thermochemical radius. We have been able to confirm this for two of the complex anions of interest. For example, in the case of the perchlorate ion we derived a crystal-chemical radius from the known lattice parameters of the (high-temperature) cubic modification of potassium, rubidium, and cesium perchlorate. The value, 2.4 A., is in excellent agreement with the thermochemical radius. Similarly, on the basis of the lattice parameters of strontium, cadmium, and barium molybdates, which all crystallize in the tetragonal Scheelite structure, which is also assumed by the alkali-perrhenates, we estimated the ionic radius of the I\/IOO~-~ ion to be about 2.6 A., in good agreement with the thermochemical d u e . Properties of the Liquid Solutions.-As we turn now to the observed interaction parameters for the aiiionanion mixtures determined in the course of the present work, we note first the small negative value of a for perchlorate-nitrate, the near zero value for sulfate, and the increasingly positive values for perrhenate, chromate, and molybdate in nitrate. We consider the negative value for the singly charged perchlorate ion in nitrate to be particularly significant. This result suggests that, in spite of‘ the radius ratio effect, a negative interaction parameter may be obtained when the size difference between two simple anions becomes suitably large compared to the common cation. It seems very desirable to test this thesis in simple halide-halide mixtures, and such investigations are now planned. Preliminary work by Kleppa, Hersh, and Toguri indicates that liquid CsC1-CsBr mixtures may be slightly exothermk8 On the other hand, there is a striking contrast between the negative and near aero interaction parameters for perchlorate-nitrate and sulfate-nitrate, and the positive values observed in the other anion systems. This contrast seems to indicate that for certain complex anions, such a,s chromate, molybdate, perrhenate, we must, in order to understand its solution behavior in a nitrate medium, take into account not only the size and charge of the anion, but also other aspects of its chemistry. It is tempting to relate these differences to the tendency of some of these ions to form associated anionic species. However, in view of the limited amount of information so far available, we consider it premature to speculate further about the details of this problem. Further work in a liquid halide medium is planned. Turning now to the interaction parameters for the four perrhenate-nitrate systems we note that the values range from +0.56 f 0.02 kcal./mole for sodium, to (8) 0. J. Kleppa, L.
S.Hersh, a n d J. &I. Toguri, t o be published.
FUSED SALTSYSTEMS
2753
$0.65 k 0.1 for potassium, +0.7g f 0.1 for rubidium, and +0.5g f 0.1 for the cesium system. I n view of the experimental uncertainties involved we do not consider these variations to be very significant. Thus, it appears that the heat of mixing in these systems is somewhat more insensitive to the cation radius than in tlie previously explored chloride-nitrate and bromidenitrate systems. It will be recalled that in these systems the interaction parameters range from about 0.4 kcal. for sodium to +0.1 kcal. for cesium. The Heats of Fusion.-In considering the new heats and entropies of fusion recorded in Table 11, it should first be noted that the entropies of fusion for rubidium perrhenste and for potassium perchlorate both fall in the range 5.5 to 6.0 cal./deg. mole; i.e., they amount to about 3 cal./deg. ion. This is typical of the order of magnitude usually observed in simple salts such as KaCl, XC1, etc. Note, however, that the sodium and potassium perrhenates have much larger entropies of fusion, 11.2 and 11.3 cal./deg. mole, respectively, while the cesium salt has an intermediate value. There is reason to believe that these variations in large measure must be related to the state of order of the complex anion in the solid state a t the melting point. The low, but otherwise “normal,” entropies of fusion of rubidium perrheiiate and of potassium perchlorate, suggest that in these salts the complex anions are already free to “rotate” in tlie solid state. On the other hand, the high values for sodium and potassium perrhenate indicate that for these salts the melting process is also a. disordering process. The entropy difference, which amounts to somewhat more than 5 cal./deg. mole, is of the same order of magnitude as the entropy change associated with producing complete disorder, in the solid state, of tetrahedral molecular groups such as CC1, and CBr4.9 A phase change, associated with an entropy change of 5.74 cal./deg. mole occurs in potassium perchlorate a t 300’. Presumably, this is the temperature a t which the perchlorate anions become disordered, Le., obtain “rotational” freedom as indicated by the X-ray diffraction work of Finbak and HasseLIO Finally, it should be noted that a completely misleading value of the heat of fusion of potassium perrhenate is reported in the literature. This value (20.16 kcal./mole) was obtained by Seumann and Costenaul’ in a study of the vapor pressure of potassium perrhenate in the solid and in the liquid state. Thus, it was derived from the difference between two large heats of vaporization. Acknowledgments.-This work has been supported by tlie National Science Foundation (Grant G-19513) and by the Office of Naval Research under Contract No. Noiir-2121 (11) with the University of Chicago. General support of the Institute for the Study of Metals by the ARC and by the ARPA also is acknowledged.
+
(9) G. B. Qnthiie and J . P. nIcCollougli, J . Plivs. Chrm. Soltds, 18, A3 (19 61). (10) C . Finbak and 0. Hnssel, 2. P h y s z k . Chem. (Lezpzzg), 32B,130 (19361. (11) K. Neumann a n d V. Costenan, zbid.. ISBA, 66 (1939).
